Simcore Modflow Software Processing - Modelagem Integrada de Fluxo de Água Subterrânea

Simcore Software Processing Modflow An Integrated Modeling Environment for the Simulation of Groundwater Flow Transport and Reactive Processes July 5 2012 No text content visible in the image Contents 1 Introduction 1 11 Supported Computer Codes 1 12 Compatibility Issues 5 2 Modeling Environment 7 21 The Grid Editor 8 22 The Data Editor 14 221 The CellbyCell Input Method 17 222 The Polygon Input Method 19 223 The Polyline Input Method 21 224 Specifying Data for Transient Simulations 22 23 The File Menu 23 231 New Model 23 232 Open Model 23 233 Convert Model 23 234 Preferences 25 235 Save Plot As 29 236 Print Plot 29 237 Animation 29 24 The Grid Menu 30 241 Mesh Size 30 242 Layer Property 30 243 Cell Status 34 2431 IBOUND MODFLOW 34 2432 ICBUND MT3DMT3DMS 35 244 Top of Layers TOP 35 VI Contents 245 Bottom of Layers BOT 36 25 The Parameters Menu 36 251 Time 36 252 Initial Prescribed Hydraulic Heads 39 253 Horizontal Hydraulic Conductivity and Transmissivity 40 254 Horizontal Anisotropy 40 255 Vertical Leakance and Vertical Hydraulic Conductivity 40 256 Vertical Anisotropy and Vertical Hydraulic Conductivity 40 257 Effective Porosity 41 258 Specific Storage Storage Coefficient and Specific Yield 41 259 Bulk Density 42 2591 Layer by Layer 42 2592 Cell by Cell 42 26 The Models Menu 42 261 MODFLOW 42 2611 MODFLOW Flow Packages Drain 42 2612 MODFLOW Flow Packages Evapotranspiration 44 2613 MODFLOW Flow Packages GeneralHead Boundary 46 2614 MODFLOW Flow Packages HorizontalFlow Barrier 48 2615 MODFLOW Flow Packages Interbed Storage 49 2616 MODFLOW Flow Packages Recharge 51 2617 MODFLOW Flow Packages Reservoir 52 2618 MODFLOW Flow Packages River 56 2619 MODFLOW Flow Packages StreamflowRouting 58 26110 MODFLOW Flow Packages TimeVariant SpecifiedHead 63 26111 MODFLOW Flow Packages Well 64 26112 MODFLOW Flow Packages Wetting Capability 65 26113 MODFLOW Solvers 67 26114 MODFLOW Head Observations 83 26115 MODFLOW Drawdown Observations 87 26116 MODFLOW Subsidence Observations 87 26117 MODFLOW Compaction Observations 87 26118 MODFLOW Output Control 87 26119 MODFLOW Run 89 26120 MODFLOW View 92 262 MT3DMSSEAWAT 98 2621 MT3DMSSEAWAT Simulation Settings 99 Contents VII 2622 MT3DMSSEAWAT Initial Concentration 105 2623 MT3DMSSEAWAT Advection 105 2624 MT3DMSSEAWAT Dispersion 110 2625 MT3DMSSEAWAT Species Dependent Diffusion 113 2626 MT3DMSSEAWAT Chemical Reaction 113 2627 MT3DMSSEAWAT Prescribed Fluid Density 118 2628 MT3DMSSEAWAT SinkSource Concentration 118 2629 MT3DMSSEAWAT MassLoading Rate 119 26210 MT3DMSSEAWAT Solver GCG 119 26211 MT3DMSSEAWAT Concentration Observations 121 26212 MT3DMSSEAWAT Output Control 121 26213 MT3DMSSEAWAT Run 123 26214 MT3DMSSEAWAT View 125 263 PHT3D 126 2631 PHT3D Simulation Settings 126 264 RT3D 130 2641 RT3D Simulation Settings 130 2642 RT3D Initial Concentration 132 2643 RT3D Advection 132 2644 RT3D Dispersion 132 2645 RT3D Sorption Layer by Layer 132 2646 RT3D Sorption Cell by Cell 133 2647 RT3D Reaction Parameters Spatially Constant 133 2648 RT3D Reaction Parameters Spatially Variable 133 2649 RT3D SinkSource Concentration 134 26410 RT3D Concentration Observations 134 26411 RT3D Output Control 135 26412 RT3D Run 135 26413 RT3D View 136 265 MOC3D 136 2651 MOC3D Subgrid 136 2652 MOC3D Initial Concentration 137 2653 MOC3D Advection 137 2654 MOC3D Dispersion Chemical Reaction 139 2655 MOC3D StrongWeak Flag 141 2656 MOC3D Observation Wells 141 2657 MOC3D SinkSource Concentration 141 2658 MOC3D Output Control 142 2659 MOC3D Concentration Observation 143 26510 MOC3D Run 143 VIII Contents 26511 MOC3D View 144 266 MT3D 145 2661 MT3D Initial Concentration 145 2662 MT3D Advection 145 2663 MT3D Dispersion 149 2664 MT3D Chemical Reaction Layer by Layer 149 2665 MT3D Chemical Reaction Cell by Cell 149 2666 MT3D SinkSource Concentration 150 2667 MT3D Concentration Observations 150 2668 MT3D Output Control 151 2669 MT3D Run 152 26610 MT3D View 154 267 MODFLOW2000 Parameter Estimation 154 2671 MODFLOW2000 Parameter Estimation Simulation Settings 156 2672 MODFLOW2000 Parameter Estimation Head Observations 161 2673 MODFLOW2000 Parameter Estimation Flow Observations 161 2674 MODFLOW2000 Parameter Estimation Run 164 2675 MODFLOW2000 Parameter Estimation View 167 268 PEST Parameter Estimation 170 2681 PEST Parameter Estimation Simulation Settings 171 2682 PEST Parameter Estimation Head Observations 194 2683 PEST Parameter Estimation Flow Observations 195 2684 PEST Parameter Estimation Run 195 2685 PEST Parameter Estimation View 197 269 PMPATH Advective Transport 199 27 The Tools Menu 199 271 Digitizer 199 272 The Field Interpolator 200 2721 Interpolation Methods for Irregularly Spaced Data 200 2722 Using the Field Interpolator 201 273 The Field Generator 206 274 2D Visualization 208 275 3D Visualization 209 276 Results Extractor 209 277 Water Budget 211 28 The Value Menu 213 281 Matrix 213 Contents IX 282 Reset Matrix 215 283 Polygons 216 284 Points 216 285 Search and Modify 217 286 Import Results 218 287 Import Package 218 29 The Options Menu 219 291 Map 219 292 Environment 222 3 The Advective Transport Model PMPATH 229 31 The Semianalytical Particle Tracking Method 230 311 Consideration of the display of the calculated pathlines 233 312 Consideration of the spatial discretization and water table layers 233 32 PMPATH Modeling Environment 235 321 Viewing Window and crosssection windows 235 322 Status bar 235 323 Tool bar 237 3231 Open model 237 3232 Set particle 237 3233 Erase Particle 240 3234 Zoom In 240 3235 Zoom Out 240 3236 Particle Color 241 3237 Run Particles Backward 241 3238 Run Particles Backward Step by Step 241 3239 Stop Particle Tracking 241 32310 Run Particles Forward Step by Step 241 32311 Run Particles Forward 242 33 PMPATH Options Menu 242 331 Environment 242 332 Particle Tracking Time 246 333 Maps 251 34 PMPATH Output Files 252 341 Plots 252 342 Hydraulic Heads 253 343 Drawdowns 253 344 Flow Velocities 253 345 Particles 253 X Contents 4 Tutorials 255 41 Your First Groundwater Model with PM 255 411 Overview of the Hypothetical Problem 255 412 Run a SteadyState Flow Simulation 256 4121 Step 1 Create a New Model 257 4122 Step 2 Assign Model Data 257 4123 Step 3 Perform the Flow Simulation 266 4124 Step 4 Check Simulation Results 267 4125 Step 5 Calculate subregional water budget 269 4126 Step 6 Produce Output 270 413 Simulation of Solute Transport 277 4131 Perform Transport Simulation with MT3DMS 279 4132 Perform Transport Simulation with MOC3D 288 414 Parameter Estimation 295 4141 Parameter Estimation with PEST 297 415 Animation 300 42 Unconfined Aquifer System with Recharge 303 421 Overview of the Hypothetical Problem 303 422 Steadystate Flow Simulation 303 4221 Step1 Create a New Model 303 4222 Step2 Generate the Model Grid 304 4223 Step 3 Refine the Model Grid 306 4224 Step 4 Assign Model Data 307 4225 Step 5 Perform steadystate flow simulation 311 4226 Step 6 Extract and view results 312 423 Transient Flow Simulation 313 43 Aquifer System with River 317 431 Overview of the Hypothetical Problem 317 4311 Step 1 Create a New Model 318 4312 Step 2 Generate the Model Grid 318 4313 Step 3 Refine the Model Grid 320 4314 Step 4 Assign Model Data 320 4315 Step 5 Perform steadystate flow simulation 325 4316 Step 6 Extract and view results 327 5 Examples and Applications 333 51 Basic Flow Problems 333 511 Determination of Catchment Areas 333 512 Use of the GeneralHead Boundary Condition 337 Contents XI 513 Twolayer Aquifer System in which the Top layer Converts between Wet and Dry 339 514 WaterTable Mount resulting from Local Recharge 342 515 Perched Water Table 345 516 An Aquifer System with Irregular Recharge and a Stream 348 517 Flood in a River 352 518 Simulation of Lakes 355 52 EPA Instructional Problems 359 53 Parameter Estimation and Pumping Test 360 531 Basic Parameter Estimation Skill 360 532 Estimation of Pumping Rates 364 533 The Theis Solution Transient Flow to a Well in a Confined Aquifer 367 534 The Hantush and Jacob Solution Transient Flow to a Well in a Leaky Confined Aquifer 370 535 Parameter Estimation with MODFLOW2000 Test Case 1 373 536 Parameter Estimation with MODFLOW2000 Test Case 2 376 54 Geotechnical Problems 379 541 Inflow of Water into an Excavation Pit 379 542 Flow Net and Seepage under a Weir 382 543 Seepage Surface through a Dam 384 544 Cutoff Wall 389 545 Compaction and Subsidence 393 55 Solute Transport 397 551 Onedimensional Dispersive Transport 397 552 Twodimensional Transport in a Uniform Flow Field 399 553 Monod Kinetics 403 554 Instantaneous Aerobic Biodegradation 405 555 FirstOrder ParentDaughter Chain Reactions 408 556 Benchmark Problems and Application Examples from Literature 410 56 PHT3D Examples 412 57 SEAWAT Examples 413 58 Miscellaneous Topics 414 581 Using the Field Interpolator 414 582 An Example of Stochastic Modeling 418 6 Supplementary Information 421 61 Limitation of PM 421 611 Data Editor 421 XII Contents 612 Boreholes and Observations 422 613 Digitizer 422 614 Field Interpolator 422 615 Field Generator 422 616 Water Budget Calculator 422 62 File Formats 422 621 ASCII Matrix File 422 622 Contour Table File 423 623 Grid Specification File 424 624 Line Map File 425 625 ASCII Time Parameter File 426 626 HeadDrawdownConcentration Observation Files 427 6261 Observation Boreholes File 427 6262 Layer Proportions File 428 6263 Observations File 428 6264 Complete Information File 428 627 Flow Observation Files 429 6271 Cell Group File 430 6272 Flow Observations Data File 430 6273 Complete Information File 430 628 Trace File 431 629 Polygon File 432 6210 XYZ File 434 6211 Pathline File 434 62111 PMPATH Format 434 62112 MODPATH Format 435 6212 Particles File 436 63 Input Data Files of the supported Model 436 631 Name File 436 632 MODFLOW96 439 633 MODFLOW20002005 440 634 MODPATH and MODPATHPLOT version 1x 441 635 MODPATH and MODPATHPLOT version 3x 441 636 MOC3D 441 637 MT3D 441 638 MT3DMSSEAWAT 442 639 RT3D 442 6310 PHT3D 442 6311 PEST 443 64 Using MODPATH with PM 443 Contents XIII 65 Define PHT3D Reaction Module 444 References 447 Index 455 stress period For transient flow simulations involving several stress periods the input parameters can be different from period to period Note that the user may move to other layers within the Data Editor and examine the grid configuration in each layer although the values are specified for each vertical column of cells Maximum ET Rate RETM LT¹ Elevation of the ET Surface hs L ET Extinction Depth d L Layer Indicator IET and Parameter Number Parameter Number is used to group cells where the RETM values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps The Evapotranspiration package removes water from the saturated groundwater regime based on the following assumptions 1 When groundwater table is at or above the elevation of the ET surface hs evaporation loss from the groundwater table is at the maximum ET Rate RETM 2 No evapotranspiration occurs when the depth of the groundwater table below the elevation of the ET surface exceeds the ET extinction depth d and 3 In between these two extremes evapotranspiration varies linearly with the groundwater table elevation These assumptions can be expressed in the equation form RET RETM if h hs RET 0 if h hs d 27 RET RETM h hs d d if hs d h hs where RET LT¹ is the evapotranspiration rate per unit surface area of groundwater table The evapotranspiration flow rate QET L³T¹ drawn from a model cell is QET RET DELR DELC 28 where DELR DELC is the map area of a model cell QET is drawn from only one cell in the vertical column beneath the map area The Evapotranspiration package provides two options for specifying the cell in each vertical column of cells where evapotranspiration is drawn from 1 Evapotranspiration is always drawn from the top layer of the model List of Figures 21 Spatial discretization of an aquifer system and the cell incides 10 22 The Model Dimension dialog box 10 23 The Grid Editor 11 24 The Grid Size dialog box 14 25 The Data Editor Grid View 15 26 The Data Editor Map View 17 27 The Data Editor Crosssectional View 18 28 The Cell Information dialog box 19 29 The Search and Modify Cell Values dialog box 19 210 The Temporal Data dialog box 22 211 The Convert Model dialog box 24 212 Telescoping a flow model using the Convert Model dialog box 25 213 The Preferences dialog box 25 214 The Layer Property dialog box 31 215 Grid configuration used for the calculation of VCONT 33 216 The Time Parameters dialog box for MODFLOW2000MODFLOW 2005 37 217 The Time Parameters dialog box for MODFLOW96 38 218 The Drain Parameters dialog box 43 219 The General Head Boundary Parameters dialog box 47 220 The HorizontalFlow Barrier dialog box 49 221 Types of finegrained beds in or adjacent to aquifers Beds may be discontinuous interbeds or continuous confining beds Adapted from Leake and Prudic 78 50 222 The Recharge Package dialog box 52 223 The Reservoir Package dialog box 55 XVI List of Figures 224 The StageTime Table of Reservoirs dialog box 55 225 The River Parameters dialog box 56 226 The Stream Parameters dialog box 59 227 Specification of the stream structure 62 228 The stream system configured by the table of Fig 227 63 229 The Wetting Capability dialog box 66 230 The Direct Solution DE45 dialog box 69 231 The Preconditioned Conjugate Gradient Package 2 dialog box 72 232 The PCGN dialog box 74 233 The Strongly Implicit Procedure Package dialog box 78 234 The SliceSuccessive Overrelaxation Package dialog box 79 235 The Geometric Multigrid Solver dialog box 80 236 The Newton Solver NWT dialog box 82 237 The Head Observation dialog box 84 238 The Modflow Output Control dialog box 88 239 The Run Modflow dialog box 90 240 The Data tab of the Scatter Diagram Hydraulic Head dialog box 92 241 Interpolation of simulated head values to an observation borehole 93 242 The Chart tab of the Scatter Diagram Hydraulic Head dialog box 94 243 The Data tab of the Time Series Curves Hydraulic Head dialog box 96 244 The Chart tab of the HeadTime Series Curves Diagram dialog box 97 245 The Initial Concentration dialog box 99 246 The Simulation Settings MT3DMSSEAWAT dialog box 100 247 The Stoichiometry tab of the Simulation Settings MT3DMSSEAWAT dialog box 101 248 The Variable Density tab of the Simulation Settings MT3DMSSEAWAT dialog box 104 249 The Advection Package MT3DMS dialog box 105 250 Initial placement of moving particles adapted from Zheng 119 a Fixed pattern 8 particles are placed on two planes within a cell b Random pattern 8 particles are placed randomly within a cell 109 251 Distribution of initial particles using the fixed pattern adapted from Zheng 1990 If the fixed pattern is chosen the number of particles placed per cell NPL and NPH is divided by the number of planes NPLANE to yield the number of particles to be placed on each plane which is then rounded to one of the numbers of particles shown here 110 252 The Dispersion Package dialog box 111 253 The Chemical Reaction MT3DMS dialog box 113 254 The Generalized Conjugate Gradient GCG dialog box 120 255 The Output Control MT3DMT3DMS dialog box 121 List of Figures XVII 256 The Output Times tab of the Output Control MT3DMT3DMS dialog box 122 257 The Run MT3DMS dialog box 123 258 The Run SEAWAT dialog box 125 259 The Chemical Reaction Module PHT3D dialog box 127 260 The Simulation Settings PHT3D dialog box 128 261 The Reaction Definition RT3D dialog box 131 262 The Sorption Parameters RT3D dialog box 133 263 The Reaction Parameters for RT3D Spatially Constant dialog box 134 264 The Run RT3D dialog box 135 265 The Subgrid for Transport MOC3D dialog box 137 266 The Parameter for Advective Transport MOC3D dialog box 138 267 The Dispersion Chemical Reaction MOC3D dialog box 140 268 The Source Concentration Constant Head dialog box 142 269 The Output Control MOC3D dialog box 143 270 The Run Moc3d dialog box 144 271 The Advection Package MTADV1 dialog box 146 272 The Chemical Reaction Package MTRCT1 dialog box 150 273 The Output Control MT3DMT3DMS dialog box 151 274 The Output Times tab of the Output Control MT3DMT3DMS dialog box 152 275 The Run MT3DMT3D96 dialog box 153 276 The Simulation Settings MODFLOW2000 dialog box 157 277 The Flow Observation River dialog box 162 278 The Flow Observation tab of the Flow Observation River dialog box 163 279 The Run MODFLOW2000 Sensitivity AnalysisParameter Estimation dialog box 165 280 The Run PESTASP MODFLOW2000 dialog box 166 281 The Simulation Settings PEST dialog box 173 282 The Parameter Groups tab of the Simulation Settings PEST dialog box177 283 The Regularization tab of the Simulation Settings PEST dialog box 181 284 The SVDSVDAssist tab of the Simulation Settings PEST dialog box 185 285 The Control Data tab of the Simulation Settings PEST dialog box 191 286 The Run PEST dialog box 195 287 The Field Interpolator dialog box 202 288 Effects of different weighting exponents 203 289 The Variogram dialog box 204 290 Linear Power and logarithmic models 206 291 Search patterns used by a the Quadrant Search method Data per sector2 and b the Octant Search method Data per sector1 206 XVIII List of Figures 292 The Field Generator dialog box 207 293 The 2D Visualization tool in action 208 294 The Result Selection dialog box 209 295 The Results Extractor dialog box 210 296 The Water Budget dialog box 212 297 The Browse Matrix dialog box 214 298 The Load Matrix dialog box 215 299 The starting position of a loaded ASCII matrix 216 2100The Reset Matrix dialog box 216 2101The Search and Modify dialog box 217 2102The Import Results dialog box 218 2103The Map Options dialog box 220 2104Scaling a vector graphic 221 2105Importing and Georeferencing a raster map 222 2106The Appearance tab of the Environment Options dialog box 223 2107The Coordinate System tab of the Environment Options dialog box 224 2108Defining the coordinate system and orientation of the model grid 225 2109The Contours tab of the Environment Options dialog box 226 2110The Color Spectrum dialog box 226 2111The Contour Labels dialog box 226 2112The Label Format dialog box 227 31 PMPATH in action 230 32 a Flow through an infinitesimal volume of a porous medium and b the finitedifference approach 231 33 Schematic illustration of the spurious intersection of two pathlines in a twodimensional cell 234 34 The PMPATH modeling environment 236 35 The Add New Particles dialog box 239 36 The Environment Options dialog box of PMPATH 242 37 The Cross Sections tab of the Environment Options dialog box of PMPATH 243 38 The Contours tab of the Environment Options dialog box of PMPATH 244 39 The Color Spectrum dialog box 246 310 The Contour Labels dialog box 246 311 The Label Format dialog box 247 312 The Particle Tracking Time dialog box 247 313 The Pathline Colors tab of the Particle Tracking Time dialog box 249 314 The RCHEVT Options tab of the Particle Tracking Time dialog box 250 315 The Maps Options dialog box 251 List of Figures XIX 316 The Save Plot As dialog box 252 41 Configuration of the hypothetical model 257 42 The spatial discretization scheme and cell indices of MODFLOW 258 43 The Model Dimension dialog box 259 44 The generated model grid 260 45 The Layer Options dialog box and the layer type dropdown list 261 46 The Data Editor displaying the plan view of the model grid 262 47 The Run Modflow dialog box 267 48 The Water Budget dialog box 270 49 The Results Extractor dialog box 273 410 The Result Selection dialog box 274 411 Contours of the hydraulic heads in the first layer 275 412 The model loaded in PMPATH 276 413 The Add New Particles dialog box 277 414 The capture zone of the pumping well vertical exaggeration 1 278 415 The capture zone of the pumping well vertical exaggeration 10 279 416 The 100day capture zone calculated by PMPATH 280 417 The Particle Tracking Time Properties dialog box 280 418 The Concentration Observation dialog box 281 419 The Reaction Definition dialog box 282 420 The Advection Package MT3DMS dialog box 283 421 The Dispersion Package MT3DMT3DMSRT3D dialog box 284 422 The Reset Matrix dialog box for chemical reaction data of MT3DMS 284 423 The Output Control MT3D Family dialog box 285 424 The Run MT3DMS dialog box 286 425 Contours of the concentration values at the end of the simulation 287 426 The Time Series Curves Concentration dialog box 288 427 The Chart tab of the Time Series Curves Concentration dialog box 289 428 The Subgrid for Transport MOC3D dialog box 290 429 The Parameters for Advective Transport MOC3D dialog box 290 430 The Dispersion Chemical Reaction MOC3D dialog box 291 431 The Output Control MOC3D dialog box 292 432 The Run Moc3d dialog box 293 433 Contours of the concentration values at the end of the simulation 294 434 The Time Series Curves Concentration dialog box 295 435 The Chart tab of the Time Series Curves Concentration dialog box 296 436 The Head Observation dialog box 297 437 The List of Parameters PEST dialog box 298 438 The Run PEST dialog box 299 XX List of Figures 439 The Scatter Diagram dialog box 300 440 The Chart tab of the Scatter Diagram dialog box 301 441 The Animation dialog box 302 442 Configuration of the hypothetical model 304 443 The Model Grid and Coordinate System dialog box 305 444 Model grid after the refinement 307 445 Model Boundaries 310 446 Steady state head distribution 313 447 a Head distribution after 240 days of pumping period 1 time step 12 b Head distribution after 120 days of recharge period 2 time step 6 316 448 Configuration of the hypothetical model 317 449 The Model Grid and Coordinate System dialog box 319 450 Model grid after the refinement 320 451 Model grid of the 1st layer and 3rd layer 322 452 Model grid of the 2nd layer 323 453 Define the river using a polyline 326 454 Parameters of the upstream vertex 326 455 Parameters of the downstream vertex 327 456 The Result Selection dialog box 328 457 Steady state hydraulic head distribution in the first model layer 328 458 Steady state hydraulic head distribution in the 3rd model layer and capture zones of the pumping wells 329 459 125year streamlines particles are started at the cell 6 5 1 and flow towards Well 2 331 51 Plan view of the model area 334 52 Catchment area and 365days isochrones of the pumping well 2Dapproach groundwater recharge is treated as distributed source within the model cells 335 53 Particles are tracked back to the groundwater surface by applying the groundwater recharge on the groundwater surface 3Dapproach 336 54 Catchment area of the pumping well 3Dapproach 336 55 Plan view of the model area 337 56 Calculated head contours for the west part of the aquifer 338 57 Calculated head contours for the entire aquifer 339 58 Configuration of the hypothetical model after McDonald and others 86 340 59 Hydrogeology and model grid configuration 343 List of Figures XXI 510 Simulated watertable along row 1 beneath a leaking pond after 190 708 2630 days and steady state conditions 345 511 Hydrogeology and model grid configuration 346 512 Simulated steady state head distribution in layer 1 348 513 Configuration of the model grid and the location of the observation well 349 514 Distribution of recharge used for analytical solution and the model after Prudic 100 350 515 Comparison of simulation results to analytical solution developed by Oakes and Wilkinson 92 352 516 Distribution of streamflow for a 30day flood event used for the simulation after Prudic 100 353 517 Model calculated river stage 354 518 Numbering system of streams and diversions after Prudic 100 355 519 Plan and crosssectional views of the model area 356 520 Steadystate hydraulic head contours in layer 4 358 521 Timeseries curve of the water stage in the lake 358 522 Configuration of the aquifer system 361 523 Plan view of the model 365 524 Location of the cutoff wall and pumping wells 366 525 Time series curve of the calculated hydraulic head at the center of the contaminated area 366 526 Plan view of the model 368 527 Timeseries curves of the calculated and observed drawdown values 369 528 Configuration of the leaky aquifer system and the aquifer parameters 370 529 Configuration of the leaky aquifer system and the aquifer parameters 372 530 Physical system for test case 1 Adapted from Hill and others 63 373 531 Test case 2 model grid boundary conditions observation locations and hydraulic conductivity zonation used in parameter estimation Adapted from Hill and others 63 377 532 Configuration of the physical system 380 533 Simulated head distribution and catchment area of the excavation pit 381 534 Configuration of the physical system 383 535 Model grid and the boundary conditions 383 536 Flowlines and calculated head contours for isotropic medium 383 537 Flowlines and calculated head contours for anisotropic medium 383 538 Seepage surface through a dam 386 539 Model grid and the boundary conditions 387 540 Calculated hydraulic heads after one iteration step 387 541 Calculated hydraulic heads distribution and the form of the seepage surface 388 XXII List of Figures 542 Model grid and boundary conditions 390 543 Plan and crosssectional views of flowlines Particles are started from the contaminated area The depth of the cutoff wall is 8 m 391 544 Plan and crosssectional views of flowlines Particles are started from the contaminated area The depth of the cutoff wall is 10 m 392 545 Model grid and boundary conditions 395 546 Distribution of the land surface subsidence maximum 011 m 396 547 Comparison of the calculated breakthrough curves with different dispersivity values 398 548 Configuration of the model and the location of an observation borehole 400 549 Calculated concentration distribution 401 550 Comparison of the breakthrough curves at the observation borehole The numerical solution is obtained by using the 3rd order TVD scheme 401 551 Comparison of the breakthrough curves at the observation borehole The numerical solution is obtained by using the upstream finite difference method 402 552 Calculated concentration values for onedimensional transport from a constant source in a uniform flow field 404 553 Calculated concentration values of hydrocarbon 406 554 Calculated concentration values of oxygen 407 555 Comparison of calculated concentration values of four species in a uniform flow field undergoing firstorder sequential transformation 409 556 Model domain and the measured hydraulic head values 414 557 Contours produced by Shepards inverse distance method 415 558 Contours produced by the Kriging method 416 559 Contours produced by Akimas bivariate interpolation 417 560 Contours produced by Renkas triangulation algorithm 417 561 Calculation of the mean safety criterion by the Monte Carlo method 419 61 Local coordinates within a cell 437 List of Tables 21 Symbols used in the present text 8 22 Summary of menus in PM 9 23 Summary of the toolbar buttons of the Grid Editor 12 24 Summary of the toolbar buttons of the Data Editor 16 25 Versions and Filenames of MODFLOW 27 26 Model Data checked by PM 91 27 Names of the MOC3D output files 142 28 Adjustable parameters through MODFLOW2000 within PM 155 29 Adjustable parameters through PEST within PM 170 210 Output from the Water Budget Calculator 213 31 Summary of the toolbar buttons of PMPATH 238 41 Output files from MODFLOW 268 42 Volumetric budget for the entire model written by MODFLOW 268 43 Output from the Water Budget Calculator 271 44 Output from the Water Budget Calculator for the pumping well 272 45 Measured hydraulic head values for parameter estimation 296 51 Volumetric budget for the entire model written by MODFLOW 357 52 River data 362 53 Measurement data 362 54 Analytical solution for the drawdown with time 371 55 Parameters defined for MODFLOW2000 test case 1 parameter values starting and estimated PARVAL 375 56 Parameters defined for MODFLOW2000 test case 2 parameter values starting and estimated PARVAL 378 XXIV List of Tables 57 PHT3D Examples 412 58 SEAWAT Examples 413 61 Assignment of parameters in the ValueI vector 434 1 Introduction Processing Modflow PM was originally developed to support the first official re lease of MODFLOW88 85 to simulate the inundation process of an abandoned opencast coal mine Since the release of MODFLOW88 many computer codes have been developed to add functionalities to MODFLOW or to use MODFLOW as a flowequation solver for solving specific problems Consequently several versions of PM172224 have been released to utilize latest computer codes to facilitate the modeling process and to free up modelers from tedious data input for more cre ative thinking The computer codes that are supported by present version of Processing Modflow are given in the following section 11 Supported Computer Codes MODFLOW 85545556635791 MODFLOW is a modular threedimensional finitedifference groundwater model published by the U S Geological Survey The first public version of MODFLOW was released in 1988 and is referred to as MODFLOW88 MODFLOW88 and the later version of MODFLOW96 5455 were originally designed to simulate sat urated threedimensional groundwater flow through porous media MODFLOW 2000 56 attempts to incorporate the solution of multiple related equations into a single code To achieve the goal the code is divided into entities called pro cesses Each process deals with a specific equation For example the Groundwater Flow Process GWF deals with the groundwaterflow equation and replaces the original MODFLOW The parameter estimation capability of MODFLOW2000 is implemented by Hill and others 63 using three processes in addition to the GWF process The Observation Process OBS calculates simulated values that are to be 2 1 Introduction compared to measurements calculates the sum of squared weighted differences between model values and observations and calculates sensitivities related to the observations The Sensitivity Process SEN solves the sensitivity equation for hy draulic heads throughout the grid and the ParameterEstimation PES Process solves the modified GaussNewton equation to minimize an objective function to find optimal parameter values Although the OBS SEN and PES processes allow MODFLOW2000 to perform a model calibration without the need for any ex ternal parameter estimation software there will still be many situations in which it is preferable to calibrate a MODFLOW model using external parameter esti mation software rather than using builtin MODFLOW2000 parameter estima tion functionality 36 To combine the strengths of PESTASP and MODFLOW 2000 a modified version of MODFLOW2000 called MODFLOWASP 35 al lows a coupled PESTASPMODFLOW2000 approach using MODFLOWASP to calculate derivatives and using PESTASP to estimate parameter values The lat est major version of MODFLOW was released in 2005 called MODFLOW2005 57 This version however does not support parameter estimation process at the time of this writing As a result users are encouraged to take advantage of ex ternal parameterestimation programs such as PEST In 2011 MODFLOWNWT 91 is released MODFLOWNWT is a standalone version of MODFLOW2005 based on the Newton Formulation and includes a new UpstreamWeighting UPW Package that provides an alternative formulation of the groundwaterflow equation provided by the BCF LPF and HUF Packages MODFLOWNWT is designed to solve groundwaterflow problems that are nonlinear due to unconfined aquifer conditions andor some combination of nonlinear boundary conditions PEST 333738 The purpose of PEST is to assist in data interpretation and in parameter estima tion If there are field or laboratory measurements PEST an adjust model param eters andor excitation data in order that the discrepancies between the pertinent modelgenerated numbers and the corresponding measurements are reduced to a minimum PEST does this by taking control of the model MODFLOW and run ning it as many times as is necessary in order to determine this optimal set of parameters andor excitations PEST includes many cuttingedge parameter es timation techniques According to Doherty 37 the most profound advance is the SVDassist scheme This method combines two important regularization methodologiestruncated singular value decomposition and Tikhonov regular ization MODPATH 959596 MODPATH is a particle tracking code written in FORTRAN To run a particle tracking simulation with MODPATH the users need to key in parameters in a text screen and have the options to save the input values in a separate file for later 11 Supported Computer Codes 3 use A graphical postprocessor such as MODPATHPLOT 97 3D Groundwater Explorer 21 or 3D Master23 is required for displaying the calculated pathlines and particle locations PMPATH 19 PMPATH is a Windowsbased advective transport model for calculating and ani mating path lines of groundwater PMPATH uses a semianalytical particletracking scheme used in MODPATH 95 to calculate the groundwater paths and travel times PMPATH supports both forward and backward particletracking schemes for steadystate and transient flow fields The graphical user interface of PMPATH allows the user to run a particle tracking simulation with just a few clicks of the mouse Pathlines or flowlines and travel time marks are calculated and displayed along with various onscreen graphical options including head or drawdown con tours and velocity vectors MOC3D 74 MOC3D is a singlespecies transport model computes changes in concentration of a single dissolved chemical constituent over time that are caused by advective transport hydrodynamic dispersion including both mechanical dispersion and dif fusion mixing or dilution from fluid sources and mathematically simple chemical reactions including decay and linear sorption represented by a retardation factor MOC3D uses the method of characteristics to solve the transport equation on the basis of the hydraulic gradients computed with MODFLOW for a given time step This implementation of the method of characteristics uses particle tracking to rep resent advective transport and explicit finitedifference methods to calculate the effects of other processes For improved efficiency the user can apply MOC3D to a subgrid of the primary MODFLOW grid that is used to solve the flow equation However the transport subgrid must have uniform grid spacing along rows and columns Using MODFLOW as a builtin function MOC3D can be modified to simulate densitydriven flow and transport MT3D 119122 MT3D is a singlespecies transport model uses a mixed EulerianLagrangian ap proach to the solution of the threedimensional advectivedispersivereactive trans port equation MT3D is based on the assumption that changes in the concentration field will not affect the flow field significantly This allows the user to construct and calibrate a flow model independently After a flow simulation is complete MT3D simulates solute transport by using the calculated hydraulic heads and various flow terms saved by MODFLOW MT3D can be used to simulate changes in concentra tion of single species miscible contaminants in groundwater considering advection dispersion and some simple chemical reactions The chemical reactions included in the model are limited to equilibriumcontrolled linear or nonlinear sorption and firstorder irreversible decay or biodegradation Since most developers focus their 4 1 Introduction efforts on supporting its successor MT3DMS 123 MT3D is considered to be obsolete in terms of further development MT3DMS 123125 MT3DMS is a further development of MT3D The abbreviation MS denotes the MultiSpecies structure for accommodating addon reaction packages MT3DMS includes three major classes of transport solution techniques ie the finite dif ference method the particle tracking based EulerianLagrangian methods and the higherorder finitevolume TVD method In addition to the explicit formulation of MT3D MT3DMS includes an implicit iterative solver based on generalized con jugate gradient GCG methods If this solver is used dispersion sinksource and reaction terms are solved implicitly without any stability constraints MT3D99 124 MT3D99 is an enhanced version of MT3DMS 123 for simulating aerobic and anaerobic reactions between hydrocarbon contaminants and any userspecified electron acceptors and parentdaughter chain reactions for inorganic or organic compounds The multispecies reactions are fully integrated with the MT3DMS transport solution schemes including the implicit solver RT3D 252627 is a code for simulating threedimensional multispecies reac tive transport in groundwater Similar to MT3D99 the code is based on MT3DMS 123 MT3D99 and RT3D can accommodate multiple sorbed and aqueous phase species with any reaction framework that the user wishes to define With the flex ibility to insert userspecific kinetics these two reactive transport models can sim ulate a multitude of scenarios For example natural attenuation processes can be evaluated or an active remediation can be simulated Simulations could potentially be applied to scenarios involving contaminants such as heavy metals explosives petroleum hydrocarbons andor chlorinated solvents PHT3D 9899 PHT3D couples MT3DMS 125 for the simulation of threedimensional advec tivedispersive multicomponent transport and the geochemical model PHREEQC 2 93 for the quantification of reactive processes PHREEQC2 in its original version is a computer program written in the C programming language that is designed to perform a wide variety of lowtemperature aqueous geochemical cal culations PHT3D uses PHREEQC2 database files to define equilibrium and ki netic eg biodegradation reactions For the reaction step PHT3D simulations might include 1 Equilibrium complexation reactionspeciation within the aque ous phase 1 Kinetically controlled reactions within the aqueous phase such as biodegradation 3 Equilibrium dissolution and precipitation of minerals 4 Ki netic dissolution and precipitation of minerals 5 Single or multisite cation ex change equilibrium and 6 Single or multisite surface complexation reactions SEAWAT 517677 12 Compatibility Issues 5 SEAWAT is designed to simulate threedimensional variabledensity saturated groundwater flow and transport The original SEAWAT program was developed by Guo and Langevin 51 based on MODFLOW88 and an earlier version of MT3DMS 123 The program has subsequently been modified to couple MODFLOW 2000 56 and a later version of MT3DMS 125 Flexible equations were added to the fourth version of the program ie SEAWAT V4 77 to allow fluid den sity to be calculated as a function of one or more MT3DMS species Fluid density may also be calculated as a function of fluid pressure The effect of fluid viscosity variations on groundwater flow was included as an option This option is how ever not supported by PM Although MT3DMS and SEAWAT are not explicitly designed to simulate heat transport temperature can be simulated as one of the species by entering appropriate transport coefficients For example the process of heat conduction is mathematically analogous to Fickian diffusion Heat conduction can be represented in SEAWAT by assigning a thermal diffusivity for the temper ature species instead of a molecular diffusion coefficient for a solute species Heat exchange with the solid matrix can be treated in a similar manner by using the mathematically equivalent process of solute sorption See Langevin and others 77 for details about heat transport Water Budget Calculator 18 This code calculates the groundwater budget of userspecified subregions and the exchange of flows between subregions 12 Compatibility Issues For many good reasons MODFLOW and most of its related groundwater simulation programs such as MT3DMS are written in FORTRAN and save simulation results in binary files This includes groundwater models distributed by the U S Geological Sur vey and most popular graphical user interfaces such as Processing Modflow ModIME 121 Groundwater Modeling System known as GMS Groundwater Vistas Argus ONE and Visual MODFLOW PM is capable of reading binary files created by the abovementioned codes Binary files are often saved in the unformatted sequential or transparent for mat An unformatted sequential file contains record markers before and after each record whereas a transparent file contains only a stream of bytes and does not contain any record markers Of particular importance is that different FORTRAN compilers of ten use different and incompatible formats for saving unformatted sequential files Thus when compiling your own codes the following rules should be followed so that PM can read the model generated binary files When Lahey Fortran compiler is used 6 1 Introduction Create a transparent file by specifying FORM UNFORMATTED and AC CESS TRANSPARENT in the OPEN statement When Intel Visual Fortran is used Create a transparent file if it is opened using FORM BINARY and AC CESS SEQUENTIAL If you are using other compilers please consult the user manual for the settings of creating transparent binary files 2 Modeling Environment This chapter is a complete reference of the user interface of PM With the exception of PHT3D PM requires the use of consistent units throughout the modeling process For example if you are using length L units of meters and time T units of seconds hydraulic conductivity will be expressed in units of ms pumping rates will be in units of m3s and dispersivity will be in units of m The values of the simulation results are also expressed in the same units Table 21 lists symbols and their units which are used in various parts of this text PHT3D requires the use of meters for the length the use of mollw for concentra tions of aqueous mobile chemicals and userdefined immobile entities such as bac teria and the use of mollv for mineral exchanger and surface concentrations where mol refers to moles lw refers to liter of pore water and lv refers to liter of bulk volume see Prommer and others 99 for details about the use of units in PHT3D PM contains the following menus File Grid Parameters Models Tools Value Options and Help The Value and Options menus are available only in the Grid Editor and Data Editor see Sections 21 and 22 for details PM uses an intelligent menu system to help you control the modeling process If a model data set has been specified the corresponding item of the Grid Parameters and Models menus will be checked To deactivate a selected item in the Models menu just select the item again If the user does not know which model data still needs to be specified one may try to run the model by selecting the menu item Run from the corresponding model in the Models menu PM will check the model data prior to running the model A summary of the menus in PM is given in Table 22 A toolbar with buttons representing PM operations or commands is displayed be low the menus The toolbar is a shortcut for the pulldown menus To execute one of these shortcuts move the mouse pointer over the toolbar button and click on it 8 2 Modeling Environment Most of the userspecified data is saved in binary files Prior to running the sup ported models or the parameter estimation programs PM will generate the required ASCII input files The names of the ASCII input files are given in Section 63 The for mats of the input files of can be found in the users guides of the corresponding model The particletracking model PMPATH retrieves the binary data files of PM directly thus no ASCII input file is required by PMPATH 21 The Grid Editor The first steps in the groundwater modeling process are to define the goals of the model select a computer code collect the necessary data develop a conceptual model of the groundwater system and define the spatial discretization of the model domain Anderson and Woessner 8 discuss the steps in going from aquifer systems to a numer ical model grid Zheng and Bennett 120 describe the design of model grids which are intended for use both in flow and transport simulations These sources provide valu able general information relating to spatial discretization and grid design in numerical groundwater modeling In the blockcentered finite difference method an aquifer system is replaced by a discretized domain consisting of an array of nodes and associated finite difference blocks cells Fig 21 shows the spatial discretization scheme of an aquifer system with a mesh of cells and nodes at which hydraulic heads are calculated The nodal grid forms the framework of the numerical model Hydrostratigraphic units can be represented by one or more model layers The thickness of each model cell and the width of each column and row can be specified The locations of cells are described in Table 21 Symbols used in the present text Symbol Meaning Unit m thickness of a model layer L HK horizontal hydraulic conductivity along model rows LT 1 V K vertical hydraulic conductivity LT 1 T transmissivity T HK m L2T 1 Ss specific storage L1 S storage coefficient or storativity S Ss m Sy specific yield or drainable porosity ne effective porosity V CONT vertical leakance T 1 HANI horizontal anisotropy HANI HK horizontal hydraulic conductivity along columns V ANI vertical anisotropy HK V K V ANI 21 The Grid Editor 9 Table 22 Summary of menus in PM Menu Description File Create new models open existing models convert models to the PM format Save and print plots Grid Generate or modify the size of a model grid input of the geometry of the aquifer Parameters Input of spatial aquifer parameters for example transmissivity Input of tem poral parameters for example simulation length or number of stress periods Models Specify modelspecific data using the module provided and call simulation programs For example the user can add wells use the recharge or river modules to MODFLOW or define the advection or dispersion parameters in MT3DMS The simulation programs are called by selecting Run from the corresponding model Tools Call the modeling tools Value Manipulate model data read or save model data in separate files import model results import an existing MODFLOW input file Options Modify the appearance of the model grid on the screen load site maps change display mode change input method Help Call Processing Modflow Pro Help terms of layers rows and columns PM uses an index notation Layer Row Column for locating the cells For example the cell located in the first layer 6th row and 2nd column is denoted by 1 6 2 To generate or modify a model grid select Grid Mesh Size If a grid does not exist a Model Dimension dialog box Fig 22 appears for specifying the extent and number of layers rows and columns of the model grid After specifying these data and clicking the OK button the Grid Editor shows the model grid Fig 23 A summary of the tool bar buttons of the Grid Editor is given in Table 23 Using the Environment Options dialog box see Section 292 the user can adjust the coordinate system the extent of the Viewing Window and the position of the model grid to fit the study site By default the origin of the coordinate system is set at the lowerleft corner of the model grid and the extent of the Viewing Window is set to twice that of the model grid The first time the Grid Editor is used the user can insert or delete columns or rows see below After leaving the Grid Editor and saving the grid the existing model grid can be subsequently refined by calling the Grid Editor again In each case the width of any column or row can be modified If the grid is refined depending on the nature of the model parameters they are either kept the same or scaled by the cell size The following rules apply 1 Pumping rates massloading rate see Section 2629 and cellbycell conduc tance values of the river drain generalhead boundary and stream are scaled by the cell volume For example if a well cell is refined to four cells all four refined 10 2 Modeling Environment Fig 21 Spatial discretization of an aquifer system and the cell incides Fig 22 The Model Dimension dialog box 21 The Grid Editor 11 Fig 23 The Grid Editor cells will be treated as wells each with 14 of the original pumping rate The sum of their pumping rates remain the same as that of the previous single well 2 The parameters of polylines which are used to define river drain generalhead boundary or stream remain the same since they are gridindependent If a stream of the StreamRouting package is defined by using cellbycell values you must redefine the segment and reach number of the stream 3 Transmissivity T and storage coefficient S values are scaled by the thickness 4 All other model parameters remain the same To change the width of a column andor a row 12 2 Modeling Environment Table 23 Summary of the toolbar buttons of the Grid Editor Button Name Action Leave editor Leave the Grid Editor and return to the main menu of PM Assign value Allows the user to move the grid cursor and change the widths of grid columns and rows Pan Moves the Viewing Window up down or sideways to display areas of the model domain which at the current viewing scale lie outside the Viewing Window By dragging the mouse the model grid and sitemaps will be moved in the same direction as the mouse cursor When the left mouse button is released the grid and maps will be redrawn Zoom in Allows the user to zoomin by dragging a window over a part of the model domain Zoom out Display the entire worksheet Rotate grid To rotate the model grid point the mouse pointer to the grid left click and hold down the mouse button and move the mouse Shift grid Allows the user to move the model grid to another position To shift the model grid point the mouse pointer to the grid left click and hold down the mouse button and move the mouse Map View Switch to the Map View display mode Column View Switch to the column crosssectional display mode Row View Switch to the row crosssectional display mode Duplication onoff If duplication is turned on the size of the current row or column will be copied to all rows or columns passed by the grid cursor Duplication is on when this button is depressed 1 Click the assign value button The grid cursor appears only if the Assign Value button is pressed down You do not need to click this button if it is already depressed 2 Move the grid cursor to the desired cell by using the arrow keys or by clicking the mouse on the desired position The sizes of the current column and row are shown on the status bar 3 Press the right mouse button once The Grid Editor shows the Grid Size dialog box Fig 24 4 In the dialog box type new values then click OK 21 The Grid Editor 13 To insert or delete a column andor a row 1 Inserting or deleting columnsrows is only possible when using the Grid Editor for the first time Click the assign value button 2 Move the grid cursor to the desired cell by using the arrow keys or by clicking the mouse on the desired position 3 Hold down the Ctrlkey and press the up or right arrow keys to insert a row or a column press the down or left arrow keys to delete the current row or column 14 2 Modeling Environment To refine a layer a row or a column 1 Refining a grid is only possible when the grid has already been saved Click the assign value button 2 Move the grid cursor to the desired cell by using the arrow keys or by clicking the mouse on the desired position 3 Press the right mouse button once The Grid Editor shows the Grid Size dialog box Fig 24 4 In the dialog box type new values then click OK Fig 24 The Grid Size dialog box 22 The Data Editor The Data Editor is used to assign parameter values to the model To start the Data Editor select a corresponding item from the Grid Parameters or Models menus For example select Parameters Porosity to assign porosity values to the model The Data Editor provides four display modes Map View Grid View Column View and Row View It has three methods for specifying parameter values Cellby cell Polygon and Polyline methods The input methods are discussed in sections 221 222 and 223 The Polyline method is available only for specifying data to the River Drain Generalhead boundary and StreamflowRouting packages In the Grid View display mode the Viewing Window is aligned with the model grid Fig 25 In the Map View display mode the Viewing Window is aligned with the orthogonal Northing and Easting coordinate axes A rotated model grid is displayed 22 The Data Editor 15 on the Map View similar to Fig 26 In the Row or Column crosssectional View the Viewing Window is aligned with the vertical axis Fig 27 Fig 25 The Data Editor Grid View Using the Environment Options dialog box see Section 292 the user can adjust the vertical exaggeration factor for the crosssectional display the coordinate system the horizontal extent of the Viewing Window and the position of the model grid to fit the condition of the study area Regardless of the display modes the mouse pointer position x y z is always expressed in the world coordinates according to the user defined coordinate system and K I J is expressed in Layer Row Column cell indices The position of the grid cursor is shown in the tool bar The grid cursor can be moved by using the arrow keys clicking the mouse on the desired position using buttons in the tool bar or typing the new position in the layerrowcolumn edit fields and pressing the Enter key The parameter values of the cell pointed to by the grid cursor are displayed from left to right in the status bar A summary of the tool bar buttons of the Data Editor is given in Table 24 16 2 Modeling Environment Table 24 Summary of the toolbar buttons of the Data Editor Button Name Action Leave editor Leave the Data Editor and return to the main menu Assign value Allow the user to move the grid cursor and assign values to model cells Pan Moves the Viewing Window up down or sideways to display areas of the model domain which at the current viewing scale lie outside the Viewing Window By dragging the mouse the model grid and sitemaps will be moved in the same direction as the mouse cursor When the left mouse button is released the grid and maps will be redrawn Zoom in Allow the user to drag a zoomwindow over a part of the model domain Zoom out Display the entire worksheet Cellbycell in put method Switch to the Cellbycell input method Polygon input method Switch to the Zone input method Polyline input method Switch to the Polyline input method Grid view Switch to the Grid View display mode Map view Switch to the Map View display mode Column View Switch to the column crosssectional display mode Row View Switch to the row crosssectional display mode Duplication onoff If duplication is turned on the size of the current row or col umn will be copied to all rows or columns passed by the grid cursor Duplication is on when this button is depressed Layer Row Column Copy onoff When this button is depressed Layerrowcolumn copy is on and the following rules apply 1 If the display mode is Grid View or Map View when moving to another layer the zones and cell values of the current layer will be copied to the desti nation layer 2 If the display mode is Row View when mov ing to another column the cell values of the current row cross section will be copied to the destination row crosssection 3 If the display mode is Column View when moving to another column the cell values of the current column crosssection will be copied to the destination column crosssection Change stress period Manage model data for transient simulations 22 The Data Editor 17 Fig 26 The Data Editor Map View 221 The CellbyCell Input Method To activate this method click the button or select Options Input Method Cell ByCell To assign new values to a cell 1 Click the assign value button It is not necessary to click this button if the button is already depressed 2 Move the grid cursor to the desired cell by using the arrow keys or by clicking the mouse on the cell The values of the current cell is are displayed in the status bar 3 Press the Enter key or press the right mouse button once The Data Editor shows a dialog box 4 In the dialog box type new values then click OK Since groundwater model data are often very complex PM provides several possibili ties for checking or modifying cellbycell model data as listed below 18 2 Modeling Environment Fig 27 The Data Editor Crosssectional View Doubleclick a cell All model cells with the same value will appear in the same color The color can be changed by repeated doubleclicks Shift left mouse button or CtrlQ Open the Cell Information dialog box Fig 28 which displays the userspecified data of the cell pointed to by the grid cursor Ctrl left mouse button Open the Search and Modify Cell Values dialog box Fig 29 This allows you to display all cells that have a value located within the Search Range to be specified According to the user specified Value and the operation Options you can easily modify the cell values For example if Add is used the userspecified value will be added to the cell value The Parameter dropdown box shows the available parameter types The user may select the parameter to which the subsequent Search and Modify operation will be applied Select Value Search and Modify or press CtrlS Open a Search and Modify dialog box for more advanced data manipulation fea tures See Section 285 for details 22 The Data Editor 19 Fig 28 The Cell Information dialog box Fig 29 The Search and Modify Cell Values dialog box 222 The Polygon Input Method The Polygon Input Method allows the user to assign parameter values to model cells with the help of polygons This input method is not allowed in the crosssectional view To activate this method click on the button or the button to switch to Grid View or Map View and then click on the button or choose Options Input Method Poly gon The use of this input method is straightforward First you draw a polygon and then assign parameter values to the polygon Finally press the button to apply the parameter values to model cells that lie within the polygon Note Polygon data is not used by PM for model computation directly If polygon data is not applied to the model cells the original values in the cells are used To draw a polygon 1 If the display mode is not Grid View or Map View click the button or the button to switch to the Grid View or Map View 20 2 Modeling Environment 2 Click the assign value button and click the button 3 Click the mouse pointer on a desired position to anchor one end of a line 4 Move the mouse pointer to another position then press the left mouse button again 5 Repeat steps 3 and 4 until the polygon is closed or press the right mouse button to abort To delete a polygon 1 If the display mode is not Grid View or Map View click the button or the button to switch to the Grid View or Map View 2 Click the assign value button and click the button 3 Move the mouse pointer into a polygon The boundary of the polygon will be highlighted 4 Press the Delete key To assign values to polygons 1 If the display mode is not Grid View or Map View click the button or the button to switch to the Grid View or Map View 2 Click the assign value button and click the button 3 Move the mouse pointer into a polygon The boundary of the polygon will be highlighted The values of the polygon will be displayed in the status bar 4 Press the right mouse button once The Data Editor displays a dialog box which allows the user to assign parameter values to the polygon 5 In the dialog box type new parameter values then click the button to apply the parameter values to the model cells within the polygon To modify a polygon 1 The user may drag vertices of a polygon by pointing the mouse pointer at a vertex node and pressing down the left mouse button while moving the mouse 2 If there are several polygons some polygons can intersect or even cover other polygons If the mouse pointer is moved into a covered polygon the boundary of the polygon will not be highlighted In this case simply move the mouse pointer into that polygon hold down the Ctrl key and press the left mouse button once The Data Editor will resort the order of the polygons and the lost polygon will be recovered 22 The Data Editor 21 223 The Polyline Input Method The Polyline Input Method is available only for the Drain Generalhead boundary River and StreamflowRouting packages This input method is not allowed in the cross sectional view To activate this method click on the button or the button to switch to Grid View or Map View and then click on the button or choose Options Input Method Polyline The use of this input method is straightforward First you draw a polyline along a drain river or stream and then assign parameter values to vertices of the polyline Within a polyline parameter values needed for constructing MODFLOW input files are assigned to at least one vertex Properties needed for cells along traces of polylines are obtained using the parameter values of vertices These property values are used in addition to the cellbycell values to generate MODFLOW input files prior to running MODFLOW To draw a polyline 1 If the display mode is not Grid View or Map View click the button or the button to switch to the Grid View or Map View 2 Click the assign value button and click the button 3 Click the mouse pointer on a desired position to anchor one end of a line 4 Move the mouse pointer to another position then press the left mouse button again 5 Repeat steps 3 and 4 until the desired polyline is drawn click on the latest vertex again to complete the polyline or press the right mouse button to abort drawing To delete a polyline 1 If the display mode is not Grid View or Map View click the button or the button to switch to the Grid View or Map View 2 Click the assign value button 3 Move the mouse pointer over a polyline The polyline will be highlighted 4 Press the Delete key Follow the steps below to assign parameter values to polylines Refer to the explana tion of the River Drain Generalhead boundary and Streamflowrouting packages for details about the required parameters of each package To assign values to polylines 1 If the display mode is not Grid View or Map View click the button or the button to switch to the Grid View or Map View 22 2 Modeling Environment 2 Click the assign value button and click the button 3 Move the mouse pointer over a vertex and rightclick The Data Editor displays a dialog box which allows the user to assign parameter values to the vertex 4 In the dialog box type new parameter values Once the parameter values are specified the display color of the vertex is changed to indicate that its parameter values are specified To modify a polyline 1 The user may drag vertices of a polyline by pointing the mouse pointer at a vertex node pressing down the left mouse button and moving the mouse 2 Use Shiftleft click on a segment of the polyline to insert a new vertex 3 Use ctrlleft click on a vertex to delete it 224 Specifying Data for Transient Simulations If a model has more than one stress period the button appears in the Tool bar Clicking on this button opens the Temporal Data dialog box Fig 210 which is used to manage model data for transient simulations The following describes the use of the dialog box Fig 210 The Temporal Data dialog box 23 The File Menu 23 The table displays the status of the model data of each stress period The boxes in the Data Status column have three states Model data has been specified and will be used for the simulation Model data has been specified but will not be used The model data from the previous stress period will be used for the simulation Model data has not been specified The model data from the previous stress period will be used for the simulation Click on the Data boxes to toggle between and Fig 210 shows an example in which the model data for the periods 1 3 4 are specified The specified data of the first period will be used throughout the first three periods The data of the fourth period will be used for the rest of the simulation The model data of the third period has been specified but will not be used for the simulation since the Data Status is Edit Data To edit model data for a particular stress period select a row of the table and click the Edit Data button After having specified the model data of a stress period the Data status changes to Copy Data To copy model data from one stress period to another 23 The File Menu 231 New Model Select New Model to create a new model A New Model dialog box allows the user to specify a filename on any available folder or drive for the new model A PM model must always have the file extension pm5 which has been kept consistent since PMWIN version 5 All file names valid under the MS Windows operating system with up to 120 characters can be used It is a good idea to save every model in a separate folder where the model and its output data will be kept This will also allow the user to run several models simultaneously multitasking 232 Open Model Use Open Model to load an existing PM model Once a model is opened PM displays the filename of the model on the title bar 233 Convert Model A Convert Models dialog box appears after selecting this menu item The options in this dialog box are grouped under 4 tabs PMWIN 4x MODFLOW8896 24 2 Modeling Environment Fig 211 The Convert Model dialog box MODFLOW20002005 and Telescoping Flow Model Fig 211 The tabs are de scribed below In addition the user can specify refinement factors for both column and row directions In this way one can load or create a model with a higher resolution for transport simulations PMWIN 4x tab This tab is used to convert groundwater models created by PMWIN 4x to PM To convert click the open file button and select a PMWIN 4x model from an Open dialog box then click the Convert button to start the con version Groundwater models created by PMWIN 5x or later are compatible with PM and do not need to be converted MODFLOW8896 tab This tab is used to import models stored in MODFLOW 88 or MODFLOW96 formats to PM To import click the open file button and select a MODFLOW Name File from an Open dialog box then click the Convert button to start the conversion Refer to Section 631 for the definition of the name file A MODFLOW8896 name file usually has lines with the file type ie Ftype BAS or BCF MODFLOW20002005 tab This tab is used to import models stored in MODFLOW 20002005 formats to PM To import click the open file button and select a MODFLOW Name File from an Open dialog box then click the Convert button to start the conversion Refer to Section 631 for the definition of the name file A MODFLOW20002005 name file usually has lines with the file type ie Ftype BAS6 BCF6 or LPF Telescoping Flow Model Fig 212 This tab creates localscale submodels from a regional scale model To create a submodel select an existing PM model and specify the subregion Then click the Convert button Prior to converting the flow simulation of existing PM model must be performed The subregion is defined by the starting and ending columns and rows PM automatically transfers the model parameters and the calculated heads from the regional model to the submodel The 23 The File Menu 25 boundary of the submodel will be set to constant head boundary for steadystate simulations or timevariant specifiedhead boundary for transient simulations Fig 212 Telescoping a flow model using the Convert Model dialog box 234 Preferences The Preferences dialog box Fig 213 defines the MODFLOW version and manages the paths to the simulation programs of an opened PM model The settings of the dialog box are described below Fig 213 The Preferences dialog box 26 2 Modeling Environment Modflow Version Several variants of MODFLOW are supported and included in PM Each variant is associated with an executable program The full paths and file names of all executable programs of MODFLOW are given in Table 25 The de fault Modflow Version is MODFLOW96 This version works with all supported transport models If you intent to do parameterestimation runs with MODFLOW 2000 Modflow Version must be set to MODFLOW2000MODFLOW2005 and the Flow Package see below must be set to LayerProperty Flow LPF or Up stream Weighting UPW Package If you want to use MODFLOWNWT you must select MODFLOW2000MODFLOW2005 LayerProperty Flow LPF or Upstream Weighting UPW Package and then activate the Newton Solver see Section 26113 Flow Package This dropdown box is locked on the BCF package if Modflow Version is MODFLOW96 This dropdown box is enabled when Modflow Ver sion is set to MODFLOW2000MODFLOW2005 Both MODFLOW2000 and MODFLOW2005 include the LayerProperty Flow LPF and the BlockCentered Flow BCF packages for formulating intercell hydraulic conductance terms The UpstreamWeighting UPW package is included in MODFLOWNWT designed to solve problems involving drying and rewetting nonlinearities of the unconfined groundwaterflow equation The input data format to the UPW package is nearly identical to that of the LPF package As the BCF or LPFUPW packages require different aquifer parameters for formulating finite difference equations of ground water flow it is important to notice the following major differences between these packages The Block Centered Flow BCF package supports four layer types Depend on the selected layer type the required aquifer parameters of a model layer are different and listed below Layer type 0 T and S Layer type 1 HK and Sy Layer type 2 T S and Sy Layer type 3 HK Sy and S Note that S and Sy are required only for a transient flow simulation All layer types use VCONT to describe the vertical conductance between two layers The LayerProperty Flow package and the UpstreamWeighting package has only two layer types confined and convertible ie convertible between con fined and unconfined Independent of the selected layer type a model layer always requires HK Ss and VK or VANI The only exception is Sy which is required only if the layer is convertible note that Ss and Sy are required only for a transient flow simulation When the LayerProperty Flow package is selected the menu items Transmissivity Vertical Leakance and Storage Co efficient of the Parameters menu are dimmed and cannot be used dont need to be used 23 The File Menu 27 Note All versions of Modflow and BCF LPF or UPW package can be used with PEST for estimating parameters However one can only estimate the required aquifer parameters of the BCF or LPFUPW package as given above As the BCF package does the not support the required parameterization method of MODFLOW2000 this package cannot be used with the builtin model calibration capability of MODFLOW2000 That is the user cannot estimate aquifer parameters when using BCF with MODFLOW2000 The settings of Modflow Version and Flow Package are saved with the model ie if the model is used on another computer these settings will remain the same Table 25 Versions and Filenames of MODFLOW Version Filename MODFLOW96 pmdirmodflw96lkmt2modflow2iexe MODFLOW2000 pmdirmf2kmf2kiexe MODFLOW2005 pmdirmodflow2005mf2005exe MODFLOWNWT pmdirmodflownwtmodflownwtexe MODFLOWNWT 64bit version pmdirmodflownwtmodflownwt 64exe pmdir is the folder in which PM is installed for example CSimcorePM8 ModuleModels The supported modules or models are listed below Each mod ulemodel is associated with a program Note that some modules are optional and may not appear on the users computer MODFLOW is groundwater flow simulation program which is used when se lecting the menu item Modflow Run PMPATH is a particletracking model also referred to as advective transport included in PM Text Viewer which can be any text editors is used to display simulation result files which are saved in ASCII MODFLOW2000 Parameter Estimation The associated program is used when selecting the menu item MODFLOW2000 Parameter Estimation Run MODFLOW2000 PEST Parameter Estimation PEST 3334 is a program for parameter es timation The associated program is used when selecting the menu item PEST Parameter Estimation Run or MODFLOW2000 Parameter Estimation Run PESTASPMODFLOW2000 Note that the latter requires PESTASP and a special version of MODFLOW2000 called MF2KASP which are au tomatically installed 28 2 Modeling Environment MT3D MT3D is a singlespecies solute transport model which has been pre pared by Zheng 119122 and has been improved subsequently over years The associated program is used when selecting the menu item MT3D Run MOC3D MOC3D 74 is a singlespecies solute transport model using the method of characteristics The associated program is used when selecting the menu item MOC3D Run MT3DMS MT3DMS 123125 is a multispecies solute transport model The associated program is used when selecting the menu item MT3DMSSEAWAT Run If the user intends to use MT3D99 124 the MT3D99 program should be assigned to this module and the MT3D99 and MODFLOW programs must be compiled with the same compiler 3D Visualization The software Seer3D is available separately When in stalled Seer3D can be started by selecting the menu item Tools 3D Visual ization RT3D The RT3D model 252627 simulates reactiveflow and transport of multiple mobile andor immobile species The PM installation includes three versions of RT3D rt3d1vexe version 1 rt3d2vexe version 2 and rt3d25vexe version 25 They can be found in the folder pmhomert3d where pmhome is the installation directory of PM The associated program is used when selecting the menu item RT3D Run PHT3D PHT3D 99 couples MT3DMS 125 for the simulation of three dimensional advectivedispersive multicomponent transport and the geochem ical model PHREEQC2 93 for the quantification of reactive processes The associated program is used when selecting the menu item PHT3D Run SEAWAT SEAWAT is designed to simulate threedimensional variabledensity saturated groundwater flow and transport The associated program is used when selecting the menu item MT3DMSSEAWAT Run Active Check or clear the active flag to activate or deactivate a modelmodule Please note that the first three modules MODFLOW PMPATH and TEXT VIEWER are required and cannot be deactivated When a module is deactivated its associ ated menu item under the Models menu is removed This feature is useful when several modules are not used and the Models menu should be kept as short as pos sible Deactivating or activating of a module does not affect the model data in any way Paths to Simulation Program File If the user intends to use an executable program located in another position click the corresponding button and select the desired program from a dialog box Note The following programs must be located in the same directory as the PEST PESTASP program mf2kaspexe mf2pestexe modboreexe par2senexe and pestchekexe 23 The File Menu 29 235 Save Plot As Use Save Plot As to save the contents of the worksheet in graphics files Three graph ics formats are available Drawing Interchange File DXF HewlettPackard Graphics Language HPGL and Windows Bitmap BMP DXF is a fairly standard format developed by Autodesk for exchanging data between CAD systems HPGL is a two letter mnemonic graphics language developed by HewlettPackard Most graphics or wordprocessing software and graphics devices can process these graphics formats To save a plot use the Format dropdown box to select a graphic format Then enter a filename into the File edit field or click and select a file from a dialog box When finished click OK Note that in the Map View display mode only the BMPformat may be used 236 Print Plot This menu item is only activated in the Data Editor After selecting this item a Print Plot dialog box is displayed with a preview window The options are described below Use full page The plot is scaled to fit the paper the original aspect ratio will not be changed Center on page The plot is placed on the center of the page Image Size millimeters Specify the width and height of the printed image in millimeters Margins millimeters Specify the left and top margins of the image in millimeters Printer A Printer dialog box allows the user to select an installed printer and spec ify the print quality the paper size source and orientation and other printing pa rameters Print Print the contents shown on the preview window Close Close the Print Plot dialog box without printing 237 Animation This menu item is only activated when the 2D Visualization Tools 2D Visualization tool is selected Before creating an animation sequence the user should use the En vironment Option and Maps Option dialog boxes refer to Section 29 for details to make sure that the model grid maps and contours are set properly To create an animation sequence 1 Select File Animation to display an Animation dialog box 30 2 Modeling Environment 2 In the Animation dialog box click the open file button to display a Save File dialog box Select an existing frame file or specify a new base file name for the frame files in the dialog box then click Open Like a movie an animation sequence is based on a series of of frames Each frame is saved by using the filename basenamennn where basename is the base file name and nnn is the serial number of the frame files Note To protect the model data the frame files must not be saved in the same folder as the model data 3 Check or clear Create New Frames Check Create New Frames if a new animation sequence should be created Clear the Create New Frame box if a saved sequence should be played back 4 Set Delays Delay is the number of seconds between frames 5 In the Animation dialog box click OK to start the animation PM will create a frame image for each time point at which the simulation results have been saved When all frames are created PM will repeat the animation indefinitely until the Esc key is pressed 24 The Grid Menu 241 Mesh Size Allows the user to generate or modify a model grid using the Grid Editor See Section 21 for how to use the Grid Editor 242 Layer Property The layer properties are defined in the Layer Property dialog box Fig 214 Many settings of this dialog box depend on the selection between the BlockCenteredFlow BCF and Layer Property Flow LPF packages Refer to Section 234 for details about the BCF and LPF package When the LPF Package is used the columns Trans missivity Leakance and Storage Coefficient are dimmed to indicate that their settings are ignored because the LPF package only uses HK VK Ss and Sy When the BCF package is used the column Vertical Anisotropy is dimmed since it is not supported by the BCF package The settings of this dialog box are described below Type The numerical formulations which are used by the BCF or LPF package to describe groundwater flow depend on the type of each model layer The available layer types are 24 The Grid Menu 31 Type 0 The layer is strictly confined For transient simulations the confined storage coefficient specific storage layer thickness is used to calculate the rate of change in storage Transmissivity of each cell is constant throughout the simulation Type 1 The layer is strictly unconfined The option is valid for the first layer only Specific yield is used to calculate the rate of change in storage for this layer type During a flow simulation transmissivity of each cell varies with the saturated thickness of the aquifer Type 2 A layer of this type is partially convertible between confined and un confined Confined storage coefficient specific storage layer thickness is used to calculate the rate of change in storage if the layer is fully saturated otherwise specific yield will be used Transmissivity of each cell is constant throughout the simulation Vertical leakage from above is limited if the layer desaturates Type 3 A layer of this type is fully convertible between confined and uncon fined Confined storage coefficient specific storage layer thickness is used to calculate the rate of change in storage if the layer is fully saturated oth erwise specific yield will be used During a flow simulation transmissivity of each cell varies with the saturated thickness of the aquifer Vertical leakage from above is limited if the layer desaturates Note that the LPF package uses only two layer types confined and convertible Layer type 0 will be interpreted by the LPF package as confined and all other layer types will be interpreted as convertible layers ie the layers are convertible between confined and unconfined Fig 214 The Layer Property dialog box 32 2 Modeling Environment Horizontal Anisotropy The ratio of the horizontal hydraulic conductivity along columns to hydraulic conductivity along rows The latter is specified by selecting Parameters Horizontal Hydraulic Conductivity When the LPF package is used a positive Horizontal Anisotropy value indi cates that horizontal anisotropy is constant for all cells in the layer and the anisotropy is the specified value A negative value indicates that horizontal anisotropy can vary at each cell in the layer The cellbycell anisotropy values are specified by selecting Parameters Horizontal Anisotropy When the BCF package is used horizontal anisotropy is constant for all cells in the layer and the anisotropy is the absolute value of the specified Horizontal Anisotropy value Vertical Anisotropy The setting of this column is either VK or VANI VK indicates that vertical hydraulic conductivity is used for the layer and is to be specified by selecting Parameters Vertical Hydraulic Conductivity VANI indicates that vertical anisotropy is used for the layer and is to be speci fied by selecting Parameters Vertical Anisotropy Transmissivity MODFLOW or exactly to say the BCF package requires trans missivity horizontal hydraulic conductivity LT 1 layer thickness L for layers of type 0 or 2 PM provides two options for each model layer to facilitate the data input Set the Transmissivity setting of a layer to UserSpecified The userspecified transmissivity values of the layer are used in the simulation Set the Transmissivity setting of a layer to Calculated PM calculates transmissivity of the layer by using userspecified horizontal hydraulic conductivity and the elevations of the top and bottom of the layer The calculated transmissivity values are used in the simulation Leakance For flow simulations involving more than one model layer MOD FLOW BCF package requires the input of the vertical conductance term known as vertical leakance VCONT array between two model layers MODFLOW uses VCONT to formulate the flow rate equation between two vertically adjacent cells PM provides two options for each model layer to facilitate the data input Set the Leakance setting of a layer to UserSpecified The userspecified vertical leakance values are used in the simulation In the Data Editor the vertical leakance between the layers i and i1 is given as the data of the ith layer The leakance data are not required for the bottom layer since MODFLOW assumes that the bottom layer is underlain by impermeable material Set the Leakance setting of a layer to Calculated PM calculates vertical leakance by using the rules explained below The calcu lated vertical leakance values are used in the simulation 24 The Grid Menu 33 As illustrated in Fig 215a when each model layer represents a different hy drostratigraphic unit or when two or more layers represent a single hydro stratigraphic unit PM uses equation 21 to calculate the vertical leakance VCONT V CONT 2 νk Kzkij νk1 Kzk1ij 21 where Kzkij and Kzk1ij are the vertical hydraulic conductivity values of layers k and k1 respectively The ratio of horizontal to vertical hydraulic conductivity ranging from 11 to 10001 is common in model application 8 A summary of hydraulic conductivity values can be found in 111 It is not uncommon to represent resistance to flow in a low hydraulic conduc tivity unit 215b semiconfining unit by lumping the vertical hydraulic con ductivity and thickness of the confining unit into a vertical leakance term be tween two adjacent layers These kinds of models are often called quasi three dimensional models because semiconfining units are not explicitly included in a simulation In this case the user must manually calculate the VCONT val ues using equation 22 and enter them into the Data Editor V CONT 2 νu Kzu νc Kzc νL KzL 22 where Kzu Kzc and KzL are the vertical hydraulic conductivity values of the upper layer semiconfining unit and lower layer respectively Fig 215 Grid configuration used for the calculation of VCONT 34 2 Modeling Environment Storage Coefficient For transient flow simulations MODFLOW BCF package requires dimensionless storage terms to be specified for each model layer For a confined layer these storage terms are given by the confined storage coefficient specific storage L1 layer thickness L If the Storage Coefficient setting is set to Calculated PM uses userspecified specific storage and the elevations of the top and bottom of each layer to calculate the confined storage coefficient Set the Storage Coefficient flag to User Specified if you want to specify the confined storage coefficient manually For an unconfined layer the storage values are equal to specific yield The setting of the Storage Coefficient flag has no influence on the specific yield Interbed Storage PM supports the InterbedStorage package for calculating stor age changes from both elastic and inelastic compaction of each model layer Check the Interbed Storage setting of a specific layer to calculate its storage changes and compaction by using the InterbedStorage package Refer to Section 2615 for details about this package 243 Cell Status 2431 IBOUND MODFLOW The flow model MODFLOW requires an IBOUND array which contains a code for each model cell A positive value in the IBOUND array defines an active cell the hydraulic head is computed a negative value defines a constant head or fixed head cell the hydraulic head is kept constant at a given value throughout the flow simula tion and the value 0 defines an inactive cell no flow takes place within the cell It is suggested to use 1 for active cells 0 for inactive cells and 1 for constant head cells Any outer boundary cell which is not a constant head cell is automatically a zero flux boundary cell Flux boundaries with nonzero fluxes are simulated by assigning appro priate infiltration or pumping wells in the corresponding cell via the well package For constant head cells the initial hydraulic head remains the same throughout the simulation The initial hydraulic head is specified by selecting Parameters Initial and Prescribed Hydraulic Heads A constant head boundary exists whenever an aquifer is in direct hydraulic contact with a river a lake or a reservoir in which the water groundwater level is known to be constant It is important to be aware that a constant head boundary can provide inexhaustible supply or sink of water A groundwater sys tem may get or lose as much water as necessary from or to such a boundary without causing any change of hydraulic heads in the constant head boundary In some situa tions this may be unrealistic Therefore care must be taken when using constant head boundaries and it is suggested to avoid using this boundary condition on the upstream side of the groundwater flow direction Consider using the GeneralHead Boundary or the TimeVariant SpecifiedHead packages if the hydraulic head at the constant 24 The Grid Menu 35 head boundary varies with time Headdependent boundary conditions are modeled by means of the general head boundary river or drain package If it is planned to use MOC3D the user should be aware that MOC3D allows one to specify zones along constant head boundaries which are associated with differ ent source concentrations Zones are defined within the IBOUND array by specifying unique negative values For example if a model has three zones one will use 1 2 and 3 for the constant head cells Note that the associated concentrations must be specified by selecting Models MOC3D SinkSource Concentration FixedHead Cells 2432 ICBUND MT3DMT3DMS The transport models MT3D MT3DMS and RT3D require an ICBUND array which contains a code for each model cell A positive value in the ICBUND array defines an active concentration cell the concentration varies with time and is calculated a negative value defines a constantconcentration cell the concentration is constant and the value 0 defines an inactive concentration cell no transport simulation takes place at such cells It is suggested to use the value 1 for an active concentration cell 1 for a constantconcentration cell and 0 for an inactive concentration cell Note that the ICBUND array applies to all species if MT3DMS or RT3D is used Other types of boundary conditions are implemented by assigning concentrations to inflows see sections 2666 and 2628 or assigning a massloading rate to a cell Section 2629 MT3D MT3DMS and RT3D automatically convert noflow or dry cells to inac tive concentration cells Active variablehead cells can be treated as inactive concen tration cells to minimize the area needed for transport simulation as long as the solute transport is insignificant near those cells For constantconcentration cells the initial concentration remains the same at the cell throughout the simulation A constant head cell may or may not be a constantconcentration cell The initial concentration is spec ified by selecting Models MT3D Initial Concentration Models MT3DMS Initial Concentration or Models RT3D Initial Concentration 244 Top of Layers TOP The top elevation of a layer is required when one of the following conditions applies PM will check these conditions except the last one prior to running a model simula tion 1 The BCF package is selected and layer type 2 or 3 is used 2 The BCF package is selected and VCONT to the underlying layer is calculated by PM 3 The BCF package is selected and T or S is calculated by PM 4 The LPF package is used 36 2 Modeling Environment 5 One of the programs PMPATH MT3D MT3DMS MOC3D RT3D PHT3D or 3D Master for 3DVisualization will be used 245 Bottom of Layers BOT The bottom elevation of a layer is required when one of the following conditions ap plies PM will check these conditions except the last one prior to running a model simulation 1 The BCF package is selected and layer type 2 or 3 is used 2 The BCF package is selected and VCONT to the underlying layer is calculated by PM 3 The BCF package is selected and T or S is calculated by PM 4 The LPF package is used 5 One of the programs PMPATH MT3D MT3DMS MOC3D RT3D PHT3D or 3D Master for 3DVisualization will be used 25 The Parameters Menu This menu is used to input time initial hydraulic head values and aquifer parameters such as HK or VK Depends on the settings of the layer properties Section 242 it is possible that an aquifer parameter is required only for certain model layers or is not required for any of the model layers In the latter case the corresponding menu item will be dimmed In the former case the Data Editor will display a short indicative message data of this layer will be used in the simulation or data of this layer will NOT be used in the simulation on the status bar to indicate whether an aquifer parameter is required for the layer being edited 251 Time Selecting this menu item to display a Time Parameters dialog box The appearance of this dialog box is affected by the setting of the Modflow version Section 234 When the Modflow Version is set to MODFLOW2000MODFLOW2005 the Transient column appears in the table of this dialog box and the Simulation Flow Type group of this dialog box is dimmed and deactivated Fig 216 since MODFLOW2000 allows individual stress periods in a single simulation to be either transient or steady state instead of requiring the entire simulation to be either steady state or transient Steady state and transient stress periods can occur in any order Commonly the first stress period is steady state and produces a solution that is used as the initial condition for subsequent transient stress periods 25 The Parameters Menu 37 Fig 216 The Time Parameters dialog box for MODFLOW2000MODFLOW2005 When the Modflow Version is not set to MODFLOW2000MODFLOW2005 the Transient column disappears and all stress periods are either steadystate or tran sient which is controlled by the options of the Simulation Flow Type group Fig 217 The columns of this dialog box are described below Period Active Length Time Step MODFLOW divides the simulation time into stress periods which are in turn divided into time steps Check the Active box to activate a stress period For each stress period the user has the option of chang ing parameters associated with headdependent boundary conditions in the River Stream Drain Evapotranspiration GeneralHead Boundary and TimeVariant SpecifiedHead Boundary packages as well as the recharge rates in the Recharge package and pumping rates in the Well package For transport simulations the user may change massloading rates MT3DMS only and source concentrations asso ciated with the fluid sources and sinks The length of stress periods and time steps is not relevant to steady state flow simu lations However if transport simulations need to be done at a later time the actual period length should be entered Transient Check the Transient box if a stress period is transient Clear the Tran sient box if a stress period is steadystate Multiplier Flow MODFLOW allows the time step to increase as the simulation progresses It uses the following equations to increase the lengths of time steps as 38 2 Modeling Environment Fig 217 The Time Parameters dialog box for MODFLOW96 a geometric progression t1 PERLEN TSMULT 1 TSMULT NST P 1 23 tm1 TSMULT tm 24 where PERLEN is the length of a stress period TSMULT is the time step multiplier NSTP is the number of time steps and tm is the length of the mth time step within a stress period Transport Step size The transport models further divide each time step into smaller time increments called transport steps Because the explicit numerical solution of the solutetransport equation has certain stability criteria associated with it the length of a time step used for a flow solution may be too large for a transport solution Each time step must therefore be divided into smaller transport steps For explicit solutions eg when the Generalized Conjugate Gradient solver is not used in MT3DMS the transport step sizes in the table are used for the simulation Considering stability criteria the transport models always calculate a maximum allowed transport step size Deltatmax Usually the smallest cell containing sinks will be the one which determines Deltatmax Therefore in transport simulations variable cell sizes are not always beneficial Setting the transport step size in the table to zero or to a value greater than Deltatmax will cause Deltatmax to be used 25 The Parameters Menu 39 for the simulation For details about the stability criteria associated with the explicit transportsolution refer to 74 119 or 120 For implicit solutions in MT3DMS ie when the Generalized Conjugate Gradient solver is used the transport step sizes in the table are the initial transport step size in each flow time step The subsequent transport step size may increase or remain constant depending on the userspecified transport step size multiplier see below If the transport step size is specified as zero the modelcalculated value based on the userspecified Courant number in the Advection Package MT3DMS dialog box is used Max No of Transport Steps If the number of transport steps within a flow time step exceeds the maximum number the simulation is terminated Multiplier Transport is the multiplier for successive transport steps within a flow time step This value is used by MT3DMS for the case that the Generalized Con jugate Gradient solver and the solution option for the advection term is the finite difference method see Section 2623 Simulation Time Unit Each time when the time unit in the Simulation Time Unit group is changed PM will update the period length in the table if Auto Update Period Length is checked Note that changing the time unit does not affect the userspecified parameter values Simulation Flow Type PM allows to perform steady state or transient flow simula tions by selecting an option from the Simulation Flow Type group It is possible to run a steady state simulation over several stress periods In this case a steady state solution is calculated for each stress period Save As and Load Using these buttons the user can save or load the contents of the table in or from a time parameter file or a ASCII time parameter file The format of the ASCII time parameter file is given in Section 625 252 Initial Prescribed Hydraulic Heads MODFLOW requires initial hydraulic heads at the beginning of a flow simulation Initial hydraulic heads at constant head cells are used as specified head values of those cells and remain constant throughout the flow simulation For transient flow simulations the initial heads must be the actual values since they are used to account for the storage terms For steadystate flow simulations the initial heads are used as starting values for the iterative equation solvers The initial heads at the constant head cells must be the actual values while all other values can be set at an arbitrary level For an unconfined or convertible layer layer type 1 or 3 the initial hydraulic head of a constant head cell should be higher than the elevation of the cell bottom because MODFLOW does not convert a dry fixedhead cell to an inactive cell If any constanthead cell becomes dry MODFLOW will stop the flow simula tion and write a message CONSTANTHEAD CELL WENT DRY SIMULATION ABORTED into the run listing file OUTPUTDAT 40 2 Modeling Environment 253 Horizontal Hydraulic Conductivity and Transmissivity Horizontal hydraulic conductivity is required for layers of types 1 or 3 Transmissivity is required for layers of types 0 or 2 Horizontal hydraulic conductivity is the hydraulic conductivity along model rows It is multiplied by an anisotropy factor specified in the Layer Property dialog box Section 242 to obtain the hydraulic conductivity along model columns Typical values and ranges of horizontal hydraulic conductivity for different types of soils are given in many groundwater textbooks for example Freeze and Cherry 46 Spitz and Moreno 111 and Fetter 44 For layers of types 0 or 2 PM uses the horizontal hydraulic conductivity and layer thickness to calculate transmissivity if the corresponding Transmissivity setting in the Layer Property dialog box Section 242 is set to Calculated The userspecified trans missivity values of a model layer are used in the simulation if the Transmissivity setting of that layer is set to Userspecified 254 Horizontal Anisotropy The LayerProperty Flow LPF package supports the use of the cellbycell horizontal anisotropy which is the ratio of horizontal hydraulic conductivity along columns to hydraulic conductivity along rows The latter is specified by selecting Parameters Horizontal Hydraulic Conductivity The menu item Horizontal Anisotropy is dimmed and cannot be used with the BlockCentered Flow BCF package The cellbycell horizontal anisotropy values of a layer are used only when the Horizontal Anisotropy value of the layer in the Layer Options dialog box Fig 214 page 31 is negative 255 Vertical Leakance and Vertical Hydraulic Conductivity The BCF package uses the vertical leakance VCONT values to formulate the flow rate equation between two vertically adjacent cells As discussed in Section 242 the user may either specify the vertical leakance values directly or specify the vertical hydraulic conductivity values and let PM calculate the required VCONT values When Vertical Leakance of a layer in the Layer Property dialog box Fig 214 is Userspecified the userspecified vertical leakance values of that layer are used in the simulation When Vertical Leakance is calculated PM calculates the VCONT values and uses them in the simulation Refer to Section 242 for details 256 Vertical Anisotropy and Vertical Hydraulic Conductivity The LayerProperty Flow LPF package supports the use of the cellbycell vertical hydraulic conductivity or vertical anisotropy which is the ratio of horizontal hydraulic 25 The Parameters Menu 41 conductivity along rows to vertical hydraulic conductivity for the model layer The menu item Vertical Anisotropy is dimmed and cannot be used with the BlockCentered Flow BCF package When Vertical Anisotropy of a layer in the Layer Property dialog box Fig 214 is VK the cellbycell vertical hydraulic conductivity of that layer is used in the sim ulation When Vertical Anisotropy is VANI the cellbycell vertical anisotropy of the layer is used 257 Effective Porosity If the total unit volume V of a soil matrix is divided into the volume of the solid portion Vs and the volume of voids Vv the porosity n is defined as n VvV Effective poros ity with the respect to flow through the medium is normally smaller than porosity because part of the fluid in the pore space is immobile or partially immobile This may occur when the flow takes place in a finetextured medium where adhesion ie the attraction to the solid surface of the porous matrix by the fluid molecules adjacent to it is important On a more macroscopic scale the effective porosity also has to accom modate the fact that unresolved conductivity variations lead to a reduction of effective porosity Transport models for example PMPATH or MT3DMS use effective porosity to calculate the average velocity of the flow through the porous medium If a dual porosity system is simulated by MT3DMS effective porosity should be specified as the portion of total porosity filled with mobile water and the immobile porosity is defined through Models MT3DMS Chemical Reaction A summary of representa tive porosity values for different soil types can be found in Zheng and Bennett 120 or Domenico and Schwartz 41 258 Specific Storage Storage Coefficient and Specific Yield For transient flow simulations MODFLOW requires dimensionless storage terms specified for each layer of the model For a steady state simulation these menu items are not used and are therefore dimmed In a confined layer the storage term is given by storativity or confined storage co efficient specific storage L1 layer thickness L The storativity is a function of the compressibility of the water and the elastic property of the soil matrix The spe cific storage or specific storativity is defined as the volume fraction of water that a unit column of aquifer releases from storage under a unit decline in hydraulic head The specific storage ranges in value from 33 106 m1 of rock to 20 102 m1 of plastic clay Domenico 40 Layers of types 0 2 and 3 require the confined storage coefficient PM uses spe cific storage and the layer thickness to calculate the confined storage coefficient if the 42 2 Modeling Environment corresponding Storage Coefficient setting in the Layer Property dialog is Calculated By setting the Storage Coefficient setting to User Specified and selecting Parameters Storage Coefficient you can specify the confined storage coefficient directly In a phreatic aquifer Layers of types 2 and 3 the storage term is given by specific yield or drainable porosity Specific yield is defined as the volume of water that an un confined aquifer releases from storage per unit surface area of aquifer per unit decline in the water table Specific yield is a function of porosity and is not necessarily equal to porosity because a certain amount of water is held in the soil matrix and cannot be removed by gravity drainage Refer to Spitz and Moreno 111 for a summary of values of specific yield Refer to Bear 1213 or Freeze and Cherry 46 for detailed explanation of storage terms and their definitions 259 Bulk Density 2591 Layer by Layer The layerbylayer bulkdensity data are used by the Chemical Reaction package of MT3D or RT3D version 1 for calculating the retardation factor or for calculating the firstorder irreversible radioactive decay or biodegradation rate of the adsorbed phase Refer to Section 2664 for details 2592 Cell by Cell The cellbycell bulkdensity data are used by the Chemical Reaction package of MT3DMS MT3D99 PHT3D SEAWAT and RT3D version 2 and later for simu lating sorption effects 26 The Models Menu 261 MODFLOW 2611 MODFLOW Flow Packages Drain The Drain package is used to simulate effects of features such as agricultural drains which remove groundwater from aquifer at a rate proportional to the head difference between the aquifer and the drain When the hydraulic head in the aquifer is greater than the drain elevation ground water flows into the drain and is removed from the groundwater model Discharge to the drain is zero when the hydraulic head is lower than or equal to the median drain elevation Recharge from the drain is always zero regardless of the hydraulic head in the aquifer 26 The Models Menu 43 Using the Data Editor a drain system is defined by using the CellbyCell or Poly gon input methods to assign parameters to model cells or by using the Polyline input method and assigning parameters to vertices of the polylines along the trace of drain system The input parameters are assumed to be constant during a given stress period For transient flow simulations involving several stress periods the input parameters can be different from period to period The input methods require different parameters as described below When using the Polyline input method rightclick on a vertex to specify its prop erties in the Drain Parameters dialog box Fig 218 If the properties are assigned to one vertex only the properties of all vertices of the polyline are assumed to be the same The settings of the dialog box are described below Layer Option and Layer Number Layer Option controls how the layer number of a drain is determined If Layer Option is Assign layer number manually the value of Layer Number defines the model layer number for all model cells downstream from a vertex until the next vertex redefines the layer number If Layer Option is Assign layer number automatically the drain is as signed to a layer where the drain elevation d see below is located between the top and bottom of the layer The layer number is set to 1 if d is higher than the top of the first layer The layer number is set to the last layer if d is lower than the bottom of the last layer Active Check this box to activate a vertex Clear the Active box to deactivate a vertex The properties of an active vertex will be used in the simulation The properties of an inactive vertex are ignored Fig 218 The Drain Parameters dialog box 44 2 Modeling Environment Equivalent Hydraulic Conductivity K LT 1 and Elevation of the Drain d L The value K describes all of the head loss between the drain and the aquifer It depends on the material and characteristics of the drain itself and the immediate environment Since the Drain package requires the input of drain hydraulic conductance Cd and drain elevation d to each cell of a drain the input values K and d at active vertices are linearly interpolated or extrapolated to each cell along the trace of the polyline and the value Cd is obtained by Cd K L 25 where L is the length of the drain within a cell The discharge rate to a drain cell Qd is calculated by Qd Cd h d 26 where h is the hydraulic head in a drain cell By default MODFLOW saves the calculated discharge rates in the BUDGETDAT Parameter Number Since Cd is usually unknown it must be estimated Parameter Number is used to group cells where the Cd values are to be esti mated by the parameter estimation programs MODFLOW2000 Section 267 or PEST Section 268 Refer to the corresponding sections for parameter es timation steps The value of Parameter Number is assigned to all model cells downstream from a vertex until the next vertex redefines the parameter number Drain Bottom Elevation L This value is used by SEAWAT to calculate ref erence head considering the density effect to to accurately simulate the flow of variabledensity ground water to a drain The ALL button Click the ALL button of a property to copy the property value to all other active vertices When using the Cellbycell or Polygon input methods the following values are to be assigned to model cells of a drain system See the explanations above for the definition of the input values Drain hydraulic conductance Cd L2T 1 Elevation of the Drain d L Parameter Number and Drain Bottom Elevation L 2612 MODFLOW Flow Packages Evapotranspiration The Evapotranspiration package simulates the effects of plant transpiration and direct evaporation in removing water from the saturated groundwater regime Evapotranspiration is defined by assigning the following parameters to each verti cal column of cells The input parameters are assumed to be constant during a given No text content visible in the image 46 2 Modeling Environment 2 Vertical distribution of evapotranspiration is specified in the Layer Indicator Array IET defines the layer where evapotranspiration is drawn from the groundwater table elevation In either case the QET has no influence on the simulation if the designated cell is either a noflow inactive cell or a constant head cell You can select an option in the Evapotranspiration Package dialog box The layer indicator array is needed only when the second option is used 2613 MODFLOW Flow Packages GeneralHead Boundary The GeneralHead Boundary GHB package is used to simulate headdependent flow boundaries Cauchy boundary conditions where flow into or out of a GHBcell from an external source is provided in proportion to the difference between the head in the cell and the head assigned to the external source Using the Data Editor a generalhead boundary is defined by using the Cellby Cell or Polygon input methods to assign parameters to model cells or by using the Polyline input method and assigning parameters to vertices of the polylines along the trace of the boundary The input parameters are assumed to be constant during a given stress period For transient flow simulations involving several stress periods the input parameters can be different from period to period The input methods require different parameters as described below When using the Polyline input method rightclick on a vertex to specify its proper ties in the General Head Boundary Parameters dialog box Fig 219 If the prop erties are assigned to one vertex only the properties of all vertices of the polyline are assumed to be the same The settings of the dialog box are described below Layer Option and Layer Number Layer Option controls how the layer number of a general head boundary is determined If Layer Option is Assign layer number manually the value of Layer Number defines the model layer number for all model cells downstream from a vertex until the next vertex redefines the layer number If Layer Option is Assign layer number automatically the boundary is assigned to a layer where Head on Boundary hb see below is located between the top and bottom of the layer The layer number is set to 1 if hb is higher than the top of the first layer The layer number is set to the last layer if hb is lower than the bottom of the last layer Active Check this box to activate a vertex Clear the Active box to deactivate a vertex The properties of an active vertex will be used in the simulation The properties of an inactive vertex are ignored 26 The Models Menu 47 Equivalent Hydraulic Conductivity K LT 1 and Head on the External Source hb L The value K depends on the material and characteristics of the medium between the external source and the model Since the GHB package requires the input of GHB hydraulic conductance Cb and head on the external source hb to each cell of a generalhead boundary the input values K and hb at active vertices are linearly interpolated or extrapolated to each cell along the trace of the polyline and the value Cb is obtained by Cb K L 29 where L is the length of the generalhead boundary within a cell Flow through a GHBcell Qb L3T 1 is calculated by Qb Cd hb h 210 where h is the hydraulic head in the aquifer By default MODFLOW saves the calculated flow rates in the BUDGETDAT Since the GHB package does not limit the value of flow in either direction a GHBcell is equivalent to a constant head cell if a very large Cb is used Therefore care must be used in utilizing the GHB package to insure that unrealistic flows into or out of the groundwater system do not develop during the course of simulation Parameter Number Since Cb is usually unknown it must be estimated Pa rameter Number is used to group cells where the Cb values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW 2000 Section 267 Refer to the corresponding sections for parameter esti mation steps The value of Parameter Number is assigned to all model cells Fig 219 The General Head Boundary Parameters dialog box 48 2 Modeling Environment downstream from a vertex until the next vertex redefines the parameter num ber GHB Elevation L This the elevation of the generalhead boundary from which the equivalent reference head is calculated This value is required by SEAWAT to accurately calculate the flow of variabledensity groundwater to the generalhead boundary Density of GHB Fluid ML3 This value represents the prescribed den sity of fluid entering the groundwater system from the generalhead bound ary This value is used by SEAWAT only if it is running in a uncoupled mode ie the densityeffect of all species are turned off see 2621 and the Density of generalhead boundary fluid options in the Simulation Settings MT3TMSSEAWAT dialog box see Fig 248 on p 104 is set as User Specified in the GHB Package The ALL button Click the ALL button of a property to copy the property value to all other active vertices When using the Cellbycell or Polygon input methods the following values are to be assigned to model cells of a generalhead boundary See the explanations above for the definition of the input values GHB hydraulic conductance Cb L2T 1 Head on the External Source hb L Parameter Number GHB Elevation L and Density of GHB Fluid ML3 2614 MODFLOW Flow Packages HorizontalFlow Barrier The HorizontalFlow Barrier package simulates thin lowpermeability geologic fea tures such as vertical faults or slurry walls which impede the horizontal flow of groundwater These geologic features are approximated as a series of horizontalflow barriers conceptually situated on the boundaries between pairs of adjacent cells in the finitedifference grid Refer to Hsieh and Freckleton 66 for the numerical implemen tation of the HorizontalFlow Barrier package A horizontalflow barrier is defined by assigning the following values to a model cell in the HorizontalFlow Barrier Package dialog box Fig 220 The location and the parameters of the barrier are assumed to be constant for the entire simulation Barrier Direction The barrier direction indicates the cell face where the barrier is located To erase an existing barrier use zero for the barrier direction Hydraulic ConductivityThickness of the barrier TDW T 1 or Transmissiv ity Thickness of the barrier TDW LT 1 The TDW represents the hydraulic 26 The Models Menu 49 Fig 220 The HorizontalFlow Barrier dialog box characteristic of the barrier If a layer is unconfined type 1 or 3 or if MODFLOW 2000 is used TDW is the barrier hydraulic conductivity divided by the thickness of the barrier If a layer is confined type 0 or 2 TDW is the barrier transmissivity divided by the thickness of the barrier Parameter Number Parameter Number is used to group cells where the TDW values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps 2615 MODFLOW Flow Packages Interbed Storage For steady state flow simulations this menu item is not used and is therefore dimmed Groundwater is released from storage under conditions of decreasing hydraulic head The released water volume is proportional to the compressibility of the soil matrix and water because a reduction of the hydraulic head results in an increase in the effective stress on the soil skeleton and a decrease of the water pressure In creasing effective stress on the soil skeleton results in deformation compaction of the soil matrix The Interbed Storage IBS package 78 calculates the water volume released from storage and simulates elastic and inelastic compaction of compressible finegrained beds in an aquifer due to groundwater extraction The term interbed is used to denote a poorly permeable bed within a relatively permeable aquifer Fig 221 The interbeds are assumed to consist primarily of highly compressible clay and silt beds from which water flows vertically to adjacent coarsegrained beds To incorporate the calculation of interbed storage of a layer check the Interbed Storage flag in the Layer Property dialog box see Section 242 Using the Cellby cell or Polygon input methods of the Data Editor the following properties of interbeds are specified to model cells 50 2 Modeling Environment Preconsolidation Head or preconsolidation stress Hc L Preconsolidation head is the previous minimum head value in the aquifer For any model cells in which the specified preconsolidation head is greater than the initial hydraulic head the value of the preconsolidation head will be set to that of the initial hydraulic head When compressible finegrained sediments are stressed beyond a previous maxi mum stress preconsolidation stress compaction is permanent inelastic Elastic Storage Factor Sfe For a confined aquifer the elastic compaction or expansion of sediments is proportional or nearly proportional to changes in hydraulic head values in the aquifer The IBS package uses the following equation to calculate the change in the thickness b L of the interbed positive for compaction and negative for expansion b h Sfe h Sske b0 211 where h L is change in hydraulic head positive for increase Sske L1 is the skeletal component of elastic specific storage b0 is the thickness of the interbed For an unconfined aquifer the elastic compaction or expansion of sediments can be expressed as b h Sfe h 1 n nw Sske b0 212 where n is porosity and nw is moisture content above water table as a fraction of total volume of porous medium Inelastic Storage Factor Sfv Fig 221 Types of finegrained beds in or adjacent to aquifers Beds may be discon tinuous interbeds or continuous confining beds Adapted from Leake and Prudic 78 26 The Models Menu 51 For a confined aquifer the IBS package uses the following equation in analogy to equation 211 to calculate the approximate inelastic compaction b L b h Sfv h Sskv b0 213 where Sskv L1 is the skeletal component of inelastic specific storage For an unconfined aquifer the inelastic compaction of sediments can be ex pressed as b h Sfv h 1 n nw Sskv b0 214 where n is porosity and nw is moisture content above water table as a fraction of total volume of porous medium Starting Compaction L Compaction values computed by the IBS package are added to the starting compaction so that stored values of compaction and land subsidence may include previous components The starting compaction does not affect the calculation of storage changes or resulting compaction Parameter Number Parameter Number is used to group cells where the sfv values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps 2616 MODFLOW Flow Packages Recharge The Recharge package is designed to simulate distributed recharge to the groundwater system Recharge is defined by assigning the following data to each vertical column of cells The input parameters are assumed to be constant during a given stress period For transient flow simulations involving several stress periods the input parameters can be different from period to period Note that the user may move to other layers within the Data Editor and examine the grid configuration in each layer although the values are specified for each vertical column of cells Recharge Flux IR LT 1 Layer Indicator IRCH Parameter Number Parameter Number is used to group cells where the IR values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps MODFLOW uses IR to calculate the recharge flow rate QR L3T 1 applied to the model cell QR IR DELR DELC 215 52 2 Modeling Environment Fig 222 The Recharge Package dialog box where DELR DELC is the map area of a model cell In MODFLOW the recharge rate QR is applied to a single cell within a vertical column of cells In the simplest situation the water table is located in the top layer of the model the top layer is des ignated as unconfined and an array of Recharge Flux IR is specified for that layer Problems may arise when the water table cuts across layers To solve this kind of problems the Recharge package provides three options for specifying the cell in each vertical column of cells that receives the recharge The user can select an option from the Recharge Package dialog box Fig 222 1 Recharge is only applied to the top grid layer 2 Vertical distribution of recharge is specified in the Layer Indicator array IRCH which defines the layer where recharge is applied 3 Recharge is applied to the highest active cell in each vertical column The user does not have to predetermine the layer to which recharge should be applied The appropriate layer is automatically selected by the Recharge package If the high est active cell is a constanthead cell recharge will be intercepted and cannot go deeper Refer to the description of the Recharge package in McDonald and Harbaugh 85 for an example of using these options 2617 MODFLOW Flow Packages Reservoir The Reservoir package 43 is designed for cases where reservoirs are much greater in area than the area represented by individual model cells More than one reservoir can be simulated using this package The area subject to inundation by each reservoir is specified by assigning the reservoir number to selected cells For reservoirs that 26 The Models Menu 53 include two or more areas of lower elevation separated by areas of higher elevation the filling of part of the reservoir may occur before spilling over to an adjacent area The package can simulate this process by specifying two or more reservoirs in the area of a single reservoir Using the Data Editor reservoirs are defined by using the CellbyCell or Polygon input methods to assign the following parameters to model cells Reservoir Number IRES Land surface elevation of the reservoir BRES L Vertical hydraulic conductivity of the reservoir bed HCRES LT 1 Thickness of the reservoir bed Rb L Layer Indicator IRESL Parameter Number Parameter Number is used to group cells where the HCRES values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps The water table elevations of reservoirs are specified in the StageTime Table of Reservoirs dialog box see below The land surface elevation within the specified area of potential inundation for each reservoir is typically defined by the average land sur face elevation of individual cells within the area At cells in which reservoir stage ex ceeds land surface elevation within the specified reservoir area the reservoir boundary is activated Similarly wherever reservoir stage is less than the land surface elevation of a cell the reservoir boundary is not activated If reservoir stage drops below the lowest land surface elevation for all cells within the specified reservoir area water exchange is not simulated between the reservoir and the underlying groundwater system In active cells water exchange between surface water and groundwater is com puted in a manner identical to the River package see Section 2618 The Reservoir package is ideally suited for cases where leakage from or to reservoirs may be a sig nificant component of flow in a groundwater system however if reservoir stage is unknown then a more complex conceptualization would be needed in which reservoir stage would be computed as part of the simulation rather than having stage specified as model input Programs that compute the lake stages based on inflows and outflows exist for example Cheng and Anderson 16 or Council 29 Three options are available for simulating leakage between a reservoir and the underlying groundwater system The first option simulates leakage only to layer 1 the second option simulates leakage to the uppermost active cell and the third option simulates leakage to a specified layer for each active reservoir cell Inherent in the simulation of reservoirs is that the reservoir only partially penetrates an active model cell If the reservoir fully penetrates a cell the reservoir leakage will be simulated in a lower cell Thus water exchange between the groundwater system and the reservoir takes place across the bottom of the reservoir and the top of the model cells 54 2 Modeling Environment Leakage between the reservoir and the underlying groundwater system is simulated for each model cell corresponding to the inundated area by multiplying the head differ ence between the reservoir and the groundwater system by the hydraulic conductance of the reservoir bed Equation 216 defines the hydraulic conductance of the reservoir bed CRES HCRES DELCI DELRJRb 216 where DELCI is the width of the model row I DELRJ is the width of the model column J Reservoir bed thickness is subtracted from the land surface elevation of the reser voir to obtain the elevation of the base of the reservoir bed sediments The elevation of the base of the reservoir bed sediments is used in computing leakage When the hydraulic head in the groundwater system is above the base of the reservoir bed sed iments leakage QRES L3T 1 from or to the groundwater system is computed by equation 217 QRES CRES HRES h 217 where HRES is the reservoir stage L and h is the hydraulic head in the aquifer un derlying the reservoir L When the hydraulic head is lower than the elevation of the base of the reservoir bed sediments HRESBOT leakage from the reservoir to the groundwater system is computed by QRES CRES HRES HRESBOT 218 To specify the water table elevations stages of reservoirs 1 Click the Stage button from the Reservoir Package dialog box Fig 223 A StageTime Table of Reservoirs dialog box appears Fig 224 2 Select a reservoir number a row from the first table The reservoir number is corresponding to the number IRES see above The de scription column is a place for the user to take notes 3 Type the observation time and the corresponding stage into the second table The observation time is measured from the start of the model simulation to which the measured stage pertains The Reservoir package requires the input of the starting and ending stages for each stress period These stage values are linearly interpolated to the beginning of each time step to determine whether the reservoir boundary is activated at that time point The stage values for each stress period are obtained by linear interpolation using the values specified in the StageTime Table of Reservoirs dialog box If the starting time of a stress period is earlier than the earliest observation time in the table the earli est observed stage is used as the starting stage for that stress period Similarly if the 26 The Models Menu 55 Fig 223 The Reservoir Package dialog box Fig 224 The StageTime Table of Reservoirs dialog box ending ending time of a stress period is beyond the latest observation time the latest observed stage is used Output Option 1 Make a stagevolumearea table for reservoirs If this option is checked reservoir stage area and volume will be printed to the Run Listing File of MODFLOW each time step 56 2 Modeling Environment 2 Number of values in the stagevolumearea table NPTS NPTS is the number of values in printed table of stage volume and area for each reservoir First and last stage value are minimum and maximum elevations within area of potential inundation A value of 15 or greater is recommended for detailed representation of stagevolume and stagearea relations 2618 MODFLOW Flow Packages River The purpose of the River package is to simulate the effect of flow between groundwater systems and surfacewater features such as rivers lakes or reservoirs Using the Data Editor a river is defined by using the CellbyCell or Polygon input methods to assign parameters to model cells or by using the Polyline input method and assigning parameters to vertices of the polylines along the trace of the river The input parameters are assumed to be constant during a given stress period For transient flow simulations involving several stress periods the input parameters can be different from period to period The input methods require different parameters as described below When using the Polyline input method rightclick on a vertex to specify its prop erties in the River Parameters dialog box Fig 225 If the properties are assigned to one vertex only the properties of all vertices of the polyline are assumed to be the same The settings of the dialog box are described below Layer Option and Layer Number Layer Option controls how the layer number of a river is determined Fig 225 The River Parameters dialog box 26 The Models Menu 57 If Layer Option is Assign layer number manually the value of Layer Number defines the model layer number for all model cells downstream from a vertex until the next vertex redefines the layer number If Layer Option is Assign layer number automatically the river is as signed to a layer where the elevation of the riverbed bottom Briv see be low is located between the top and bottom of the layer The layer number is set to 1 if Briv is higher than the top of the first layer The layer number is set to the last layer if RBOT is lower than the bottom of the last layer Active Check this box to activate a vertex Clear the Active box to deactivate a vertex The properties of an active vertex will be used in the simulation The properties of an inactive vertex are ignored Hydraulic Conductivity of Riverbed Kriv LT 1 Head in the river Hriv L Elevation of the Riverbed bottom Briv L Width of the river Wriv L and Thickness of the riverbed Mriv L The value Kriv describes all of the head loss between the river and the aquifer It depends on the material and characteristics of the riverbed itself and the immediate environment Since the river package requires the input of Hriv Briv and river hydraulic conductance CRIV to each cell of a river the input values Kriv Hriv and Briv at active vertices are linearly interpolated or extrapolated to each cell along the trace of the polyline and the value Criv is obtained by Criv Kriv L Wriv Mriv 219 where L is the length of the river within a cell Parameter Number Since Criv is usually unknown it must be esti mated Parameter Number is used to group cells where the Criv values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps The value of Parameter Number is assigned to all model cells downstream from a vertex until the next vertex redefines the pa rameter number Density of River Fluid ML3 This value represents the prescribed density of fluid entering the groundwater system from the river This value is used by SEAWAT only if it is running in a uncoupled mode ie the densityeffect of all species are turned off see 2621 and the Density of river fluid options in the Simulation Settings MT3TMSSEAWAT dialog box see Fig 248 on p 104 is set as UserSpecified in the River Package The ALL button Click the ALL button of a property to copy the property value to all other active vertices 58 2 Modeling Environment When using the Cellbycell or Polygon input methods the following values are to be assigned to model cells of a river See the explanations above for the definition of the input values Hydraulic Conductance of the riverbed Criv L2T 1 Head in the river Hriv L Elevation of the Riverbed bottom Briv L Parameter Number Thickness of the riverbed Mriv L and Density of River Fluid ML3 In a model cell containing river parameters the flow rate Qriv between the river and groundwater is calculated by equations 220 and 221 By default MODFLOW saves the calculated flow rates in the BUDGETDAT which can be used for water balance calculations If the groundwater hydraulic head h is greater than RBOT the leakage rate QRIV from the river to the aquifer is calculated by Qriv Criv hriv h if h Briv 220 The value of QRIV is negative if the hydraulic head h is greater than HRIV It means that water flows from the aquifer into the river and is removed from the ground water system When h falls below the bottom of the riverbed the leakage rate through the riverbed is given by Qriv Criv hriv Briv if h Briv 221 2619 MODFLOW Flow Packages StreamflowRouting The StreamflowRouting STR package Prudic 100 is designed to account for the amount of flow in streams and to simulate the interaction between surface streams and groundwater Streams are divided into segments and reaches Each reach corresponds to individual cells in the finitedifference grid A segment consists of a group of reaches connected in downstream order Streamflow is accounted for by specifying flow for the first reach in each segment and then computing streamflow to adjacent downstream reaches in each segment as inflow in the upstream reach plus or minus leakage from or to the aquifer in the upstream reach The accounting scheme used in this package assumes that streamflow entering the modelled reach is instantly available to down stream reaches This assumption is generally reasonable because of the relatively slow rates of groundwater flow Streamflow into a segment that is formed from tributary streams is computed by adding the outflows from the last reach in each of the specified tributary segments If a segment is a diversion then the specified flow into the first reach of the segment is 26 The Models Menu 59 subtracted from flow in the main stream However if the specified flow of the diversion is greater than the flow out of the segment from which flow is to be diverted then no flow is diverted from that segment Using the Data Editor a stream is defined by using the CellbyCell or Polygon in put methods to assign parameters to model cells or by using the Polyline input method and assigning parameters to vertices of the polylines along the trace of the stream The input parameters are assumed to be constant during a given stress period For transient flow simulations involving several stress periods the input parameters can be different from period to period The input methods require different parameters as described below When using the Polyline input method rightclick on a vertex to specify its prop erties in the River Parameters dialog box Fig 226 If the properties are assigned to one vertex only the properties of all vertices of the polyline are assumed to be the same The settings of the dialog box are described below Fig 226 The Stream Parameters dialog box 60 2 Modeling Environment Calculate stream stages in reaches If this option is selected the stream wa ter depth dstr in each reach is calculated from Mannings equation under the assumption of a rectangular stream channel See equation 225 below Options apply to the selected polyline Layer Option and Layer Number Layer Option controls how the layer number of a stream reach is determined If Layer Option is Assign layer number manually the value of Layer Number defines the model layer number for all model cells downstream from a vertex until the next vertex redefines the layer number If Layer Option is Assign layer number automatically the river is assigned to a layer where the elevation of the Streambed bottom Botstr see below is located between the top and bottom of the layer The layer number is set to 1 if Botstr is higher than the top of the first layer The layer number is set to the last layer if Botstr is lower than the bottom of the last layer Segment Number is a number assigned to a polyline Segments must be numbered in downstream order The maximum number allowed is 1000 Inflow to this Segment L3T 1 is the streamflow entering a segment poly line When inflow into a segment is the sum of outflow from a specified number of tributary segments the segment inflow values are specified as 1 Parameters apply to the selected vertex Active Check this box to activate a vertex Clear the Active box to deac tivate a vertex The input parameters at active vertices are linearly interpo lated or extrapolated to each cell along the trace of the polyline and used in the simulation The parameters of an inactive vertex are ignored Hydraulic Conductivity of Streambed Kstr LT 1 Width of the Stream Channel Wstr L Elevation of the Streambed Top Topstr L and El evation of the Streambed Bottom Botstr L The value Kstr describes all of the head loss between the stream and the aquifer It depends on the material and characteristics of the streambed itself and the immediate en vironment Since the STR package requires the input of stream hydraulic conductance Cstr to each reach of a stream the input parameters at active vertices are linearly interpolated or extrapolated to each cell along the trace of the polyline and Cstr is obtained by Cstr Kstr L Wstr Topstr Botstr 222 where L is the length of the stream within a cell Stream Stage hs L is the head in the stream In a model cell containing a stream reach the leakage rate Qstr between the reach and groundwater is calculated by equations 223 and 224 By default MODFLOW saves the calculated leakage rates in the BUDGETDAT which can be used for water balance calculations Qstr Cstr hs h if h Botstr 223 Qstr Cstr hs Botstr if h Botstr 224 Slope of the Streambed Channel Sstr and Mannings roughness coeff nC These parameters are used only when the option Calculate stream stages in reaches is selected To obtain the stream stage the stream water depth dstr is calculated using the Mannings equation under the assumption of a rectangular stream channel The calculated water depth is added to the streambed top to get the stream stage The Mannings equation for a rectangular stream channel is dstr Q n C Wstr Sstr12 35 225 where Q L3 T1 is the calculated stream discharge n is Mannings roughness coefficient Wstr L is the width of the channel and C is a conversion factor which depends on the length and time units of the model C 1 m13s 86400 m13day 1486 ft13s 128383 ft13day 226 Although n and C appear separately in equation 225 only the values of nC or Cn are used in the computer code The user needs therefore only to specify the value of nC Some of the experimental values of the Mannings roughness coefficient can be found in the documentation of the STR package 100 Parameter Number Since Cstr is usually unknown it needs to be estimated Parameter Number is used to group cells where the Cstr values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps The value of Parameter Number is assigned to all model cells downstream from a vertex until the next vertex redefines the parameter number 62 2 Modeling Environment Fig 227 Specification of the stream structure The ALL button Click the ALL button of a property to copy the property value to all other active vertices Stream Structure describes the configuration of a stream system Each row in the table Fig 227 represents a stream segment in the model Each segment can have up to 10 tributary segments The numbers of the tributary segments are specified in the columns 1 to 10 The column Iupseg is the number of the upstream segment from which water is diverted For a segment that is not a diversion Iupseg must be specified as zero Iupseg is used only when the option Simulate diversions from segments is checked The values in Fig 227 indicate that segment 2 is diverted from segment 1 segment 1 is a tributary segment of segment 3 and segments 2 and 4 are tributary segments of segment 5 The configuration of the stream system is shown in Fig 228 When using the Cellbycell or Polygon input methods the following values are to be assigned to model cells alone the trace of a stream See the explanations above for the definition of the input values Segment Number Inflow to this Segment L3T 1 26 The Models Menu 63 Fig 228 The stream system configured by the table of Fig 227 Reach Number is a sequential number in a segment that begins with one for the farthest upstream reach and continues in downstream order to the last reach in the segment Using the Cellbycell or Polygon methods only one reach can be assigned to a model cell although the STR package allows the user to assign more than one reach in different segments to the same model cell Stream Stage hs L Streambed Hydraulic Conductance Cstr L2T 1 Elevation of the Streambed Top TOPstr L Elevation of the Streambed Bottom BOTstr L Width of the Stream Channel Wstr L Slope of the Streambed Channel Str Mannings roughness coeff nC Parameter Number 26110 MODFLOW Flow Packages TimeVariant SpecifiedHead For transient simulations the TimeVariant SpecifiedHead package 78 allows con stant head cells to take on different head values for each time step A timevariant specified head boundary is defined by using the CellbyCell or Polygon input methods of the Data Editor to assign the following parameters to model cells Flag A nonzero value indicates that a cell is specified as a timevariant specifiedhead boundary Start Head hs L This value is the prescribed hydraulic head of a cell at the start of the stress period 64 2 Modeling Environment End Head he L This value is the prescribed hydraulic head of a cell for the last time step of a stress period This package does not alter the way contant head boundaries are formulated in the finitedifference equations of MODFLOW It simply sets the element in the IBOUND array to a negative value for all cells where a timevariant specifiedhead boundary is selected Flag 0 For each time step within a period the package linearly interpo lates prescribed hydraulic heads h for each timevariant specifiedhead boundary cell by using the equation h hs he hs PERTIM PERLEN 227 where PERTIM is the starting time of a time step within a stress period and PERLEN is the length of the stress period The interpolated head values remain con stant during a time step If a cell is specified as a timevariant specifiedhead boundary for a stress period and omitted in the specification for a subsequent period it remains a fixedhead boundary with a head equal to that at the end of the previous period 26111 MODFLOW Flow Packages Well An injection or a pumping well is defined by using the CellbyCell or Polygon input methods of the Data Editor to assign the following parameters to model cells The input parameters are assumed to be constant during a given stress period For transient flow simulations involving several stress periods the input parameters can be different from period to period Recharge rate of the well Qw L3T 1 Negative values are used to indicate pumping wells while positive cell values indicate injection wells The injection or pumping rate of a well is independent of both the cell area and the hydraulic head in the cell MODFLOW assumes that a well penetrates the full thickness of the cell To simulate wells that penetrate more than one model layer the injection or pumping rate for each layer has to be specified The total injection or pumping rate for a multilayer well is equal to the sum of those from the individual layers For confined layers the injection or pumping rate for each layer Qk can be ap proximately calculated by dividing the total rate Qtotal in proportion to the layer transmissivities McDonald and Harbaugh 85 Qk Qtotal Tk ΣT 228 where Tk is the transmissivity of layer k and ΣT is the sum of the transmissiv ity values of all layers penetrated by the multilayer well Another possibility to 26 The Models Menu 65 simulate a multilayer well is to set a very large vertical hydraulic conductivity or vertical leakance eg 1 ms to all cells of the well The total pumping rate is then assigned to the lowest cell of the well For display purposes a very small pump ing rate say 1 1010m3s can be assigned to other cells of the well In this way the exact extraction rate from each penetrated layer can be obtained by using the Water Budget Calculator See Section 4125 for how to calculate subregional water budget Parameter Number Parameter Number is used to group cells where the Qw values are to be estimated by the parameter estimation programs PEST Section 268 or MODFLOW2000 Section 267 Refer to the corresponding sections for parameter estimation steps Density of Injection Fluid ML3 This value is used by SEAWAT only if it is run ning in a uncoupled mode ie the densityeffect of all species are turned off see 2621 and the Density of Injection Well Fluid options in the Simulation Settings MT3TMSSEAWAT dialog box see Fig 248 on p 104 is set as UserSpecified in the Well Package 26112 MODFLOW Flow Packages Wetting Capability The wetting capability of the BlockCentered Flow 2 BCF2 package 86 allows the simulation of a rising water table into unsaturated dry model layers The BCF2 package is identical to the BCF1 package of MODFLOW88 85 except for the wetting and drying of cells A cell falls dry when the head is below the bottom elevation of the cell When a cell falls dry IBOUND is set to 0 which indicates a no flow or an inactive cell all conductance values to the dry cell are set to zero No water can flow into the cell as the simulation proceeds and the cell remains inactive even if neighboring water tables rise again To overcome this problem a value THRESH called wetting threshold is intro duced to the BCF2 package or later versions of this package The computer code uses this value to decide whether a dry or an inactive cell can be turned into a wet active cell If THRESH 0 the dry cell or the inactive cell cannot be wetted If THRESH 0 only the cell below the dry cell or inactive cell can cause the cell to become wet If THRESH 0 the cell below the dry cell or inactive cell and the four horizon tally adjacent cells can cause the cell to become wet A dry cell or an inactive cell can be turned into an active cell if the head from the previous iteration in a neighboring cell is greater than or equal to the turnon threshold TURNON 66 2 Modeling Environment Fig 229 The Wetting Capability dialog box TURNON BOT THRESH 229 where BOT is the elevation of the bottom of the cell To improve the stability of the numerical solution a neighboring cell cannot be come wet as a result of a cell that has become wet in the same iteration only variable head cells either immediately below or horizontally adjacent to the dry cell can cause the cell to become wet When a cell is wetted its IBOUND value is set to 1 which in dicates a variablehead cell vertical conductance values are set to the original values and the hydraulic head h at the cell is set by using one of the following equations h BOT WETFCT hn BOT 230 h BOT WETFCT THRESH 231 where hn is the head at the neighboring cell that causes the dry cell to wet and WETFCT is a userspecified constant called the wetting factor The user may se lect between equations 230 and 231 in the Wetting Capability dialog box Fig 229 This dialog box appears after selecting Models MODFLOW Flow Packages Wet ting Capability The dialog box allows the user to specify the iteration interval for attempting to wet cells IWETIT Wetting is attempted every IWETIT iterations When using the PCG2 solver 59 this applies to outer iterations and not inner iterations The reason for adjusting IWETIT is that the wetting of cells sometimes produces erroneous head changes in neighboring cells during the succeeding iteration which may cause erroneous conversions of those cells Waiting a few iterations until heads have had a chance to adjust before testing for additional conversions can prevent these erroneous conversions When setting IWETIT greater than one there is some risk that cells may be prevented from correctly converting from dry to wet If the solution for a time step is obtained in less than IWETIT iterations then there will be no check during that time step to see if cells should be converted from dry to wet The potential for this prob 26 The Models Menu 67 lem to occur is greater in transient simulations which frequently require only a few iterations for a time step The method of wetting and drying cells used in the BCF2 Package can cause prob lems with the convergence of the iterative solvers used in MODFLOW Convergence problems can occur in MODFLOW even without the wetting capability but problems are more likely to occur when the wetting capability is used Symptoms of a problem are slow convergence or divergence combined with the frequent wetting and drying of the same cells It is normal for the same cell to convert between wet and dry several times during the convergence process but frequent conversions are an indication of problems As a matter of fact situations exist where the real solution oscillates such as in the case of a well causing a drawdown which makes the well cells fall dry This in turn switches off the well and leads to a rise of the water table and wetting of the well cell etc The user can detect such situations by examining the model run record file OUTPUTDAT a message is printed each time a cell converts The basic tools at hand to combat convergence problems are Choose vertical discretization such that only few cells will fall dry Choose wetting from below only ie set THRESH0 Change to a different preconditioner if the PCG2 solver is used Change to a different solver Increase the modulus of THRESH Increase IWETIT Decrease pumping rates of wells 26113 MODFLOW Solvers To calculate heads in each cell in the finitedifference grid MODFLOW prepares one finite difference equation for each cell expressing the relationship between the head at a node and the heads at each of the six adjacent nodes at the end of a time step Because each equation may involve up to seven unknown values of head and because the set of unknown head values changes from one equation to the next through the grid the equations for the entire grid must be solved simultaneously at each time step The system of simultaneous finite difference linear equations can be expressed in matrix notation as A x b 232 where A is a coefficient matrix assembled by MODFLOW using userspecified model data b is a vector of defined flows terms associated with headdependent boundary conditions and storage terms at each cell x is a vector of hydraulic heads at each cell One value of the hydraulic head for each cell is computed at the end of each time step PM supports five packages solvers for solving systems of simultaneous linear 68 2 Modeling Environment equations and the Newton Solver NWT package for solving systems of nonlinear equations Direct Solution DE45 package Preconditioned ConjugateGradient 2 PCG2 package Preconditioned ConjugateGradient with improved nonlinear control PCGN pack age Strongly Implicit Procedure SIP package SliceSuccessive Over Relaxation SSOR package Geometric Multigrid Solver GMG package and Newton Solver NWT package Input parameters of these solution methods are discussed below See McDonald and Harbaugh 85 59 Harbaugh 53 Wilson and Naff 117 Niswonger and others 91 and Naff and Banta 90 for detailed mathematical background and numerical implementation of these solvers Various comparisons between the solution methods can be found in Trescott 114 Kuiper 75 Behie and Forsyth 14 Scandrett 108 and Hill 60 Hill60 indicates that the greatest differences in solver efficiency on scalar computers occur for threedimensional nonlinear problems For these types of problems it may be well worth the time and effort to try more than one solver Note The GMG solver 117 is only implemented in MODFLOW2000 and MODFLOW2005 The PCGN solver is implemented in MODFLOW2005 The NWT solver is only available in MODFLOWNWT and must be used together with the UPW package see Section 234 for details When the NWT solver is activated MODFLOWNWT will be used as the simulation engine and the settings of the linear solvers will be ignored 26 The Models Menu 69 MODFLOW Solvers DE45 Although a direct solver requires more memory and typically requires more compu tational effort than iterative solvers it may execute faster than an iterative solver in some situations The Direct Solution package 53 uses Gaussian elimination with an alternating diagonal equation numbering scheme that is more efficient than the stan dard method of equation numbering It is the most efficient when solving small linear problems Use the Direct Solution DE45 dialog box Fig 230 to specify required parame ters as described below Maximum iterations external or internal is the maximum number of iterations in each time step Set this number to 1 if iteration is not desired Ideally iteration would not be required for direct solution however it is necessary to iterate if the flow equation is nonlinear see Problem type below or if computer precision lim itations result in inaccurate calculations as indicated by a large water budget error For a non linear flow equation each iteration is equally time consuming because the coefficient matrix A is changed with each iteration and Gaussian elimination is required after each change This is called external iteration For a linear equation iteration is significantly faster because A is changed at most once per time step Thus Gaussian elimination is required at most once per time step This is called internal iteration Max equations in upper part of A This is the maximum number of equations in the upper part of the equations to be solved This value impacts the amount of Fig 230 The Direct Solution DE45 dialog box 70 2 Modeling Environment memory used by the solver If specified as 0 the program will calculate the value as half the number of cells in the model which is an upper limit The actual number of equations in the upper part will be less than half the number of cells whenever there are no flow and constant head cells because flow equations are not formulated for these cells The solver prints the actual number of equations in the upper part when it runs The printed value can be used in future runs in order to minimize memory usage Max equations in lower part of A This is the maximum number of equations in the lower part of the equations to be solved This value impacts the amount of memory used by the solver If specified as 0 the program will calculate the value as half the number of cells in the model which is an upper limit The actual number of equations in the lower part will be less than half the number of cells whenever there are no flow and constant head cells because flow equations are not formulated for these cells The solver prints the actual number of equations in the lower part when it runs The printed value can be used in future runs in order to minimize memory usage Max band width of AL This value impacts the amount of memory used by the solver If specified as 0 the program will calculate the value as the product of the two smallest grid dimensions which is an upper limit Head change closure criterion L If iterating iteration stops when the absolute value of head change at every node is less than or equal to this value The criterion is not used when not iterating but a value must always be specified RelaxationAccelleration Parameter ACCL ACCL is a multiplier for the com puted head change for each iteration Normally this value is 1 A value greater than 1 may be useful for improving the rate of convergence when using external iteration to solve nonlinear problems ACCL should always be 1 for linear prob lems When Maximum Iterations 1 ACCL is changed to 1 regardless of the input value Printout From the Solver If the option All available information is selected the maximum head change and residual positive or negative are saved in the run listing file OUTPUTDAT for each iteration of a time step whenever the time step is an even multiple of Printout Interval If the option The number of iterations only is checked the printout of maximum head change and residual is suppressed Select the option None to suppress all printout from the solver A positive integer is required by Printout Interval Problem Type The choice of problem type affects the efficiency of solution sig nificant work can be avoided if it is known that A remains constant all or part of the time Linear indicates that the flow equations are linear To meet the linearity require ment all model layers must be confined and there must be no formulations 26 The Models Menu 71 that change based upon head such as seepage from a river changing from head dependent flow to a constant flow when head drops below the bottom of the riverbed Examples of nonlinearity are cases with riverbed conductance drain conductance maximum evapotranspiration rate evapotranspiration extinction depth general head boundary conductance and reservoirbed conductance Nonlinear indicates that a nonlinear flow equation is being solved which means that some terms in A depend on simulated head Example of head de pendent terms in A are transmissivity for watertable layers which is based on the saturated thickness flow terms for rivers drains and evapotranspira tion convert between head dependent flow and constant flow and the change in storage coefficient when a cell converts between confined and unconfined When a nonlinear flow equation is being solved external iteration is normally required in order to accurately approximate the nonlinearities Note that when nonlinearities caused by water table calculations are part of a simulation there are not necessarily any obvious signs in the output from a simulation that does not use external iteration to indicate that iteration is needed In particular the budget error may be acceptably small without iteration even though there is significant error in head because of nonlinearity To understand this consider the water table correction for transmissivity For each iteration a new transmis sivity value is calculated based on the previous head Then the flow equations are solved and a budget is computed using the new head with the same trans missivities No budget discrepancy results because heads are correct for the transmissivity being used at this point however the new heads may cause a significant change in transmissivity The new transmissivity will not be cal culated unless there is another iteration Therefore when one or more layers are under water table conditions iteration should always be tried The maxi mum change in head during each iteration printed by the solver provides an indication of the impact of all nonlinearities MODFLOW Solvers PCG2 The required parameters for the PCG2 package are specified in the Preconditioned ConjugateGradient Package 2 dialog box Fig 231 They are described below Preconditioning Method The PCG2 package provides two preconditioning op tions the modified incomplete Cholesky preconditioner MICCG 10 and the Neu man Series Polynomial preconditioner POLCG 107 Relaxation Parameter is used with MICCG Usually this parameter is equal to 1 Ashcraft and Grimes 9 found out that for some problems a value of 099 098 or 097 would reduce the number of iterations required for convergence 72 2 Modeling Environment The option Calculate the upper bound on the maximum eigenvalue is only avail able when POLCG is selected Check this box if the solver should calculate the upper bound on the maximum eigenvalue of A Otherwise a value of 2 will be used The upper bound is estimated as the largest sum of the absolute values of the components in any row of A Estimation of the upper bound uses slightly more execution time per iteration Allowed Iteration Numbers MXITER is the maximum number of outer iterations For each outer iteration A and b equation 232 are updated by using the newly calculated hydraulic heads For a linear problem MXITER should be 1 unless more that ITER1 in ner iterations are required A larger number generally less than 100 is required for a nonlinear problem Outer iterations continue until the final convergence criteria see below are met on the first inner iteration ITER1 is the maximum number of inner iterations Equation 232 with a new set of A and b is solved in inner iterations The inner iterations continue until ITER1 iterations are executed or the final convergence criteria see below are met Convergence Criteria Fig 231 The Preconditioned Conjugate Gradient Package 2 dialog box 26 The Models Menu 73 Head Change L is the head change criterion for convergence When the max imum absolute value of the head change at all nodes during an iteration is less than or equal to the specified Head Change and the criterion for Residual is satisfied see below iteration stops Residual L3T 1 is the residual criterion for convergence Residual is calcu lated as A x b for each inner iteration When the maximum absolute value of the residual at all cells during an iteration is less than or equal to Residual and the criterion for Head Change is satisfied see above iteration stops Printout From the Solver Printout Interval requires a positive integer If the option All available information is selected the maximum head change and residual pos itive or negative are saved in the run listing file OUTPUTDAT for each iteration of a time step whenever the time step is an even multiple of Printout Interval If the option The number of iterations only is checked the printout of maximum head change and residual is suppressed Select the option None to suppress all printout from the solver Damping Parameter The Damping Parameter is a multiplier for the computed head change for each iteration Normally this value is 1 A value smaller than 1 may be useful for unstable systems MODFLOW Solvers PCGN MODFLOW2005 and higher The preconditioned conjugate gradient solver with improved nonlinear control PCGN 90 is a solver package for MODFLOW2005 According to the authors of PCGN the principal objective of the PCGN package is to provide the modeler with more options when faced with a poorly converging nonlinear problem This menu item can be ac cessed only if the MODFLOW Version in the Preference dialog box Figure 213 is set to MODFLOW2000MODFLOW2005 The required parameters for the PCG package are specified in the PCGN dialog box Fig 232 and are outlined below Re fer to the input instruction of the users guide of the PCGN package 90 for details General Solver Parameters ITER MO is the maximum number of Picard outer iterations allowed For nonlinear problems this variable must be set to some number greater than one depending on the problem size and degree of nonlinearity If ITER MO is set to 1 then the PCGN solver assumes that the problem is linear and the input requirements are greatly truncated ITER MI is the maximum number of PCG inner iterations allowed Generally this variable is set to some number greater than one depending on the matrix size degree of convergence called for and the nature of the problem For a nonlinear problem ITER MI should be set large enough 74 2 Modeling Environment CLOSE R is the residualbased stopping criterion for iteration This parameter is used differently depending on whether it is applied to a linear or nonlinear problem ITER MO 1 CLOSE R is used as the value in the absolute convergence criterion for quitting the PCG iterative solver ITER MO 1 For a nonlinear problem CLOSE R is used as a criterion for quitting the Picard outer iteration CLOSE H is used as an alternate stopping criterion for the Picard iteration needed to solve a nonlinear problem The maximum value of the head change is obtained for each Picard iteration after completion of the inner PCG iter ation If this maximum head change is less than CLOSE H then the Picard iteration is considered tentatively to have converged However as nonlinear problems can demonstrate oscillation in the head solution the Picard iteration Fig 232 The PCGN dialog box 26 The Models Menu 75 is not declared to have converged unless the maximum head change is less than CLOSE H for three Picard iterations If these Picard iterations are sequential then a good solution is assumed to have been obtained If the Picard iterations are not sequential then a warning is issued advising that the convergence is conditional and the user is urged to examine the mass balance of the solution Parameters related to PCG Solver RELAX is the socalled relaxation parameter for the modified incomplete Cholesky MIC preconditioner under MIC preconditioning row sum agree ment between the original matrix and the preconditioning matrix is created by pivot modification When RELAX 0 then the MIC corresponds to the or dinary incomplete Cholesky preconditioner the effect of the modifications to the incomplete Cholesky having been nullified When RELAX 1 then these modifications are in full force enerally speaking it is of advantage to use the modifications to the incomplete Cholesky algorithm a value of RELAX such that 09 RELAX 1 is generally advised for most problems IFILL is the fill level of the MIC preconditioner Preconditioners with fill lev els of 0 and 1 are available IFILL 0 and IFILL 1 respectively Generally the higher the fill level the more preconditioning imparted by a MIC precon ditioner Parameters related to Damping These parameters are used only if the problem is nonlinear ITER MO 1 ADAMP defines the mode of damping applied to the linear solution In general damping determines how much of the head changes vector j shall be applied to the hydraulic head vector hj in Picard iteration j hj hj1 θ j where θ is the damping parameter The available damping modes are ADAMP 0 Ordinary damping is employed and a constant value of damp ing parameter θ DAMP will be used throughout the Picard iteration This option requires a valid value for DAMP see below ADAMP 1 Adaptive damping is employed Adaptive damping changes the damping parameter θ in response to the difficulty the nonlinear solver encounters in solving a given problem Essentially the nonlinear solver looks to increase θ should the convergence of the Picard iteration pro ceed satisfactorily but otherwise causes θ to decrease Adaptive damp ing can be useful for problems that do not converge readily but otherwise should be avoided as it generally requires more total iterations This op tion requires valid values for variables DAMP DAMP LB RATE D and CHGLIMIT Adaptive damping also admits the possibility of directly lim iting the the maximum head change applicable to update the hydraulic heads see CHGLIMIT below If this option is not desired then CHGLIMIT should be set to zero 76 2 Modeling Environment ADAMP 2 Enhanced damping algorithm in which the value of θ is in creased but never decreased provided the Picard iteration is proceeding satisfactorily This enhanced damping allows θ to increase from a mini mum value to a maximum value DAMP by a rate equal to RATE D The minimum value in the first stress period is DAMP LB for subsequent stress periods it is the geometric mean of DAMP and DAMP LB This option re quires valid values for DAMP DAMP LB and RATE D DAMP The variable DAMP restricts the damping parameter θ generally 0 DAMP 1 Its function for the various modes of ADAMP are ADAMP 0 The damping parameter θ takes on the value DAMP and is maintained constant throughout the simulation ADAMP 0 The value of DAMP will be treated as the upper limit for θ in the enhanced damping or adaptive damping algorithms DAMP LB represents a bound placed on θ generally 0 DAMP LB DAMP For the various modes of ADAMP 0 DAMP LB serves the fol lowing purposes ADAMP 1 In the adaptive damping algorithm DAMP LB represents the lower limit to which θ under adverse adaptive damping conditions will be allowed to fall ADAMP 2 In the enhanced damping algorithm DAMP LB is the starting value or a component of the starting value for the damping parameter θ used in the initial Picard iteration of every stress period RATE D is a rate parameter generally 0 RATE D 1 For the various modes of ADAMP 0 RATE D serves the following purposes ADAMP 1 RATE D sets the recovery rate for the damping factor θ in response to the progress in the Picard iteration it also forms a limit on the response function to progress in the Picard iteration Typical values for RATE D under this scenario are 001 RATE D 01 Under adaptive damping if the user finds that the damping factor θ increases too rapidly then reducing RATE D will slow the rate of increase ADAMP 2 Provided the Picard iteration is progressing satisfactorily RATE D adjusts the damping factor θ upward such that θj θj1 RATE D θj1 where j is the Picard iteration number Typical values for RATE D under this scenario are 001 RATE D 01 although larger or smaller values may be used CHGLIMIT limits the maximum head change applicable to the updated hy draulic heads in a Picard iteration Provided that the current damping factor is greater than the ratio of CHGLIMIT to the maximum head change and that this ratio is less than one then the damping factor is reset to the value of the ratio 26 The Models Menu 77 This option is available only in association with adaptive damping ACNVG 1 If CHGLIMIT 00 then adaptive damping proceeds without this feature Parameters related to Convergence of Inner Iteration ACNVG defines the mode of convergence applied to the PCG solver In gen eral the relative stopping criterion for PCG iteration is νi ε ν0 where ν0 is the weighted residual norm on entry to the PCG solver ε is the relative con vergence parameter and νi is the same norm at PCG iteration i The available convergence modes are ACNVG 1 The standard convergence scheme is employed The standard relative convergence is denoted by εs and takes the value 01 this value is assigned to the relative convergence ε No additional variables are used ACNVG 1 Adaptive convergence is employed The adaptive convergence scheme adjusts the relative convergence ε of the PCG iteration based on a measure of the nonlinearity of the problem Under this scheme ε is allowed to vary such that CNVG LB ε εs where the exact value of ε is depen dent on the measure of nonlinearity This option requires a valid value for variable CNVG LB ACNVG 2 Enhanced convergence is employed If the variable enhance ment option is employed RATE C 0 then εs is taken as the upper limit for ε This option requires valid values for variables MCNVG and RATE C CNVG LB is used only in convergence mode ACNVG 1 CNVG LB is the minimum value that the relative convergence ε is allowed to take under the self adjusting convergence option The objective here is to prevent ε from becoming so small that the PCG solver takes an excessive number of iterations Valid range for variable 0 CNVG LB εs a value of CNVG LB 0001 usually produces reasonable results MCNVG is used only in convergence mode ACNVG 2 MCNVG increases the relative PCG convergence criteria by a power equal to MCNVG that is letting p MCNVG then the relative convergence criterion ε is enhanced such that ε εsp where 0 p 6 RATE C is used only in convergence mode ACNVG 2 this option results in variable enhancement of ε If 0 RATE C 1 then enhanced relative conver gence is allowed to decrease by increasing ε as follows εj εj1 RATE C εj1 where j is the Picard iteration number this change in ε occurs so long as the Picard iteration is progressing satisfactorily If RATE C 0 then the value of ε set by MCNVG remains unchanged through the Picard iteration Typi cal values for RATE C are 001 RATE C 01 although larger or smaller values may be used Print Progress Report If checked a record of progress made by the Picard it eration for each time step is printed in the MODFLOW Listing file This record 78 2 Modeling Environment consists of the total number of dry cells at the end of each time step as well as the total number of PCG iterations necessary to obtain convergence MODFLOW Solvers SIP The required parameters for the SIP package are specified in the Strongly Implicit Procedure Package dialog box Fig 233 The parameters are described below MXITER is the maximum number of iterations in one time step in an attempt to solve the system of finitedifference equations IPRSIP is the printout interval for this package A positive integer is required The maximum head change positive or negative is saved in the run record file OUT PUTDAT for each iteration of a time step whenever the time step is an even multi ple of IPRSIP This printout also occurs at the end of each stress period regardless of the value of IPRSIP NPARM is the number of iteration parameters to be used Five parameters are gen erally sufficient ACCL is the acceleration parameter It must be greater than zero and is generally equal to one Head Change L is the head change criterion for convergence When the maxi mum absolute value of head change from all cells during an iteration is less than or equal to Head Change iteration stops Fig 233 The Strongly Implicit Procedure Package dialog box 26 The Models Menu 79 MODFLOW Solvers SSOR The required parameters for SSOR package are specified in the Slice Successive Over relaxation Package dialog box Fig 234 The parameters are described below Fig 234 The SliceSuccessive Overrelaxation Package dialog box MXITER is the maximum number of iterations in one time step in an attempt to solve the system of finitedifference equations IPRSOR is the printout interval for SSOR A positive integer is required The maximum head change positive or negative is saved in the run record file OUT PUTDAT for each iteration of a time step whenever the time step is an even multi ple of IPRSOR This printout also occurs at the end of each stress period regardless of the value of IPRSOR ACCL is the acceleration parameter usually between 10 and 20 Head Change is the head change criterion for convergence When the maximum absolute value of head change from all cells during an iteration is less than or equal to Head Change iteration stops MODFLOW Solvers GMG MODFLOW2000 Only The required parameters for the GMG package 117 are specified in the Geometric Multigrid Solver dialog box Figure 235 The parameters are described below Iteration Control 80 2 Modeling Environment Maximum Number of Outer Iteration MXITER MXITER is the maximum number of outer iterations For linear problems MXITER can be set to 1 Fornonlinear problems MXITER needs to be larger but rarely more than 100 Head Change Closure Criterion HCOLOSE HCLOSE is the head change con vergence criterion for nonlinear problems After each linear solve inner itera tion themaximum head change is compared against HCLOSE HCLOSE can be set to a large number for linear problems HCLOSE is ignored if MXITER 1 Maximum number of inner PCGiterations IITER IITER defines the max imum number of PCG iterations for each linear solution A value of 100 is typically sufficient It is frequently useful to specify a smaller number for non linear problems so as to prevent an excessive number of inner iterations Budget Closure Criterion RCLOSE RCLOSE is the residual convergence cri terion for the inner iteration The PCG algorithm computes the l2norm of the residual and compares it against RCLOSE Typically RCLOSE is set to the same value as HCLOSE If RCLOSE is set too high then additional outer iterations may be required due to the linear equation not being solved with suf ficient accuracy On the other hand a too restrictive setting for RCLOSE for nonlinear problems may force an unnecessarily accurate linear solution This may be alleviated with the IITER parameter or with damping Damping Control Fig 235 The Geometric Multigrid Solver dialog box 26 The Models Menu 81 Damping Method Two damping methods are available Fixed Damping Value If this method is selected then the Damping Value see below is used as a constant damping parameter Cooleys method If this method is selected then the Damping Value is used for the first outer iteration nonlinear iteration The damping parameter is adaptively varied on the basis of the head change using Cooleys method as described in Mehl and Hill 87 for subsequent iterations Damping value This defines the value of the damping parameter For linear problems a value of 10 should be used For nonlinear problems a value less than 10 but greater than 00 may be necessary to achieve convergence A typi cal value for nonlinear problems is 05 Damping also helps to alleviate exces sive inner PCGiterations Preconditioner Control Smoother Type ILU Smoothing Select this option to implement ILU0 smoothing in the multigrid preconditioner This smoothing requires an additional vector on each multigrid level to store the pivots in the ILU factorization Symmetric GaussSeidel SGS Smoothing Select this option to implement the Symmetric GaussSeidel SGS smoothing in the multigrid precondi tioner No additional storage is required for this smoother users may want to use this option if available memory is exceeded or nearly exceeded when using ILU Smoothing Using SGS smoothing is not as robust as ILU smoothing additional iterations are likely to be required in reducing the residuals In extreme cases the solver may fail to converge as the residuals cannot be reduced sufficiently SemiCoarsening This option controls semicoarsening in the multigrid pre conditioner The possible options and their meanings are given as follows Coarsen RowsColumnsLayers rows columns and layers are all coars ened Coarsen RowsColumns rows and columns are coarsened but the layers are not Coarsen ColumnsLayers columns and layers are coarsened but the rows are not Coarsen RowsLayers rows and layers are coarsened but the columns are not No Coarsening there is no coarsening Typically the options Coarsen RowsColumnsLayers or Coarsen RowsCol umns should be selected In the case that there are large vertical variations in the hydraulic conductivities then the option Coarsen RowsColumns should be used If no coarsening is implemented the GMG solver is comparable to 82 2 Modeling Environment Fig 236 The Newton Solver NWT dialog box the PCG2 ILU0 solver described in Hill 59 and uses the least amount of memory Relaxation Parameter This parameter can be used to improve the spectral con dition number of the ILU preconditioned system The value of relaxation pa rameter should be approximately one However the relaxation parameter can cause the factorization to break down If this happens then the GMG solver will report an assembly error and a value smaller than one for relaxation pa rameter should be tried Relaxation Parameter is used only if the option No Coarsening is selected MODFLOW Solvers Newton MODFLOWNWT This menu item is available only if the MODFLOW Version in the Preference dialog box Figure 213 is set to MODFLOW2000MODFLOW2005 and the Flow Pack age is set to LayerProperty Flow LPF or Upstream Weighting UPW Package When this menu item is selected checked MODFLOWNWT will be used as the simulation engine and the settings of the other linear solvers eg PCG2 DE45 etc will be ignored The required parameters for Newton package are specified in the Newton Solver NWT dialog box Fig 236 The parameters are described below LINMETH determines which matrix solver will be used 26 The Models Menu 83 OPTIONS contains three sets of preconfigured solver input values See table 2 of the MODFLOWNWT user guide 91 for the solver input values that will be used for the available options SIMPLE indicates that default solver input values will be defined that work well for nearly linear models This would be used for models that do not include nonlinear stress packages and models that are either confined or consist of a single unconfined layer that is thick enough to contain the water table within a single layer MODERATE indicates that default solver input values will be defined that work well for moderately nonlinear models This would be used for models that in clude nonlinear stress packages and models that consist of one or more uncon fined layers The MODERATE option should be used when the SIMPLE option does not result in successful convergence COMPLEX indicates that default solver input values will be defined that work well for highly nonlinear models This would be used for models that include nonlinear stress packages and models that consist of one or more unconfined layers representing complex geology and swgw interaction The COMPLEX option should be used when the MODERATE option does not result in success ful convergence IBOTAV is a flag that indicates whether corrections will be made to groundwater head relative to the cellbottom altitude if the cell is surrounded by dewatered cells A correction will be made if this box is checked This setting is problem specific and both checked and unchecked should be tested IPHDRY is a flag that indicates whether groundwater head will be set to HDRY when the groundwater head is less than 1E04 above the cell bottom HEADTOL L is the maximum head change between outer iterations for solution of the nonlinear problem FLUXTOL L3T is the maximum rootmeansquared flux difference between outer iterations for solution of the nonlinear problem MAXITEROUT is the maximum number of iterations to be allowed for solution of the outer nonlinear problem THICKFACT is the portion of the cell thickness length used for smoothly adjust ing storage and conductance coefficients to zero See the symbol Ω in equation 9 of the MODFLOWNWT user guide 91 26114 MODFLOW Head Observations Select Head Observations from the MODFLOW menu or from MODFLOW2000 Pa rameter Estimation or PEST Parameter Estimation menus to specify the locations of the head observation boreholes and their associated observed measurement data 84 2 Modeling Environment Fig 237 The Head Observation dialog box in the Head Observations dialog box Fig 237 Using the Save button the user can save the tables in separate ASCII files see Section 626 for the formats which can be loaded at a later time by using the Load button The other options of this dialog box are described below The Observations Tab Observation Borehole The Name OBSNAM and the coordinates expressed in the world coordinates according to the userdefined coordinate system of each borehole are given in this table The Name should be unique for each observation A borehole is active if the Active flag is checked To input a new borehole scroll down to the end of the table and simply type the name and coordinates to the last blank row To delete a borehole the user selects the row to be deleted by clicking on its record selector before the first column of the table then pressing the Del key After a simulation the user may select View Head Scatter Diagram from the Modflow or PEST menus to compare the calculated and observed values The user can also select View HeadTime Curves of these menus to display timeseries curves of both the calculated and observed values The Observation Data group contains two tables Layer Proportion and Head Observations These tables contain the data of the selected borehole which is marked by on the Observation Borehole table The Layer Proportions table PM supports multilayer observations by using this table If an observation borehole is screened over more than one model layer and the observed hydraulic head is affected by all screened layers then the associated simulated value is a weighted average of the calculated hydraulic heads of the screened layers The simulated head value h is calculated by h sum from i1 to nlay of Hi PRi sum from i1 to nlay of PRi 233 Where nlay is the number of model layers Hi and PRi are the calculated head value and the proportion value of the ith layer respectively The proportion values generally are assigned using the thickness screened within each layer and the local hydraulic properties A more realistic representation of this problem would be produced by calculating proportions that are based on the flowsystem and hydraulic properties 63 For a singlelayer borehole simply specify a nonzero proportion value to the layer where the borehole is screened and assign a proportion value of zero to all other layers If the proportion values of all layers are zero the observation borehole is considered as inactive and thus no graphical display can be generated for this borehole 86 2 Modeling Environment The Head Observations table When specifying head observations for MOD FLOW2000 the third column of this table is Statistic otherwise it is Weight Inserting or deleting an observation row is identical to the table for Observa tion Borehole described above Time The observation time to which the measurement pertains is mea sured from the beginning of the model simulation You may specify the observation times in any order By clicking on the column header or the OK button the observation times and the associated values will be sorted in ascending order When calibrating a steady state flow model with one stress period the observation time should be the length of the period Of particular note is that when calibrating a transient flow model with PEST the observation times and the associated HOBS Weight and Statistic val ues are linearly interpolated to the simulation times at the end of each stress period or time step The interpolated values are then used for parameter es timation When running MODFLOW2000 the specified observation times and values are used for parameter estimation directly without interpolation HOBS The hydraulic head observed at the observation time Weight The Weight of an observation gives a relative confidence level of the observed value The higher the value the better is the measurement The weight can be set at zero if needed meaning that the observation takes no part in the calculation of the objective function during a parameter es timation process but it must not be negative Refer to the documents of PEST 333436 for the function of weights in the parameter estimation process Statistic MODFLOW2000 reads statistics from which the weights are cal culated The physical meaning of Statistic is controlled by the Options tab see below The Options Tab This tab is only used by MODFLOW2000 for parameter estimation There are two options Parameter Estimation Option When the option temporal changes in hydraulic heads are used as observations is selected the temporal change is calculated as a specified hydraulic head minus the first hydraulic head specified for that location The first hydraulic head at a location is included in the regression The advantage of matching temporal changes in hydraulic head is that errors that are constant in time such as well elevation are expunged 63 Statistic Option This option defines the physical meaning of Statistic specified in the Head Observations table It also defines how the weights are calculated 26 The Models Menu 87 Refer to Hill 62 for more details about the role of statistics and weights in solving regression problems Note The PEST interface of PM can only handle singlelayer observation boreholes Multilayer boreholes are ignored when using PEST However multilayer boreholes will be used when using PESTASPMODFLOW2000 26115 MODFLOW Drawdown Observations Select Drawdown Observations from the MODFLOW menu or from the PEST menu to specify the locations of the drawdown observation boreholes and their associated ob served measurement data in a Drawdown Observations dialog box Its use is identical to the Head Observation dialog box The only difference is that the head observations are replaced by drawdown observations Note that MODFLOW2000 does not use drawdown observations for parameter estimation Instead the temporal changes in specified hydraulic heads are used 26116 MODFLOW Subsidence Observations Select this menu item to open a Subsidence Observation dialog box Except the Layer Proportion table the use of this dialog box is identical to the Head Observation dialog box The Layer Proportions table is not used here because the subsidence is the sum of the compactions in all model layers The specified subsidence values are solely for display purposes and not used by PEST or MODFLOW2000 for parameter estimation 26117 MODFLOW Compaction Observations Select this menu item to open a Compaction Observation dialog box The use of this dialog box is identical to the Head Observation dialog box except the Layer Pro portion table The layer Proportions values are used as a flag here When displaying compactiontime curves or a compaction scatter diagram the sum of the compaction values of the layers which have a positive layer proportion value is assign to the ob servation borehole The specified compaction values are solely for display purposes and not used by PEST or MODFLOW2000 for parameter estimation 26118 MODFLOW Output Control The primary output file of MODFLOW is the run listing file OUTPUTDAT MOD FLOW calculates a volumetric water budget for the entire model at the end of each 88 2 Modeling Environment time step and saves it in the run listing file The volumetric water budget provides an indication of the overall acceptability of the numerical solution In numerical solution techniques the system of equations solved by a model actually consists of a flow con tinuity statement for each model cell Continuity should therefore also exist for the total flows into and out of the entire model or a subregion This means that the differ ence between total inflow and total outflow should equal the total change in storage It is recommended to read the listing file by selecting Models Modflow View Run Listing File The run listing file also contains other essential information In case of dif ficulties this supplementary information could be very helpful If the computational accuracy is inadequate decrease the convergence criterion in the selected solver In addition to the run listing file various simulation results can be saved by check ing the corresponding output terms in the MODFLOW Output Control dialog box Fig 238 The settings are described below Output Terms The output terms and the corresponding result files are described below All result files are saved in the folder in which the model data are saved Hydraulic Heads are the primary result of a MODFLOW simulation Hydraulic heads in each finitedifference cell are saved in the unformatted binary file HEADSDAT Drawdowns are the differences between the initial hydraulic heads and the cal culated hydraulic heads Drawdowns in each cell are saved in the unformatted binary file DDOWNDAT Cellbycell Flow Terms are flow terms for individual cells including four types Fig 238 The Modflow Output Control dialog box 26 The Models Menu 89 1 cellbycell stress flows or flows into or from an individual cell due to one of the external stresses excitations represented in the model eg pumping well or recharge 2 cellbycell storage terms which give the rate of accumulation or depletion of storage in an individual cell 3 cellbycell constanthead flow terms which give the net flow to or from individual constant head cells and 4 internal cellbycell flows which are the flows across individual cell faces that is between adjacent model cells The cellbycell flow terms are used for calculating water budgets and for particle tracking and transport simu lations by PMPATH and MOC3D The cellbycell flow terms are saved in the unformatted binary file BUDGETDAT Subsidence is the sum of the compaction of all model layers for which the interbed storage calculation is turned on see Section 242 Compaction of individual layers is the sum of the calculated compaction and the userspecified starting compaction in each layer Preconsolidation head is the previous minimum head value in the aquifer For model cells in which the specified preconsolidation head is greater than the corresponding value of the starting head the preconsolidation head will be set to the starting head Subsidence compaction and preconsolidation head are saved in the unformatted binary file INTERBEDDAT Interface file to MT3D is an unformatted binary file containing the computed heads fluxes across cell interfaces in all directions and locations and flow rates of the various sinkssources The interface file is created for the transport mod els MT3D MT3DMS RT3D and PHT3D Output Frequency The simulation results are saved whenever the time steps and stress periods are an even multiple of the output frequency and the results for the first and last stress periods and time steps are always saved Use 0 zero for the output frequency if only the result of the last stress period or the last time step should be saved Predefined Head Values The predefined heads for noflow cells HNOFLO and dry cells HDRY are given in the Predefined Head Values group 26119 MODFLOW Run Select this menu item to open the Run Modflow dialog box Fig 239 to run the flow simulation with MODFLOW or to check the model data The available settings of the dialog box are described below The File Table has three columns 90 2 Modeling Environment Generate Prior to running a flow simulation PM uses the userspecified data to generate input files for MODFLOW and MODPATH An input file will be generated if it does not exist or if the corresponding Generate box is checked Normally we do not need to worry about these boxes since PM will take care of the settings Note that MODPATH 9697 andor MODPATHPLOT 97 cannot be started from PMWIN directly In most cases however the user does not need to use these programs since PMPATH includes all their features and is far easier to use Refer to Section 64 for how to run MODPATH Description gives the names of the packages used in the flow model Destination File shows the paths and names of the input files of the flow model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Generate input files only dont start MODFLOW Check this option if the user does not want to run MODFLOW The simulation can be started at a later time or can be started at the Command Prompt DOS box by executing the batch file MODFLOWBAT Check the model data If this option is checked PM will check the geometry of the model and the consistency of the model data as given in Table 26 before Fig 239 The Run Modflow dialog box 26 The Models Menu 91 Table 26 Model Data checked by PM Term Checking Criteria Layer thickness May not be zero or negative Top and bottom elevation of layers Model layers may not overlap each other Initial head at constant head cells A constant head cell may not be dry at the beginning of a simulation Horizontal hydraulic conduc tivity transmissivity vertical hydraulic conductivity ver tical leakance or effective porosity May not be zero or negative Storage coefficient specific storage or specific yield May not be negative River package 1 A river cell may not be a fixedhead cell and should not be an inactive cell 2 Elevation of the riverbed should be higher than the ele vation of the cell bottom 3 The river stage must be higher than elevation of the riverbed StreamflowRouting package A STRcell may not be a constant head cell and should not be an inactive cell Drain package 1 A drain cell may not be a fixedhead cell and should not be an inactive cell 2 Elevation of the drain should be higher than the eleva tion of the cell bottom General head boundary A GHBcell may not be a fixedhead cell and should not be an inactive cell Well package A wellcell may not be a fixedhead cell and should not be an inactive cell creating data files The errors if any are saved in the file CHECKLIS located in the same folder as the model data OK Click OK to generate MODFLOW input files In addition to the input files PM creates a batch file MODFLOWBAT in the model folder When all input files are generated PM automatically runs MODFLOWBAT in a Command Prompt window DOS box During a flow simulation MODFLOW writes a detailed run record to the file OUTPUTDAT saved in the model folder MODFLOW saves the simulation results in various unformatted binary files only if a flow simulation has been successfully completed See MODFLOW Output Control page 87 for details about the output terms of MODFLOW 92 2 Modeling Environment 26120 MODFLOW View MODFLOW View Run Listing File Select this menu item to use the Text Viewer see Section 234 to display the run list file OUTPUTDAT which contains a detailed run record saved by MODFLOW MODFLOW View Head Scatter Diagram This menu item is available only if Head Observations have been defined see Section 26114 Select this menu item to open the Scatter Diagram Hydraulic Head dia log box Fig 240 The options are grouped under two tabs Data and Chart as described below The Data Tab contains a table showing the observed and calculated values at ac tive observation boreholes see Section 26114 for the definition of observation boreholes The columns of this table are listed Plot A borehole will be displayed on the scatter diagram only when its Plot box is checked Color Defines the plot color for each borehole Click the button to change the color Fig 240 The Data tab of the Scatter Diagram Hydraulic Head dialog box Fig 241 Interpolation of simulated head values to an observation borehole OBSNAM Displays the name of each observation borehole specified in the Head Observation dialog box Section 26114 Calculated value Displays simulated head values at observation boreholes If a borehole lies in an inactive or dry cell the default value for dry cells defined in Models MODFLOW Output Control is displayed As observation boreholes are rarely located at cell centers simulated head values at observation boreholes need to be calculated by means of interpolation At an observation borehole screened in the ith layer singlelayer observation PM calculates the simulated hydraulic head value Hi by interpolating within the layer using the following equation Hi sum from j1 to 4 of hj Aj sum from j1 to 4 of Aj Aj 0 for inactive cells 234 where Aj are the areas and hj are the computed values at the center of the cells surrounding the observation borehole Fig 241 For a multilayer observation borehole the simulated head value is calculated by equation 233 page 85 using the Hi values of all screened layers Observed Value The userspecified observed values in the Head Observations dialog box Section 26114 are linearly interpolated to the simulation times and displayed in this column 94 2 Modeling Environment Fig 242 The Chart tab of the Scatter Diagram Hydraulic Head dialog box Simulation Time Displays the times at the end of each stress period or time step to which the calculated values and observed values pertain Save Table Press this button to save the data of OBSNAM Calculated Value Observed Value and Simulation Time in an ASCII file This button is enabled only when the Data tab is chosen The Chart Tab Fig 242 displays the scatter diagram using the calculated and observed data Scatter diagrams are often used to present the quality of calibration results The observed values are plotted on one axis against the corresponding cal culated values on the other If there is an exact agreement between measurement and simulation all points lie on a 45 line The narrower the area of scatter around this line the better is the match The available settings are summarized below Scatter Diagram The Scatter Diagram has a lot of builtin features Rightclick on the scatter diagram to open a 2DChart Control Properties dialog box which allows the user to change the titles and axes settings Most options of this dialog box are selfexplanatory however the user can click the Help button for detailed descriptions of all options To zoom an area of the scatter diagram Press the Shift or the Ctrl key and hold down left mouse button Drag mouse to select zoom area and release the mouse button Performing a zoom with the Ctrl key enlarges the selected area of a chart while not necessarily showing the axes To remove the zooming effect press the r key 26 The Models Menu 95 Label Check the boxes to display the name of the observation boreholes or the observation times on the scatter diagram Observation Select Use results of all observations if all Plotmarked obser vations listed in the Data table should be used If the option Use results of the following OBSNAM is chosen only the results of the selected observation borehole OBSNAM are displayed Simulation Time Select Use results of all simulation times if all results listed in the Data table should be used If the option Use results of the following simulation time is chosen only the results of the selected simulation time are displayed Axes Bounds The bounds of the axes are defined by Upper Bound and Lower Bound which are determined automatically if the Fix Bounds box is not checked or if the Reset Bounds button is pressed When editing the upper and lower bounds the scatter diagram will be updated accordantly if Fix Bounds is not checked Check it to fix the bounds at specified values Variance is the mean squared error between observed and calculated value of Plotmarked observations which are displayed on the scatter diagram Copy to Clipboard Press this button to place a copy of the scatter diagram on the clipboard The user can recall this copy by pressing Ctrlv in almost all word or graphics processing software This button is enabled only when the Chart tab is chosen Save Plot As Press this button to save the scatter diagram in Windows bitmap or Metafile formats This button is enabled only when the Chart tab is chosen MODFLOW View Drawdown Scatter Diagram This menu item is available only if Drawdown Observations have been defined see Section 26115 Select this menu item to open a Scatter Diagram Drawdown dia log box which is identical to the Scatter Diagram Hydraulic Head dialog box Fig 240 except the drawdown values replace the head values Note that drawdown is defined by h0 h where h0 is the userspecified initial hydraulic head and h is the calculated head at time t MODFLOW View Subsidence Scatter Diagram This menu item is available only if Subsidence Observations have been defined see Section 26116 Select this menu item to open a Scatter Diagram Subsidence dia log box which is identical to the Scatter Diagram Hydraulic Head dialog box Fig 240 except the subsidence values replace the head values 96 2 Modeling Environment MODFLOW View Compaction Scatter Diagram This menu item is available only if Compaction Observations have been defined see Section 26117 Select this menu item to open a Scatter Diagram Compaction dia log box which is identical to the Scatter Diagram Hydraulic Head dialog box Fig 240 except the compaction values replace the head values MODFLOW View HeadTime Curves This menu item is available only if Head Observations have been defined see Section 26114 Select this menu item to open the Time Series Curves Hydraulic Head dialog box Fig 243 The options are grouped under two tabs Data and Chart as described below The Data Tab The Data tab contains two tables The table to the left shows the names OBSNAM of the observation boreholes and their Plot and Color settings The table to the right shows the Observation Time Calculated Values and Observed Values OBSNAM This column displays the name of each observation borehole speci fied in the Head Observation dialog box Fig 237 Fig 243 The Data tab of the Time Series Curves Hydraulic Head dialog box 26 The Models Menu 97 Plot The timeseries curves of a borehole will be displayed only when its Plot box is checked Color This column defines the plot color for each borehole Click the button to change the color Simulation Time Displays the times at the end of each stress period or time step to which the calculated values and observed values pertain Calculated value Displays simulated head values at observation boreholes If a borehole lies in an inactive or dry cell the default value for dry cells defined in Models MODFLOW Output Control is displayed Refer to MODFLOW View Head Scatter Diagram page 92 for details of interpolating simulated heads to the observation boreholes Observed Value The userspecified observed values in the Head Observations dialog box Fig 237 are linearly interpolated to the simulation times and dis played in this column Save Table Press this button to save the data of OBSNAM Simulation Time Calculated Value Observed Value in an ASCII file This button is enabled only when the Data tab is chosen The Chart Tab The Chart tab Fig 244 displays timeseries curves using the cal culated and observed values The available settings are summarized below Chart The Chart has a lot of builtin features Fig 244 The Chart tab of the HeadTime Series Curves Diagram dialog box 98 2 Modeling Environment Rightclick on the chart to open a 2DChart Control Properties dialog box which allows the user to change the titles and axes settings Most options of this dialog box are selfexplanatory however the user can click the Help button for detailed descriptions of all options To zoom an area of the scatter diagram Press the Shift or the Ctrl key and hold down left mouse button Drag mouse to select a zoom area and release the mouse button Performing a zoom with the Ctrl key enlarges the selected area of a chart while not necessarily showing the axes To remove the zooming effect press the r key XAxis Time The bounds of the time axis are defined by Upper Bound and Lower Bound which are determined automatically if the check box Fix Bounds is clear or if the Reset Bounds button is pressed When editing the upper and lower bounds the chart will be updated accordantly if Fix Bounds is not checked Check it to fix the bounds at specified values Check Logarithmic to display the timeaxis in the logarithmic scale YAxis The bounds of this axis are defined by Upper Bound and Lower Bound which are determined automatically if the check box Fix Bounds is clear or if the Reset Bounds button is pressed When editing the upper and lower bounds the chart will be updated accordantly if Fix Bounds is not checked Check it to fix the bounds at specified values Check Logarithmic to display the Yaxis in the logarithmic scale Data Type Check the Calculated or Observed box to display the timeseries curves based on the calculated or observed values respectively The chart uses solid lines for displaying calculated curves Observation curves are dashed Se lect Use results of all observations if all Plotmarked observations listed in the Data table should be used If the option Use results of the following OBSNAM is chosen only the curves of the selected observation borehole OBSNAM are displayed Copy to Clipboard Press this button to place a copy of the chart on the clip board The user can recall this copy by pressing Ctrlv in almost all word or graphics processing software This button is enabled only when the Chart tab is chosen Save Plot As Press this button to save the chart in Windows bitmap or Metafile formats This button is enabled only when the Chart tab is chosen 262 MT3DMSSEAWAT The first step to use MT3DMS or SEAWAT is to define the simulation mode species and type of reactions to be simulated in the Simulation Settings dialog box Section 2621 Once the simulation settings are defined the appropriate menu items of the 26 The Models Menu 99 MT3DMSSEAWAT menu will be enabled allowing the user to specify required model parameters If the user selects menu items involving speciesdependent parameters PM will display a dialog box for selecting a species for which the parameter is to be specified For example if you select MT3DMSSEAWAT Initial Concentration the Initial Concentration dialog box Fig 245 will appear and the following options are available Select a species and click the Edit button to specify the initial concentration for that species Click the Close button to close the dialog box and to stop editing data The Data box has three types of status as given below Once the data is specified you may click on the Data box to check or clear it Data has been specified and will be used for simulation Data has been specified but will not be used the default value of zero will be used Data is not available the box is dimmed and deactivated the default value of zero will be used 2621 MT3DMSSEAWAT Simulation Settings The Simulation Settings dialog box Fig 246 controls the type of reaction and the species involved in the simulation It also controls whether variable density flow andor transport should be simulated The available settings are described as follows Fig 245 The Initial Concentration dialog box 100 2 Modeling Environment Simulation Mode Constant Density Transport with MT3DMS If this option is selected the con stant density flow solution of MODFLOW will be used by MT3DMS to sim ulate solute transport processes It is assumed that the solution concentration does not affect the fluid density and the flow field MT3DMS simulations are carried out on the basis of flowfields computed beforehand by MODFLOW Variable Density Flow and Transport with SEAWAT If this option is selected SEAWAT will be used to simulate coupled variabledensity flow and solute transport With this option fluid density is calculated by using an equation of state and the simulated solute concentration values of involved species The densityeffect of a particular species may be turned on or off in the Species tab see below The flow and transport processes are computed by MODFLOW and MT3DMS that are incorporated in SEAWAT Type of Reaction Select a type of reaction that you want to simulate from this dropdown box MT3DMS includes the type of Firstorder irreversible reaction only The last three reaction types are supported by the proprietary MT3D99 code 124 If you do not have access to MT3D99 or need to simulate more complex Fig 246 The Simulation Settings MT3DMSSEAWAT dialog box 26 The Models Menu 101 reaction scenarios consider using the multicomponent reactive transport model PHT3D see Section 263 for details The required parameters for the selected chemical reaction type are specified by selecting MT3DMSSEAWAT Chemical Reaction see Section 2626 No kinetic reaction is simulated Select this one to turn off the simulation of kinetic reactions Firstorder irreversible reaction simulates radioactive decay or biodegradation Monod kinetics MT3D99 implements the Monod kinetics only for the dissolved phase of an organic compound Firstorder parentdaughter chain reactions can be used to model radioac tive chain reaction and biodegradation of chlorinated solvents for exam ple the transformation of perchloroethene PCE trichloroethene TCE dichloroethene DCE vinyl chloride VC The species are defined in the Species tab and the yield coefficients between species pairs are to be specified in the Stoichiometry tab of the Simulation Settings dialog box Fig 247 Fig 247 The Stoichiometry tab of the Simulation Settings MT3DMSSEAWAT di alog box 102 2 Modeling Environment Instantaneous reaction among species MT3D99 uses the approach of Bor den and Bedient 15 and Rifai and others 104105 to simulate the aerobic and anaerobic biodegradation of common hydrocarbon contaminants includ ing benzene touluene ethylbenzene and xylene BTEX Stoichiometric ratios between the first species and other species are required to simulate this type of reaction and are to be specified in the Stoichiometry tab Fig 247 Species tab Fig 246 The columns of the table are described below Number This column displays the readonly species number Active Check the Active box to add a species to the simulation Description Type the name or description of the species here Density On This item is used by SEAWAT only Check the box to include the concentration of the simulated species in the fluid density calculation If the fluid density is independent of all simulated species ie Density On boxes of all species are cleared SEAWAT will run in a uncoupled mode and the user specified fluid density array see Section 2627 will be used in the simulation DRHODC This item is used by SEAWAT only DRHODC ie ρC is the slope that relates fluid density ρ to solute concentration C Separate values for DRHODC are entered for individual species DRHODC is ignored if the Density On box of the corresponding species is not checked Any measurement unit can be used for solute concentration provided DRHODC and the reference fluid density DENSEREF see below are set properly CRHOREF This item is used by SEAWAT only CRHOREF is the reference concentration for the species For most simulations CRHOREF should be specified as zero Stoichiometry tab Fig 247 is used to specify yield coefficients or stoichiometric ratios between species pairs A yield coefficient Y12 between two species means consuming of one mass unit of species 1 will yield Y12 mass units of species 2 For example if Y12 3 then consuming of 1 g of species 1 will yield 3 g of species 2 The stoichiometric ratio F1k between species 1 and species k means one mass unit of species 1 reacts with F1k mass units of species k For example if F14 3 then 1 g of species 1 will react with 3 g of species 4 SEAWAT tab Fig 248 is used to specify SEAWAT simulation control parameters The available settings are given below Activate the variabledensity watertable correction IWTABLE Check this option to activate the variabledensity watertable corrections eq 82 of 51 Method for calculating internodal density values This option determines how the internodal density values used to conserve fluid mass will be calculated Flow and transport coupling procedure OneTimestep lag Flow and transport will be explicitly coupled using a one timestep lag as described in Guo and Langevin 51 With the explicit 26 The Models Menu 103 approach the flow equation is formulated using fluid densities from the previous transport timestep The explicit coupling option is normally much faster than the iterative option and is recommended by the authors of SEA WAT 77 for most applications Nonlinear Iterative The solution of the flow and transport equations is obtained in an iterative sequence for each timestep until the consecutive differences in the calculated fluid densities are less than a userspecified value See Guo and Langevin 51 for detailed explanations Conditional The flow solution will be recalculated only for 1 The first transport step of the simulation or 2 The last transport step of the MOD FLOW timestep or 3 The maximum density change at a cell is greater than the Density change threshold for recalculating flow solution see be low Maximum number of nonlinear coupling iterations This value is used only if the Flow and transport coupling procedure is Nonlinear Iterative SEAWAT will stop execution after the given number iterations for the flow and transport solutions if convergence has not occurred Density change convergence criterion for coupling iterations ML3 This value is used only if the Flow and transport coupling procedure is Nonlinear Iterative If the maximum fluid density difference between two consecutive implicit coupling iterations is less than then given value SEAWAT will advance to the next timestep Otherwise SEAWAT will continue to iterate on the flow and transport equations or will terminate if Maximum number of nonlinear coupling iterations is reached Density change threshold for recalculating flow solution ML3 This value is used only if the Flow and transport coupling procedure is Conditional If the fluid density change between the present transport timestep and the last flow solution at one or more cells is greater than the given value then SEAWAT will update the flow field by solving the flow equation with the updated density field Length of the first transport time step FIRSTDT This is the length of the first transport timestep used to start the simulation Reference fluid density DENSEREF DENSEREF is the fluid density at the reference concentration temperature and pressure For most simulations DENSEREF is specified as the density of freshwater at 25 C and at a reference pressure of zero Minimum Fluid Density DENSEMIN If DENSEMIN 0 If the computed fluid density is less than DENSEMIN the density value is set to DENSEMIN If DENSEMIN 0 The computed fluid density is not limited by DENSEMIN 104 2 Modeling Environment Maximum Fluid Density DENSEMAX If DENSEMAX 0 If the computed fluid density is greater than DENSE MAX the density value is set to DENSEMAX If DENSEMAX 0 The computed fluid density is not limited by DENSE MAX Density Options uncoupled mode When the all Density On boxes in the Species tab are cleared ie SEAWAT runs in a uncoupled mode the user has the option to determine the density of the source fluid at wells river and generalhead boundaries If Reference Fluid Density is selected then density value of the source fluid is equal to DENSEREF otherwise the userspecified density values to the respective packages will be used Fig 248 The Variable Density tab of the Simulation Settings MT3DMSSEAWAT dialog box 26 The Models Menu 105 2622 MT3DMSSEAWAT Initial Concentration At the beginning of a transport simulation MT3DMS and SEAWAT require the initial concentration of each active species at each active concentration cell ie ICBUND 0 2623 MT3DMSSEAWAT Advection The available settings of the Advection Package MT3DMS dialog box Fig 249 are described below Fig 249 The Advection Package MT3DMS dialog box Solution Scheme MT3DMS provides five solution schemes for the advection term as described below The method of characteristics MOC scheme was implemented in the transport models MOC 73 and MOC3D see Section 2653 and has been widely used One of the most desirable features of the MOC technique is that it is virtually free of numerical dispersion which creates serious difficulty in many numerical schemes The major drawback of the MOC scheme is that it can be slow and requires a large amount of computer memory when a large number of particles is required Also the computed concentrations sometimes tend to show artificial oscillations 106 2 Modeling Environment The modified method of characteristics MMOC uses one particle for each finitedifference cell and is normally faster than the MOC technique At each new time level a particle is placed at the nodal point of each finitedifference cell The particle is tracked backward to find its position at the old time level The concentration associated with that position is used to approximate the advectionrelevant average concentration at the cell where the particle is placed The MMOC technique is free of artificial oscillations if implemented with a lowerorder velocity interpolation scheme such as linear interpolation used in MT3D and MT3DMS However with a lowerorder velocity interpo lation scheme the MMOC technique introduces some numerical dispersion especially for sharp front problems The hybrid method of characteristics HMOC attempts to combine the strengths of the MOC and MMOC schemes by using an automatic adaptive scheme con ceptually similar to the one proposed by Neumann 89 The fundamental idea behind the scheme is automatic adaptation of the solution process to the na ture of the concentration field When sharp concentration fronts are present the advection term is solved by MOC through the use of moving particles dy namically distributed around each front Away from such fronts the advection term is solved by MMOC The criterion for controlling the switch between the MOC and MMOC schemes is given by DCHMOC see below The finitedifference method is implicit with the Generalized Conjugate Gradi ent solver GCG package see Section 26210 Due to the problems of numerical dispersion and artificial oscillation the up stream finite difference method is only suitable for solving transport problems not dominated by advection When the grid Peclet number Pe Pe xαL x is the grid spacing and αL is the longitudinal dispersivity is smaller than two the upstream finite difference method is reasonably accurate However it is advisable to use the upstream finite difference method for obtaining first approximations in the initial stages of a modeling study The thirdorder TVD method is based on the ULTIMATE algorithm 80 8182 which is in turn derived from the earlier QUICKEST algorithm 79 With the ULTIMATE scheme the solution is mass conservative without ex cessive numerical dispersion and artificial oscillation Weighting Scheme is needed only when the implicit finitedifference method is used ie the solution scheme is finitedifference and the iterative GCG solver is used In the finitedifference method when computing the mass flux into a model cell by advection the concentration values at the cell interfaces between two neigh boring cells are used For the upstream weighting scheme the interface concentra tion in a particular direction is equal to the concentration at the upstream node along the same direction For the centralinspace weighting scheme the interface concentration is obtained by linear interpolation of the concentrations at the two neighboring cells As denoted in Zheng and Wang 123 the centralinspace scheme does not lead to intolerable numerical dispersion when the grid spacing is regular However if transport is dominated by advection the upstream weighting is preferred as the centralinspace weighting scheme can lead to excessive artificial oscillation Particle Tracking Algorithm is used in combination with the method of characteristics Using the firstorder Euler algorithm numerical errors tend to be large unless small transport steps are used The allowed transport step t of a particle is determined by MT3D using equation 235 Δt γc R MIN Δxvx Δyvy Δzvz 235 where Δx Δy and Δz are the cell widths along the row column and layer directions respectively c is the Courant number The particle velocities vx vy and vz at the position x y z are obtained by linear interpolation from the specific discharges at the cell faces The minimum Δt of all particles is used in a transport step The basic idea of the fourthorder RungeKutta method is to calculate the particle velocity four times for each tracking step one at the initial point twice at two trial midpoints and once at a trial end point A weighted velocity based on values evaluated at these four points is used to move the particle to a new position The fourthorder RungeKutta method permits the use of larger tracking steps However its computational effort is considerably larger than the firstorder Euler method For this reason a mixed option combining both methods is introduced in MT3DMS The mixed option is implemented by automatic selection of the fourthorder RungeKutta algorithm for particles located in cells which contain or are adjacent to sinks or sources and automatic selection of the firstorder Euler algorithm for particles located elsewhere Simulation Parameters Depends on the selected Solution Scheme one or more of the following parameters may be required Maximum number of total moving particles MXPART is the number of particles allowed in a simulation Courant number PERCEL is the number of cells or a fraction of a cell any particle will be allowed to move in any direction in one transport step Generally 05 PERCEL 1 Concentrationweighting factor WD lies between 0 and 1 The value of 05 is normally a good choice This number can be adjusted to achieve better mass 108 2 Modeling Environment balance Generally it can be increased toward 1 as advection becomes more dominant Negligible relative concentration gradient DCEPS is a criterion for placing particles A value around 105 is generally adequate If DCEPS is greater than the relative cell concentration gradient DCCELLkij equation 236 NPH particles are placed in the cell k i j otherwise NPL particles are placed see NPH and NPL below DCCELLkij CMAXkij CMINkij CMAX CMIN 236 where CMAXkij and CMINkij are the maximum and minimum concen tration values in the immediate vicinity of the cell k i j CMIN and CMAX are the minimum and maximum concentration values in the entire grid respec tively Pattern for initial placement of particles NPLANE is used to select a pattern for initial placement of moving particles NPLANE 0 the random pattern is selected for initial placement Particles are distributed randomly in both the horizontal and vertical directions Fig 250b This option generally leads to smaller mass balance discrepancy in nonuniform or divergingconverging flow fields NPLANE 0 the fixed pattern is selected for initial placement The value of NPLANE serves as the number of planes on which initial particles are placed within each cell Fig 250a This fixed pattern may work better than the random pattern only in relatively uniform flow fields For two di mensional simulations in plan view set NPLANE1 For cross sectional or three dimensional simulations NPLANE2 is normally adequate Increase NPLANE if more resolution in the vertical direction is desired No of particles per cell in case of DCCELL DCEPS NPL is the number of initial particles per cell to be placed at cells where the relative cell concentration gradient DCCELL is less than or equal to DCEPS Generally NPL can be set to zero since advection is considered insignificant under the condition DCCELL DCEPS Setting NPL equal to NPH causes a uniform number of particles to be placed in every cell over the entire grid ie the uniform approach No of particles per cell in case of DCCELL DCEPS NPH is the number of initial particles per cell to be placed at cells where the relative cell con centration gradient DCCELL is greater than DCEPS The selection of NPH depends on the nature of the flow field and also the computer memory limi tation Generally use a smaller number in relatively uniform flow fields and a larger number in relatively nonuniform flow fields However values exceed ing 16 in twodimensional simulations or 32 in three dimensional simulations 26 The Models Menu 109 Fig 250 Initial placement of moving particles adapted from Zheng 119 a Fixed pattern 8 particles are placed on two planes within a cell b Random pattern 8 parti cles are placed randomly within a cell are rarely necessary If the random pattern is chosen NPH particles are ran domly distributed within the cell If the fixed pattern is chosen NPH is divided by NPLANE to yield the number of particles to be placed per plane which is rounded to one of the values shown in Fig 251 Minimum number of particles allowed per cell NPMIN If the number of particles in a cell at the end of a transport step is fewer than NPMIN new particles are inserted into that cell to maintain a sufficient number of particles NPMIN can be set to 0 in relatively uniform flow fields and a number greater than zero in divergingconverging flow fields Generally a value between zero and four is adequate Maximum number of particles allowed per cell NPMAX If the number of particles in a cell exceeds NPMAX particles are removed from that cell until NPMAX is met Generally NPMAX 2 NPH SRMULT is a multiplier for the particle number at source cells SRMULT 1 In most cases SRMULT 1 is sufficient However better results may be obtained by increasing SRMULT Pattern for placement of particles for sink cells NLSINK is used to select a pattern for initial placement of particles to approximate sink cells in the MMOC scheme The convention is the same as that for NPLANE and it is generally adequate to set NLSINK equivalent to NPLANE Number of particles allowed to approximate sink cells NPSINK is used in the MMOC scheme The convention is the same as that for NPH and it is generally adequate to set NPSINK equivalent to NPLANE 110 2 Modeling Environment Fig 251 Distribution of initial particles using the fixed pattern adapted from Zheng 1990 If the fixed pattern is chosen the number of particles placed per cell NPL and NPH is divided by the number of planes NPLANE to yield the number of particles to be placed on each plane which is then rounded to one of the numbers of particles shown here Critical relative concentration gradient DCHMOC is used to select between MOC and MMOC in the HMOC solution scheme MOC is selected at cells where DCCELL DCHMOC MMOC is selected at cells where DCCELL DCHMOC 2624 MT3DMSSEAWAT Dispersion The following values must be specified for each layer in the Dispersion Package dialog box Fig 252 TRPT is the ratio of the horizontal transverse dispersivity to the longitudinal dis persivity The longitudinal dispersivity for each finitedifference cell is specified in the Data Editor Longitudinal dispersivity is used to approximate the spreading of the solute concentration in groundwater caused by the irregular shape of the inter connected pore space and the velocity variations at the microscopic level as well as the unresolved macroscopic level The velocity of groundwater varies according to the size of the pores and water moves faster at the internal points between soil grains than on the solid surface This spreading is often referred to as mechanical 26 The Models Menu 111 Fig 252 The Dispersion Package dialog box dispersion and it occurs in all three spatial directions The coefficient of mechani cal dispersion is defined by αivi where αi is the dispersivity and vi is the average linear velocity in the idirection The sum of mechanical dispersion and molecular diffusion is called hydrodynamic dispersion Values of dispersivity used for simulations generally depend on the scale of a con centration plume being considered While a plume grows it will not only un dergo the microscopic mechanical dispersion but also the dispersion caused by macroscopic heterogeneities This results in a trend of increasing dispersivity val ues with the scale of observation Summaries of the scaledependent dispersiv ity values can be found in Anderson 67 Gelhar et al 4950 and Spitz and Moreno 111 Note that all heterogeneity which is not explicitly represented in the model should be incorporated into the dispersion coefficients TRPV is the ratio of the vertical transverse dispersivity to the longitudinal disper sivity DMCOEF is the effective molecular diffusion coefficient D L2T 1 equation 238 DMCOEF describes the diffusive flux of a solute in water from an area of greater concentration toward an area where it is less concentrated The mass flux is pro portional to the concentration gradient and is given by Ficks first law F D C 237 where F ML2T 1 is the mass flux of solute per unit area per unit time D L2T 1 is the diffusion coefficient C ML3 is the solute concentration and 112 2 Modeling Environment C ML3L1 is the concentration gradient In porous media the solute mass cannot diffuse as fast as in free water because the ions must move along longer pathways through the pore space To account for this tortuosity effect an effective diffusion coefficient D must be used D ω D 238 According to Freeze and Cherry 46 ω ranges from 05 to 001 for laboratory stud ies of diffusion of nonadsorbed ions in porous geologic materials The diffusion coefficients D of the major ions Na K Mg2 Ca2 Cl CO2 3 HCO 3 SO2 4 are temperaturedependent and range from 1 109 to 2 109m2s at 25C 83 106 At 5C the coefficients are about 50 smaller The molecular diffusion coefficient is generally very small and negligible compared to the me chanical dispersion see below and is only important when groundwater velocity is very low In MT3DMS the concentration change due to dispersion alone is solved with a fully explicit central finitedifference scheme There is a certain stability criterion associated with this scheme To retain stability the transport step size cannot exceed an upper limit defined by equation 239 t 05 R Dxx x2 Dyy y2 Dzz z2 239 where x y and z are the widths of the cell along the row column and layer directions R is the retardation factor The components of the hydrodynamic dispersion coefficient Dxx Dyy and Dzz are calculated by equation 240 Dxx αL v2 x v αT H v2 y v αT V v2 z v D Dyy αL v2 y v αT H v2 x v αT V v2 z v D 240 Dzz αL v2 z v αT H v2 x v αT V v2 y v D where αL L is the longitudinal dispersivity αT H L is the horizontal transverse dispersivity αT V L is the vertical transverse dispersivity vx vy and vz LT 1 are components of the flow velocity vector along the x y and z axes and v v2 x v2 y v2 z12 241 26 The Models Menu 113 Equation 239 is calculated for each active cell and the minimum t is taken as the maximum allowed step size for solving the dispersion term This criterion is compared with other transport step size constraints to determine the minimum step size for the simulation Generally a higher flow velocity for example the velocity in the immediate vicinity of a pumping well will cause larger values of Dxx Dyy and Dzz which in turn result in a smaller t in equation 239 When t is too small the required CPU time will become enormous To overcome this problem an implicit formulation is implemented in MT3DMS See Section 26210 for details 2625 MT3DMSSEAWAT Species Dependent Diffusion Select this item to enter diffusion coefficient for individual species The specified data will be used by MT3DMS or SEAWAT to replace the effective molecular diffusion coefficient in the Dispersion package The specified data are used only if the Dispersion package is activated 2626 MT3DMSSEAWAT Chemical Reaction The Chemical Reaction package can be used to simulate sorption and chemical reac tions The type of reaction is selected in the Simulation Settings MT3DMSSEAWAT dialog box Fig 246 The type of sorption and the parameters for sorption and chem ical reactions are defined in the the Chemical Reaction MT3DMS dialog box Fig 253 of the Data Editor The required parameters for the selected sorption and reaction types are summarized below Fig 253 The Chemical Reaction MT3DMS dialog box 114 2 Modeling Environment Type of Sorption Sorption is implemented in MT3DMS through use of the retar dation factor R No sorption Sorption is not simulated Linear isotherm equilibrium assumes that the sorbed concentration Ckij is directly proportional to the dissolved concentration Ckij equation 242 The retardation factor is therefore independent of the concentration values and is calculated only once for each cell at the beginning of the simulation by equation 243 Ckij Kd Ckij 242 Rkij 1 ρb nkij Kd 243 where nkij is the porosity of the porous medium in the cell k i j Kd L3M 1 is the distribution coefficient that depends on the solute species na ture of the porous medium and other conditions of the system and ρb ML3 is the bulk density of the porous medium The bulk density is the ratio of the mass of dried soil to total volume of the soil Freundlich isotherm nonlinear equilibrium is expressed by equation 244 The retardation factor at the beginning of each transport step is calculated by equation 245 Ckij Kf Ca kij 244 Rkij 1 ρb nkij a Ca1 kij Kf 245 where Ckij is the solute concentration in the cell in the cell k i j at the beginning of each transport step a is the Freundlich exponent and Kf L3M 1 is the Freundlich constant Langmuir isotherm nonlinear equilibrium is defined by equation 246 The retardation factor at the beginning of each transport step is calculated by equa tion 247 Ckij KL S Ckij 1 KL Ckij 246 Rkij 1 ρb nkij KL S 1 KL Ckij2 247 where KL L3M 1 is the Langmuir constant and S MM 1 is the maximum amount of the solute that can be adsorbed by the soil matrix Firstorder kinetic sorption nonequilibrium When the local equilibrium as sumption is not valid MT3DMS assumes that sorption can be represented by a firstorder reversible kinetic sorption defined by equation 248 ρb Ct β C CKd 248 where β T1 is the firstorder mass transfer rate between the dissolved and sorbed phases ρb M L3 is the bulk density of the porous medium C is the sorbed concentration and Kd L3 M1 is the distribution coefficient that depends on the solute species nature of the porous medium and other conditions of the system Using the Firstorder kinetic sorption option the user has the choice of specifying the initial concentration for the sorbed or immobile phase for each species To do this simply check Use the initial concentration for the nonequilibrium sorbed or immobile liquid phase and specify the concentration value to Initial concentration for the sorbed phase or Initial concentration for the immobile liquid phase in the Chemical Reaction MT3DMS dialog box If the box Use the initial concentration for the nonequilibrium sorbed or immobile liquid phase is not checked it is assumed that the initial concentration of the sorbed or immobile liquid phase is in equilibrium with the initial concentration of the dissolved phase Equation 248 can be rearranged in C CKd ρbβ Ct 249 If sufficient time is available for the system to reach equilibrium for example the flow velocity of groundwater is very slow then there is no further change in C and Ct 0 so that equation 249 is reduced to linear sorption equation 242 If the firstorder mass transfer rate is infinitely large the righthand side of equation 249 is equal to zero which also leads to linear sorption For very small values of β the lefthandside of equation 248 becomes negligible ie there is no change in the sorbed concentration and sorption is negligible Dualdomain mass transfer without sorption and Dualdomain mass transfer with sorption Dualdomain means that two kinds of continuum eg a fractured medium and the porous medium exist simultaneously in the same spatial region ie the same model cells In fractured aquifers the water moves faster along fractures than it does in a rock formation and the solute transport is often controlled by advection along the fractures and dominated by dispersion in the porous block along the fractures MT3DMS uses the dualdomain concept to approach extremely heterogeneous porous media or media composed of fractures and pores In this approach the effective porosity specified in Parameters Effective Porosity is used as the primary porosity for the pore spaces filled with mobile water ie fractures and the secondary porosity for the pore spaces filled with immobile water ie rock formation is defined in the Chemical Reaction MT3DMS dialog box Fig 253 The sum of the primary and the secondary porosities is the total porosity of the medium The exchange of solutes between the mobile and immobile domains can be defined through equation 250 nim Cimt ζ Cm Cim 250 where nim is the secondary porosity ie the portion of total porosity filled with immobile water Cm ML3 is the concentration in the mobile domain Cim ML3 is the concentration in the immobile domain and ζ T1 is the firstorder mass transfer rate between the mobile and immobile domains As the mass transfer rate ζ increases the dualdomain model functions more and more like the singledomain model with a porosity approaching the total porosity of the porous medium For a very small value of ζ the righthandside of equation 250 approaches zero ie there is no change of the concentration in the immobile domain and the model functions like a singleporosity model with the primary effective porosity One of the advantages of this approach is that the fracture structure does not need to be known However a problem may arise when one tries to estimate the mass transfer rate ζ by measuring the concentrations Cm and Cim When the concentration is measured at a certain point only one value is obtained which cannot be distinguished between mobile and immobile concentration It is therefore more likely that ζ must be estimated through a model calibration using Cm values only Type of Reaction No kinetic reaction is simulated reaction is not simulated Firstorder irreversible reaction The required parameters are Firstorder reaction rate for the dissolved phase 1T Firstorder reaction rate for the sorbed phase 1T The concentration change due to the chemical reaction from one transport step to another transport step at cell kij can be expressed as ΔCRCTkij ΔtRkij λ1 Ckij λ2 ρbnkij Ckij 251 where λ1 T1 is the firstorder rate for the dissolved phase λ2 T1 is the firstorder rate for the sorbed phase Δt is the transport timestep and Ckij is the mass of the solute species adsorbed on the solids per unit bulk dry mass of the porous medium at the beginning of each transport step Ckij is in equilibrium with solute concentration Ckij in the cell kij 26 The Models Menu 117 The rate constant λ is usually given in terms of the halflife t12 equation 255 Generally if the reaction is radioactive decay λ2 should be set equal to λ1 However for certain types of biodegradation λ2 may be different from λ1 Monod kinetics MT3D99 implements the Monod kinetics only for the dis solved phase of an organic compound The required parameters are Product of total microbial concentration and the maximum specific growth rate of the bacterium Mt µmax ML3T HalfSaturation constant Ks ML3 According to Rifai and others 105 and Zheng 124 the change in the sub strate concentration within a transport timestep using the Monod growth func tion is calculated as follows C t Mt µmax C Ks C 252 Where C ML3 is the substrate concentration t T is the length of a transport timestep Mt ML3 is the total microbial concentration µmax T 1 is the maximum specific growth rate of the bacterium and the half saturation constant Ks ML3 represents the substrate concentration at which the rate of growth is half the maximum rate 4 Firstorder parentdaughter chain reactions The firstorder parentdaughter chain reactions is implemented in MT3D99 for both dissolved and sorbed phases In addition to the yield coefficients between speciespairs see Section 2621 the required parameters for each involved species are Firstorder reaction rate coefficient for the dissolved phase T 1 Firstorder reaction rate coefficient for the sorbed phase T 1 Considering the dissolved phase the changes in the concentration values of involved species within a transport timestep are calculated in the following sequential order C1 t λ1 C1 C2 t λ2 C2 Y12λ1 C1 253 Ck t λk Ck Yk1kλk1 Ck1 Where Ck ML3 is the concentration of species k t T is the length of a transport timestep λk T 1 is the first order reaction rate coefficient for the dissolved phase for species k and Yk1k is the yield coefficient between species k1 and k 118 2 Modeling Environment Instantaneous reaction among species Required stoichiometric ratios between the species are to be specified in the Stoichiometry tab Fig 247 of the Sim ulation Settings MT3DMSSEAWAT dialog box in Section 2621 Use the initial concentration for nonequilibrium sorbed or immobile liquid phase This check box is only used with if the type of sorption is Firstorder kinetic sorption nonequilibrium Dualdomain mass transfer without sorption or Dual domain mass transfer with sorption For Firstorder kinetic sorption nonequilibrium If this box is checked the initial concentration of all species for the sorbed phase need to be entered in this dialog box see below If this box is cleared the sorbed phase is assumed to be in equilibrium with the dissolved phase For Dualdomain mass transfer If this box is checked the initial concentration of all species for the immobile liquid phase need to be entered in this dialog box see below If this box is cleared the concentration of immobile liquid phase is assumed to be zero 2627 MT3DMSSEAWAT Prescribed Fluid Density The prescribed fluid density is used by SEAWAT if the simulation mode is set as Vari able Density Flow and Transport with SEAWAT and the densityeffect of all the simu lated species is turned off Refer to the Species tab of Section 2621 for details 2628 MT3DMSSEAWAT SinkSource Concentration This menu is used for specifying the concentration associated with the fluid of point or spatially distributed sources or sinks The concentration value of a particular source or sink is specified in the Data Editor Point sources include wells general head bound ary cells fixedhead cells rivers and streams Recharge is the only spatially distributed source whereas evapotranspiration is the only sink whose concentration can be speci fied The concentration of a sink cannot be greater than that of the groundwater at the sink cell If the sink concentration is specified greater than that of the groundwater it is automatically set equal to the concentration of the groundwater Therefore setting a big sink concentration value eg 1 1030 to evapotranspiration ensures that the groundwater concentration is used for the computation Note that MT3DMS does not allow the concurrent use of the rivers and the streams This does not cause problems in any case because the Streamflow Routing package has all functions of the River package Menu items of this menu are dimmed if the corresponding hydraulic features given in the Models MODFLOW menu are not used checked The user may or may not 26 The Models Menu 119 specify the concentration for the sources or sinks when they are used in the flow sim ulation The specified concentration will be used in the transport simulation if a corre sponding menu item is checked If a checked item is no longer necessary for a trans port simulation simply select the item again and deactivate it If the concentration of a source or sink is not specified the default value for the concentration is zero Using the menu item Time Variant Specified Concentration the user may define constant concentration cells anywhere in the model grid and different concentration values may be specified for different stress periods A time varying specified concen tration cell is defined by setting the following data in the Data Editor Flag A non zero value indicates that a cell is specified as a constant concen tration cell In a multiple stress period simulation a constantconcentration cell once defined remains a constantconcentration cell during the simulation but its concentration value can be specified to vary in different stress period To change the concentration value in a particular stress period simply set a nonzero value to Flag and assign the desired concentration value to Specified Concentration In a multispecies simulation the Flag is applied to all species Specified Concentration ML3 This value is the concentration in the cell from the beginning of a stress period If the constantconcentration condition does not apply to a particular species assign a negative concentration value for that species The negative value is used by MT3DMS to skip assigning the constant concentration for the designated species 2629 MT3DMSSEAWAT MassLoading Rate Instead of specifying a source concentration associated with a fluid source the mass loading rate MT 1 into the groundwater system can directly be specified by using this menu item This is of interest for example for the case where dissolution of an oil spill occurs and the groundwater flowing through the residually saturated oil body picks up hydrocarbons 26210 MT3DMSSEAWAT Solver GCG MT3DMS includes a generalpurpose iterative solver based on the generalized conju gate gradient method for solving the system of the transport equations The solver is implemented in the Generalized Conjugate Gradient package A detailed description of the method can be found in Zheng and Wang 123 This solver must always be activated Using this solver dispersion sinksource and reaction terms are solved implicitly without any stability constraints on the trans port step size The required settings and parameters for this package are specified in the Generalized Conjugate Gradient GCG dialog box Fig 254 120 2 Modeling Environment Preconditioning Method The GCG package has three preconditioning options Ja cobi Symmetric Successive Overrelaxation SSOR and the Modified Incomplete Cholesky MIC The MIC preconditioner usually takes less iterations than the other methods but it requires significantly more memory Max Number of Outer Iterations MXITERand Max Number of Inner Iterations ITER1 The GCG solver has two iteration loops an inner loop and an outer loop Like the PCG2 solver of MODFLOW see page 71 within the inner loop all co efficients in the transport matrix A and the righthandside vector b remain unchanged during inner iterations The inner loop continues until ITER1 itera tions are executed or the convergence criterion is met If some of the coefficients in A are dependent on the concentration being solved as in the case of nonlinear sorption they must be updated in outer iterations So MXITER should be set to an integer greater than one only when a nonlinear sorption isotherm is included in the simulation For ITER1 a value between 30 and 50 should be adequate for most problems Relaxation Factor is only used for the SSOR option a value of 10 is generally adequate Concentration Closure Criterion is the convergence criterion a value between 106 and 104 is generally adequate Before solving the system of transport equa tions it is normalized by dividing the concentration terms by the maximum con centration of all cells When the change of the normalized concentration at all cells during a inner iteration is less than or equal to this value iteration stops When it takes only one inner iteration to converge the solution is considered to have converged and the simulation proceeds to the next transport step Concentration Change Printout Interval The maximum concentration changes are printed out whenever the iteration number is an even multiple of this printout interval Set it to zero for printing only at the end of each stress period Fig 254 The Generalized Conjugate Gradient GCG dialog box 26 The Models Menu 121 Fig 255 The Output Control MT3DMT3DMS dialog box Include full dispersion tensor memory intensive This is a flag for treatment of dispersion tensor cross terms If this option is not used all dispersion cross terms will be lumped to the righthandside of the system of transport equations Omitting the cross terms represents a method of approximation which is highly efficient It must be noted however that for critical applications the full dispersion tensor should be included 26211 MT3DMSSEAWAT Concentration Observations Select this menu item from the MT3DMS menu or from MOC3D MT3D or RT3D to specify the locations of the concentration observation boreholes and their associ ated observed measurement data in a Concentration Observations dialog box Its use is identical to the Head Observation dialog box see Section 26114 The only differ ence is that the head observations are replaced by concentration observations 26212 MT3DMSSEAWAT Output Control Use the Output Control MT3DMT3DMS dialog box Fig 255 to set the output op tions of MT3D The options in this dialog box are grouped under three tabs described below Output Terms The MT3DMS transport model always generates a listing file OUT PUTMTM which documents the details of each simulation step Optionally you 122 2 Modeling Environment Fig 256 The Output Times tab of the Output Control MT3DMT3DMS dialog box can save other output terms by checking the corresponding output terms in this tab All output terms denoted by ASCII are also saved in the listing file The cal culated dissolvedphase concentration values are saved in the unformatted binary files MT3DnnnUCN where nnn is the species number The calculated sorbed phase or immobileliquid phase concentration values are saved in the unformatted binary files MT3DnnnSUCN All output files are located in the same folder as your model You can use the Result Extractor to read the unformatted binary files Output Times The value of the output frequency NPRS indicates whether the output is produced in terms of total elapsed simulation time or the transport step number If NPRS0 simulation results will only be saved at the end of simulation If NPRS 0 simulation results will be saved whenever the number of transport steps is an even multiple of NPRS If NPRS 0 simulation results will be saved at times as specified in the table shown in Fig 256 There are two ways for specifying the output times The user may click the table header Output Time and then enter a minimum time a maximum time and a time interval between each output into an Output Time dialog box PM will use these entries to calculate NPRS and the output times The other way is to specify a positive NPRS and press the Tab key then enter the output times into the table Note that the output times are measured from the beginning of the simulation Misc CINACT is the predefined concentration value for an inactive concentration cell ICBUND 0 This value is a marker for these cells only and has no physical 26 The Models Menu 123 meaning THKMIN is the minimum saturated thickness in a cell expressed as the deci mal fraction of the model layer thickness below which the cell is considered inactive NPRMAS indicates how frequently the mass budget information should be saved in the mass balance summary file MT3DnnnMAS where nnn is the species number 26213 MT3DMSSEAWAT Run If the Simulation Mode is set as Constant Density Transport with MT3DMS the Run MT3DMS dialog box Fig 257 will be displayed If the Simulation Mode is set as Variable Density and Transport with SEAWAT the Run SEAWAT dialog box Fig 258 will be displayed in place of the Run MT3DMS dialog box Fig 257 The Run MT3DMS dialog box Run MT3DMS dialog box The available settings of the Run MT3DMS dialog box are described below The File Table has three columns Generate Prior to running a transport simulation PM uses the userspecified data to generate input files for MT3DMS An input file will be generated if it 124 2 Modeling Environment does not exist or if the corresponding Generate box is checked Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Generate input files only dont start MT3DMS Check this option if the user does not want to run MT3DMS The simulation can be started at a later time or can be started at the Command Prompt DOS box by executing the batch file MT3DMSBAT Use Legacy Name File Format eg MT3D99 The Name File of later ver sions of MT3DMS uses the same format as MODFLOW2000 However old versions of MT3D MT3DMS and its variants such as MT3D99 use an older format Check this box if you are running MT3D99 or older versions of MT3DMS OK Click OK to generate MT3DMS input files In addition to the input files PM creates a batch file MT3DMSBAT in the model folder When all input files are generated PM automatically runs MT3DMSBAT in a Command Promptwindow DOS box During a simulation MT3DMS writes a detailed run record to the file OUTPUTMTM saved in the model folder See Section 26212 on page 121 for details about the output terms Run SEAWAT dialog box The available settings of the Run SEAWAT dialog box are described below The File Table has three columns Generate Prior to running a transport simulation PM uses the userspecified data to generate input files for SEAWAT An input file will be generated if it does not exist or if the corresponding Generate box is checked Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Generate input files only dont start SEAWAT Check this option if the user does not want to run SEAWAT The simulation can be started at a later time or 26 The Models Menu 125 Fig 258 The Run SEAWAT dialog box can be started at the Command Prompt DOS box by executing the batch file SEAWATBAT OK Click OK to generate SEAWAT input files In addition to the input files PM creates a batch file SEAWATBAT in the model folder When all input files are generated PM automatically runs SEAWATBAT in a Command Promptwindow DOS box During a simulation SEAWAT writes a detailed run record to the file OUTPUTSWT saved in the model folder See Section 26212 on page 121 for details about the output terms 26214 MT3DMSSEAWAT View MT3DMSSEAWAT View Run Listing File Select this menu item to use the Text Viewer see Section 234 to display the run list file OUTPUTMTM of MT3DMS or OUTPUTSWT of SEAWAT which contains a detailed run record saved by MT3DMS or SEAWAT respectively MT3DMSSEAWAT View Concentration Scatter Diagram This menu item is available only if Concentration Observations have been defined see Section 26211 on page 121 Select this menu item to open a Scatter Diagram Con 126 2 Modeling Environment centration dialog box which is identical to the Scatter Diagram Hydraulic Head dialog box Fig 240 on page 92 except the concentration values replace the head values MT3DMSSEAWAT View ConcentrationTime Curves This menu item is available only if Concentration Observations have been defined see Section 26211 on page 121 Select this menu item to open a Time Series Curves Concentration dialog box which is identical to the Time Series Curves Hydraulic Head dialog box Fig 243 on page 96 except the concentration values replace the head values 263 PHT3D With the exception of userdefinable reaction modules that use PHREEQC2 as the reaction simulator the PHT3D interface of PM is identical to the MT3DMSSEAWAT interface with the Simulation Mode setting to Constant Density Transport with MT3DMS see Section 2621 As is the case with MT3DMS the composition of a PHT3D model starts with Simulation Settings and PHT3D simulations are carried out on the basis of flowfields computed beforehand by MODFLOW Thus as given by Prommer and others 99 PHT3D cannot reproduce the potential impact of reactive processes on the ground water flow field and the model is not suitable to predict for example the impact of bioclogging or mineral precipitation on the hydraulic properties of an aquifer The si multaneous use of the MT3DMS chemical reaction package RCT and PHREEQC2 as reaction simulators is possible However this should be done with appropriate care ie control of potential operatorsplitting errors 2631 PHT3D Simulation Settings The simulation settings of PHT3D are completed in two dialog boxes The Chemical Reaction Module PHT3D dialog box Fig 259 will appear first allowing the user to select a predefined chemical reaction module For simpler problems such as those that only include equilibrium reactions all of the aqueous species components and miner als are already included in the original PHREEQC2 Standard database In addition PM includes more than 10 reaction modules from PHT3D examples See Section 56 for a complete list of PHT3D examples In some cases a problemspecific reaction module needs to be prepared and added to PM before using PHT3D See Section 65 for the steps of defining a customized reaction module 26 The Models Menu 127 Fig 259 The Chemical Reaction Module PHT3D dialog box Once a reaction module is selected and the Chemical Reaction Module PHT3D di alog box is closed the Simulation Settings PHT3D dialog box Fig 260 appears The tabs of the dialog box are described below Component equilibrium This tab contains a table and each row of the table de fines an aqueous component that are assumed to be in chemical equilibrium The columns of the table are defined as follows Active Check the box to include the respective component in the simulation A transport simulation will be carried out for each of the included aqueous components except for pH and pe As pH and pe are included in all simulation they cannot be deactivated Component Name of the component Options This is an optional argument that is passed to the PHREEQC2 input file to take advantage of the numerous options in PHREEQC to define concen tration values For example the charge option can be invoked or the option to calculate the input concentration of an element from equilibrium with a pure phase See the PHREEQC2 manual 93 for more details Component kinetic This tab contains two tables that define mobile kinetic reac tants and immobile kinetic reactants respectively For each reactant a rate expres sion is defined in the databasefile of the selected reaction module and the local equilibrium assumption is assumed to be invalid The columns of the tables are defined as follows Active Check the box to include the respective reactant in the simulation 128 2 Modeling Environment Fig 260 The Simulation Settings PHT3D dialog box Component Name of the reactant Stoichiometry Stoichiometry is expressed in the form of reactant1 mole r1 reactant2 mole r2 product1 mole p1 product2 mole p2 and is predefined in the databasefile of the selected reaction module Parm 1 to 8 Parameters used to define the reaction rate The parameters are predefined in the databasefile of the selected reaction module Minerals equilibrium Each row of the table contains a mineral for which the local equilibrium assumption LEA is assumed to be valid Check the Active of a row to include the respective mineral in the simulation No transport step is carried out for minerals The columns of the table are defined as follows Active Check the box to include the respective mineral in the simulation Mineral Name of the mineral Options This is an optional argument that can be entered for each of the miner als that are included in a simulation This value represents the target Saturation Index SI for a pure phase in the aqueous phase Equation This column contains the exact definitions of the minerals Minerals kinetic Each row of the table contains a mineral for which a rate ex pression is defined in the databasefile of the selected reaction module and the 26 The Models Menu 129 local equilibrium assumption is assumed to be invalid The columns of the table are defined as follows Active Check the box to include the respective mineral in the simulation Mineral Name of the mineral Stoichiometry Stoichiometry is expressed in the form of reactant1 mole r1 reactant2 mole r2 product1 mole p1 product2 mole p2 and is predefined in the databasefile of the selected reaction module Parm 1 to 8 Parameters used to define the reaction rate The parameters are predefined in the databasefile of the selected reaction module Exchange Species Each row of the table contains an exchange species involved in cationexchanging reactions with an exchanger The columns of the table are defined as follows Active Check the box to include the respective species in the simulation Exchange Species Name of the exchange species Surfaces The dropdown box Surface Complexation Model contains the information on which type of SCM calculation will be executed by PHREEQC Each row of the table contains a Surface Master Species defined in the databasefile of the selected reaction module Active Check the box to include the respective surface master species in the simulation Surface Master Species The name of surface master species Surface Area defines the specific surface area of a surface either in m2g when the number of sites and mass of a surface are entered explicitly or in m2mol when the amount of surface sites is coupled to a pure phase or a kinetic reactant Mass defines the mass of solid and is used to calculate the surface area Al though a value must always be specified here it is only used when the number of sites and mass are defined explicitly ie when not coupled to a pure phase or kinetic reactant PhaseReactant Switch PhaseReactant is an optional argument to define a pure phase or kinetic reactant to which the surface binding site must be cou pled The number of moles of surface sites will be calculated from the num ber of moles of the phasereactant SWITCH is an optional argument to define whether a pure phase is used PhaseReactant equilibrium phase or a ki netic reactant PhaseReactant kinetic reactant PhaseReactant only works in conjunction with PhaseReactant that is there is no need to specify it un less PhaseReactant is defined If no value is specified the default is equilibrium phase Options 130 2 Modeling Environment Simulation Options Temperature of the aqueous solution is is the temperature in Celsius used in chemical reactions for which a temperature dependence is defined in the database file The default value is 25C Output File Format determines ASCII files extension ACN andor Binary files UCN that contain the computed concentrations for all gridcells and for all output times that are defined in the PHT3D Output Control CB OFFSET is a number that acts as a flag to indicate if the charge im balance carried by a solution is to be transported If CB OFFSET 0 the charge imbalance of solutions is transported This is achieved by adding CB OFFSET to the charge imbalance of all solution The resulting values are used as the concentrations in the transport equations to calculate the redistribution of the charge imbalanceIf CB OFFSET 0 the charge im balance is not transported Default value for CB OFFSET is 005 Threshold values for executing PHREEQC Changes in aqueous concentration values is the PHREEQC2 activationdeactivation criteria as described in the PHT3D manual At the beginning of each reac tion step PHT3D checks for each cell by which amount the concentration of the mobile species have changed during the previous reaction step If the change in a cell is smaller than Changes in aqueous concentration values no reactions are calculated for that cell The user should always verify that the selected value has negligible effect on the simulation outcome If the value is set to 0 PHREEQC2 will be executed for all gridcells except fixed concentration boundaries in all reaction steps Changes in pH is the PHREEQC2 activationdeacvtivation as described in the PHT3D manual This value is only used when greater than zero and when Changes in aqueous concentration values is greater than zero 264 RT3D 2641 RT3D Simulation Settings The available settings of the Reaction Definition RT3D dialog box Fig 261 are described below Reaction Module Currently seven preprogrammed reaction modules are avail able Their purposes taken from the RT3D manual are described briefly below Refer to Clement 25 for their reaction algorithms No Reaction tracer transport chemical reaction is not simulated Instantaneous aerobic decay of BTEX Simulates aerobic degradation of BTEX using an instantaneous reaction model The reaction simulated are similar to those simulated by BIOPLUMEII 104 26 The Models Menu 131 Instantaneous degradation of BTEX using multiple electron acceptors Simu lates instantaneous biodegradation of BTEX via five different degradation path ways aerobic respiration O2 denitrification NO 3 iron reduction Fe2 sulfate reduction SO2 4 and methanogenesis CH4 Kineticlimited degradation of BTEX using multiple electron acceptors Sim ulates kineticlimited biodegradation of BTEX via five different degradation pathways aerobic respiration O2 denitrification NO 3 iron reduction Fe2 sulfate reduction SO2 4 and methanogenesis CH4 Ratelimited sorption reactions Simulates firstorder reversible kinetic sorp tion This option is equivalent to Firstorder kinetic sorption in the chemical reaction package of the MT3DMS Models MT3DMSSEAWAT Chemical Reaction Double Monod model Simulates the reaction between an electron donor and an electron acceptor mediated by actively growing bacteria cells living in both aqueous and soil phases Sequential decay reactions Simulates reactive transport coupled by a series of sequential degradation reactions up to four components under anaerobic conditions Anaerobic and aerobic biodegradation of PCETCEDCEVC Simulates se quential degradation of perchloroethene PCE trichloroethene TCE dichloroethene DCE vinyl chloride VC via both aerobic and anaerobic paths Sorption Parameter Defines whether the sorption parameters are going to be spec ified layerbylayer Use LayerbyLayer mode or cellbycell Use CellbyCell Fig 261 The Reaction Definition RT3D dialog box 132 2 Modeling Environment mode The latter can only be used by RT3D version 20 or later The sorption parameters are specified using Models RT3D Sorption Parameters Convergence Criteria for iterative solver The table contains a list of species for the selected reaction module Reaction solvers of RT3D use absolute tolerance atol and relative tolerance rtol values to control convergence errors The following rule of thumb may be used to set the atol and rtol values If m is the number of significant digits required in a solution component set rtol 10m1 and set atol to a small value at which the absolute value of the component is essentially insignificant Note that the values of atol and rtol should always be positive 2642 RT3D Initial Concentration At the beginning of a transport simulation RT3D requires the initial concentration of each active species at each active concentration cell ie ICBUND 0 2643 RT3D Advection Select this menu item to open an Advection Package RT3D dialog box The use of this dialog box is identical to the Advection Package MT3DMS dialog box Fig 249 on page 105 2644 RT3D Dispersion Select this menu item to open a Dispersion Package dialog box Its use is identical to the Dispersion Package of MT3DMS see Section 2624 for details 2645 RT3D Sorption Layer by Layer This menu item is available only if Sorption Parameter of the Simulation Settings RT3D dialog box see Section 2641 is set to Use LayerbyLayer mode The avail able settings of the Sorption Parameters RT3D dialog box Fig 262 are given below Type of Sorption RT3D supports three sorption types ie linear equilibrium isotherm Freundlich nonlinear equilibrium isotherm and Langmuir nonlinear equilibrium isotherm See Section 2626 for details Species Select a species for which the sorption coefficients are to be specified Sorption Coefficients Use this table to specify the required parameters on a layer bylayer basis Refer to Section 2664 for details about the sorption coefficients 26 The Models Menu 133 Fig 262 The Sorption Parameters RT3D dialog box 2646 RT3D Sorption Cell by Cell This menu item is available only if Sorption Parameter of the Simulation Settings RT3D dialog box see Section 2641 is set to Use CellbyCell mode RT3D 20 and later only Using the Data Editor sorption coefficients may be entered on a three dimensional cell by cell basis This option provides the ability to have different coeffi cients for different areas 2647 RT3D Reaction Parameters Spatially Constant In RT3D reaction parameter values of each species can be spatially constant for the en tire model or can be variable from cell to cell Select this menu item to assign spatially constant parameter values to the Reaction Parameters for RT3D Spatially Constant dialog box Fig 263 2648 RT3D Reaction Parameters Spatially Variable Select this menu item to specify spatially variable cellbycell reaction parameters Note that this menu item cannot be used if the Reaction Module in the Simulation Set tings RT3D dialog box Fig 261 is one of the following No Reaction tracer trans port Instantaneous aerobic decay of BTEX or Instantaneous degradation of BTEX using multiple electron acceptors 134 2 Modeling Environment Fig 263 The Reaction Parameters for RT3D Spatially Constant dialog box 2649 RT3D SinkSource Concentration The use of this menu is the same as MT3D SinkSource Concentration except the use of the menu item TimeVariant Specified Concentration A time varying specified concentration cell is defined by setting the following data in the Data Editor Flag A non zero value indicates that a cell is specified as a constant concen tration cell In a multiple stress period simulation a constantconcentration cell once defined remains a constantconcentration cell during the simulation but its concentration value can be specified to vary in different stress period To change the concentration value in a particular stress period simply set a nonzero value to Flag and assign the desired concentration value to Specified Concentration In a multispecies simulation the Flag is applied to all species Specified Concentration ML3 This value is the concentration in the cell from the beginning of a stress period If the constantconcentration condition does not apply to a particular species assign a negative concentration value for that species The negative value is used by RT3D to skip assigning the constantconcentration for the designated species 26410 RT3D Concentration Observations Select this menu item from the RT3D menu or from MOC3D MT3DMS or MT3D to specify the locations of the concentration observation boreholes and their associ ated observed measurement data in a Concentration Observations dialog box Its use is identical to the Head Observation dialog box see Section 26114 The only differ ence is that the head observations are replaced by concentration observations 26 The Models Menu 135 26411 RT3D Output Control The output control of RT3D is the same as that of MT3DMSSEAWAT See Section 26212 on page 121 for details 26412 RT3D Run The available settings of the Run RT3D dialog box Fig 264 are described below Fig 264 The Run RT3D dialog box The File Table has three columns Generate Prior to running a transport simulation PM uses the userspecified data to generate input files for RT3D An input file will be generated if it does not exist or if the corresponding Generate box is checked The user may click on a box to check or clear it Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs 136 2 Modeling Environment Generate input files only dont start RT3D Check this option if the user does not want to run RT3D The simulation can be started at a later time or can be started at the Command Prompt DOS box by executing the batch file RT3DBAT OK Click OK to start generating RT3D input files In addition to the input files PM generates a batch file MT3DMSBAT saved in the model folder When all necessary files are generated PM automatically runs RT3DBAT in a Command Promptwindow DOS box During a simulation RT3D writes a detailed run record to the file OUTPUTRT3 saved in the model folder See Section 26212 on page 121 for details about the output terms 26413 RT3D View RT3D View Run Listing File Select this menu item to use the Text Viewer see Section 234 to display the run list file OUTPUTMTM which contains a detailed run record saved by MT3DMS RT3D View Concentration Scatter Diagram This menu item is available only if Concentration Observations have been defined see Section 26410 on page 134 Select this menu item to open a Scatter Diagram Con centration dialog box which is identical to the Scatter Diagram Hydraulic Head dialog box Fig 240 on page 92 except the concentration values replace the head values RT3D View ConcentrationTime Curves This menu item is available only if Concentration Observations have been defined see Section 26410 on page 134 Select this menu item to open a Time Series Curves Concentration dialog box which is identical to the Time Series Curves Hydraulic Head dialog box Fig 243 on page 96 except the concentration values replace the head values 265 MOC3D 2651 MOC3D Subgrid Within the finitedifference grid used to solve the flow equation in MODFLOW the user may specify a window or subgrid over which MOC3D will solve the solute transport equation This feature can significantly enhance the overall efficiency of the 26 The Models Menu 137 model by avoiding calculation effort where it is not needed However MOC3D re quires that within the area of the transport subgrid row and column discretization must be uniformly spaced that is x and y must be constant although they need not be equal to each other The spatial discretization or rows and columns beyond the boundaries of the subgrid can be nonuniform as allowed by MODFLOW to permit calculations of head over a much larger area than the area of interest for transport simulation Vertical discretization defined by the cell thickness can be variable in all three dimensions However large variability may adversely affect numerical accuracy For details refer to Konikow et al 74 for the model assumptions that have been incorporated into the MOC3D model The subgrid is defined in the Subgrid for Transport MOC3D dialog box Fig 265 MOC3D assumes that the concentration outside of the subgrid is the same within each layer so only one concentration value is specified for each layer within or adja cent to the subgrid by using the C Outside of Subgrid table of this dialog box The values of other layers which are not within or adjacent to the subgrid are ignored Fig 265 The Subgrid for Transport MOC3D dialog box 2652 MOC3D Initial Concentration MOC3D requires initial concentration of each cell within the transport subgrid at the beginning of a transport simulation The values specified here are shared with MT3D 2653 MOC3D Advection Use the Parameter for Advective Transport MOC3D dialog box Fig 266 to specify the required data as described below 138 2 Modeling Environment Interpolation scheme for particle velocity In MOC3D the advection term of a so lute transport process is simulated by the Method of Characteristics MOC Using the MOC scheme a set of moving particles is distributed in the flow field at the beginning of the simulation A concentration and a position in the Cartesian co ordinate system are associated with each of these particles Particles are tracked forward through the flow field using a small time increment At the end of each time increment the average concentration at a cell due to advection alone is eval uated from the concentrations of particles which happen to be located within the cell The other terms in the governing equation ie dispersion chemical reaction and decay are accounted for by adjusting the concentrations associated with each particle after the redistribution of mass due to those processes on the grid A moving particle in a groundwater flow system will change velocity as it moves due to both spatial variation in velocity and temporal variations during transient flow During a flow time step advection is determined from velocities computed at the end of the flow time step Temporal changes in velocity are accounted for by a step change in velocity at the start of each new flow time step After the flow equation is solved for a new time step the specific discharge across every face of each finitedifference cell is recomputed on the basis of the new head distribution and the movement of particles during this flow time step is based only on these specific discharges MOC3D provides two interpolation options linear and bilinear interpolation for calculating the spatial variation of the particle velocity from the specific discharges Konikow and others 74 indicate that if transmissivity within a layer is homoge neous or smoothly varying bilinear interpolation of velocity yields more realistic pathlines for a given discretization than linear interpolation And in the presence Fig 266 The Parameter for Advective Transport MOC3D dialog box 26 The Models Menu 139 of strong heterogeneities between adjacent cells within a layer it would usually be preferable to select the linear interpolation scheme Maximum number of particles NPMAX Maximum number of particles available for particle tracking of advective transport in MOC3D If it is set to zero the model will calculate NPMAX according to equation 254 NPMAX 2 NPTPND NSROW NSCOL NSLAY 254 where NPTPND is the initial number of particles per cell see below The values NSROW NSCOL and NSLAY are the number of rows columns and layers of the transport subgrid respectively Courant number CELDIS is the number of cells or the fraction of a cell that a particle may move through in one step typically 05 CELDIS 10 Fraction limit for regenerating initial particles FZERO If the fraction of active cells having no particles exceeds FZERO the program will automatically regener ate an initial particle distribution before continuing the simulation typically 001 FZERO 005 Initial number of particles per cell NPTPND Valid options for default geometry of particle placement include 1 2 3 or 4 for onedimensional transport simulation 1 4 9 or 16 for twodimensional transport simulation and 1 8 or 27 for three dimensional transport simulation The user can also customize initial placement of particles by specifying a negative number to NPTPND pressing the Tabkey and entering local particle coordinates into table in the lower part of the dialog box shown in Fig 266 where PNEWL PNEWR and PNEWC are relative positions for the initial placement of particles in the layer row and column direction respec tively The local coordinate system range is from 05 to 05 and represents the relative distance within the cell about the node location at the center of the cell so that the node is located at 00 in each direction 2654 MOC3D Dispersion Chemical Reaction The types of reactions incorporated into MOC3D are restricted to those that can be represented by a firstorder rate reaction such as radioactive decay or by a retardation factor such as instantaneous reversible sorptiondesorption reactions governed by a linear isotherm and constant distribution coefficient Kd Use the Dispersion Chemical Reaction MOC3D dialog box Fig 267 to spec ify the required data for each model layer as described below Simulate Dispersion Check this option if dispersion should be included in the simulation 140 2 Modeling Environment Fig 267 The Dispersion Chemical Reaction MOC3D dialog box Firstorder decay rate λ T 1 typically represents radioactive decay of both the free and sorbed solute A radioactive decay rate is usually expressed as a halflife t12 The half life is the time required for the concentration to decrease to one half of the original value The decay rate λ is calculated by λ ln 2 t12 255 Effective molecular diffusion coefficient L2T 1 describes the diffusive flux of a solute in water from an area of greater concentration toward an area where it is less concentrated Refer to Section 2624 page 110for more about the molecular diffusion coefficient and dispersivity Longitudinal dispersivity αL L horizontal transverse dispersivity αT H L and vertical transverse dispersivity αT V L describe the spreading of the solute con centration in groundwater caused by the irregular shape of the interconnected pore space and the velocity variations at the microscopic level as well as the unresolved macroscopic level See Section 2624 for details Retardation factor R For a linear isotherm R is independent of the concentra tion field R is calculated by R 1 ρb ne Kd 256 where ne is the effective porosity and rhob is the bulk density of the porous medium 26 The Models Menu 141 2655 MOC3D StrongWeak Flag A flag is required for each cell within the transport subgrid Where a fluid source is strong new particles are added to replace old particles as they are advected out of that cell Where a fluid sink is strong particles are removed after they enter that cell and their effect has been accounted for Where sources or sinks are weak particles are neither added nor removed and the sourcesink effects are incorporated directly into appropriate changes in particle positions and concentrations A strong source or sink cell is indicated by the cell value of 1 2656 MOC3D Observation Wells Cells of the transport subgrid can be designated as observation wells by assigning the value of 1 to the cells At each observation well the time head and concentration after each particle move will be written to the separate output file MOCOBSOUT saved in the same folder as your model data Note that this feature is to facilitate graphical postprocessing of the calculated data using other software packages outside of PM 2657 MOC3D SinkSource Concentration This menu is used for specifying the concentrations of point or distributed sources including constant head cells generalhead boundary cells rivers wells and recharge cells Except the concentrations associated with constant head cells all source concen tration values are specified in the Data Editor If the concentration of a fluid source is not specified the default value for the concentration is zero The source concentration associated with the constant head cells are specified in the Source Concentration Con stant Head dialog box Fig 268 The constant head cells are grouped into zones which are defined by specifying unique negative values to the IBOUND array see Section 2431 Each zone has an associated source concentration value The concentration in the fluid leaving the aquifer at fluid sinks is assumed to have the same concentration as the fluid in the aquifer However if the fluid sink is associ ated with evaporation or transpiration it is assumed that the fluid discharge mechanism will exclude dissolved chemicals which results in an increase in concentration at the location of the sink Items of this menu are dimmed if the corresponding package in the Models MOD FLOW Flow Packages menu are not used checked The specified concentration will be used by MOC3D if a corresponding menu item is checked If a checked item is no longer necessary for a transport simulation simply select the item again and deactivate it 142 2 Modeling Environment Fig 268 The Source Concentration Constant Head dialog box 2658 MOC3D Output Control The main output file of MOC3D is the listing file MOC3DLST MOC3D includes output options to create separate ASCII or binary files for concentration velocity and the location of particles Optionally the dispersion equation coefficients on cell faces can be written to the listing file The dispersion equation coefficient is a combination of dispersion coefficient D porosity ne thickness b and an appropriate grid dimension factor For example the dispersion equation coefficient for the interface between cells k j i and k j1 i in the column direction is ne b Dxxkj12ix The output options for MOC3D are given in the Output Control MOC3D dialog box Fig 269 Most items in this dialog box are selfexplanatory The names of the separate ASCII or binary output files are given in Table 27 Table 27 Names of the MOC3D output files Output Term Filename Listing file PathMOC3Dlst Concentration file ASCII Pathmocconcasc Concentration file binary Pathmocconcbin Velocity ASCII Pathmocvelasc Velocity binary Pathmocvelbin Particle location ASCII Pathmocprtasc Particle location binary Pathmocprtbin Path is the folder in which the model is saved 26 The Models Menu 143 Fig 269 The Output Control MOC3D dialog box 2659 MOC3D Concentration Observation Select this menu item from the MOC3D menu to specify the locations of the concen tration observation boreholes and their associated observed measurement data in a Concentration Observations dialog box Its use is identical to the Head Observation dialog box see Section 26114 The only difference is that the head observations are replaced by concentration observations 26510 MOC3D Run Select this menu item to open the Run Moc3d dialog box Fig 270 The available settings of this dialog box are described below The File Table has three columns Generate Prior to running a flow simulation PM uses the userspecified data to generate input files for MODFLOW and MOC3D An input file will be gen erated if it does not exist or if the corresponding Generate box is checked The user may click on a box to check or clear it Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Check the model data If this option is checked PM will check the geometry of the model and the consistency of the model data as given in Table 26 before 144 2 Modeling Environment creating data files The errors if any are saved in the file CHECKLIS located in the same folder as the model data Generate input files only dont start MOC3D Check this option if the user does not want to run MOC3D The simulation can be started at a later time or can be started at the Command Prompt DOS box by executing the batch file MOC3DBAT OK Click OK to generate MODFLOW and MOC3D input files In addition to the input files PM creates a batch file MOC3DBAT in the model folder When all files are generated PM runs MOC3DBAT in a Command Promptwindow DOS box During a simulation MOC3D writes a detailed run record to the file MOC3DLST saved in the model folder MOC3D saves the simulation results in various unformatted binary files only if a transport simulation has been success fully completed See the previous section for details about the output terms and the corresponding result files from MOC3D 26511 MOC3D View MOC3D View Run Listing File Select this menu item to use the Text Viewer see Section 234 to display the run list file MOC3DLST which contains a detailed run record saved by MOC3D Fig 270 The Run Moc3d dialog box 26 The Models Menu 145 MOC3D View Concentration Scatter Diagram This menu item is available only if Concentration Observations have been defined see Section 2659 Select this menu item to open a Scatter Diagram Concentration di alog box which is identical to the Scatter Diagram Hydraulic Head dialog box Fig 240 except the concentration values replace the head values MOC3D View ConcentrationTime Curves This menu item is available only if Concentration Observations have been defined see Section 2659 Select this menu item to open a Time Series Curves Concentration dialog box which is identical to the Time Series Curves Hydraulic Head dialog box Fig 243 except the concentration values replace the head values 266 MT3D 2661 MT3D Initial Concentration MT3D requires the initial concentration of each active concentration cell ie ICBUND 0 at the beginning of a transport simulation The values specified here are shared with MOC3D 2662 MT3D Advection The available settings of the Advection Package MTADV1 dialog box Fig 271 are described below Note that some of the simulation parameters are only required when a particular solution scheme is selected Solution Scheme MT3D provides four solution schemes for the advection term in cluding the method of characteristics MOC modified method of characteristics MMOC hybrid method of characteristics HMOCand upstream finite difference method Due to the problems of numerical dispersion and artificial oscillation the upstream finite difference method is only suitable for solving transport problems not dominated by advection When the grid Peclet number Pe Pe xαL x is the grid spacing and αL is the longitudinal dispersivity is smaller than two the upstream finite difference method is reasonably accurate It is advisable to use the upstream finite difference method anyway for obtaining first approximations in the initial stages of a modeling study The method of characteristics MOC scheme was implemented in the transport models MOC 73 and MOC3D see Section 2653 and has been widely used One of the most desirable features of the MOC technique is that it is 146 2 Modeling Environment virtually free of numerical dispersion which creates serious difficulty in many numerical schemes The major drawback of the MOC scheme is that it can be slow and requires a large amount of computer memory when a large number of particles is required Also the computed concentrations sometimes tend to show artificial oscillations The modified method of characteristics MMOC uses one particle for each finitedifference cell and is normally faster than the MOC technique At each new time level a particle is placed at the nodal point of each finitedifference cell The particle is tracked backward to find its position at the old time level The concentration associated with that position is used to approximate the advectionrelevant average concentration at the cell where the particle is placed The MMOC technique is free of artificial oscillations if implemented with a lowerorder velocity interpolation scheme such as linear interpolation used in MT3D and MT3DMS However with a lowerorder velocity interpo lation scheme the MMOC technique introduces some numerical dispersion especially for sharp front problems The hybrid method of characteristics HMOC attempts to combine the strengths of the MOC and MMOC schemes by using an automatic adaptive scheme con ceptually similar to the one proposed by Neumann 89 The fundamental idea behind the scheme is automatic adaptation of the solution process to the na ture of the concentration field When sharp concentration fronts are present the advection term is solved by MOC through the use of moving particles dy Fig 271 The Advection Package MTADV1 dialog box 26 The Models Menu 147 namically distributed around each front Away from such fronts the advection term is solved by MMOC The criterion for controlling the switch between the MOC and MMOC schemes is given by DCHMOC see below Particle Tracking Algorithm MT3D provides three particle tracking options a firstorder Euler algorithm a fourthorder RungeKutta algorithm and a combi nation of these two Using the firstorder Euler algorithm numerical errors tend to be large unless small transport steps are used The allowed transport step t of a particle is de termined by MT3D using equation 235 on page 107 The basic idea of the fourthorder RungeKutta method is to calculate the par ticle velocity four times for each tracking step one at the initial point twice at two trial midpoints and once at a trial end point A weighted velocity based on values evaluated at these four points is used to move the particle to a new posi tion The fourthorder RungeKutta method permits the use of larger tracking steps However the computational effort required by the fourthorder Runge Kutta method is considerably larger than that required by the firstorder Euler method For this reason a mixed option combining both methods is introduced in MT3D The mixed option is implemented by automatic selection of the fourthorder RungeKutta algorithm for particles located in cells which contain or are adja cent to sinks or sources and automatic selection of the firstorder Euler algo rithm for particles located elsewhere Maximum number of total moving particles MXPART is the number of particles allowed in a simulation Courant number PERCEL is the number of cells or a fraction of a cell any particle will be allowed to move in any direction in one transport step Generally 05 PERCEL 1 Concentrationweighting factor WD lies between 0 and 1 The value of 05 is nor mally a good choice This number can be adjusted to achieve better mass balance Generally it can be increased toward 1 as advection becomes more dominant Negligible relative concentration gradient DCEPS is a criterion for placing par ticles A value around 105 is generally adequate If DCEPS is greater than the relative cell concentration gradient DCCELLkij equation 236 on page 108 the higher number of particles NPH is placed in the cell k i j otherwise the lower number of particles NPL is placed see NPH and NPL below Pattern for initial placement of particles NPLANE is used to select a pattern for initial placement of moving particles NPLANE 0 the random pattern is selected for initial placement Particles are distributed randomly in both the horizontal and vertical directions Fig 250b 148 2 Modeling Environment on page 109 This option generally leads to smaller mass balance discrepancy in nonuniform or divergingconverging flow fields NPLANE 0 the fixed pattern is selected for initial placement The value of NPLANE serves as the number of planes on which initial particles are placed within each cell Fig 250a on page 109 This fixed pattern may work better than the random pattern only in relatively uniform flow fields For two dimen sional simulations in plan view set NPLANE1 For cross sectional or three di mensional simulations NPLANE2 is normally adequate Increase NPLANE if more resolution in the vertical direction is desired No of particles per cell in case of DCCELL DCEPS NPL is the number of initial particles per cell to be placed at cells where the relative cell concentration gradient DCCELL is less than or equal to DCEPS Generally NPL can be set to zero since advection is considered insignificant under the condition DCCELL DCEPS Setting NPL equal to NPH causes a uniform number of particles to be placed in every cell over the entire grid ie the uniform approach No of particles per cell in case of DCCELL DCEPS NPH is the number of initial particles per cell to be placed at cells where the relative cell concentration gradient DCCELL is greater than DCEPS The selection of NPH depends on the nature of the flow field and also the computer memory limitation Generally use a smaller number in relatively uniform flow fields and a larger number in relatively nonuniform flow fields However values exceeding 16 in twodimensional simu lations or 32 in three dimensional simulations are rarely necessary If the random pattern is chosen NPH particles are randomly distributed within the cell If the fixed pattern is chosen NPH is divided by NPLANE to yield the number of par ticles to be placed per plane which is rounded to one of the values shown in Fig 251 on page 110 Minimum number of particles allowed per cell NPMIN If the number of parti cles in a cell at the end of a transport step is fewer than NPMIN new particles are inserted into that cell to maintain a sufficient number of particles NPMIN can be set to 0 in relatively uniform flow fields and a number greater than zero in diverg ingconverging flow fields Generally a value between zero and four is adequate Maximum number of particles allowed per cell NPMAX If the number of parti cles in a cell exceeds NPMAX particles are removed from that cell until NPMAX is met Generally NPMAX 2 NPH SRMULT is a multiplier for the particle number at source cells SRMULT 1 In most cases SRMULT 1 is sufficient However better results may be obtained by increasing SRMULT Pattern for placement of particles for sink cells NLSINK is used to select a pattern for initial placement of particles to approximate sink cells in the MMOC scheme 26 The Models Menu 149 The convention is the same as that for NPLANE and it is generally adequate to set NLSINK equivalent to NPLANE Number of particles allowed to approximate sink cells NPSINK is used in the MMOC scheme The convention is the same as that for NPH and it is generally adequate to set NPSINK equivalent to NPLANE Critical relative concentration gradient DCHMOC is used to select between MOC and MMOC in the HMOC solution scheme MOC is selected at cells where DCCELL DCHMOC MMOC is selected at cells where DCCELL DCHMOC 2663 MT3D Dispersion The use of this menu item is the same as MT3DMS Dispersion See Section 2624 on page 110 for details 2664 MT3D Chemical Reaction Layer by Layer Chemical reactions supported by MT3D include equilibriumcontrolled sorption and firstorder irreversible rate reactions such as radioactive decay or biodegradation It is generally assumed that equilibrium conditions exist between the aqueousphase and solidphase concentrations and that the sorption reaction is fast enough relative to groundwater velocity so that it can be treated as instantaneous Consider using MT3DMS if nonequilibrium ratelimited sorption needs to be simulated Use this menu item to open the Chemical Reaction Package MTRCT1 dialog box Fig 272 to specify the required parameters on a layerbylayer basis The parameters are described below Type of sorption Sorption is implemented in MT3D through use of the retarda tion factor R MT3D supports sorption types of Linear isotherm equilibrium Freudlich isotherm nonlinear equilibrium and Langmuir isotherm nonlinear equilibrium See Section 2626 for details Simulate the radioactive decay or biodegradation Check this box to simulate the effect of the firstorder irreversible rate reactions See the description of the reac tion type Firstorder irreversible reaction on page 116 for details 2665 MT3D Chemical Reaction Cell by Cell Using the Data Editor chemical reaction coefficients may be entered on a three di mensional cell by cell basis This option provides the ability to have different reaction coefficients for different areas in a single model layer 150 2 Modeling Environment Fig 272 The Chemical Reaction Package MTRCT1 dialog box 2666 MT3D SinkSource Concentration The use of this menu is the same as MT3DMSSEAWAT SinkSource Concentration except the use of the menu item TimeVariant Specified Concentration A time variant specified concentration cell is defined by specifying the following data in the Data Editor Note that Time Variant Specified Concentration may not be supported by some earlier version of MT3D Flag A non zero value indicates that a cell is specified as a constant concentra tion cell In a multiple stress period simulation a constantconcentration cell once defined will remain a constantconcentration cell for the duration of the simula tion but its concentration value can be specified to vary in different stress periods To change the concentration value in a particular stress period simply set Flag to a nonzero value and assign the desired concentration value to Specified Concen tration Specified Concentration ML3 This value is the concentration in the cell at the beginning of a stress period 2667 MT3D Concentration Observations Select this menu item from the MT3D menu to specify the locations of the concen tration observation boreholes and their associated observed measurement data in a Concentration Observations dialog box Its use is identical to the Head Observation dialog box see Section 26114 The only difference is that the head observations are replaced by concentration observations 26 The Models Menu 151 2668 MT3D Output Control Use the Output Control MT3DMT3DMS dialog box Fig 273 to set the output op tions of MT3D The options in this dialog box are grouped under three tabs described below Output Terms The MT3D transport model always generates a listing file OUT PUTMT3 which documents the details of each simulation step Optionally you can save other output terms by checking the corresponding output terms in this tab All output terms denoted by ASCII are also saved in the listing file The calcu lated concentration values are saved in the unformatted binary file MT3DUCN In addition MT3D96 can save the mass contained in each cell in the unformat ted binary file MT3DCBM All output files are located in the same folder as your model You can use the Result Extractor to read the unformatted binary files Output Times The value of the output frequency NPRS indicates whether the output is produced in terms of total elapsed simulation time or the transport step number If NPRS 0 simulation results will only be saved at the end of simulation If NPRS 0 simulation results will be saved whenever the number of transport steps is an even multiple of NPRS If NPRS 0 simulation results will be saved at times as specified in the table shown in Fig 274 There are two ways for specifying the output times The user may click the table header Output Time and then enter a minimum time a maximum time and a time interval between each output into an Output Time dialog box PM will use these entries to calculate NPRS and the Fig 273 The Output Control MT3DMT3DMS dialog box 152 2 Modeling Environment Fig 274 The Output Times tab of the Output Control MT3DMT3DMS dialog box output times The other way is to specify a positive NPRS and press the Tab key then enter the output times into the table Note that the output times are measured from the beginning of the simulation Misc CINACT is the predefined concentration value for an inactive concentration cell ICBUND 0 This value is a marker for these cells only and has no physical meaning THKMIN is the minimum saturated thickness in a cell expressed as the deci mal fraction of the model layer thickness below which the cell is considered inactive THKMIN is only used by MT3D96 or later NPRMAS indicates how frequently the mass budget information should be saved in the mass balance summary file MT3DMAS 2669 MT3D Run The available settings of the Run MT3DMT3D96 dialog box Fig 275 are described below The File Table has three columns Generate Prior to running a transport simulation PM uses the userspecified data to generate input files for MT3D An input file will be generated if it does not exist or if the corresponding Generate box is checked The user may click 26 The Models Menu 153 Fig 275 The Run MT3DMT3D96 dialog box on a box to check or clear it Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Generate input files only dont start MT3D Check this option if the user does not want to run MT3D The simulation can be started at a later time or can be started at the Command Prompt DOS box by executing the batch file MT3DBAT OK Click OK to generate MT3D input files In addition to the input files PM creates a batch file MT3DBAT saved in the model folder When all files are gen erated PM automatically runs MT3DBAT in a Command Promptwindow DOS box During a simulation MT3D writes a detailed run record to the file OUT PUTMT3 saved in the model folder See the previous section for details about the output terms 154 2 Modeling Environment 26610 MT3D View MT3D View Run Listing File Select this menu item to use the Text Viewer see Section 234 to display the run list file OUTPUTMT3 which contains a detailed run record saved by MT3D MT3D View Concentration Scatter Diagram This menu item is available only if Concentration Observations have been defined see Section 2667 on page 150 Select this menu item to open a Scatter Diagram Con centration dialog box which is identical to the Scatter Diagram Hydraulic Head dialog box Fig 240 on page 92 except the concentration values replace the head values MT3D View ConcentrationTime Curves This menu item is available only if Concentration Observations have been defined see Section 2667 on page 150 Select this menu item to open a Time Series Curves Concentration dialog box which is identical to the Time Series Curves Hydraulic Head dialog box Fig 243 on page 96 except the concentration values replace the head values 267 MODFLOW2000 Parameter Estimation This section describes the interface for the builtin parameter estimation capability of MODFLOW2000 The parameters andor excitations which can be estimated by MODFLOW2000 are listed in Table 28 Since the BCF package does not support pa rameterization of aquifer parameters it cannot be used with the parameter estimation procedures of MODFLOW2000 In other words if the user plans to use MODFLOW 2000 to estimate aquifer parameters then one has to use the LPF package with ad justable aquifer parameters HK VK HANI VANI Ss and Sy See Section 234 for how to switch between the BCF and LPF packages During a parameter estimation process MODFLOW2000 searches optimum pa rameter values for which the sum of squared deviations between modelcalculated and observed hydraulic heads at the observation boreholes is reduced to a minimum The coordinates of the observation boreholes and observed head values are given in MODFLOW2000 Parameter Estimation Head Observations It is to note that MODFLOW2000 does not accept drawdown observations rather it has an option of using the temporal changes in hydraulic heads as observations see Section 26114 for details Of particular note is that a simultaneous fit of highly correlated parameters 26 The Models Menu 155 for example HK and recharge values on the basis of observed heads only is of little value in steadystate problems due to the nonuniqueness of such a fit In those cases the ability of using prior information and flow observation data in MODFLOW2000 could help in solving problems The parameters to be estimated are defined in the following steps To define an adjustable parameter for estimation 1 Select a parameter or a package from the Parameters or Models MODFLOW Flow Packages menus for example Horizontal Hydraulic Conductivity Recharge or Well 2 Assign a parameter number and initial guessed parameter values to the cells where the parameter values should be estimated The parameter number needs to be unique within a parameter type eg HK or Ss and may be any integer ranging between 1 and 500 Set the parameter number to zero if the specified parameter value should not be estimated Please note the following rules when assigning parameter values and parameter numbers During a parameter estimation process the parameter values for an estimation iteration are calculated as the product of the parameters initial cellvalues and a parameter multiplier PARVAL The latter is to be estimated by MODFLOW 2000 It is to note that if the parameters initial cellvalues are heterogeneously distributed then the result is also a distribution scaled by the estimated param eter multiplier In contrast if the value of 1 is used as the parameters initial cellvalue then the estimated parameter multiplier represents the physical pa rameter value To estimate the conductance values of headdependent cells eg drain gen eral headboundary river or stream cells or pumping rates of wells a nonzero Table 28 Adjustable parameters through MODFLOW2000 within PM Packages Abbreviation Adjustable Parameters BlockCentered Flow BCF No aquifer parameters can be estimated LayerProperty Flow LPF All layer types HK HANI VANI VK Ss and Sy Drain DRN Conductance of drain cells Evapotranspiration EVT Maximum evapotranspiration rate GeneralHead Boundary GHB Conductance of GHB cells Horizontal Flow Barrier HFB6 Hydraulic characteristic of barrier Recharge RCH Recharge flux River RIV Conductance of RIV cells StreamFlow Routine STR Conductance of STR cells Well WEL Pumping or injection rates of WEL cells 156 2 Modeling Environment conductance value or pumping rate must be assigned to those cells Conduc tance values or pumping rate will not be adjusted if the userspecified values are equal to zero In a transient flow model when a parameter is varying with time parameter numbers should not be repeated in different stress periods That is different parameter numbers should be used for different stress periods 3 Select MODFLOW2000 Parameter Estimation Parameter List to open a List of Parameters MODFLOW2000 dialog box which lists all parameters defined in previous steps and provides an overview of all parameters The dialog box also allows selecting or unselecting parameters for estimation see Section 2671 2671 MODFLOW2000 Parameter Estimation Simulation Settings The required parameters and execution options for MODFLOW2000 are specified in the List of Parameters MODFLOW2000 dialog box Fig 276 The available settings are grouped under four tabs described below Using the Save button the user can save the settings in separate ASCII files which can be loaded at a later time by using the Load button Click the Update button to retrieve the estimated parameter values saved in the MF2KOUT B file The Update button is disabled and dimmed if this file is not available The Parameters Tab The Parameters Tab contains a table that gives an overview of the initial values and properties of estimated parameters The initial value PARVAL of parameter is the arithmetical mean of the cell values of that parameter The parameters lower bound PARLBND and upper bound PARUBND default to two orders lower andhigher than PARVAL respectively If a parameter is removed by changing the parameter number to zero in the Data Editor the corresponding parameter in the table is ignored PM does not delete that adjustable parameter from the table To delete the parameter click on its record selector before the first column of the table then press the Del key Note that the user cannot manually add a parameter to the table If a parameter is deleted by mistake simply click the Cancel button to discard all changes or click the OK button to accept changes and then open the Simulation Settings MODFLOW2000 dialog box again to recover the lost parameter The meaning of each column of the table is described below By clicking on a column header the parameters can be sorted in ascending order using the values of that column 26 The Models Menu 157 PARNAM While editing data of a certain aquifer parameter or flow package the spatial extent of an estimated parameter is defined by assigning a parameter number to the cells of interest PM automatically assigns a PARNAM by combining that parameter number with the short names of the aquifer parameter ie HK VK VANI HANI SS and SY or package For example if parameter numbers 1 and 2 are specified for the Recharge package then RCH 1 and RCH 2 are assigned to PARNAM Fig 276 Modification of the assigned names is not allowed Active The value of an estimated parameter will only be adjusted if Active is checked Otherwise the userspecified cell values will be used for the simulation When switching from the BCF to LPF or from LPF to BCF package some aquifer parameters might become unadjustable eg T S are not adjustable when using the LPF package and they will be indicated by gray background color Normally the total number of active parameters should not exceed 10 although PM allows 500 parameters Description A text describing the parameter can be entered here optional for example recharge zone one A maximum of 120 characters is allowed PARVAL is the initial parameter multiplier for PARNAM Minimum and Maximum are the reasonable minimum and maximum scaling fac tors for the parameter These values are used solely to determine how the final optimized value of this parameter compares to a reasonable range of values For Fig 276 The Simulation Settings MODFLOW2000 dialog box 158 2 Modeling Environment logtransformed parameters untransformed values should be used Logtransform Check this flag to logtransform the parameter Typically logtrans formed parameters are those for which negative values are not reasonable for ex ample hydraulic conductivity The Prior Information Tab It often happens that we have some information concerning the parameters that we wish to optimize and that we obtained this information independently of the current experiment This information may be in the form of other unrelated estimates of some or all of the parameters or of relationships between parameters It is often useful to in clude this information in the parameter estimation process because it may lend stability to the process To define prior information first check the Active box in the Prior Information tab and then enter the prior information equation in the Prior Information column The syntax of a prior information line is Eqnam Prm Sign Coef Pnam Sign Coef Pnam Sign STAT Statp Statflag PlotSymbol 257 All components of equation 257 must be separated by one space Following Hill and others 63 the components are defined below Eqnam is a usersupplied name up to 10 nonblank characters for a priorinformation equation Prm is the prior estimate for priorinformation equation Eqnam Prm always needs to be specified as a native untransformed value That is even if the parameter is specified as being logtransformed see the Parameters tab above Prm needs to be the untransformed value indicates the equal sign Sign is either or The Sign after is optional and is assumed to be unless otherwise specified Coef is the multiplication coefficient for the parameter following the in the prior information equation Coef can be specified with or without a decimal point and can be specified in scientific notation eg 3123E03 indicates multiplication Pnam is the parameter name For aquifer parameters ie HK VK HANI VANI SS and SY Pnam is the same as PARNAM given in the Parameters tab see above For timevarying parameters eg RCH WEL Pnam is a combination of PAR NAM and the stress period number to which Pnam pertains For example for parameter number 2 of recharge RCH 2 in the stress period 3 Pnam RCH 2 3 26 The Models Menu 159 If the parameter is designated as being logtransformed the priorinformation equation may contain only one parameter name STAT must be entered literally Statp is the value from which the weight for priorinformation equation Eqnam is calculated as determined using Statflag Statflag is a flag identifying how the weight for priorinformation equation Eq nam is to be calculated This depends both on whether the user chooses to spec ify the variance standard deviation or coefficient of variation and whether for logtransformed parameters the user chooses to specify the statistic related to the native untransformed parameter or to the transformed parameter 1 Statflag 0 Statp is the variance associated with Prm and is related to the native prior value Weight 1Statp unless the parameter is defined as log transformed in which case equation 27 of Hill and others 63 is used to convert Statp which equals σ2 b of equation 27 to σ2 ln b and Weight 1σ2 ln b 2 Statflag 1 Statp is the standard deviation associated with Prm and is related to the native prior value Weight 1Statp2 unless the parameter is defined as logtransformed in which case equation 27 of Hill and others 63 is used to convert Statp which equals σb of equation 27 to σ2 ln b and Weight 1σ2 ln b 3 Statflag 2 Statp is the coefficient of variation associated with Prm and is related to the native prior value Weight 1Statp Prm2 unless the parameter is defined as logtransformed in which case equation 27 of Hill and others 63 is used to convert Statp which equals σbb of equation 27 to σ2 ln b and Weight 1σ2 ln b 4 Statflag 10 Statp is the variance associated with the log base 10 transform of Prm Weight 1Statp 230262 5 Statflag 11 Statp is the standard deviation associated with the log base 10 transform of Prm Weight 1Statp2 230262 6 Statflag 12 Statp is the coefficient of variation associated with the log base 10 transform of Prm Weight 1Statp log10PRM2 230262 PlotSymbol is an integer that will be written to output files intended for graphical analysis to allow control of the symbols used when plotting data related to the prior information The following lines show some examples refer to Hill 62 p 43ff and Hill and others 63 p 83ff for more details about the use of the prior information PRCH1 22 36500 RCH11 STAT 50 1 4 PHK1 10 HK1 STAT 05 11 5 PS12 002 20 SS1 30 SS2 STAT 05 11 5 160 2 Modeling Environment The Control Data Tab The control data are used to control the regression calculations The control data are written in the input file PESDAT for the Parameter Estimation Process Following Hill and others 63 the items of the control data are described below MAXITER is the maximum number of parameterestimation iterations If MAX ITER 0 the program calculates the variancecovariance matrix on parameters and related statistics the parameter correlation coefficients generally are of most interest using the starting parameter values and parameter estimation stops after oneiteration Note that the starting parameter values are obtained by multiplying PARVAL with the cellvalues of the parameter see Parameters Tab MAXCHANGE is the maximum fractional change for parameter values in one iteration step MAXCHANGE commonly equals to 20 or less if parameter values are unstable during parameterestimation iterations TOL is the parameterestimation closure criterion as a fractional change in pa rameter values TOL commonly equals 001 Larger values often are used during preliminary calibration processes value as small as 0001 may be used for theoret ical works SOSC is the second convergence criterion discussed in Hill 62 p12 If SOSC 00 parameter estimation will converge if the leastsquares objective function does not decrease more than SOSC 100 percent over two parameterestimation iterations SOSC usually equals 00 Typical nonzero values of SOSC are 001 and 005 RMAR is used along with RMARM to calculate the Marquardt parameter which is used to improve regression performance for illposed problems Theil 113 Seber and Wild 109 Initially the Marquardt parameter is set to zero for each parameterestimation iteration For iterations in which the parameter changes are unlikely to reduce the value of the objective function the Marquardt parameter is increased according to mnew r RMARM mold r RMAR until the condition is no longer met or until mnew r is greater than 1 Typically RMAR 0001 RMARM is the Marquardt parameter multiplier which is used along with RMAR to determine the Marquardt parameter see above CSA is the searchdirection adjustment parameter used in the Marquardt procedure Usually equals 008 FCONV is a flag and a value used to allow coarser solver convergence criteria for early parameterestimation iterations If FCONV equals zero coarser convergence criteria are not used Commonly FCONV 00 Typical nonzero values would be 50 or 10 and these can produce much smaller execution times in some circum stances 26 The Models Menu 161 The Options Tab Two options are available Run Mode Perform Parameter Estimation is the default run mode which instructs MOD FLOW2000 to estimate values of active parameters listed in the Parameters tab Perform Sensitivity Analysis directs MODFLOW2000 to evaluate sensitivities using the initial PARVAL and parameter values Using this option MODFLOW 2000 calculates onepercent sensitivities for hydraulic heads for the entire grid The onepercent sensitivities can be contoured just like hydraulic heads can be countered The onepercent scaled sensitivity map can be used to identify where additional observations of hydraulic head would be most important to the estimation of different parameters and to compare the sensitivity of hydraulic heads throughout the model to different parameters Perform Forward Model Run using PARVAL values given in the Parameters tab This option directs MODFLOW2000 to replace the model parameters by the product of PARVAL values and the cellvalues of parameters and then perform a forward model run MaxChange This option determines whether MAXCHANGE specified in the Control Data tab is applied to the native parameter value or to the log transform of the parameter value This option only applies to logtransformed parameters 2672 MODFLOW2000 Parameter Estimation Head Observations Select Head Observations from the MODFLOW2000 Parameter Estimation menu or MODFLOW or PEST menus to specify the locations of the head observation bore holes and their associated observed measurement data in a Head Observation dialog box see Section 26114 on page 83 for details When this menu item is selected and checked the Head Observation package of MODFLOW2000 will use the head observation data for the parameter estimation If you do not want to use the Head Observation package and the head observation data select the menu item again and click the Deactivate button 2673 MODFLOW2000 Parameter Estimation Flow Observations This menu is used for specifying the flow observation data associated with drain gen eral head boundary river or constant head boundary cells Each submenu is enabled only if the corresponding flow package is in use When a submenu is selected and checked its flow observation data will be used for the parameter estimation If the Fig 277 The Flow Observation River dialog box user does not want to use the flow observation data select the submenu again and click the Deactivate button Flow observations are defined by assigning parameters to model cells using the Flow Observation dialog box Fig 277 of the Data Editor The dialog box consists of two tabs as described below The Group Number Tab A flow observation is commonly represented by a group of cells with the same Group Number For each cell group MODFLOW2000 compares the simulated flow rate gain or loss with the observation data specified in the Flow Observation tab The simulated flow rate of a cell group y L3 T1 is calculated by yn1nqcl fnqn 258 where nqcl is the number of cells in the cell group fn is a userspecified multiplicative factor qn L3T1 is the simulated flow rate at one cell Generally fn10 However if a gauging site is located within a cell instead of at the edge of the cell fn needs to be less than 10 so that only part of the simulated flow for the cell is included in y 26 The Models Menu 163 Fig 278 The Flow Observation tab of the Flow Observation River dialog box The Flow Observation Tab The Flow Observation tab Fig 278 is used to specify the names of cell groups and their associated observed measurement data The options of this tab are described below 1 Cell Group Each row of the table pertains to a group of cells The name OB SNAM and the associated group number Group Number of each cell group are to be specified in the table A cell group is active if the Active flag is checked To add a cell group scroll down to the end of the table and simply type the name and group number to the last blank row To delete a cell group the user selects the row to be deleted by clicking on its record selector before the first column of the table then pressing the Del key After a simulation the user may select View Scatter Diagram from the MOD FLOW2000 Parameter Estimation menu to compare the observed and calculated values The user may also select View Time Series Curves from the same menu to display timeseries curves of both the calculated and observed values 2 Flow Observation Data of the selected Cell Group contains the data pertained to the cell group marked by on the Cell Group table Inserting or deleting an observation row is identical to the Cell Group table a Time The observation time to which the measurement pertains is measured from the beginning of the model simulation The user may specify the obser 164 2 Modeling Environment vation times in any order By clicking on the column header or the OK button the observation times and the associated values will be sorted in ascending order b Observation values HOBS contain the flow rates observed at the observation times Negative values should be assigned when water leaves the groundwater system c Statistic MODFLOW2000 reads statistics from which the weights are calcu lated The physical meaning of Statistic is controlled by the Option tab see below The Options Tab The Statistic Option defines the physical meaning of Statistic specified in the Flow Observation tab It also defines how the weights are calculated Refer to Hill 62 for more details about the role of statistics and weights in solving regression problems 2674 MODFLOW2000 Parameter Estimation Run MODFLOW2000 Select this menu item to start MODFLOW2000 The available settings of the Run MODFLOW2000 Sensitivity AnalysisParameter Estimation dialog box Fig 279 are described below The File Table has three columns Generate Prior to running the program PM uses the userspecified data to generate input files for MODFLOW2000 An input file will be generated if it does not exist or if the corresponding Generate box is checked The user may click on a box to check or clear it Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Generate input files only dont start MODFLOW2000 Check this option if the user does not want to run MODFLOW2000 The simulation can be started at a later time or can be started at the Command Prompt DOS box by execut ing the batch file MF2KBAT 26 The Models Menu 165 Check the model data If this option is checked PM will check the geometry of the model and the consistency of the model data as given in Table 26 page 91 before creating data files The errors if any are saved in the file CHECKLIS located in the same folder as the model data OK Click OK to generate MODFLOW2000 input files In addition to the in put files PM creates a batch file MF2KBAT in the model folder When all files are generated PM automatically runs MF2KBAT in a Command Promptwindow DOS box During the parameter estimation process the user will notice that the parameter names PARNAM of timevarying parameters eg RCH WEL are further combined with the stress period number to which the parameter pertains For example parameter number 2 of recharge in stress period 3 is indicated by RCH 2 3 For steady state simulations the string 1 is used After completing the parameter estimation process MODFLOW2000 prints the optimized parameter values to the file MF2KOUT b in the model folder The model results after the parameter estimation process are calculated by using the optimized parameter values During a parameter estimation process MODFLOW 2000 does not modify the original model data This provides a greater security for the model data because a parameter estimation process does not necessarily lead to a success Fig 279 The Run MODFLOW2000 Sensitivity AnalysisParameter Estimation di alog box 166 2 Modeling Environment PESTASPMODFLOW2000 Select this menu item to start parameter estimation with the coupled approach PEST ASP MODFLOW2000 In this case the derivatives of model outputs with respect to adjustable parameters are calculated by MODFLOWASP35a modified version of MODFLOW2000 and the parameter estimation is done by PESTASP This approach combines the strengths of both programs The available settings of the Run PESTASP MODFLOW2000 dialog box Fig 280 are described below The File Table has three columns Generate Prior to running the program PM uses the userspecified data to generate input files for MODFLOWASP and PESTASP An input file will be generated only if the corresponding Generate box is checked The user may click on a box to check or clear it Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Fig 280 The Run PESTASP MODFLOW2000 dialog box 26 The Models Menu 167 Generate input files only dont start PESTASP Check this option if the user does not want to run PESTASP MODFLOW2000 The simulation can be started at a later time or can be started at the Command Prompt DOS box by executing the batch file PESTMF2KBAT Check the model data If this option is checked PM will check the geometry of the model and the consistency of the model data as given in Table 26 page 91 before creating data files The errors if any are saved in the file CHECKLIS located in the same folder as the model data Let PESTASP calculate Derivatives Although the derivatives calculated by MODFLOWASP using the sensitivity equation method is more accurate sometimes the slight loss of numerical precision incurred through the use of derivatives calculated by PESTASP using the perturbation finitedifference method appears to abet rather than hinder the parameter estimation process This option should be tried if a parameter estimation process fails to converge OK Click OK to generate the input files In addition PM creates a batch files PESTMF2KBAT in the model folder When all files are generated PM automat ically runs PESTMF2K in a Command Promptwindow DOS box After com pleting the parameter estimation process PESTASP MODFLOW2000 prints the optimized parameter values to the file MF2KOUT B in the model folder The model results after the parameter estimation process are calculated by using the optimized parameter values During a parameter estimation process PESTASP MODFLOW2000 does not modify the original model data This provides a greater security to the model data because a parameter estimation process does not neces sarily lead to a success 2675 MODFLOW2000 Parameter Estimation View MODFLOW2000 Parameter Estimation View Global Listing File Select this menu item to use the Text Viewer see Section 234 to display the global listing file MF2KGLOBAL LISTING which contains the parameter values and statis tics for parameterestimation iterations the optimized value of each adjustable param eter together with that parameters 95 confidence interval It tabulates the set of field measurements their optimized modelcalculated counterparts the difference between each pair and certain functions of these differences MODFLOW2000 Parameter Estimation View Forward Run Listing File During a parameter estimation process forward runs are repeated and the run record is saved in the listing file OUTPUTDAT Listing files are overwritten during subsequent 168 2 Modeling Environment forward model runs and thus only the listing file unique to final parameter values is available for inspection with the Text Viewer see Section 234 Parameter estimation processes are often terminated unexpectedly because the groundwater flow process of MODFLOW2000 fails to complete a flow calculation due to an unsuitable parameter combination used by an estimationiteration In that case MODFLOW2000 writes error messages to the OUTPUTDAT file and terminates the simulation It is therefore recommended to check this file when MODFLOW2000 fails to complete the parameter estimation iterations MODFLOW2000 Parameter Estimation View Estimated Parameter Values At the end of each optimizationiteration MODFLOW2000 writes the estimated pa rameter set to a file named MF2KOUT B Select this menu item to use the Text Viewer see Section 234 to display this file The estimated parameter values are displayed using the parameter name PARNAM given in the Parameters tab of the List of Param eters MODFLOW2000 dialog box Fig 276 The parameter names PARNAM of timevarying parameters eg RCH WEL are combined with the stress period number to which the parameter pertains For example parameter number 2 of recharge in stress period 3 is indicated by RCH 2 3 For steady state simulations the string 1 is used as the stress period number Using values from intermediate parameterestimation iterations that are likely to be closer to the optimal parameter values often reduces execution time MODFLOW2000 Parameter Estimation View Dimensionless Scaled Sensi tivities Select this menu item to use the Text Viewer see Section 234 for linking a Text Viewer with PM to display the file MF2KOUT SD which contains dimensionless scaled sensitivity values that can be used to compare the importance of different obser vations to the estimation of a single parameter or the importance of different parame ters to the calculation of a simulated value Hill 62 MODFLOW2000 Parameter Estimation View Composite Scaled Sensitivities Select this menu item to use the Text Viewer see Section 234 for linking a Text Viewer with PM to display the file MF2KOUT SC which contains composite scaled sensitivity values that indicate the total amount of information provided by the obser vations for the estimation of one parameter If some parameters have composite scaled sensitivities that are less than about 001 times the largest composite scaled sensitivity 26 The Models Menu 169 it is likely that the regression will have trouble converging Hill 62 A parameter with large composite scaled sensitivity and many large dimensionless scaled sensitivi ties is probably more reliably estimated than a parameter with a large composite scaled sensitivity and one large dimensionless scaled sensitivity because the error of the sin gle important observation is propagated directly into the estimate Hill 63 MODFLOW2000 Parameter Estimation View OnePercent Scaled Sensitivi ties Select this menu item to use the Text Viewer see Section 234 for linking a Text Viewer with PM to display the file MF2KOUT S1 which contains onepercent scaled sensitivity values that indicate an approximate amount of information provided by the observations for the estimation of one parameter MODFLOW2000 Parameter Estimation View OnePercent Scaled Sensitivi ties Arrays The onepercent sensitivities for hydraulic heads are calculated for the entire grid and can be contoured just like hydraulic heads can be contoured The onepercent scaled sensitivity map can be used to identify where additional observations of hydraulic head would be most important to the estimation of different parameters and to compare the sensitivity of hydraulic heads throughout the model to different parameters 62 MODFLOW2000 Parameter Estimation View Scatter Diagram This menu item is available only if head observations see Section 26114 or flow ob servations Section 2673 have been defined Select this menu item to open a Scatter Diagram dialog box which is identical as the Scatter Diagram Hydraulic Head dialog box as described in Section 26120 with two exceptions The userspecified observation times and observed values are given in the columns Simulation Time and Observed Value directly without interpolating to the times at the end of each stress period or time step The Calculated Value column contains the values calculated by MODFLOW2000 ie the values are not calculated by pmp using equation 234 A Result Type option appears in the Data tab The first result type is Observed values versus simulated values When the second result type Weighted observed values versus weighted simulated values is chosen the observed and calculated values are multiplied by a weighting factor which is the square root of weight defined in the Option tab of the Head Observations Fig 436 or Flow Observation Fig 277 dialog boxes 170 2 Modeling Environment MODFLOW2000 Parameter Estimation View TimeSeries Curves This menu item is available only if head observations see Section 26114 or flow observations Section 2673 have been defined Select this menu item to open a Time Series Curves dialog box which is identical as the TimeSeries Curves Hydraulic Head dialog box as described in Section 26120 The only exception is that the user specified observation times and observed values are given in the columns Simulation Time and Observed value directly without interpolating to the times at the end of each stress period or time step The Calculated Value column contains the values calculated by MODFLOW2000 ie the values are not calculated by PM using equation 234 page 93 268 PEST Parameter Estimation This menu provides an interface between PM MODFLOW and PEST All versions of MODFLOW can be used with PEST The parameters andor excitations which may be estimated by regression are listed in Table 29 The adjustable aquifer parameters depend on the selection of BCF or LPF package and layer types During a parameter estimation process PEST searches optimum parameter values for which the sum of squared deviations between modelcalculated and observed values of hydraulic heads or drawdowns at the observation boreholes is reduced to a min imum The coordinates of the observation boreholes and observed values are given Table 29 Adjustable parameters through PEST within PM Packages Abbreviation Adjustable Parameters BlockCentered Flow BCF Layer type 0 T S and VCONT Layer type 1 HK Sy and VCONT Layer type 2 T S Sy and VCONT Layer type 3 HK S Sy and VCONT LayerProperty Flow LPF All layer types HK HANI VANI VK Ss and Sy Drain DRN Conductance of drain cells Evapotranspiration EVT Maximum evapotranspiration rate GeneralHead Boundary GHB Conductance of GHB cells Horizontal Flow Barrier HFB6 Hydraulic characteristic of barrier Interbed Storage IBS Inelastic storage factor Recharge RCH Recharge flux Reservoir RES Conductance of RES cells River RIV Conductance of RIV cells StreamFlow Routine STR Conductance of STR cells Well WEL Pumping or injection rates of WEL cells 26 The Models Menu 171 in PEST Parameter Estimation Head Observations or Drawdown Observations Note that a simultaneous fit of highly correlated parameters for example transmissiv ity and recharge values on the basis of observed heads or drawdowns only is of little value in steadystate problems due to the nonuniqueness of such a fit The parameters to be estimated are defined in the following steps To define an adjustable parameter for estimation 1 Select a parameter from the Parameters menu or select a package from the Models Flow Simulation MODFLOW Flow Packages menu for example Transmis sivity or Well 2 Assign an initial guess of the parameter value and a parameter number to cells within an area where the parameter value should be estimated The parameter number needs to be unique within a parameter type eg T S or Ss and may be any integer ranging between 1 and 500 Set the parameter number to zero if the specified parameter value should not be estimated 3 Select PEST Parameter Estimation Simulation Settings to open a Simulation Settings PEST dialog box which provides an overview of all parameters defined in previous steps and interfaces for setting control parameters The dialog box also allows selecting or deselecting parameters for estimation see Section 2681 Note 1 Using the Calculated settings in the Layer Options dialog box PM allows the user to specify HK VK or Ss instead of T VCONT and S values to layers of types 0 or 2 However when using PEST to estimate T VCONT or S values the user must define the adjustable parameters by selecting Transmissivity Vertical Leakance or Storage Coefficient from the Parameters menu regardless whether the Calculated or UserSpecified settings are used 2 To estimate the conductance values of headdependent cells eg drain general headboundary river or stream cells or pumping rates of wells a nonzero con ductance value or pumping rate must be assigned to those cells with adjustable parameters Conductance values or pumping rates will not be adjusted if the user specified cell values are zero 2681 PEST Parameter Estimation Simulation Settings The required inputs and options for running PEST are specified in the Simulation Set tings PEST dialog box Fig 281 The names of most input variables of this di alog box are inherited from the PEST manual37 and the Addendum to the PEST Manual39 which provide a great inside into to the theory and application of PEST 172 2 Modeling Environment The user is encourage to download and consult these references as needed The Op eration Mode dropdown box Fig 281is used to define how PEST should run and the rest of the available settings are grouped under six tabs described in the following sec tions below The functions of Operation Mode dropdown box and the push buttons are defined as follows Operation Mode Parameter Estimation PEST will use the available information to estimate pa rameters defined in the Parameters Tab by running the model as many times as needed Sensitivity Analysis When this option is selected the maximum number of optimization iterations see NOPTMAX in the Control Data tab will be set to 1 PEST will run in the Parameter Estimation mode but will terminate execu tion immediately after it has calculated the Jacobian matrix for the first time The parameter covariance correlation coefficient and eigenvector matrices will be written to the run record file and parameter sensitivities will be written to the sensitivity file these are based on the initial parameter set defined in the Parameters tab Forward Model Run using PARVAL values given in the Parameters tab When this option is selected the maximum number of optimization iterations see NOPTMAX in the Control Data tab will be set to 0 PEST will run in the Pa rameter Estimation mode but will not calculate the Jacobian matrix Instead it will terminate execution after just one model run This setting can thus be used when you wish to calculate the objective function corresponding to a particu lar parameter set andor to inspect observation residuals corresponding to that parameter set Regularization Within each optimization iteration PESTs task when working in regularization mode is identical to its task when working in parameter es timation mode ie it must minimize an objective function using a linearized version of the model encapsulated in a Jacobian matrix However just before calculating the parameter upgrade vector PEST calculates the appropriate reg ularization weight factor to use for that iteration This is the factor by which all of the weights pertaining to regularization information are multiplied in accordance with equation 233 of the PEST manual 37 prior to formulating the overall objective function whose task it is for PEST to minimize on that iteration As parameters shift and the Jacobian matrix changes an outcome of the nonlinear nature of most models the regularization weight factor also changes Hence it needs to be recalculated during every optimization iteration Use of PEST in regularization mode is fully described in Chapters 7 and 8 of the PEST manual The user is required to supply control variables listed in the 26 The Models Menu 173 Regularization tab and to supply at least one prior information equation with the name of observation group Obgnme set to regul Save and Load Using the Save button the user can save the settings in separate files which can be loaded at a later time by using the Load button Update Click the Update button to retrieve the estimated parameter values saved in the PESTCTLPAR file that contains the estimated parameter values PESTCTLPAR is created by PEST after running it in the parameter estimation mode The Update button is disabled and dimmed if this file is not available The Parameters Tab The Parameters Tab contains a table that gives an overview of the initial values and properties of estimated parameters The initial value PARVAL of parameter is the arithmetical mean of the cell values of that parameter The parameters lower bound PARLBND and upper bound PARUBND default to two orders lower andhigher than PARVAL respectively If a parameter is removed by changing the parameter number to zero in the Data Editor the corresponding parameter in the table is ignored PM does not delete that adjustable parameter from the table To delete the parameter click on its record selector before the first column of the table then press the Del key Note that the user Fig 281 The Simulation Settings PEST dialog box 174 2 Modeling Environment cannot manually add a parameter to the table If a parameter is deleted by mistake simply click the Cancel button to discard all changes or click the OK button to accept changes and then open the Simulation Settings PEST dialog box again to recover the lost parameter The meaning of each column of the table is described below By clicking on a column header the parameters can be sorted in ascending order using the values of that column PARNAM While editing data of a certain aquifer parameter or flow package the spatial extent of an adjustable parameter is defined by assigning a parameter num ber to the cells of interest PARNAM is a combination of that parameter number and the short name of the aquifer parameter ie HK HANI VK VANI SS SY T S or VCONT or package For example if parameter numbers 1 and 2 are spec ified for the Recharge package then RCH 1 and RCH 2 are assigned to PARNAM Fig 281 Modification of the assigned names is not allowed Active The value of an estimated parameter will only be adjusted if Active is checked Otherwise the userspecified cell value will be used for the simulation When switching from the BCF to LPF or from LPF to BCF package some aquifer parameters might become unadjustable eg T S are not adjustable when using the LPF package and they will be indicated by gray background color Normally the total number of active parameters should not exceed 10 although PM allows 500 parameters Description A text describing the parameter can be entered here optional for example recharge zone one A maximum of 120 characters is allowed PARVAL1 is a parameters initial value For a fixed parameter this value remains invariant during the optimization process For a tied parameter see PARTRANS below the ratio of PARVAL1 to the parent parameters PARVAL1 sets the ratio be tween these two parameters to be maintained throughout the optimization process For an adjustable parameter PARVAL1 is the parameters starting value which to gether with the starting values of all other adjustable parameters it is successively improved during the optimization process To enhance optimization efficiency the user should choose an initial parameter value which is close to the guessed op timized value The user should note the following repercussions of choosing an initial parameter value of zero Limitation of the parameter adjustment is not possible see the discussion on RELPARMAX and FACPARMAX during the first optimization iteration if the starting value of a parameter is zero Furthermore FACORIG cannot be used to modify the action of RELPARMAX and FACPARMAX for a particular pa rameter throughout the optimization process if that parameters original value is zero 26 The Models Menu 175 A relative increment for derivatives calculation cannot be evaluated during the first iteration for a parameter whose initial value is zero If the parameter be longs to a group for which derivatives are in fact calculated as Relative see INCTYP and DERINC below a non zero DERINCLB variable must be pro vided for that group If a parameter has an initial value of zero the parameter can be neither a tied nor a parent parameter as the tiedparent parameter ratio cannot be calculated PARLBND and PARUBND are a parameters lower and upper bounds respectively For adjustable parameters the initial parameter value PARVAL1 must lie between these two bounds For fixed and tied parameters PARLBND and PARUBND are ignored PARTRANS controls the parameter transformation By clicking on a cell of the PARTRANS column this flag can be set as None Logtransformed Tied or Fixed Use Logtransformed if you wish that a parameter be log transformed throughout the estimation process this is recommended for transmissivities and hydraulic con ductivities A parameter which can become zero or negative in the course of the parameter estimation process must not be log transformed hence if a parameters lower bound is zero or less PEST will disallow logarithmic transformation for that parameter Note that by using an appropriate scale and offset you can ensure that parameters never become negative Thus if you are estimating the value for a pa rameter whose domain as far as the model is concerned is the interval 999 10 you can shift this domain to 001 20 for PEST by designating a scale of 10 and an offset of 100 Similarly if a parameters model domain is entirely negative you can make this domain entirely positive for PEST by supplying a scale of 10 and an offset of 00 See the discussion on the SCALE and OFFSET variables below If a parameter is fixed taking no part in the optimization process PARTRANS must be specified as Fixed If a parameter is linked to another parameter this is signified by a PARTRANS value of Tied In the latter case the parameter plays only a limited role in the estimation process However the parameter to which the tied parameter is linked this parent parameter must be neither fixed nor tied itself takes an active part in the parameter estimation process the tied parameter simply piggy backs on the parent parameter the value of the tied parameter maintaining at all times the same ratio to the parent parameter as the ratio of their initial values If a parameter is neither fixed nor tied and is not log transformed the parameter transformation variable PARTRANS must be supplied as None PARCHGLIM is used to designate whether an adjustable parameter is relative limited or factorlimited See the discussion on RELPARMAX and FACPARMAX page 191 For tied or fixed parameters PARCHGLIM has no significance PARGP is the number of the group to which a parameter belongs Parameter groups are discussed in Group Definitions below 176 2 Modeling Environment PARTIED is the name of the parent parameter to which the parameter is tied You can select a name from a drop down list SCALE and OFFSET Just before a parameter value is written to an input file of MODFLOW it is multiplied by the real variable SCALE after which the real variable OFFSET is added The use of these two variables allows you to redefine the domain of a parameter Because they operate on the parameter value at the last moment before it is sent they take no part in the estimation process in fact they can conceal from PEST the true value of a parameter as seen by the model PEST optimizing instead the parameter bp where bp bm offsetscale 259 Here bp is the parameter optimized by PEST bm is the parameter seen by the model while scale and offset are the scale and offset values for that parameter respectively If you wish to leave a parameter unaffected by scale and offset enter the SCALE as 10 and the OFFSET as 00 The Parameter Groups Tab In PEST the input variables that define how derivatives are calculated pertain to pa rameter groups rather than to individual parameters These input variables are specified in the Parameter Groups tab of the Simulation Settings PEST dialog box Fig 282 Thus derivative data do not need to be entered individually for each parameter how ever if you wish you can define a group for every parameter and set the derivative variables for each parameter separately In many cases parameters fall neatly into sep arate groups which can be treated similarly in terms of calculating derivatives Number is the group number The maximum number of parameter groups is 150 Description A text describing the estimated parameter can be entered here op tional for example Transmissivity Group 1 A maximum of 120 characters is allowed INCTYP and DERINC INCTYP defines the type of parameter increment per turbation used for forward difference calculation of derivatives with respect to any parameter belonging to the group INCTYP can be Relative Absolute or Rel to max INCTYP Relative The parameter increment is calculated as a fraction of the current value of that parameter that fraction is specified in DERINC A DERINC value of 001 is often appropriate INCTYP Absolute The parameter increment is fixed at the value of DER INC No suggestion for an appropriate DERINC value can be provided for this 26 The Models Menu 177 Fig 282 The Parameter Groups tab of the Simulation Settings PEST dialog box option the most appropriate increment will depend on the parameter magni tudes INCTYP Rel to max The parameter increment is calculated as a fraction of the group member with highest absolute value that fraction again being DER INC A DERINC value of 001 is often appropriate If a group contains mem bers which are fixed andor tied the user should note that the values of these parameters are taken into account when calculating parameter increments DERINCLB is the absolute lower limit of parameter increments for all group mem bers If a parameter increment is calculated as Relative it may become too low if the parameter values become very small And if a parameter increment is calcu lated as Rel to max it may become too low if the modulus of the largest parameter in the group is very small A parameter increment becomes too low if it does not allow reliable derivatives to be calculated with respect to that parameter because of round off errors incurred in the subtraction of nearly equal model generated values DERINCLB is used to bypass this possibility Set DERINCLB to zero if the user does not wish to place a lower limit on param eter increments in this fashion Note that if INCTYP is Absolute DERINCLB is ignored 178 2 Modeling Environment FORCEN can be Always 2 Always 3 or Switch It determines how to calculate derivatives for group members FORCEN Always 2 Derivatives for all parameters belonging to that group will always be calculated using the forward difference method FORCEN Always 3 PEST will use the central difference method to calculate the derivatives In this case twice as many model runs as there are parameters within the group will be required however the derivatives will be calculated with greater accuracy and this will probably have a beneficial effect on the performance of PEST FORCEN Switch Derivatives calculations for all adjustable group members will begin using the forward difference method switching to the central method for the remainder of the estimation process after the relative objective function reduction between successive iterations is less than PHIREDSWH as defined in the Control Data below Experience has shown that in most instances the most appropriate value for FORCEN is Switch This allows speed to take precedence over accuracy in the early stages of the optimization process when accuracy is not critical to objective function improvement and accuracy to take precedence over speed later in the process when realization of a normally smaller objective function improvement requires that derivatives be calculated with as much accuracy as possible espe cially if parameters are highly correlated and the normal matrix thus approaches singularity DERINCMUL If a three point derivatives calculation is employed the value of DERINC is multiplied by DERINCMUL Set DERINCMUL to a value of 10 if the user does not wish the parameter increment DERINC to be changed Alter natively if for some reason the user wishes the increment to be reduced if three point derivatives calculation is employed DERINCMUL should be less than 10 Experience shows that a value between 10 and 20 is usually satisfactory DERMTHD defines the variant of the central ie three point method used for derivatives calculation and is used only when FORCEN is Always 3 or Switch PEST provides three variants Parabolic Best fit or Outside pts Refer to the man ual of PEST for details about these methods The Prior Information Tab It often happens that we have some information concerning the parameters that we wish to optimize and that we obtained this information independently of the current experiment This information may be in the form of other unrelated estimates of some or all of the parameters or of relationships between parameters It is often useful to in 26 The Models Menu 179 clude this information in the parameter estimation process because it may lend stability to the process To define prior information first check the Active box in the Prior Information tab and then enter the prior information equation in the Prior Information column The syntax of a prior information equation is Pilbl Pifac Parnme Pifac logParnme Pival Weight Obgnme 260 The variables of the prior information equations are defined as follows All variables and symbols must be separated from by at least one space Pilbl Each prior information article must begin with a case insensitive prior infor mation label The label must be no more than twenty characters in length and must be unique to each prior information article Pifac and Parnme Pifac is a parameter factor Parnme is parameter name Both are required To the left of the sign there are one or more combinations Pifac and Parnme with a log prefix to Parnme if appropriate Pifac and Parnme are separated by a character signifying multiplication All parameters referenced in a prior information equation must be adjustable parameters ie you must not include any fixed or tied parameters in an article of prior information Furthermore any particular parameter can be referenced only once in any one prior information equation however it can be referenced in more than one equation Pival Pival is the value of the right side of the prior information equation Weight Weight is the weight assigned to the article of prior information in the parameter estimation process The prior information weight should ideally be in versely proportional to the standard deviation of Pival it can be zero if you wish but must not be negative In practice the weights should be chosen such that the prior information equation neither dominates the objective function or is dwarfed by other components of the objective function In choosing observation and prior information weights remember that the weight is multiplied by its respective resid ual and then squared before being assimilated into the objective function Obgnme Obgnme is observation group to which the prior information belongs and Obgnme must be twelve characters or less in length When running PEST in the Regularization mode see Regularization tab below Obgnme of at least one of the prior information equations must be regul PEST can accommo date multiple regularization groups Any observation group name Obgnme begins with the letters regul is considered to be a regularization group See Sec 82 of the PEST manual for details about multiple regularization groups Some examples of prior information equations are given below refer to the PEST manual 37 for more details 180 2 Modeling Environment The parameter factor must never be omitted Suppose for example that a prior information equation consists of only a single term viz that an untransformed ad justable parameter named par1 has a preferred value of 2305 and that you would like PEST to include this information in the optimization process with a weight of 10 If this article of prior information is given the label pi1 the pertinent prior informa tion line can be written as pi1 10 par1 2305 10 prinfo If a parameter is logtransformed you must provide prior information pertinent to the log of that parameter rather than to the parameter itself Furthermore the parameter name must be placed in brackets and preceded by log note that there is no space between log and the following opening bracket Thus in the above example if parameter par1 is logtransformed the prior information article should be rewritten as pi1 10 logpar1 362671 10 prinfo Note that logs are taken to base 10 Though not illustrated you will also need to review the weight which you attach to this prior information article by comparing the extent to which you would permit the log of par1 to deviate from 0362671 with the extent to which modelgenerated observations are permitted to deviate from their corresponding measurements The left side of a prior information equation can be comprised of the sum andor difference of a number of factorparameter pairs of the type already illus trated these pairs must be separated from each other by a or sign with a space to either side of the sign For example pi2 10 par2 343435 par4 2389834 par3 109e3 300 grouppr Prior information equations which include logtransformed parameters must express a relationship between the logs of those parameters For example if you would like the ratio between the estimated values of parameters par1 and par2 to be about 400 the prior information article may be written as pi3 10 logpar1 10 logpar2 160206 20 grouppr The Regularization Tab Tikhonov regularization is the most commonly used method of regularization and is incorporated in PEST In its broadest sense regularization is a term used to describe the process whereby a large number of parameters can be simultaneously estimated 26 The Models Menu 181 without incurring the numerical instability that normally accompanies parameter non uniqueness Numerical stability is normally achieved through the provision of supple mentary information to the parameter estimation process Such supplementary infor mation often takes the form of preferred values for parameters or for relationships between parameters ie prior information Thus if for a particular parameter the information content of the observation dataset is such that a unique value cannot be es timated for that parameter on the basis of that dataset alone uniqueness can neverthe less be achieved by using the supplementary information provided for that parameter through the regularization process Regularization is particularly useful in estimating values for parameters which de scribe the spatial distribution of some property over a two or threedimensional model domain of a ground water model The user is no longer required to subdivide the model domain into a small number of zones of piecewise parameter constancy Rather a large number of parameters can be used to describe the distribution of the spatial property and PESTs regularization functionality can be used to estimate values for these pa rameters Fig 283 The Regularization tab of the Simulation Settings PEST dialog box 182 2 Modeling Environment To run PEST in the regularization mode select Regularization from the Operation Mode dropdown box assign appropriate control parameters to the Regularization tab of of the Simulation Settings PEST dialog box Fig 283 You must also define at least one prior information equation see above and set the observation group Obgnme of the prior information equation to regul Refer to chapter 7 of the PEST manual 37 for further details about regularization Target measurement objective function PHIMLIM This is the upper limit of the measurement objective function ie the upper level of modeltomeasurement misfit that is tolerable when trying to minimize the reg ularization objective function In some cases a PEST regularization run will post date a normal parameter estimation run If the latter run was successful it will have informed the user of how low the measurement objective function can be if all parameters are adjusted without reference to any regularization conditions PHIMLIM should be set somewhat above this for the imposition of regularization constraints will mostly result in a slight diminution of PESTs ability to fit the field data exactly Acceptable measurement objective function PHIMACCEPT During each optimization iteration just after it has linearized the problem through calculating the Jacobian matrix and just before it begins calculation of the param eter upgrade vector PEST calculates the optimal value of the regularization weight factor for that iteration This is the value which under the linearity assumption en capsulated in the Jacobian matrix results in a parameter upgrade vector for which the measurement component of the objective function is equal to PHIMLIM How ever due to the approximate nature of the linearity assumption PEST may not be able to lower the measurement component of the objective function to PHIMLIM on that iteration in spite of the fact that it uses a number of different values for the Marquardt lambda in attempting to do so If it cannot lower the measurement objective function to an acceptable level it simply accepts the upgraded parame ters proceeds to the next optimization iteration and tries again However if it does succeed in lowering the measurement objective function to an acceptable level or if it has succeeded in doing this on previous iterations then PEST slightly alters its philosophy of choosing new Marquardt lambdas in that it now attempts to lower the regularization component of the objective function while maintaining the mea surement component of the objective function below this acceptable level This acceptable level is PHIMACCEPT it should be set slightly higher than PHIMLIM in order to give PEST some room to move FRACPHIM Optional PEST ignores the value supplied for FRACPHIM unless it is greater than zero A value of between zero and 10 but normally less than about 03 can be supplied 26 The Models Menu 183 for this variable if you are unsure what value to use for PHIMLIM See Section 734 of the PEST manual 37 for a full discussion of this variable Initial regularization weight factor WFINIT This is the initial regularization weight factor During every optimization iteration PEST calculates a suitable regu larization weight factor to use during that optimization iteration using an iterative numerical solution procedure its initial value when implementing this procedure for the first optimization iteration is WFINIT Minimum regularization weight factor WFMIN and Maximum regularization weight factor WFMAX These are the minimum and maximum permissible values that the regularization weight factor is allowed to take If a regularization scheme is poor and does not lend too much stability to an already unstable parameter es timation process selection of appropriate values for WFMIN and WFMAX may be quite important for these can prevent PEST from calculating outrageous values for the regularization weight factor in an attempt to compensate for inadequacies of the regularization scheme Regularization weight factor adjustment factor WFFAC and Convergence crite rion for regularization weight factor WFTOL When PEST calculates the appropriate regularization weight factor to use during any optimization iteration it uses an iterative procedure which begins at the value of the regularization weight factor calculated for the previous optimization itera tion for the first optimization iteration it uses WFINIT to start the procedure In the process of finding the weight factor which will result in a measurement objective function of PHIMLIM PEST first travels along a path of progressively increas ing or decreasing weight factor In undertaking this exploration it either multiplies or divides the weight factor by WFFAC it continues to do this until it has found two successive weight factors which lie on either side of the optimal weight factor for that optimization iteration Once it has done this it uses Newtons method to calculate the optimal weight factor through a series of successive approximations When two subsequent weight factors calculated in this way differ from each other by no more than a relative amount of WFTOL the optimal weight factor is deemed to have been calculated Continue optimizing regularization objective function even if measurement objec tive function less than PHIMLIM Under normal circumstances when working in regularization mode PEST ceases execution immediately if the measurement objective function falls below PHIM LIM There are some circumstances however where minimization of the regu larization objective function is just as important as allowing the measurement ob jective function to reach PHIMLIM If this box is checked the variable REGCON TINUE of the PEST control data file will be as continue to ensure that PEST will continue optimizing regularization objective function after reached PHIMLIM 184 2 Modeling Environment Activate conservation of memory at cost of execution speed and quantity of model output MEMSAVE If this box is checked the variable MEMSAVE of the PEST control data file will be set as memsave and Nonessential PEST tasks which are curtailed include the following The parameter covariance matrix and matrices derived from it are not calcu lated by PEST at regular intervals during the parameter estimation process for recording in the matrix file casemtt nor are these matrices calculated at the end of the inversion process for recording in the run record file caserec Be cause the covariance matrix is unavailable parameter uncertainties cannot be calculated and hence are also not recorded in the run record file In a regular ization context these have little meaning anyway Some avenues for increasing the efficiency of regularization calculations are no longer available under the leaner storage regime that prevails when mem ory conservation is active including the benefits gained through the LINREG variable and through the placing of regularization observations behind other observations involved in the parameter estimation process This can lead to significant runtime penalties in problems involving many parameters unfor tunately these are the very contexts in which memory conservation is most likely to be warranted All regularization constraints are linear LINREG If this box is checked the vari able LINREG of the PEST control data file will be set to linreg As is discussed in chapter 7 of the PEST manual 37 regularization constraints can be supplied through observations through prior information or through both of these mecha nisms Prior information relationships are always linear Regularization constraints supplied as observations for which the current value of pertinent relationships is calculated by the model can be linear or nonlinear in either case derivatives of these relationships with respect to adjustable parameters are reevaluated by PEST during each optimization iteration If regularization information is entirely linear there are many matrix operations carried out as part of PESTs regularization func tionality which do not need to be repeated from iteration to iteration If repetition of these calculations can be avoided in parameter estimation contexts involving many regularization constraints significant gains in efficiency can be made Perform interregularization group weight factor adjustment IREGADJ If this box is checked the variable MEMSAVE of the PEST control data file will be set to 1 In this case PEST takes account of both the number and sensitivities of regular ization observations and prior information equations in each group in determining relative interregularization group weighting so that the contribution made by each group to the overall set of regularization constraints is balanced 26 The Models Menu 185 The SVDSVDAssist Tab SVD Truncated Singular Value Decomposition Truncated singular value decomposition ie truncated SVD is another popular method of solving inverse problems Using SVD the dimensionality of parameter space is reduced to that point at which a unique solution to the parameter estima tion problem is possible Furthermore this simplification is carried out in a way that is mathematically optimal with respect to the dataset available for calibration Thus it effectively allows the estimation of parameter combinations rather than parameters themselves these combinations being such as to be most receptive to the data at hand In this way the problem simplification necessary to achieve numerical stability of the parameter estimation process is undertaken by the process itself Furthermore the inclusion of many parameters in the model calibration process can be justified by ob serving that the inclusion of such parameterization detail allows the truncated SVD mechanism more flexibility in determining an appropriate simplification strategy than by undertaken preemptive simplification through reducing the number of model pa rameters externally to the parameter estimation process Fig 284 The SVDSVDAssist tab of the Simulation Settings PEST dialog box 186 2 Modeling Environment The required settings for using PESTs SVD functionality are given in the SVD Truncated Singular Value Decomposition group of Fig 284 and are explained below Activate SVD for solution of inverse problem Check this box to activate PESTs SVD functionality Set PEST variables RLAMBDA1 to zero and NUMLAM to one Check this box to set Marquardt lambda RLABMDA1 and the number of trial lambdas NUM LAM to the values recommended by the PEST manual Create complete SVD output file uncheck this box to save only eigenvalues to the output file When SVD is activated PEST writes a file named modelnamesvd in addition to its normal output files This contains singular values arranged in de creasing order and corresponding eigenvectors computed on each occasion that singular value decomposition is carried out It also records the number of singular values that are actually used in computation of the parameter upgrade vector ie the number of singular values remaining after truncation Singular value decom position is carried out at least once per iteration corresponding to the testing of different Marquardt lambdas including the sole Marquardt lambda value of zero if RLAMBDA1 is set to zero and NUMLAM is set to 1 as suggested above mul tiple incidences of singular value decomposition are required in any optimization iteration in which parameters hit their bounds The SVD output file can become very large not all of the information contained in it is always worth reading However an inspection of singular values can often provide assistance in determining best values for MAXSING and EIGTHRESH see below By clearing this box only singular values and not their correspond ing eigenvectors are written to modelnamesvd thus reducing its size consider ably The number of singular values used during each parameter upgrade is also recorded Number of singular values at which truncation occurs MAXSING In other words MAXSING is the maximum number of singular values to include in the inver sion process equivalent to the maximum number of eigenvalues and the maxi mum number of degrees of freedom in parameter solution space This is problem dependent Experience with a particular problem may dictate its optimal value set it high enough to obtain a good fit between model outputs and field data but not so high that numerical instability or overfitting of model outputs to measure ments occurs resulting in unrealistic parameter values Alternatively set MAXS ING very high for example equal to the number of estimable parameters and let EIGTHRESH determine the number of singular values employed in the parameter estimation process Eigenvalue ratio threshold for truncation EIGTHRESH EIGTHRESH is the ra tio of lowest to highest eigenvalue at which truncation is implemented this then determines the number of singular values that are used in the inversion process for 26 The Models Menu 187 only those singular values are used whose ratio to the maximum singular value is above this threshold Limited experience to date indicates that 106 or 107 is a good setting for EIGTHRESH set it higher eg 105 if numerical instability or overfitting occurs SVDAssist SVDAssist is a hybrid method which combines the strengths of the Tikhonov and SVD regularization methods while accomplishing enormous gains in efficiency is described in this section Although truncated SVD can be used with Tikhonov regular ization this process is not expected to be as efficient as the SVDassist methodology It is fairly easy to setup a SVDAssisted run with the help of PM The user is encouraged to consult Sec 85 of the PEST manual 37 for detailed explanation of the mechanism of SVDassisted parameter estimation The available settings of the SVDAssist group of Fig 284 are listed below Activate SVDAssist Check this box to enable SVDassisted parameter estimation With SVDAssist activated PM will create two PEST control files namely presvdapst and base svdapst prior to running PEST The former is used for the purpose of derivatives calculation by a preSVDassist PEST run The latter is used by the utility program SVDAPREP which is a part of PEST to create a third PEST control file used for the estimation of super parameters PM will also create a batch file called pestbat which encapsulates the individual steps of an SVDassisted PEST run as follows 1 Commence a preSVDassist PEST Run Copy presvdapst to svdapst and then run PEST with svdapst This step will create a file called svdajco storing the Jacobian matrix 2 Execute SVDAPREP Copy basesvdapst to svdapst and then run SVDAPREPEXE to generate the third PEST control file pestctlpst based on svdapst and a new batch file svd abatchbat The required input data to SVDAPREPEXE are entered in the present interface and are stored in the svdaprepdat file prior to running PEST The svdabatchbat file encapsulates necessary steps for running the model 3 Run PEST PEST is executed to use the pestctlpst file generated in the previous step This PEST run will create two files namely pestctlpar and svdabpa The former stores the estimated values of super parameters the latter contains the esti mated values of the base parameters 4 Rename pestctlpar and svdabpa Once the parameter estimation process is complete the pestctlpar file is re named to pestctl par and svdabpa is copied to pestctlpar When you click on 188 2 Modeling Environment Models PEST Parameter Estimation View Estimated Parameter Values the pestctlpar file is displayed When you click on the Update button of Fig 284 the initial parameter values PARVAL1 of the Parameters tab are updated with the values stored in pestctlpar Automatic calculation of first iteration super parameter derivatives If this box is cleared super parameter derivatives calculation takes place through finite differences in the usual manner during the first optimization iteration of the inversion process If this box is checked PEST calculates super parameter deriva tives internally for the first iteration of the SVDassisted parameter estimation pro cess removing the necessity for any model runs to be undertaken in calculating these derivatives Computation of super parameters Super parameters can be calculated internally by PEST on the basis of sensitivi ties supplied in the Jacobian matrix ie the svdajco file mentioned aboveFour options are available here SVD on Qˆ12X This option sets SVDA EXTSUPER to 0 in the PEST control file ie the aforementioned pestctlpst file PEST will formulate super parameters through singular value decomposition of Q12X where X represents the base parame ter Jacobian matrix contained in the nominated base Jacobian matrix file SVD on XtQX This option sets SVDA EXTSUPER to 3 in the PEST control file which directs PEST to formulate super parameters through singular value decomposition of XtQX LSQR without orthogenalization This option sets SVDA EXTSUPER to 2 in the PEST control file which directs PEST to calculate super parameters using the first m v vectors computed by the LSQR algorithm where m is the number of super parameters see below LSQR with orthogonalization Same as above however the vectors are orthogonalized before being employed for definition of super parameters This option sets SVDA EXTSUPER to 2 in the PEST control file Number of super parameters to estimate Enter an appropriate number It is sometimes wise to enter a number here which is somewhat above the expected dimensionality of estimable parameter space to accommodate shortcomings in the linearity assumption involved in determination of super parameters from base parameters Inclusion of Tikhonov regularization in the inversion process or use of singular value decomposition will guarantee numerical stability of the SVDassisted process In either case this number should be less often significantly less than the number of base estimable parameters pa 26 The Models Menu 189 rameter reduction factors of up to 10 are not uncommon Where parameters are outnumbered by observations the number of super parameters should be at most equal to the number of observations available for model calibration It is important to note that parameters that are fixed or tied will remain fixed and tied when defin ing super parameters hence the SVDassisted parameter estimation process will respect their status Offset for super parameters In the SVDassisted parameter estimation process super parameters are provided with a starting value of zero signifying zero perturbation of initial base parame ters However zero valued parameters can create problems for PEST especially in the enforcement of parameter change limits Hence it is best to supply an offset for such parameters to keep their values away from zero A value of 10 is suitable on most occasions of SVDassisted parameter estimation Parameter relative change limit RELPARMAX Base parameters are designated as relative limited by SVDAPREP On most oc casions a value of 01 will be adequate though you should be prepared to alter this upwards if PEST convergence is too slow or downwards if parameter oscillation occurs or parameters hit their bounds too quickly Parameter scaling control variable SVDA SCALADJ PEST provides a variety of automatic base parameter scaling mechanisms to combat the problems associated with base parameter hypersensitivity described in Section 28 of Addendum to the PEST Manual 39 When some parame ters are not logtransformed parameter scaling is essential Permissible values of SVDA SCALADJ are 4 3 2 1 0 1 2 3 and 4 No base parameter scaling is undertaken if SVDA SCALADJ is set to zero Save Multiple BPA files If this box is checked SVDA MULBPA in the PEST control file ie pestctlpst is set to 1 meaning that a series of BPA files will be recorded in the course of the parameter estimation process Each BPA file contains base parameter values as estimated during subsequent optimization iterations ie svdabpa0 contains the initial base parameters svdabpa1 contains the base parameters after the first optimization iteration and so on In addition a final BPA file ie svdabpa will created at the end of optimization iterations Note that not all optimization itera tions will be represented in this sequenceonly those iterations will be represented where base parameters are improved from those previously achieved during the current parameter estimation process In normal operation when the parameter estimation process is complete PEST undertakes a single model run using optimized parameters before terminating ex ecution thus model input and output files contain bestfit parameter values and corresponding bestfit model outputs This is not possible when undertaking SVD 190 2 Modeling Environment assisted parameter estimation However based on the contents of the svdabpa file which is copied to PESTCTLPAR by PM at the end of the parameter estimation process the user can carry out such a model run by simply clicking on the Up date button to import the estimated base parameter values from PESTCTLPAR to the Parameter tab set Operation Mode Fig 284 to Forward Model Run using PARVAL values given in the Parameters tab and then run PEST Save Multiple JCO files If this box is checked PEST will write a Jacobian matrix file ie a JCO file at the end of each optimization iteration this containing the Jacobian matrix em ployed for that particular iteration Save Multiple REI files If this box is checked PEST will write a residuals file ie a REI file at the end of each optimization iteration The Control Data Tab The control data are used to set internal array dimensions of PEST and tune the op timization algorithm to the problem at hand The items of the Control Data tab Fig 285 are described in detail below When in doubt the user should use the default values RLAMBDA1 is the initial Marquardt lambda PEST attempts parameter improve ment using a number of different Marquardt lambdas during any optimization it eration In the course of the overall parameter estimation process the Marquardt lambda generally gets smaller An initial value of 10 to 100 is appropriate for many models though if PEST complains that the normal matrix is not positive def inite you will need to provide a higher initial Marquardt lambda For high values of the Marquardt parameter and hence of the Marquardt lambda the parameter estimation process approximates the gradient method of optimization While the latter method is inefficient and slow if used for the entire optimization process it often helps in getting the process started especially if initial parameter estimates are poor PEST reduces lambda if it can However if the normal matrix is not posi tive definite or if a reduction in lambda does not lower the objective function PEST has no choice but to increase lambda RLAMFAC is the factor by which the Marquardt lambda is adjusted RLAMFAC must be greater than 10 When PEST reduces lambda it divides by RLAMFAC when it increases lambda it multiplies by RLAMFAC PHIRATSUF is the first criterion for moving to the next optimization iteration Dur ing any optimization iteration PEST tries lots of parameter sets and will consider that the goal of the iteration has been achieved if 26 The Models Menu 191 Fig 285 The Control Data tab of the Simulation Settings PEST dialog box φi φi1 PHIRATSUF 261 where φi1 is the lowest objective function calculated for optimization iteration i1 and hence the starting value for the ith optimization iteration and φi is the objective function corresponding to a parameter set during optimization iteration i A value of 03 is often appropriate for PHIRATSUF If it is set too low model runs may be wasted in search of an objective function reduction which it is not possible to achieve If it is set too high PEST may not be given the opportunity of refining lambda in order that its value continues to be optimal as the parameter estimation process progresses NUMLAM is the maximum number of lambdas parameter sets that PEST can test during any optimization iteration It should normally be set between 5 and 10 For cases where parameters are being adjusted near their upper or lower limits and for which some parameters are consequently being frozen thus reducing the dimension of the problem in parameter space experience has shown that a value closer to 10 may be more appropriate than one closer to 5 RELPARMAX and FACPARMAX are used to limit parameter adjustments REL PARMAX is the maximum relative change that a parameter is allowed to undergo 192 2 Modeling Environment between iterations whereas FACPARMAX is the maximum factor change that a parameter is allowed to undergo A parameter is denoted as either relative limited or factor limited through PARCHGLIM see page 175 If a parameter b is relative limited the relative change of the parameter value between optimization iterations i1 and i is defined as bi1 bi bi1 262 The absolute value of this relative change must be less than RELPARMAX If a parameter upgrade vector is calculated such that the relative adjustment for one or more relative limited parameters is greater than RELPARMAX the magnitude of the upgrade vector is reduced such that this no longer occurs If parameter b is factor limited the factor change between optimization itera tions i1 and i is defined as bi1bi if bi1 bi bibi1 if bi1 bi 263 This factor change must be less than FACPARMAX If a parameter upgrade vector is calculated such that the factor adjustment for one or more factor lim ited parameters is greater than FACPARMAX the magnitude of the upgrade vector is reduced such that this no longer occurs It is important to note that a factorlimit will not allow a parameter to change sign If a parameter must be free to change sign during an optimization process it must be relative limited furthermore RELPARMAX must be set at greater than unity or the change of sign will be impossible Similarly if a parameters upper or lower limit is zero it cannot be factor limited and RELPARMAX must be at least unity Suitable values for RELPARMAX and FACPARMAX can vary enormously from case to case If you are unsure of how to set these parameters a value of 5 for each of them is often suitable For highly non linear problems these values are best set low If they are set too low however the estimation process can be very slow An inspection of the PEST run record by pressing the ESC key will often show whether you have set these values too low for PEST records the maximum parameter factor and relative changes are recorded on this file at the end of each optimization iteration If these changes are always at their upper limits and the estimation process is showing no signs of instability it is quite possible that REL PARMAX andor FACPARMAX are too low and could be increased Note that FACPARMAX can never be less than 1 RELPARMAX can be less than 1 as long as no parameters upper and lower bounds are of opposite sign If neces sary use OFFSET to shift the parameter domain so that it does not include zero 26 The Models Menu 193 FACORIG is a criterion for modifying RELPARMAX and FACPARMAX If in the course of an estimation process the absolute value of a parameter falls below the product of FACORIG and its original value then the product is substituted for the denominators of equation 262 or equation 263 to prevent the denominators becoming zero or too small FACORIG is not used to adjust limits for log trans formed parameters FACORIG must be greater than zero A value of 0001 is often adequate PHIREDSWH is a criterion for switching the calculation method of derivatives between the forward finite difference method and the central finite difference method If for the ith iteration the relative reduction in the objective func tion between successive optimization iterations is less than PHIREDSWH PEST will switch to three point derivatives calculation for those parameter groups with FORCEN Switch The relative reduction in the objective function is defined by φi1 φiφi1 where φi is the objective function calculated on the basis of the upgraded parameter set determined in the ith iteration A value of 01 is often suitable for PHIREDSWH If it is set too high PEST may make the switch to three point derivatives calculation too early The result will be that more model runs will be required than are really needed at that stage of the estimation process If PHIREDSWH is set too low PEST may waste an optimiza tion iteration or two in lowering the objective function to a smaller extent than would have been possible if it had made an earlier switch to central derivatives calculation Note that PHIREDSWH should be set considerably higher than PHIREDSTP see below which sets one of the termination criteria on the basis of the relative ob jective function reduction between optimization iterations NOPTMAX is the maximum number of optimization iterations A value of 20 to 30 is often adequate If you want to ensure that PEST termination is triggered by other criteria more indicative of parameter convergence to an optimal set or of the futility of further processing you should set this variable very high PHIREDSTP and NPHISTP are convergence criteria For many cases 001 and 3 are suitable values for PHIREDSTP and NPHISTP respectively If in the course of the parameter estimation process there have been NPHISTP optimization itera tions for which φi φmin φi PHIREDSTP 264 φi being the objective function value at the end of the ith optimization iteration and φmin being the lowest objective function achieved to date PEST will end the optimization process 194 2 Modeling Environment NPHINORED is the first termination criterion A value of 3 is often suitable If PEST has failed to lower the objective function over NPHINORED successive iterations the program stops RELPARSTP and NRELPAR represent the second termination criterion If the mag nitude of the maximum relative parameter change between optimization iterations is less than RELPARSTP over NRELPAR successive iterations the program stops The relative parameter change between optimization iterations for any parameter is calculated using equation 355 For many cases a value of 001 for RELPARSTP and a value of 3 for NRELPAR are adequate Output Options When the optimization process is complete one of the termina tion criteria having been met or perhaps another termination criterion such as zero objective function or zero objective function gradient for which no user supplied settings are required PEST writes some information concerning the optimized parameter set to its run record file PESTCTLREC This file is saved in the data directory of your model It tabulates the optimal values and the 95 confidence in tervals pertaining to all adjustable parameters It also tabulates the model calculated values based on these parameters together with the residuals ie the differences between measured and model calculated values Write covariance matrix If checked PEST will write the parameter covariance matrix to the run record file PESTCTLREC Write correlation coefficient matrix If checked PEST will write the parameter correlation coefficient matrix to the run record file PESTCTLREC Write normalized eigenvectors of covariance matrix If checked PEST will write the normalized eigenvectors of the covariance matrix to the run record file PESTCTLREC Save data for a possible restart If checked PEST will dump the contents of many of its data arrays to a binary file at the beginning of each optimization iteration this allows PEST to be restarted later if execution is prematurely ter minated If subsequent PEST execution is initiated using the r command line switch see the PEST manual34 for details it will recommence execution at the beginning of the iteration during which it was interrupted Include decimal point even if redundant If cleared PEST will omit the dec imal point from parameter values on model input files if the decimal point is redundant thus making room for the use of one extra significant figure If this option is checked PEST will ensure that the decimal point is always present 2682 PEST Parameter Estimation Head Observations Select the Head Observations from the PEST Parameter Estimation menu or from MODFLOW MODFLOW2000 Parameter Estimation to specify the locations of 26 The Models Menu 195 the head observation boreholes and their associated observed measurement data in a Head Observation dialog box See Section 26114 for details When this menu item is selected and checked PEST uses the head observation data for the parameter estimation 2683 PEST Parameter Estimation Flow Observations Select Drawdown Observations from the PEST Parameter Estimation or MODFLOW menu to specify the locations of the drawdown observation boreholes and their asso ciated observed measurement data in a Drawdown Observations dialog box Its use is identical to the Head Observation dialog box The only difference is that the head observations are replaced by drawdown observations See Section 26114 for details When this menu item is selected and checked PEST uses the drawdown obser vation data for the parameter estimation 2684 PEST Parameter Estimation Run Select this menu item to start a parameter estimation model calibration process with PEST The available settings of the Run PEST dialog box Fig 286 are described below Fig 286 The Run PEST dialog box 196 2 Modeling Environment The File Table has three columns Generate PM uses the userspecified data to generate input files for MOD FLOW and PEST An input file will be generated if it does not exist or if the corresponding Generate box is checked The user may click on a box to check or clear it Normally we do not need to worry about these boxes since PM will take care of the settings Description gives the names of the packages used in the model Destination File shows the paths and names of the input files of the model Options Regenerate all input files Check this option to force PM to generate all input files regardless the setting of the Generate boxes This is useful if the input files have been deleted or overwritten by other programs Generate input files only dont start PEST Check this option if the user does not want to run PEST The program can be started at a later time or can be started at the Command Prompt DOS box by executing the batch file PESTBAT Perform PESTCHEK prior to running PEST PESTCHEK reads the PEST in put files generated by PM making sure that every item is consistent with every other item and writes errors to the file PESTCHK It is recommended to use PESTCHEK as PM and PEST do not carry out consistency checks of all user specified control data and parameters Check the model data If this option is checked PM will check the geometry of the model and the consistency of the model data as given in Table 26 before creating data files The errors if any are saved in the file CHECKLIS located in the same folder as the model data OK Click OK to generate MODFLOW and PEST input files In addition to the in put files PM creates a batch files PESTBAT and MODELRUNBAT in the model folder When all files are generated PM automatically runs PESTBAT in a Com mand Promptwindow DOS box PESTBAT will call the other batch file MOD ELRUNBAT During a parameter estimation process PEST prints the estimated parameter values to the run record file PESTCTLREC in the model folder and writes the estimated parameter values to the corresponding input files of MOD FLOW BCFDAT WELDAT etc So after a parameter process the simu lation results of MODFLOW are updated by using the most recently estimated parameter values PEST does not modify the original model data This provides a greater security to the model data since a parameter estimation process does not necessarily lead to a success 26 The Models Menu 197 2685 PEST Parameter Estimation View PEST Parameter Estimation View Run Record File Select this menu item to use the Text Viewer see Section 234 to display the run record file PESTCTLREC which contains the optimized value of each adjustable pa rameter together with that parameters 95 confidence interval It tabulates the set of field measurements their optimized modelcalculated counterparts the difference be tween each pair and certain functions of these differences PEST Parameter Estimation View Forward Run Listing File During a parameter estimation process forward runs are repeated and the run record is saved in the listing file OUTPUTDAT Listing files are overwritten during subsequent forward model runs and thus only the listing file unique to final parameter values is available for inspection with the Text Viewer see Section 234 Parameter estimation processes are often terminated unexpectedly because MOD FLOW fails to complete a flow calculation due to an unsuitable parameter combination used by an estimationiteration In that case MODFLOW writes error messages to the listing file OUTPUTDAT and terminates the simulation It is therefore recommended to check this file when PEST fails to complete the parameter estimation iterations 198 2 Modeling Environment PEST Parameter Estimation View Estimated Parameter Values At the end of each optimizationiteration PEST writes the best parameter set achieved so far ie the set for which the objective function is lowest to a file named PESTCTLPAR Select this menu item to use the Text Viewer see Section 234 to display this file The first line of the PESTCTLPAR file contains the values for the character variables PRE CIS and DPOINT which were used in the PEST control file Then follows a line for each parameter each line containing a parameter name its current value and the val ues of the SCALE and OFFSET variables for that parameter Refer to Doherty 34 for details about PRECIS DPOINT SCALE and OFFSET Using values from intermediate parameterestimation iterations that are likely to be closer to the optimal parameter values often reduces execution time PEST Parameter Estimation View Composite Parameter Sensitivities Select this menu item to use the Text Viewer see Section 234 to display the Param eter Sensitivity file PESTCTLSEN which contains composite parameter sensitivity values The composite sensitivity of a parameter is defined in Equation 51 of the PEST manual 34 As given in the PEST manual composite parameter sensitivities are useful in identifying those parameters which may be degrading the performance of the parameter estimation process through lack of sensitivity to model outcomes PEST Parameter Estimation View Composite Observation Sensitivities Select this menu item to use the Text Viewer see Section 234 to display the Ob servation Sensitivity file PESTCTLSEO which contains all observation values and corresponding modelcalculated values as well as composite sensitivities for all ob servations The composite sensitivity of an observation is a measure of the sensitivity of that observation to all parameters involved in the parameter estimation process A high value of composite observation sensitivity normally indicates that an observation is particularly crucial to the inversion process Refer to Section 516 of the PEST man ual 34 for more details PEST Parameter Estimation View Head Scatter Diagram This menu item is available only if Head Observations have been defined see Section 26114 Select this menu item to open a Scatter Diagram Hydraulic Head dialog box Refer to Section 26120 for details 27 The Tools Menu 199 PEST Parameter Estimation View Drawdown Scatter Diagram This menu item is available only if Drawdown Observations have been defined see Section 26115 Select this menu item to open a Scatter Diagram Drawdown dia log box which is identical to the Scatter Diagram Hydraulic Head dialog box except the drawdown values replace the head values Refer to Section 26120 for details PEST Parameter Estimation View HeadTime Curves This menu item is available only if Head Observations have been defined see Section 26114 Select this menu item to open a Time Series Curves Hydraulic Head dialog box Refer to Section 26120 for details PEST Parameter Estimation View DrawdownTime Curves This menu item is available only if Drawdown Observations have been defined see Section 26115 Select this menu item to open a Time Series Curves Drawdown dialog box which is identical to the Time Series Curves Hydraulic Head dialog box except the drawdown values replace the head values Refer to Section 26120 for details 269 PMPATH Advective Transport Select this menu to call the particletracking model PMPATH which runs indepen dently from PM Refer to Chapter 3 for details Note PMPATH can be started by selecting this menu or from the Start menu of Windows When PMPATH is started from PM it will automatically load the model currently used by PM If the model data have been subsequently modified and a flow simulation has been performed the modified model must be reloaded into PMPATH to ensure that it can recognize the modifications 27 The Tools Menu 271 Digitizer The Digitizer is based on the Data Editor Using the Digitizer the user can digitize shift or delete points and assign values to the points The menu item Points in the Value menu allows the user to save delete or load points PM saves or loads points tofrom XYZ files An XYZ file stores the number of points the x y coordinates 200 2 Modeling Environment and the associated values of all points Refer to Section 6210 for the format To digitize a point 1 Click the Digitize button It is not necessary to click the button if it is already depressed 2 Click the mouse pointer on the desired position to set a point To shift a digitized point 1 Click the Digitize button 2 Point the mouse pointer to a digitized point leftclick and hold down the mouse button and then move the mouse to drag the digitized point 3 Release the mouse button when the point is moved to the desired position To delete a digitized point 1 Click the Digitize button 2 Hold down the Ctrl key and leftclick on the point to be deleted To assign a value to a digitized point 1 Click the Digitize button 2 Move the mouse pointer to the point to be assigned a value 3 Rightclick on the point The Digitizer shows a dialog box 4 In the dialog box type a new value then click OK 272 The Field Interpolator 2721 Interpolation Methods for Irregularly Spaced Data Numerical groundwater models require parameters eg hydraulic conductivity hy draulic heads elevations of geological layers etc assigned to each model cell Hy drogeologists however often obtain a parameter distribution in the form of scattered irregular data points xi yi fi i 1 N N is the number of measurement points xi and yi are the coordinates and fi is the parameter value at point i A fundamental problem is how to estimate the parameter values for each model cell from these data A number of interpolation or extrapolation methods for solving this kind of prob lems do exist Some of the methods are used by commercial contouring software eg 27 The Tools Menu 201 GEOKRIG GRIDZO SURFER or TECKONEM Some implementations are pub lished and available at no cost eg GSLIB 31 In an earlier time a common ap proach used by many modelers is that contour maps are first created either by using software packages or manually then overlaid on the model grid for assigning parameter values to model cells The process is indirect and somewhat cumbersome The Field Interpolator provides a more direct way for assigning cell values by using the Kriging method and methods developed by Shepard 110 Akima 12 and Renka 102103 The programs interpolate or extrapolate the measurement data to each model cell The model grid can be irregularly spaced Interpolation results are saved in the ASCII Matrix format see Section 621 which can be imported by the Data Editor into the model grid Depending on the interpolation method and the interpolation parameters the results may be different Using the Data Editor the user may create contour maps of the interpolation results and visually choose a best one Theory is not emphasized in this description since it is introduced in extensive liter ature For example Watson 115 presents a guide to the analysis and display of spatial data including several interpolation methods Franke 45 provides a brief review and classification of 32 algorithms Hoschek and Lasser 64 give a comprehensive discus sion of theories in geometrical data processing and extensive references in the area of data interpolation and computer graphics techniques Akin and Siemes 3 and Davis 30 provide fundamental mathematical background on the statistics and data analysis in geology 2722 Using the Field Interpolator The Field Interpolator runs independently from PM To start the program select Tools Field Interpolator from PM or select Field Interpolator from the Start menu of Win dows The settings of the Field Interpolator Fig 287 are grouped under three tabs Files Grid Position and SearchGridding Method These tabs are described below To start the interpolation simply click the GO button The Field Generator creates and writes the settings and the coordinates to a batch file PMDISBAT and two ASCII files PMDIS IN1 and PMDIS IN2 After having created these files PMDISBAT starts in a DOSwindow The created ASCII files are used by the interpolation pro gram The Files Tab PMWIN Model If the user has already opened a model within PM and started the Field Interpolator from the Tools menu this field contains the model file name If the text string Open a model first is shown click and select a PM model from an Open File dialog box A PM model file always has the extension PM5 202 2 Modeling Environment Input File An input file contains the measurement data which are saved as an XYZ file see Section 6210 for the format An input file can be prepared with the Digitizer or other software Click to select an existing input file The maximum number of data points is 5000 Output file An output file contains the interpolated data for each model cell and is saved in the ASCII matrix format See Section 621 for the format of the ASCII matrix file The Grid Position Tab Using the rotation angle and the coordinates Xo Yo of the upperleft corner of the model grid the user may rotate and place the grid at any position The rotation angle is expressed in degrees and is measured counterclockwise from the positive xdirection See Section 292 for details about the coordinate system of PM As we normally de fine the grid position and the coordinate system at the beginning of a modeling process the grid position will rarely need to be changed here The Gridding Method Tab PMWIN provides four gridding methods The user may select a method from the drop down box There is a corresponding interpolation program for each gridding method The interpolation programs are written in FORTRAN and were compiled with the Lahey FORTRAN 95 compiler The following sections give details of the gridding or interpolation methods Shepards Inverse Distance The Shepards inverse distance method uses Equation 265 to interpolate data for finitedifference cells Fig 287 The Field Interpolator dialog box Fig 288 Effects of different weighting exponents f i1N fidiF i1N 1diF 265 Where di is the distance between data point i and the center of a model cell fi is the value at the ith data point F is the weighting exponent and f is the estimated value at the model cell The weighting exponent must be greater than zero and less than or equal to 10 Fig 288 shows the effects of different weighting exponents Five data points are regularly distributed along the xaxis Using higher values for the exponent eg F4 the interpolated cell values will approach the value of the nearest data point The surface is therefore relatively flat near all data points Lower values of the exponent eg F 1 produce a surface with peaks to attain the proper values at the data points A value of F2 is suggested by Shepard 110 Akimas bivariate interpolation This method creates a triangulation of the measurement data points and performs interpolation by using a bivariate fifth order Hermite polynomial for the interpolation within a triangle It uses a userspecified number of data points closest to a model cell for estimating the value at the cell Renkas triangulation This method first creates a triangulation of the measurement data points and then uses a global derivativeestimation procedure to compute estimated partial derivatives at each point The program determines a piecewise cubic function Fxy F has continuous first derivatives over the created mesh and extends beyond the mesh boundary allowing extrapolation 204 2 Modeling Environment Kriging The Kriging method has been popularized by Matheron 84 and is named in honor of D G Krige a noted South African mining geologist and statistician PM assumes that the measurement data are stationary and isotropic The Kriging method estimates the value at a model cell from a userspecified number of adjacent data values while considering the interdependence expressed in the variogram A variogram is a plot of semivariance γh versus vector distance h The vari ogram is used to define the relationship of the measurement values or to estimate the distance over which measurement values are interdependent When Kriging is selected as the gridding method a Variogram button appears Click this button to display the Variogram dialog box Fig 289 The user needs to select a variogram model from the dropdown box and specify the parameters for the selected vari ogram model PM does not provide a procedure for fitting the selected variogram curve to the measurement data This is a task for geostatistical software eg Var ioWin 94 or GEOEAS 42 and beyond the objective of this software Consider other interpolation methods if the variogram type is unknown The meaning of necessary parameters and the equations for the variogram models are listed below Power and linear model γh α hω c0 α 0 and 0 ω 2 266 Logarithmic model γh 3 α logh c0 α 0 267 Fig 289 The Variogram dialog box 27 The Tools Menu 205 Spherical model γh C 32 ha h3 2 a3 c0 h a γh C c0 h a 268 Gaussian model γh C 1 EXPh2 a2 co 269 Exponential model γh C 1 EXPha co 270 Where C is the variance of measurement data and is calculated by the program a is the correlation length c0 the nugget variance α the slope and ω the power factor of the power model ω 1 yields the linear model Fig 290 The Search Method Tab The interpolation algorithms use three search methods to find a certain number of the measurement data points to interpolate a cell value The search methods are called SIMPLE QUADRANT and OCTANT The search radius is assumed to be infinitely large The SIMPLE search method finds the data points nearest to the model cell The QUADRANT or OCTANT search methods find closest data points from each quadrant or octant around a model cell Figures 291a and 291b The number of data points used in a search is defined by the Data Per Sector value If fewer than Data Per Sector points are found in a sector the program uses the other nearest points found in the entire model The valid range of Data Per Sector is SIMPLE 3 Data Per Sector 30 QUADRANT 1 Data Per Sector 7 OCTANT 1 Data Per Sector 3 The search method defaults to OCTANT search Octant or quadrant searches are usually used when the measurement points are grouped in clusters These search methods force the interpolation programs to use measurement data points radially distributed around the model cell They usually introduce more smoothing than a SIMPLE search Note that the entries in Search Method are ignored when Renkas triangulation algorithm is used 206 2 Modeling Environment Fig 290 Linear Power and logarithmic models Fig 291 Search patterns used by a the Quadrant Search method Data per sector2 and b the Octant Search method Data per sector1 273 The Field Generator The Field Generator Frenzel 47 can generate fields with heterogeneously dis tributed transmissivity or hydraulic conductivity values This allows the user to per form stochastic modeling by considering parameter distributions within PM In stochas tic modeling uncertainty due to unknown spatial variability of the model parameters is addressed directly by assuming that the parameters are random variables Hydraulic conductivity or transmissivity is commonly assumed to be lognormally distributed We denote the hydraulic conductivity by X and define a variable Y logX When Y 27 The Tools Menu 207 Fig 292 The Field Generator dialog box is normally distributed with a mean value µ and standard deviation σ then X has a lognormal distribution The Field Generator runs independently from PM To start the program select Tools Field Generator from PM or select Field Generator from the Start menu of Windows The program displays one dialog box Fig 292 and is fairly easy to use It uses the correlation scales in both I row and J column directions and the mean value µ and standard deviation σ of logtransformed measurement values to generate a quantitative description a realization of the hydraulic conductivity or transmissivity field The size of the field number of cells and the number of desired realizations are specified in the dialog box Realizations are saved in the ASCII Matrix format see Section 621 using the file names filenamennn where filename is the output file name specified in the dialog and nnn is the realization number Note that filename must not be the same as the name of the model The generated field is lognormally to base 10 distributed Using the Data Editor the user can load the generated field into an area of the model grid where the columns and rows are regularly spaced see Section 281 for how to load an ASCII matrix file The simulation of the hydraulic conductivity distribution produced in this way is not constrained to match the measurement values In a constrained simulation existing measurements are used which reduce the space of possible realizations A constrained simulation of a single realization proceeds in five steps 1 The parameter value for each model cell is interpolated from the measurements using the Kriging method The correlation length is determined from the measure ments 2 An unconstrained generation is performed using the Field Generator with the same correlation length correlation scale 208 2 Modeling Environment Fig 293 The 2D Visualization tool in action 3 The unconstrained generated values at the measurement locations are used to in terpolate values for each model cell by using the Kriging method again 4 The distribution from step 3 is subtracted from the distribution from step 2 yielding krigingresiduals 5 The Krigingresiduals are added to the distribution from step 1 yielding a real ization which has the same correlation length and passes through the measured values at the measurement points 274 2D Visualization The 2D Visualization tool is based on the Data Editor and displays the contours of a selected model result type on the model grid Fig 293 The simulation result type is selected by using the Result Selection dialog box Fig 294 which is displayed after selecting the menu item Tools 2D Visualization The dialog box contains several tabs each corresponds to a simulation model Use these tabs to select the desired result type and click the OK button to proceed to the 2D Visualization tool The 2D Visualization tool will load the selected model result and automatically display 11 contour levels ranging from the minimum to maximum values For a timedependent result type the user can select a time point from the Simulation Time dropdown box on the tool bar 27 The Tools Menu 209 Fig 294 The Result Selection dialog box 275 3D Visualization Select this menu item to start the 3D Visualization program defined in the Preferences dialog box see Section 234 for details Currently PM is supported by two 3D visu alization software packages 3D Groundwater Explorer 21 and 3D Master 23 276 Results Extractor Normally simulation results from MODFLOW MT3DMS and other transport models are saved in unformatted binary files and cannot be examined by using usual text editors Using the Results Extractor the user may extract specific results from the result files and save them in ASCII Matrix see Section 621 for the format or Surfer Data files The Result Extractor dialog box Fig 295 is described below Spreadsheet The spreadsheet displays a series of columns and rows which corre spond to the columns and rows of the finitedifference grid By clicking the Read button the selected result type will be read and put into the spreadsheet Orientation and Layer Simulation results can be loaded layer column or row wise Orientation decides how the results should be loaded If Orientation is Plan View the user is asked to enter a layer number into the edit field If Xsection column or Xsection row is selected the user should enter a column or row number into the edit field next to dropdown box Column Width This dropdown box is used to change the appearance width of the columns of the spreadsheet Tabs Each tab corresponds to a simulation model MODFLOW The available Result Types include hydraulic head drawdown preconsolidation head compaction subsidence and cellbycell flow terms see Section 26118 for the definition of each term The stress period and time step from which the result is read are given in the corresponding edit fields MOC3D The available Result Types are concentration and velocity terms The simulation time from which the result is read can be selected from the Total 210 2 Modeling Environment Elapsed Time dropdown box This dropdown box is empty if the selected simulation result does not exist MT3D The primary result of MT3D is concentration When using MT3D96 two additional result types ie solute mass and sorbed mass can be selected The simulation time from which the result is read can be selected from the To tal Elapsed Time dropdown box This dropdown box is empty if the selected simulation result does not exist MT3DMS The primary result of MT3DMS is concentration When using MT3D99 124 two additional result types ie solute mass and sorbed mass can be selected The species number and simulation time from which the re sult is read can be selected from the Species Number and Total Elapsed Time dropdown boxes These dropdown boxes are empty if simulation results do not exist RT3D The primary result of RT3D is concentration The species number and simulation time from which the result is read can be selected from the Species Number and Total Elapsed Time dropdown boxes These dropdown boxes are empty if simulation results do not exist Save and Read To extract a certain result type simply click the Read button The spreadsheet is saved by clicking the Save button and specifying the file name and the file type in a Save Matrix As dialog box There are four file types ASCII Matrix Fig 295 The Results Extractor dialog box 27 The Tools Menu 211 Warp form ASCII Matrix SURFER files and SURFER files realworld An ASCII Matrix file may be loaded into the model by the Data Editor at a later time The format of the ASCII matrix file is described in Section 621 A SURFER file has three columns containing the x y coordinates and the value of each cell If the file type is SURFER files the origin of the coordinate system for saving the file is set at the lowerleft corner of the model grid If the file type is SURFER files realworld the coordinates system as defined in the Environment Options dialog box Fig 2107 is used 277 Water Budget There are situations in which it is useful to calculate flow terms for various subregions of the model To facilitate such calculations MODFLOW saves the computed flow terms for individual cells in the file BUDGETDAT These individual cell flows are re ferred to as cellbycell flow terms and are of four types 1 cellbycell stress flows or flows into or from an individual cell due to one of the external stresses excitations represented in the model eg pumping well or recharge 2 cellbycell storage terms which give the rate of accumulation or depletion of storage in an individual cell 3 cellbycell constanthead flow terms which give the net flow to or from individual constanthead cells and 4 internal cellbycell flows which are the flows across in dividual cell faces In the file BUDGETDAT the flow between the cells K I J and K I J1 is denoted by FLOW RIGHT FACE the flow between the cells K I J and K I1 J is denoted by FLOW FRONT FACE and the flow between the cells K I J and K1 I J is FLOW LOWER FACE Follow the steps below to compute water budgets for the entire model user specified subregions and in and outflows between adjacent subregions To calculate water budget 1 Select Tools Water Budget to display the Water Budget dialog box Fig 296 2 Change the settings in the Time group as needed PM calculates the water budget for the given stress period and time step If the flow simulation has more than one time step you can select Create time series of water budget to calculate water budget terms of all stress periods and time steps 3 Modify the Output Options as needed 4 Click the Define Subregions button to use the Data Editor to define subregions for which a water budget is to be calculated A subregion is indicated by a subregion number ranging from 0 to 50 A subregion number must be assigned to each model cell The number 0 indicates that a cell is not associated with any subregion 212 2 Modeling Environment 5 Once the desired subregions are defined in the Data Editor select File Leave Editor and save the changes 6 Click OK in the Water Budget dialog box to perform the water budget calculation PM saves the flows in the file WATERBDGDAT as shown in Table 210 If Cre ate time series of water budget is selected the flow terms are saved in the file WA TERBDGCSV which is saved in a commaseparated value format and can easily be imported into MS Excel or similar Spreadsheet applications The unit of the flows is L3T 1 Flows are calculated for each subregion in each layer and each time step Flows are considered IN if they are entering a subregion Flows between subregions are given in a Flow Matrix The term HORIZ EXCHANGE gives the flow rate horizon tally across the boundary of a subregion The term EXCHANGE UPPER gives the flow rate coming from IN or going to OUT to the upper adjacent layer The term EXCHANGE LOWER gives the flow rate coming from IN or going to OUT to the lower adjacent layer For example consider EXCHANGE LOWER of REGION1 and LAYER1 the flow rate from the first layer to the second layer is 26107365E03 m3s The percent discrepancy is calculated by 100 IN OUT IN OUT2 271 Fig 296 The Water Budget dialog box 28 The Value Menu 213 Table 210 Output from the Water Budget Calculator WATER BUDGET OF SUBREGIONS WITHIN EACH INDIVIDUAL LAYER REGION 1 IN LAYER 1 FLOW TERM IN OUT INOUT CONSTANT HEAD 18595711E04 24354266E04 57585552E05 EXCHANGE LOWER 00000000E00 26107365E03 26107365E03 RECHARGE 26880163E03 00000000E00 26880163E03 SUM OF THE LAYER 28739735E03 28542792E03 19694213E05 DISCREPANCY 069 REGION 2 IN LAYER 2 WATER BUDGET OF THE WHOLE MODEL DOMAIN CONSTANT HEAD 22167889E03 37117251E03 14949362E03 WELLS 00000000E00 12000003E03 12000003E03 RECHARGE 26880163E03 00000000E00 26880163E03 SUM 49048052E03 49117254E03 69201924E06 DISCREPANCY 014 FLOW RATES BETWEEN SUBREGIONS The value of the element ij of the following flow matrix gives the flow rate from the ith region to the jth region Where i is the column index and j is the row index FLOW MATRIX 1 2 1 26107E03 0000 2 0000 19323E03 28 The Value Menu 281 Matrix Use the Browse Matrix dialog box Fig 297 to examine cell values The spreadsheet displays a series of columns and rows which corresponds to the columns and rows of the finitedifference grid The cell data are shown in the spreadsheet If the user is editing a particular package in which a cell has more than one value for example 214 2 Modeling Environment the River package requires three values for each cell the parameter type can be se lected from the Parameter dropdown box The Column Width dropdown box is used to change the appearance width of the columns of the spreadsheet The cell data may be edited within the Browse Matrix dialog box The user may also assign a value to a group of cells by using the mouse to mark the cells and then enter the desired value The user may save the cell data by clicking the Save button and specifying the file name and the file type in a Save Matrix As dialog box There are four file types ASCII Matrix Wrap form ASCII Matrix SURFER files and SURFER files realworld An ASCII Matrix file may be loaded into the spreadsheet at a later time The format of the ASCII matrix file is described in Section 621 A SURFER file has three columns containing the x y coordinates and the value of each cell If the file type is SURFER files the origin of the coordinate system for saving the file is set at the lowerleft corner of the model grid If the file type is SURFER files realworld the coordinate system defined in the the Environment Options dialog box see Section 292 will be saved To import an ASCII Matrix or a SURFER GRD file 1 Click the Load button to display the Load Matrix dialog box Fig 298 2 Click and select a file type ie ASCII Matrix or SURFER GRD and a file from an Open File dialog box 3 Specify the starting position As shown in Fig 299 the starting position indicates the column and row at which a matrix will be loaded Numbers of rows and columns of the loaded matrix need not to be identical to those of the finitedifference grid This allows to replace Fig 297 The Browse Matrix dialog box 28 The Value Menu 215 only part of the cell data by the matrix For example the user can use the Field Generator to generate a matrix with heterogeneously distributed data from statistic parameters and load it into the grid as a subregion 4 Select an option from the Options group Before a matrix is loaded to the spread sheet its values will be modified according to the following options a Replace The cell data in the spreadsheet are replaced by those of the ASCII Matrix b Add The cell values of the ASCII Matrix are added to those of the spread sheet c Subtract The cell data in the spreadsheet are subtracted from those of the loaded matrix d Multiply The cell data in the spreadsheet are multiplied by those of the loaded matrix e Divide The cell data in the spreadsheet are divided by those of the loaded matrix If a cell value of the loaded matrix is equal to zero the corresponding cell value in the spreadsheet remains unchanged Note A SURFER GRD file may only be used with regularly spaced model grids since SURFER is limited to regular spaced grids Furthermore PM only accepts SURFER GRD files saved in ASCII Consider using the Field Interpolator see Section 272 if the model grid is irregularly spaced 282 Reset Matrix Select this menu to open the Reset Matrix dialog box Fig 2100 which is used to assign uniform values to the current model layer or to the entire model The options Apply to the entire model and Apply to the current layer are available when editing Cell Status arrays IBOUND or ICBUND aquifer parameters or concentration values 1 Apply to the entire model the specified values in the Reset Matrix dialog box will be applied to all cells of the entire model Fig 298 The Load Matrix dialog box 216 2 Modeling Environment Fig 299 The starting position of a loaded ASCII matrix Fig 2100 The Reset Matrix dialog box 2 Apply to the current layer is the default option which assigns the specified values to all cells of the current layer 283 Polygons The Polygons menu allows the user to save or load the zones in or from a Polygon file All polygons in the layer being edited can be deleted by selecting Polygons Delete All Using Polygon files the user can transfer polygon information between parameters or between models with different grid configurations The format of the polygon file is given in Section 629 284 Points The Points menu appears only in the Digitizer Refer to Section 271 for details about the Digitizer and the Points menu 28 The Value Menu 217 Fig 2101 The Search and Modify dialog box 285 Search and Modify Use the Search and Modify dialog box Fig 2101 to modify cell data of the current layer or to create solid fill plots based on the cell data The options of the dialog box are described below The Trace Table The user defines a search range and its attributes in an active row of the table A row is active when the Active flag is checked The search range is given by the minimum lower limit and the maximum upper limit The color in the Color column will be assigned to the finitedifference cells that have a value located within the search range Regularly spaced search ranges can be assigned to each active row by clicking on one of the headers Minimum or Maximum and then enter a minimum and a maximum value to a Search Level dialog box The colors can be automatically assigned to get a gradational change from one color to another To do this click the header Color of the table and assign a min imum color and a maximum color to a Color Spectrum dialog box To change the color individually click on the colored cell a button appears then click on the button and select a color from a Color dialog box Cell values are modified according to the userspecified value in the Value column and the operation option in the Options column The available operations are listed below Display Only No operation takes place Replace The cell values are replaced by the userspecified value Add The userspecified value is added to the cell values 218 2 Modeling Environment Fig 2102 The Import Results dialog box Multiply The cell values are multiplied by the userspecified value Parameter dropdown box For particular packages in which a cell has more than one value eg the River package of MODFLOW this dropdown box contains the available parameter types Choose the parameter type for which the Search and Modify operation will apply Ignore Inactive Cells If this box is checked the Search and Modify operation will only be applied to active cells Maps The user may display background maps DXF or Line Map by using the Maps Options dialog box See Section 291 for details Save and Load The entries in the Trace Table can be saved or loaded in trace files The format of the trace file is given in Section 628 286 Import Results To import the model results select this menu item to open the Import Results dialog box Fig 2102 The dialog box contains several tabs each corresponds to a simulation model Use these tabs to select the desired result type simulation time and click the OK button to import Depends on the selected model simulation time is expressed in terms of stress period time step or elapsed time 287 Import Package When editing flow packages of MODFLOW the user may select this menu item to import existing input files saved in the MODFLOW8896 format Refer to McDon ald and others 85 or Harbaugh and others 54 for input file format The following packages are supported Drain Package Evapotranspiration Package GeneralHead Boundary Package HorizontalFlow Barrier Package InterbedStorage Package 29 The Options Menu 219 Recharge Package Reservoir Package River Package StreamflowRouting Package TimeVariant Specified Head Package Well Package 29 The Options Menu There are five menu items in the Options menu Maps Environment Display Cell In formation Display Mode and Input Method The menu item Display Cell Information opens a Cell Information dialog box Fig 28 which displays the userspecified data of the cell pointed by the grid cursor The menu items Display Mode and Input Method are described in Section 22 The use of the menu items Maps and Environment is de scribed below 291 Map The Maps Options dialog box Fig 2103 allows the user to display up to 5 DXF maps 3 Line maps and one georeferenced raster bitmap graphics The options in this dialog box are grouped under two tabs described below The Vector Graphics Tab The Vector Graphics Tab is used to import DXF or Linemaps A DXF file contains detailed data describing numerous CAD entities An entity is a line or symbol placed on a drawing by the CAD system PM supports the following entities LINE POLY LINE POINT ARC SOLID CIRCLE and TEXT The other entities are ignored There is no size limit to the number of the acceptable entities A LineMap consists of a series of polylines Each polyline is defined by a header line and a series of coordinate pairs The header line only contains the number of the coordinate pairs Refer to Section 624 for the format of the Line Map files To import a DXFmap or a Line map 1 Select the Vector Graphics tab 2 Right Click on any of the DXF File or Line Map File fields and then select a file from a Map Files dialog box 220 2 Modeling Environment 3 If necessary use a scale factor to enlarge or reduce the appearance size of the map Then use the values in X and Y to shift the scaled map to the desired position For details see the section Scaling a vector graphic below 4 Click the colored button in the front of the edit field and select a color for the DXFmap from a Color dialog box The color will be assigned to a DXFgraphics entity if the entitys color is not defined in the DXF file A line map will always use the selected color 5 Check the box at the front of the edit field The map will be displayed only when the box is checked Scaling a vector graphic X and Y should be 0 and Scale should be 1 if a DXF file is generated by PM Since different length units are often used by various drawing or CAD software pack ages DXF files created by those packages may not be correctly imported into PM without modifying the scale factor and the X Y values If these values are incorrect a DXFmap will be displayed too small too large or outside the Viewing Window If this happens use the Environment options dialog box to define a very large Viewing Win dow ensuring that the map can be displayed within the window Then check the units on the imported map by moving the mouse around the map and looking at the X and Y coordinates displayed in the status bar Choose two points that are a known distance Fig 2103 The Map Options dialog box 29 The Options Menu 221 apart and check their distance with the status bar If the distance is incorrect compute a scale factor and import the map again Once the correct scale factor is found the user may shift the scaled DXFmap to the desired position by using X and Y Fig 2104 uses a triangle as an example to demonstrate the use of X Y and the scale factor The Raster Graphics Tab Using the Raster Graphics tab raster graphics saved in Windows Bitmap bmp or JPEG jpg format can be imported and georeferenced To import a raster graphics map 1 Click the Raster Graphics tab 2 Click the open file button and select a file from a Raster Graphics dialog box The map is displayed in the Maps Options dialog box Fig 2105 Using the following methods to increase or decrease the magnification level of the display To move a part of the image to the center of the display simply click the desired position To zoom in hold down the Shift key and click the image To zoom out hold down the Ctrl key and click the image To display entire map hold down the Alt key and click the image 3 Follow the steps below to set georeference points a Click the Set button from the Point 1 or Point 2 group The mouse pointer turns into a crosshairs Fig 2104 Scaling a vector graphic 222 2 Modeling Environment Fig 2105 Importing and Georeferencing a raster map b Place the crosshairs at a point with known x y realworld coordinates and press the left mouse button c Enter the x y coordinates into the corresponding edit fields of the group Point 1 or Point 2 d Repeat the previous steps to set the other reference point Note that the geo reference points must not lie on a vertical or horizontal line eg the x and ycoordinates of the points must not be the same 292 Environment The Environment Options dialog box Fig 2106 allows the user to configure the coor dinate system and modify appearance of the model grid Available settings are grouped under three tabs Appearance Coordinate System and Contours which are described below The checkbox Display zones in the cellbycell mode is used to force PM to display the userspecified polygons when using the cellbycell input method The Appearance Tab The Appearance Tab Fig 2106 allows the user to change the visibility and appear ance color of each simulated component A simulated component is visible if the cor responding Visibility box is checked To select a new color click on the colored cell a 29 The Options Menu 223 Fig 2106 The Appearance tab of the Environment Options dialog box button appears then click on the button and select a color from a Color dialog box The Vertical Exaggeration edit field controls the vertical exaggeration factor seen in the Row or Column view The Coordinate System Tab The Coordinate System Tab is used to define the extent and location of the the Viewing Window and to define location and orientation of the model grid As illustrated in Fig 2107 the Viewing Window is a window to the realworld your model grid is placed within the Viewing Window The extent and location of the Viewing Window are defined by specifying the realworld coordinates of its lower left and upperright corners ie by the coordinates X1 Y1 and X2 Y2 as shown in Fig 2107 and Fig 2108 The location and orientation of the model grid are defined by the coordinates Xo Yo of its leftupper corner and a rotation angle The rotation angle is expressed in degrees and is measured counterclockwise from the positive x direction 224 2 Modeling Environment Fig 2107 The Coordinate System tab of the Environment Options dialog box The Contours Tab The Data Editor displays contours based on the cell data The Contours tab Fig 2109 controls the display of the contour levels labels and colors The options of this tab are listed below Visible Contours are visible if this box is checked Display contour lines Contour lines and labels are displayed if this box is checked Fill contours Checking this box causes the space between contour lines to be filled with the color defined in the contour level table Orient label uphill If this box is checked the contour labels are displayed so that they are always oriented uphill ie oriented towards places with higher cell val ues Ignore inactive cells If this box is checked the data of inactive cells will not be used for creating contours Parameter When editing a particular package in which a cell has more than one value for example the River package requires three values for each cell the user can select the parameter type from this drop down box PM uses the data associated with the selected parameter type to create contours Contour level table The user may click on each cell of the table and modify the values or click on the column header of the table to change the values for all cells of that column 29 The Options Menu 225 Fig 2108 Defining the coordinate system and orientation of the model grid Level To produce contours on regular intervals click the header of this col umn A Contour Levels dialog box allows the user to specify the contour range and interval By default this dialog box displays the lowest and highest values found in the current layer After clicking OK the contour levels in the table are updated to reflect the changes Line and Fill Define the color of a contour line and the fill color between two contour lines Click on the headers Line or Fill to display the Color Spectrum dialog box Fig 2110 which can be used to assign a gradational change of contour colors from the lowest contour level to the highest contour level To change the colors correspond to the lowest or highest contour levels simply click on one of the colored buttons and select a color from a Color dialog box After clicking OK the contour colors levels in the table are updated to reflect the changes Label Defines whether a contour should be labeled The user may click on an individual box of the Label column to turn label on or off Click on the header to display the Contour Labels dialog box Fig 2111 which can be used to define the display frequency of contour labels First labeled contour line defines the first contour line to be labeled Labeled line frequency specifies how often the contour lines are labeled After clicking OK the flags in the table 226 2 Modeling Environment Fig 2109 The Contours tab of the Environment Options dialog box are Label height Specifies the appearance height of the label text It uses the same length unit as the model Fig 2110 The Color Spectrum dialog box Fig 2111 The Contour Labels dialog box 29 The Options Menu 227 Label spacing Specifies the distance between two contour labels It uses the same length unit as the model Label Format The Label Format dialog box Fig 2112 allows the user to specify the format for the labels The elements of this dialog box are described below Fixed This option displays numbers at least one digit to the left and N digits to the right of the decimal separator where N is the value specified in Decimal digits Exponential This option displays numbers in scientific format and E is inserted between the number and its exponent Decimal digits The value of Decimal digits determines the number of digits to the right of the decimal separator For example if Decimal digits 2 the value 12412 will be displayed as 124120 for the fixed option or 124E03 for the exponential option Prefix is a text string that appears before each label Suffix is a text string that appears after each label Restore Defaults Clicking on this button PM sets the number of contour lines to 11 and uses the maximum and minimum values found in the current layer as the minimum and maximum contour levels The label height and spacing will also be set to their default values Load and Save The contents of the contour level table can be loaded from or saved in separate Contour files Refer to Section 622 for the format Fig 2112 The Label Format dialog box xt₂ x₁ vₓt₁ eAₓΔT vₓ₁ Aₓ yt₂ y₁ vᵧt₁ eAᵧΔT vᵧ₁ Aᵧ zt₂ z₁ vzt₁ eAzΔT vz₁ Az 36 where ΔT t₂ t₁ For steadystate flow fields the location of the particle at time t₂ must still be within the same cell as at time t₁ Given any particles starting location within a cell at time t₁ Pollocks algorithm allows determining the particles exit time t₂ and exiting point from the cell directly without having to calculate the actual path of the particle within the cell The particle tracking sequence is repeated until the particle reaches a discharge point or until a userspecified time limit is reached Backward particle tracking is implemented by multiplying all velocity terms in equation 33 by 1 For transient flow fields in addition to the condition for steadystate flow fields t₁ and t₂ must lie within the same time step In PMPATH each particle may be associated with a set of attributes ie the retardation factor the starting forward and backward travel times and positions If a particle is traveling across the end forward tracking or the beginning backward tracking of a time step of a flow simulation PMPATH sets t₂ to the end or beginning time of this time step and forces the particle to wait until the flow field of the next time step forward tracking or the previous time step backward tracking is read If the end or beginning time of a transient flow simulation is reached the most recent flow field can be treated as steady state and the movement of particles can go on 311 Consideration of the display of the calculated pathlines Because of the capability of calculating a particles exit point from a cell directly pathlines displayed by PMPATH may sometimes intersect each other Consider the case shown in Fig 33 two particles within a twodimensional cell start at the same time The dashed curves represent the actual paths of these two particles The solid lines are the pathlines displayed by PMPATH The pathlines intersect each other although the particles exit points are exactly equal to that of the actual paths This spurious effect can be prevented by using a smaller particle tracking step length such that intermediate particle positions between starting point and exit point can be calculated See Particle Tracking Time Properties dialog box Section 332 for how to change the particle tracking step length 312 Consideration of the spatial discretization and water table layers The method described above is based on the assumption that the model domain was discretized into an orthogonal finitedifference mesh ie all model cells in the same 3 The Advective Transport Model PMPATH PMPATH is an advective transport model running independently from PM PMPATH retrieves the groundwater models and simulation result from PM and MODFLOW A semianalytical particletracking scheme Pollock 9596 is used to calculate the groundwater paths and travel times Through the interactive graphical modeling envi ronment of PMPATH the user can place particles and perform particle tracking with just a few mouse clicks While most available particle tracking models need post processors for visualization of computed paths and times data PMPATH calculates and animates the pathlines simultaneously Fig 31 Moreover PMPATH provides various onscreen graphical options including head contours drawdown contours and velocity vectors for any selected model layer and time step Both forward and backward particle tracking are allowed for steady state and tran sient flow simulations For transient flow simulations particles can start from the be ginning of any time step During the simulation the particletracking algorithm will check the current time of every particle If a particle reaches the end forward track ing or the beginning backward tracking of a time step PMPATH forces the particle to wait until the flow field of the next time step has been read The particle track ing simulation proceeds until all particles have left the model via sinks or until the userspecified time limit is reached The time length of a single particle tracking step and the maximum number of tracking steps can be specified Each particle can have its own color and retardation factor With these features PMPATH can be used to simulate advective transport in groundwater to delineate contaminant capture zones injection zones and wellhead protection areas or to find the point of origin of water in specified zones PMPATH creates several output files including hydraulic heads distribution velocity field the xyz coordinates and travel times of particles Furthermore the coordinates along the 230 3 The Advective Transport Model PMPATH Fig 31 PMPATH in action path of each particle can be saved and used by 3D Master 23 for advanced 3D Visu alization 31 The Semianalytical Particle Tracking Method Assume that the density of groundwater is constant Consider an infinitesimal volume of a porous medium as shown in Fig 32a and the law of conservation of mass The three dimensional form of the partial differential equation for transient groundwater flow in saturated porous media at constant density can be expressed as vsx x vsy y vsz z w Ss h t 31 where vsx vsy and vsz LT 1 are values of the specific discharge or Darcy velocity through the unit volume along the x y and z coordinate axes 31 The Semianalytical Particle Tracking Method 231 w T 1 is a volumetric flux per unit volume and represents internal sources andor sinks of water Ss L1 is the specific storage coefficient of saturated porous media h L is the hydraulic head and t L is time For a threedimensional finitedifference cell as shown in Fig 32b the finite difference form of equation 31 can be written as Qx2 Qx1 y z x Qy2 Qy1 x z y Qz2 Qz1 x y z W x y z Ss h t 32 where Qx1 Qx2 Qy1 Qy2 Qz1 and Qz2 L3T 1 are are volume flow rates across the six cell faces x y and z L are the dimensions of the cell in the respective coordinate directions W L3T 1 is flow to internal sources or sinks within the cell and h L is the change in hydraulic head over a time interval of length t T Equation 32 is the volume balance equation for a finitedifference cell The left hand side of equation 32 represents the net rate of outflow per unit volume of the porous medium and the right hand side is the rate production per unit volume due to internal sourcessinks and storage Substitution of Darcys law for each flow term in Fig 32 a Flow through an infinitesimal volume of a porous medium and b the finitedifference approach 232 3 The Advective Transport Model PMPATH equation 32 ie Q h K Ax yields an equation expressed in terms of unknown heads at the center of the cell itself and adjacent cells An equation of this form is written for every cell in the mesh in which head is free to vary with time Once the system of equations is solved and the heads are obtained the volume flow rates across the cell faces can be computed from Darcys law The average pore velocity components across each cell face are vx1 Qx1ne y z vx2 Qx2ne y z vy1 Qy1ne x z vy2 Qy2ne x z 33 vz1 Qz1ne x y vz2 Qz2ne x y where ne is the effective porosity and vx1 vx2 vy1 vy2 vz1 and vz2 LT 1 are the average pore velocity components across each cell face Pollocks semianalytical particle tracking scheme is based on the assumption that each velocity component varies linearly within a model cell in its own coordinate direc tion The semianalytical particletracking algorithm uses simple linear interpolation to compute the principal velocity components at any points within a cell Given the start ing location x y z of the particle and the starting time t1 the velocity components are expressed in the form vxt1 Axx x1 vx1 vyt1 Ayy y1 vy1 34 vzt1 Azz z1 vz1 where x1 y1 and z1 are defined in Fig 32b Ax Ay and Az T 1 are the compo nents of the velocity gradient within the cell Ax vx2 vx1x Ay vy2 vy1y 35 Az vz2 vz1z Using a direct integration method described in Pollock 95 and considering the move ment of the particle within a cell the particle location at time t2 is No text present 234 3 The Advective Transport Model PMPATH Fig 33 Schematic illustration of the spurious intersection of two pathlines in a two dimensional cell layer have the same thickness In practice variable layer thickness is often preferred for approaching varying thickness of stratigraphic geohydrologic units In order to calculate approximate groundwater paths for this kind of discretization PMPATH uses a local vertical coordinate instead of the realworld zcoordinate The local vertical coordinate is defined for each cell as ZL z z1z2 z1 37 where z1 and z2 are the elevations of the bottom and top of the cell respectively According to this equation the local vertical coordinate zL is equal to 0 at the bottom of the cell and is equal to 1 at the top of the cell For water table layers z2 is set equal to the head in the cell In MODFLOW model layers of type 1 unconfined are always water table layers model layers of type 2 or 3 confinedunconfined are water table layers when the hydraulic head in the cell is beneath the elevation of the cell top When a particle moves laterally from one cell to another the exit point in the one and the entry point in the other cell have the identical local vertical coordinates This causes vertical discontinuities of pathlines if bottoms and tops of cells of the neighbor ing cells are different This discontinuity does not introduce error it is merely unes thetic It can be kept small if the discretization is kept fine enough to have relatively small celltocell variations of bottoms and tops 32 PMPATH Modeling Environment 235 32 PMPATH Modeling Environment The PMPATH modeling environment Fig 34 consists of the Worksheet the cross section windows the tool bar and the status bar They are described in the following sections 321 Viewing Window and crosssection windows PMPATH as well as PM use the same spatial discretization convention as MODFLOW An aquifer system is discretized into mesh blocks or cells An K I J indexing system is used to describe the locations of cells in terms of layers rows and columns The K I and Jaxes are oriented along the layer row and column directions respectively The origin of the cell indexing system is located at the upper top left cell of the model MODFLOW numbers the layers from the top down an increment in the K index corresponds to a decrease in elevation z PMPATH always displays the model grid parallel to the Viewing Window while the user may shift and rotate a model grid by giving the rotation angle A and the co ordinates Xo Yo of the upperleft corner of the grid The relation between the model grid and the realworld x y z coordinate system is illustrated in Fig 34 The View ing Window displays the plan view of the current model layer and the projection of pathlines on the horizontal plane The crosssection windows display the projection of pathlines on the IK and JKplanes The Environment Options dialog box of PMPATH see Section 331 allows the user to change the appearance of these windows The projection of pathlines on the crosssections is useful when running PMPATH with a threedimensional multilayer flow field The user should always keep in mind that only the projections of pathlines are displayed The projection of a pathline may be intersected by another or even itself particularly if a threedimensional flow field or a transient flow field is used 322 Status bar The Status bar displays the following messages 1 Current position of the mouse pointer in both x y z coordinates and K I J indices 2 Hydraulic head at the cell K I J 3 Average horizontal pore velocity at the center of the cell K I J 4 Average vertical pore velocity at the center of the cell K I J 5 Current stress period of the flow simulation 6 Current time step of the flow simulation and 7 Number of particles 236 3 The Advective Transport Model PMPATH Fig 34 The PMPATH modeling environment 32 PMPATH Modeling Environment 237 See Particle Tracking Time Properties dialog box Section 332 for how to change the current stress period and time step The hydraulic heads at the current stress period and time step are calculated by MODFLOW The x and y components of the average horizontal pore velocity at the center of a cell is obtained by averaging the velocities vx1 vx2 and vy1 vy2 respectively Equation 33 The average vertical pore velocity at the center of a cell is the average of the velocities vz1 vz2 Equation 33 The vertical velocity is defined as positive when it points in the Kdirection 323 Tool bar The tool bar provides quick access to commonly used commands in the PMPATH modeling environment You click a button on the tool bar once to carry out the action represented by that button To change the current layer or the local vertical coordinate click the corresponding edit field in the tool bar and type the new value then press ENTER See equation 37 for the definition of the local vertical coordinate Table 31 summarizes the use of the tool bar buttons which are described in the following sec tions 3231 Open model The Open model button opens an existing model created by PM A model file for PM always has the extension PM5 Prior to opening a model the flow simulation must be performed By default PMPATH reads the unformatted binary files HEADSDAT and BUDGETDAT from the same folder as the loaded model Note The first time PMPATH is started from PM the model currently used by PM will be loaded into PMPATH automatically If model data has been modified and a flow simulation has been performed the modified model must be reloaded into PMPATH to ensure that it can recognize the modifications 3232 Set particle Use the following two methods to place particles in the current layer The current layer is shown in the tool bar Fig 34 Change it first if particles need to be placed in another layer Note that particles cannot be placed in inactive cells or fixedhead cells constant head cells To place a group of particles 1 Click the Set particle button 2 Move the mouse pointer to the active model area The mouse pointer turns into crosshairs 238 3 The Advective Transport Model PMPATH Table 31 Summary of the toolbar buttons of PMPATH Button Name Action Open model Opens a model created by PMWIN Set Particle Allows the user to place particles in the model domain Erase particle Activates the erase particle tool Zoom in Allows the user to drag a zoomwindow over a part of the model domain Zoom out Forces PMPATH to display the entire model grid Particle color Allow the user to select a color for new particles from a color dialog box Run particles back ward Execute backward particle tracking for a time length The product of the number of particle tracking steps and the particle tracking step length defines the time length Run particles back ward step by step Execute backward particle tracking for a userspecified particle tracking step length Stop particletracking Stop the particle tracking or stops drawing particles Run particles forward step by step Execute forward particle tracking for a userspecified particle tracking step length Run particles forward Execute forward particle tracking for a time length The product of the number of particle tracking steps and the particle tracking step length defines the time length 3 Place the crosshairs where the user wants a corner of the Set Particle window 4 Drag the crosshairs until the window covers the subregion over which particles will be placed then release the mouse button The Add New Particles box appears Fig 35 Where NK NI and NJ are the number of particles in layer row and column directions respectively Particles can be placed either on cell faces or within cells which lie in the Set Particle window These numbers NK NI and NJ can range from 0 to 999 In the case shown in Fig 35 8 2 2 2 particles will be placed within each cell 3 3 1 particles will be placed on each cell face and 15 particles will be placed around each cell at a distance of 20 The particles will get the color and the retardation 32 PMPATH Modeling Environment 239 factor given in the Properties tab of this dialog box To place a single particle 1 Click the Set particle button 2 Change the local vertical coordinate and the particle color for the definition of the local vertical coordinate see equation 37 3 Place a particle by rightclicking the desired position This particle will have the retardation factor see below specified in the Properties tab of the Add New Parti cles dialog box Once particles are placed their color and retardation factor cannot be changed any more The retardation factor R is defined by R 1 ρb ne Kd 38 where ρb is the bulk density of the porous medium ne is the effective porosity and Kd is the distribution coefficient A detailed description of these parameters can be found in the literature eg Freeze and Cherry 46 The retardation factor was first applied to groundwater problems by Higgins 58 and Baetsle 11 Baetsle indicated that it may be used to determine the retardation of the center of mass of a contaminant moving from a point source while undergoing adsorption PMPATH uses the retardation factor to modify the average pore velocity of the groundwater flow The velocity vectors in Equation 33 become Fig 35 The Add New Particles dialog box 240 3 The Advective Transport Model PMPATH vx1 Qx1ne y zR vx2 Qx2ne y zR vy1 Qy1ne x zR vy2 Qy2ne x zR 39 vz1 Qz1ne x yR vz2 Qz2ne x yR 3233 Erase Particle The user can only erase particles located in the current layer The current layer is shown in the tool bar Change it first if the user needs to erase particles in another layer To erase particles 1 Click the Erase particle button 2 Move the mouse pointer to where the user wants a corner of the Erase window 3 Drag the mouse pointer until the window covers the particles to be deleted 4 Release the mouse button 3234 Zoom In By default PMPATH displays the entire model grid Zoom in is useful for viewing a part of the model domain in greater detail or for saving plots of a certain part of the model area see Section 341 for how to save plots To zoom in on a part of the model 1 Click the Zoom In button 2 Move the mouse pointer to where the user wants a corner of the Zoom window 3 Drag the mouse pointer until the window covers the model area to be displayed 4 Release the mouse button 3235 Zoom Out Clicking on the Zoom Out button forces PMPATH to display the entire model grid 32 PMPATH Modeling Environment 241 3236 Particle Color Clicking on the Particle color button allows the user to select a color for new parti cles from a Color dialog box Particles with different colors are useful for determining the capture zones of various pumping wells In this case particles with a certain color are placed around or on the cellfaces of each pumping well Through backward track ing capture zones of each pumping well can be recognized by their different colors 3237 Run Particles Backward Click to execute backward particle tracking for a specified time length The time length is the product of the number of particle tracking steps and the particle tracking step length given in the Particle Tracking Time Properties dialog box See Section 332 for details 3238 Run Particles Backward Step by Step Click to move particles backward a single particletracking step The particle track ing step length is defined in the Particle Tracking Time Properties dialog box See Section 332 for details 3239 Stop Particle Tracking Click to stop particle tracking or stop redrawing particles when this button is high lighted ie the rectangle on the button is colored in red PMPATH redraws the particles whenever the PMPATH window has been covered by other windows and becomes visible again For example if the user switches to to another application and then returns to PMPATH it will redraw all particles If too many particles are placed it might be necessary to keep PMPATH from redrawing all of the particles all over again Under some circumstances PMPATH will take a long time to calculate the coordi nates of flow paths and travel times This is especially true if the flow velocities and the userspecified time step length of particle tracking are very small Click the Stop Particle Tracking button if the particle tracking simulation appears too slow 32310 Run Particles Forward Step by Step Click to move particles forward a single particle tracking step The particle tracking step length is defined in the Particle Tracking Time Properties dialog box See Section 332 for details 242 3 The Advective Transport Model PMPATH 32311 Run Particles Forward Click to execute forward particle tracking for a specified time length The time length is the product of the number of particle tracking steps and the particle tracking step length given in the Particle Tracking Time Properties dialog box See Section 332 for details 33 PMPATH Options Menu 331 Environment The Environment Options dialog box Fig 36 allows modifying the appearance of the model The available settings are grouped under 4 tabs namely Appearance Cross Sections Velocity vectors and Contours These tabs are described below The Appearance Tab The Appearance Tab Fig 36 allows changing the visibility and appearance color of each simulated component A simulated component is visible if the corresponding Visibility box is checked To select a new color click on the colored cell a button appears then click on the button and select a color from a Color dialog box The Cross Sections Tab Fig 36 The Environment Options dialog box of PMPATH 33 PMPATH Options Menu 243 The options of the Cross Sections tab Fig 37 is given below Fig 37 The Cross Sections tab of the Environment Options dialog box of PMPATH Visible Check this box to display the cross section windows If the model thick ness or the exaggeration value see below is too small such that the appearance thickness on the screen is smaller than 1 pixel PMPATH will clear this box and turn off the display of the cross sections In this case the Visible check box will be cleared automatically Show grid Check this box to display the model grid Show Groundwater surface Potential Check this box to display the groundwater surface or the hydraulic heads of the highest active cells on the cross sections Exaggeration scaling factor for the height Use this value to change the appear ance height of the cross sections A larger exaggeration value lets PMPATH draw the projection of the pathlines on the cross section windows in greater details The exaggeration value can range from 001 to 1000 Projection Row and Projection Column PMPATH uses the grid cursor Fig 34 to define the column and row for which the cross sectional plots should be made The grid cursor can be moved by holding down the Ctrlkey and click the left mouse button on the desired position Alternatively type the row and column in the Projection Row and Projection Column edit boxes Minimum Elevation and Maximum Elevation The visible part on the cross sec tional plots is defined by Minimum Elevation and Maximum Elevation By de fault the maximum elevation is set to the highest elevation of the model grid or 244 3 The Advective Transport Model PMPATH the largest hydraulic head The minimum elevation is set to the lowest elevation of the model grid or the smallest hydraulic head The Velocity Vectors Tab Velocity vectors describe the direction of water movement at any instant of a given time step of the simulation see Section 332 for the definition of time step Check ing the Visible check box the projection of velocity vectors of each active model cell will be displayed on the Viewing Window and cross section windows Click the color button next to the Visible check box to change the appearance color of the velocity vectors The appearance size of the largest velocity vector is defined by the Vector size in pixels which defaults to 25 and can be ranged from 1 to 32767 The Contours Tab PMPATH displays contours based on the calculated hydraulic head or drawdown val ues The Contours tab Fig 38 controls the display of the contour levels labels and colors The options of this tab are listed below Visible Contours are visible if this box is checked Orient label uphill If this box is checked the contours labels are displayed so that they are always oriented uphill ie oriented towards places with higher cell values Fig 38 The Contours tab of the Environment Options dialog box of PMPATH 33 PMPATH Options Menu 245 Head or Drawdown Use the options Head or Drawdown to decide which kind of contours should be displayed Contour level table The user may click on each cell of the table and modify the values or click on the column header of the table to change the values for all cells of that column Level To produce contours on regular intervals click the header of this col umn A Contour Levels dialog box allows the user to specify the contour range and interval By default this dialog box displays the lowest and highest values found in the current layer After clicking OK the contour levels in the table are updated to reflect the changes Color Defines the color of a contour line Click on the header to display the Color Spectrum dialog box Fig 39 which can be used to assign a gradational change of contour colors from the lowest contour level to the highest contour level To change the colors correspond to the lowest or highest contour levels simply click on one of the colored buttons and select a color from a Color dialog box After clicking OK the contour colors levels in the table are updated to reflect the changes Label Defines whether a contour should be labeled The user may click on an individual box of the Label column to turn label on or off Click on the header to display the Contour Labels dialog box Fig 310 which can be used to define the display frequency of contour labels First labeled contour line defines the first contour line to be labeled Labeled line frequency specifies how often the contour lines are labeled After clicking OK the flags in the table are updated to reflect the changes Label height Specifies the appearance height of the label text It uses the same length unit as the model Label spacing Specifies the distance between two contour labels It uses the same length unit as the model Label height specifies the appearance height of the label text It uses the same length unit as the model Label spacing specifies the distance between two contour labels It uses the same length unit as the model Label Format The Label Format dialog box Fig 311 allows the user to specify the format for the labels The options of this dialog box are described below Fixed This option displays numbers at least one digit to the left and N digits to the right of the decimal separator where N is the value specified in Decimal digits Exponential This option displays numbers in scientific format and E is inserted between the number and its exponent 246 3 The Advective Transport Model PMPATH Decimal digits The value of Decimal digits determines the number of digits to the right of the decimal separator For example if Decimal digits 2 the value 12412 will be displayed as 124120 for the fixed option or 124E03 for the exponential option Prefix is a text string that appears before each label Suffix is a text string that appears after each label Restore Defaults Clicking on this button PMPATH sets the number of contour lines to 11 and uses the maximum and minimum values found in the current layer as the minimum and maximum contour levels The label height and spacing will also be set to their default values Load and Save The contents of the contour level table can be loaded from or saved to separate Contour files Refer to Section 622 for the format 332 Particle Tracking Time The available settings of the Particle Tracking Time dialog box Fig 312 are grouped under three tabs Simulation ModeTime Pathline Colors and RCHEVT options These tabs are described below The Simulation ModeTime Tab Fig 39 The Color Spectrum dialog box Fig 310 The Contour Labels dialog box 33 PMPATH Options Menu 247 Fig 311 The Label Format dialog box Fig 312 The Particle Tracking Time dialog box The options of the Simulation ModeTime tab Fig 312 are described below Current Time In MODFLOW simulation time is divided into stress periods which are in turn divided into time steps The time length of each stress period and time step is defined in PM In PMPATH the user can move to any stress period and time step as long as the resulting heads and budget data are saved for that stress periodtime step The starting time of each particle is always the beginning of the time step defined in Current Time Tracking Step To select a time unit for Step length click the down arrow on the Unit drop down box The step length is the time length that particles may move when one of the buttons or is pressed Maximum steps is the allowed number 248 3 The Advective Transport Model PMPATH of particle tracking steps Each time one of the buttons or is pressed particles will move backward or forward for a time length defined by the product of Step length and Maximum steps Time Mark PMPATH places a time mark on pathlines for each nth tracking step where n is given in Interval Check the corresponding Visible boxes to see time marks on the Viewing Window or the cross section windows The appearance size of the time marks is defined by Size in pixels The default value of Size is 10 for the Viewing Window and 3 for the cross section windows The sizes can be ranged from 1 to 2147483647 Simulation Mode PMPATH can be used to calculate flowlines or pathlines Flow lines indicate the instantaneous direction of flow throughout a system at all times of a steady state flow simulation or at a given time step of a transient flow simula tion Pathlines map the route that an individual particle of water follows through a region of flow under steady state or transient conditions In a steady state flow sys tem pathlines will coincide with flowlines In this case only the option Flowline use the flow field from the current time step is available In the case of a transient flow simulation where groundwater flow varies from time step to time step the flowlines and pathlines do not coincide Use the option Pathlines use transient flow fields to calculate transient pathlines Stop Conditions In general particles will stop when the allowed travel time de fined in Tracking Step is reached or when the particles reach specified head cells In addition to these conditions two stop conditions are available Particles stop when they enter cells with internal sinks The flow model MOD FLOW includes the options to simulate wells drains rivers general head boundaries streams evapotranspiration and recharge Except the last two op tions they are treated as internal distributed sources or sinks by PMPATH If the internal sink of a cell is sufficiently strong flow will be into the cell from all cell faces In that case every particle that enters the cell will be discharged If the sink is weak flow will be into the cell from some cell faces and a part of the flow will leave the cell through other faces A particle entering such a cell may be discharged or may leave the cell again In the finite difference approach however it is impossible to determine whether that particle should be discharged or pass through the cell If this option is selected particles will be discharged when they enter cells with internal sinks regardless of the flow condition Particles stop when the simulation time limit is reached This option is avail able only if the simulation mode Pathlines use transient flow fields is se lected In PMPATH the starting time of each particle is always the beginning of the time step defined in Current Time For the forward particletracking scheme the simulation time limit is the end of a transient flow simulation 33 PMPATH Options Menu 249 For the backward particletracking scheme on the other hand the simulation time limit is the beginning of the simulation Backward particle tracking will not work if this stop option is checked and particles are started from the be ginning of a transient flow simulation In this case particles will be stopped immediately after the start Note that PMPATH cannot start backward particle tracking from the end of a transient flow simulation rather PMPATH can only start particles from the beginning of the last simulation time step If the simu lation time limit is reached and this option is not checked PMPATH calculates flowlines by assuming that the flow field of the first or last time step is steady state The Pathline Colors Tab Normally the color of each pathline is the same as the color of each particle However it is sometimes useful when the colors of pathlines are distinguished by layers instead of particles There are two ways to change the color of each layer To change the color individually 1 Click on a colored cell of the table Fig 313 a button appears in the cell 2 Click on the button and select a color from a Color dialog box Fig 313 The Pathline Colors tab of the Particle Tracking Time dialog box 250 3 The Advective Transport Model PMPATH Fig 314 The RCHEVT Options tab of the Particle Tracking Time dialog box To Change the color using the Color Spectrum dialog box 1 Click the header button Color A Color Spectrum dialog box appears Using the Color Spectrum dialog box the color of each layer can be automatically assigned to get a gradational change from one color to another 2 In the Color Spectrum dialog box click the Minimum Color button to display a Color dialog box In the Color dialog box select a color and click OK Repeat this procedure for the Maximum Color button 3 In the Color Spectrum dialog box click OK A gradation of colors from the mini mum to the maximum is assigned to each layer The RCHEVT Options Tab The RCHEVT Options tab 314 provides two options Recharge The option is disabled if recharge is not used MODFLOW treats recharge as an internal distributed source of a cell and does not assign it to any of the six cell faces The distributed source approximation is usually only appro priate for two dimensional areal flow models The flow velocity across the top face of a cell in the top model layer is zero if the existing recharge is not assigned to the top face Consequently particles cannot be tracked backwards to the top face In PMPATH recharge may be treated as a distributed source or assigned to the top face or bottom face of a cell by selecting a corresponding option from the dialog 33 PMPATH Options Menu 251 box If the option Assign recharge to top and bottom cell faces is chosen positive recharge values will be assigned to the top face and negative recharge values will be assigned to the bottom face Evapotranspiration The option is disabled if evapotranspiration is not used Sim ilar to Recharge evapotranspiration can be assigned to top face of a cell or treated as a distributed sink 333 Maps The Maps Options dialog box Fig 315 allows the user to display up to 5 DXFmaps and 3 Line Maps A DXFfile contains detailed data describing numerous CAD enti ties An entity is a line or symbol placed on a drawing by the CAD system PMPATH supports the following entities LINE POLYLINE POINT ARC SOLID CIRCLE and TEXT The other entities are ignored There is no size limit to the number of the acceptable entities A Line Map consists of a series of polylines Each polyline is defined by a header line and a series of coordinate pairs The header line only contains the number of the coordinate pairs Refer to Section 624 for the format of the Line Map files To import a DXFmap or a Line Map 1 Rightclick on any of the DXF File or Line Map File edit fields and select a file from a Map Files dialog box Fig 315 The Maps Options dialog box 252 3 The Advective Transport Model PMPATH 2 If necessary use a scale factor to enlarge or reduce the appearance size of the map Then use the values in X and Y to shift the scaled map to the desired position For details see Scaling a vector graphic in Section 2104 3 Click the colored button in the front of the edit field and select a color for the DXFmap from a Color dialog box The color will be assigned to a DXFgraphics entity if the entitys color is not defined in the DXF file A line map will always use the selected color 4 Check the check box next to the edit field The map will be displayed only when the box is checked 34 PMPATH Output Files 341 Plots To create plot files 1 Select File Save Plot As to display the Save Plot As dialog box Fig 316 2 Select a format from the Format dropdown box The following five formats are available Drawing Interchange Format DXF Hewlett Packard Graphics Lan guage HPGL MODPATH PMPATH and Windows Bitmap BMP If the MODPATH or PMPATH format is chosen coordinates along the path of each particle are recorded in the file specified below The file contains the start ing coordinates of a particle and the coordinates at every point where a particle leaves a cell exit point In addition coordinates of intermediate points are saved whenever a particle tracking step length is reached The saved files can be used by 3D Master 23 or 3D Groundwater Explorer 22 for advanced 3D visualiza tion Refer to Sections 62112 and 62111 for the format of the MODPATH and PMPATH files Fig 316 The Save Plot As dialog box 34 PMPATH Output Files 253 3 Type in the file name in the File edit field directly or rightclick the edit field and select a file from a Plot File dialog box 4 Click OK to save the file Note that cross sectional plots can only be included in the DXF or BMP format PMPATH uses the same color resolution as the video screen to capture and save Windows Bitmap files A DXFfile is saved more compact and can be processed by graphics software more efficiently if the option Use Polyline to save contours is used However some graphics software packages do not support the POLYLINE feature Use this feature only if the users graphics software package accepts the DXF entity POLYLINE 342 Hydraulic Heads Select File Save Heads As to save the hydraulic head values of the current layer at the current stress period and time step in an ASCII Matrix file see Section 621 343 Drawdowns Select File Save Heads As to save the drawdown values of the current layer at the current stress period and time step in an ASCII Matrix file see Section 621 344 Flow Velocities Select File Save Velocity As and specify a file name in a File Save As dialog box to save flow velocities of the current layer at the current stress period and time step in an ASCII Matrix file see Section 621 The file saves average pore velocities at the center of each cell In addition the velocity components along the I J and Kaxes are added to the end of the file The default velocity at inactive cells is 10 1030 345 Particles Select File Save Particles As and specify a file name in a Save Particle As dialog box to save the particle position and attributes in a Particles file see Section 6212 for the format By selecting a Save as type in this dialog box either the starting position or end position after backward or forward tracking of the particles can be saved A Particles file can be loaded by selecting File Load Particles When a particle file is loaded PMPATH just adds the additional particles to the model Already existing particles will not be removed No text present 4 Tutorials The tutorials provide an overview of the modeling process with PM describe the basic skills you need to use PM and take you step by step through hypothetical problems Each tutorial is divided into three parts It starts out with Folder where you can find the readytorun model for example pmdirexamples utorials utorial1 where pmdir is the installation folder of PM Next youll find a discussion of the hypothetical prob lem and the stepbystep tutorial will walk you through the tasks 41 Your First Groundwater Model with PM Folder pmdirexamples utorials utorial1 411 Overview of the Hypothetical Problem It takes just a few minutes to build your first groundwater flow model with PM First create a groundwater model by choosing New Model from the File menu Next de termine the size of the model grid by choosing Mesh Size from the Grid menu Then specify the geometry of the model and set the model parameters such as hydraulic conductivity effective porosity etc Finally perform the flow simulation by selecting Models MODFLOW Run After completing the flow simulation you can use the modeling tools provided by PM to view the results to calculate water budgets of particular zones or graphically display the results such as head contours You can also use PMPATH to calculate and save path lines or use the finite difference transport models MT3DMS or MOC3D to simulate transport processes As shown in Fig 41 an aquifer system with two stratigraphic units is bounded by no flow boundaries on the North and South sides The West and East sides are bounded 256 4 Tutorials by rivers which are in full hydraulic contact with the aquifer and can be considered as fixed head boundaries The hydraulic heads on the west and east boundaries are 9 m and 8 m above reference level respectively The aquifer system is unconfined and isotropic The horizontal hydraulic conduc tivities of the first and second stratigraphic units are 00001 ms and 00005 ms respectively Vertical hydraulic conductivity of both units is assumed to be 10 percent of the horizontal hydraulic conductivity The effective porosity is 25 percent The ele vation of the ground surface top of the first stratigraphic unit is 10m The thickness of the first and the second units is 4 m and 6 m respectively A constant recharge rate of 8109 ms is applied to the aquifer A contaminated area lies in the first unit next to the west boundary The task is to isolate the contaminated area using a fully penetrating pumping well located next to the eastern boundary A numerical model has to be developed for this site to calculate the required pump ing rate of the well The pumping rate must be high enough so that the contaminated area lies within the capture zone of the pumping well We will use PM to construct the numerical model and use PMPATH to compute the capture zone of the pumping well Based on the calculated groundwater flow field we will use MT3DMS to sim ulate the contaminant transport We will show how to use PEST to calibrate the flow model and finally we will create an animation sequence displaying the development of the contaminant plume To demonstrate the use of the transport models we assume that the contaminant is dissolved into groundwater at a rate of 1104 µgsm2 The longitudinal and trans verse dispersivity values of the aquifer are 10 m and 1 m respectively The distribution coefficient for the linear equilibrium sorption is 0000125 The bulk density of the porous medium is 2000 kgm3 The initial concentration molecular diffusion co efficient and decay rate are assumed to be zero We will calculate the concentration distribution after a simulation time of 3 years and display the breakthrough curves concentrationtime series at two points X Y 290 310 390 310 in both units 412 Run a SteadyState Flow Simulation Six main steps must be performed in a steadystate flow simulation 1 Create a new model 2 Assign model data 3 Perform the flow simulation 4 Check simulation results 5 Calculate subregional water budget 6 Produce output 41 Your First Groundwater Model with PM 257 Fig 41 Configuration of the hypothetical model 4121 Step 1 Create a New Model The first step in running a flow simulation is to create a new model To create a new model 1 Select File New Model A New Model dialog box appears Select a folder for saving the model data such as CModels utorial1 and type the file name TU TORIAL1 as the model name A model must always have the file extension PM5 All file names valid under MSWindows with up to 120 characters can be used It is a good idea to save every model in a separate folder where the model and its output data will be kept This will also allow PM to run several models simultane ously multitasking 2 Click OK PM takes a few seconds to create the new model The name of the new model name is shown in the title bar 4122 Step 2 Assign Model Data The second step in running a flow simulation is to generate the model grid mesh specify cell status and assign model parameters to the model grid PM requires the use of consistent units throughout the modeling process For ex ample if you are using length L units of meters and time T units of seconds hy draulic conductivity will be expressed in units of ms pumping rates will be in units of m3s and dispersivities will be in units of m 258 4 Tutorials In MODFLOW an aquifer system is replaced by a discretized domain consisting of an array of nodes and associated finite difference blocks cells Fig 42 shows the spa tial discretization scheme of an aquifer system with a mesh of cells and nodes at which hydraulic heads are calculated The nodal grid forms the framework of the numerical model Hydrostratigraphic units can be represented by one or more model layers The thickness of each model cell and the width of each column and row may be variable PM uses an index notation Layer Row Column for locating the cells For example the cell located in the first layer 6th row and 2nd column is denoted by 1 6 2 In Fig 42 The spatial discretization scheme and cell indices of MODFLOW this example the model domain is discretized in cells of horizontal dimensions of 20 m by 20 m The first stratigraphic layer is represented by the first model layer and the second stratigraphic layer is represented by two model layers It is to note that a higher resolution in the vertical direction is often required in order to correctly simulate the migration of contaminants To generate the model grid 1 Select Grid Mesh Size The Model Dimension dialog box appears Fig 43 2 Enter 3 for the number of layers 10 for model thickness 0 for the model top elevation 30 for the numbers of rows and columns 600 for the model extent in both row and column directions and 10 for the vertical exaggeration 41 Your First Groundwater Model with PM 259 Fig 43 The Model Dimension dialog box PM generates a uniform grid based on the specified dimensions Later the grid may be refined and the layer elevations can be adjusted In this example the first and second stratigraphic units will be represented by one and two model layers respectively Note that the model extent for the J Dimension is 600 m instead of 580 m because MODFLOW counts the distance between the center of the cells of the fixedhead boundaries 3 Click OK PM changes the pulldown menus and displays the generated model grid Fig 44 PM allows you to shift or rotate the model grid change the width of each model column or row or to adddelete model columns or rows For this example you do not need to modify the model grid Refer to Section 21 for more information about the Grid Editor 4 Select File Leave Editor or click the leave editor button The next step is to specify the type of layers and the cell status array of the flow model The cell status array IBOUND array contains a code for each model cell which indi cates whether 1 the hydraulic head is computed referred to as active variablehead cell or active cell 2 the hydraulic head is kept fixed at a given value referred to as fixedhead cell constanthead cell or timevarying specifiedhead cell or 3 no flow takes place within the cell referred to as inactive cell Use 1 for an active cell 1 for a constanthead cell and 0 for an inactive cell For this example the value 1 needs to be assigned to the cells on the west and east boundaries and the value 1 to all other cells 260 4 Tutorials Fig 44 The generated model grid Any outer boundary cell which is not a constanthead cell is automatically a zero flux boundary cell Flux boundaries with nonzero fluxes are simulated by assigning appropriate infiltration or pumping wells in the corresponding active cell via the well package Headdependent boundary conditions are modeled on active cells by means of the general head boundary package or the river package To define the layer properties 1 Select Grid Layer Property A Layer Options dialog box appears 2 Click a cell of the Type column a dropdown button will appear within the cell By clicking the dropdown button a list containing the available layer types Fig 45 will be displayed 3 Select 1 Unconfined for the first layer and 3 ConfinedUnconfined for the other layers then click OK to close the dialog box To assign the cell status to the flow model 1 Select Grid Cell Status IBOUND Modflow The Data Editor of PM appears and displays the model grid Fig 46 A grid cursor is located over the current 41 Your First Groundwater Model with PM 261 cell The value of the current cell is shown at the bottom of the status bar The default value of the IBOUND array is 1 The grid cursor can be moved by using the arrow keys by clicking the mouse on the desired position or by using buttons in the tool bar To jump to another layer click the Layer edit box in the tool bar type the new layer number and then press enter Note A DXFmap is loaded by using the Maps Options dialog box See Section 291 for details 2 Move the grid cursor to the cell 1 1 1 and press the Enter key or the right mouse button to display a Cell Value dialog box 3 Type 1 in the dialog box then click OK The upperleft cell of the model has been specified to be a constanthead cell 4 Now turn on duplication by clicking the duplication button Duplication is on if the duplication button is depressed The current cell value will be duplicated to all cells passed by the grid cursor if it is moved while duplication is on Duplication is turned off by clicking the duplication button again 5 Move the grid cursor from the upperleft cell 1 1 1 to the lowerleft cell 1 30 1 of the model grid The value of 1 has now been duplicated to all cells on the west side of the model 6 Move the grid cursor to the upperright cell 1 1 30 by clicking on this cell 7 Move the grid cursor from the upperright cell 1 1 30 to the lowerright cell 1 30 30 The value of 1 has now been duplicated to all cells on the east side of the model 8 Turn on layer copy by clicking the layer copy button Layer copy is on if the layer copy button is depressed The cell values of the Fig 45 The Layer Options dialog box and the layer type dropdown list 262 4 Tutorials current layer will be copied to other layers if model layer is changed while layer copy is on Layer copy can be turned off by clicking the layer copy button again 9 Move to the second layer and then to the third layer by pressing the PgDn key twice The cell values of the first layer are copied to the second and third layers 10 Select File Leave Editor or click the leave editor button Fig 46 The Data Editor displaying the plan view of the model grid The next step is to specify the geometry of the model To specify the elevation of the top of model layers 1 Select Grid Top of Layers TOP A Top of Layers TOP dialog box appears and asks if the layer bottom elevation should be used for the layer top elevation 2 In the Top of Layers TOP dialog box click No PM displays the model grid 3 Move the grid cursor to the first layer if it is not in the first layer 41 Your First Groundwater Model with PM 263 4 Select Value Reset Matrix or press CtrlR A Reset Matrix dialog box appears 5 Enter 10 in the dialog box then click OK The elevation of the top of the first layer is set to 10 6 Move to the second layer by pressing PgDn 7 Repeat steps 3 and 4 to set the top elevation of the second layer to 6 and the top elevation of the third layer to 3 8 Select File Leave Editor or click the leave editor button To specify the elevation of the bottom of model layers 1 Select Grid Bottom of Layers BOT 2 Repeat the same procedure as described above to set the bottom elevation of the first second and third layers to 6 3 and 0 respectively 3 Select File Leave Editor or click the leave editor button We are going to specify the temporal and spatial parameters of the model The spatial parameters for sample problem include the initial hydraulic head horizontal and ver tical hydraulic conductivities and effective porosity To specify the temporal parameters 1 Select Parameters Time A Time Parameters dialog box appears The temporal parameters include the time unit and the numbers of stress periods time steps and transport steps In MOD FLOW the simulation time is divided into stress periods ie time intervals dur ing which all external excitations or stresses are constant which are in turn divided into time steps Most transport models divide each flow time step further into smaller transport steps The length of stress periods is not relevant to a steady state flow simulation However as we want to perform contaminant transport sim ulation the actual time length must be specified in the table 2 Enter 946728E07 seconds for the Length of the first period 3 Click OK to accept the other default values This implies that a steady state flow simulation will be carried out Now we need to specify the initial hydraulic head for each model cell The initial hy draulic head at a constanthead boundary will be kept the same throughout the flow simulation The other hydraulic head values are used as starting values in a transient simulation or first guesses for the iterative solver in a steadystate simulation Here we firstly set all values to 8 and then correct the values on the west side by overwriting them with a value of 9 264 4 Tutorials To specify the initial hydraulic head 1 Select Parameters Initial Prescribed Hydraulic Heads to display the model grid 2 Move the grid cursor to the first layer 3 Select Value Reset Matrix or press CtrlR and enter 8 in the dialog box then click OK 4 Move the grid cursor to the cell 1 1 1 and press the Enter key or the right mouse button to display a Cell Value dialog box 5 Enter 9 into the Cell Value dialog box then click OK 6 Now turn on duplication by clicking on the duplication button 7 Move the grid cursor from the upperleft cell 1 1 1 to the lowerleft cell 1 30 1 of the model grid The value of 9 is duplicated to all cells on the west side of the model 8 Turn on layer copy by clicking the layer copy button 9 Move to the second layer and the third layer by pressing PgDn twice The cell values of the first layer are copied to the second and third layers 10 Select File Leave Editor or click the leave editor button To specify the horizontal hydraulic conductivity 1 Select Parameters Horizontal Hydraulic Conductivity PM displays the model grid 2 Move the grid cursor to the first layer 3 Select Value Reset Matrix or press CtrlR enter 00001 in the dialog box then click OK 4 Move the grid cursor to the second layer 5 Select Value Reset Matrix or press CtrlR enter 00005 in the dialog box then click OK 6 Move the grid cursor to the third layer 7 Select Value Reset Matrix or press CtrlR enter 00005 in the dialog box then click OK 8 Select File Leave Editor or click the leave editor button To specify the vertical hydraulic conductivity 1 Select Parameters Vertical Hydraulic Conductivity PM displays the model grid 2 Move the grid cursor to the first layer 3 Select Value Reset Matrix or press CtrlR enter 000001 in the dialog box then click OK 41 Your First Groundwater Model with PM 265 4 Move the grid cursor to the second layer 5 Select Value Reset Matrix or press CtrlR enter 000005 in the dialog box then click OK 6 Move the grid cursor to the third layer 7 Select Value Reset Matrix or press CtrlR enter 000005 in the dialog box then click OK 8 Select File Leave Editor or click the leave editor button To specify the effective porosity 1 Select Parameters Effective Porosity PM displays the model grid Since the default value of 025 is the same as the pre scribed value nothing needs to be done here Note that although a flow simulation does not require the effective porosity it is necessary for the computation of travel times and contaminant transport processes 2 Select File Leave Editor or click the leave editor button To specify the recharge rate 1 Select Models MODFLOW Recharge 2 Select Value Reset Matrix or press CtrlR enter 8E9 for Recharge Flux LT in the dialog box then click OK 3 Select File Leave Editor or click the leave editor button The last step before performing the flow simulation is to specify the location of the pumping well and its pumping rate In MODFLOW an injection or a pumping well is represented by a node or a cell The user specifies an injection or a pumping rate for each node It is implicitly assumed that the well penetrates the full thickness of the cell MODFLOW can simulate the effects of pumping from a well that penetrates more than one aquifer or layer provided that the user supplies the pumping rate for each layer The total pumping rate for the multilayer well is equal to the sum of the pumping rates from the individual layers The pumping rate for each layer Qk can be approximately calculated by dividing the total pumping rate Qtotal in proportion to the layer transmissivity McDonald and Harbaugh 1988 Qk Qtotal Tk ΣT 41 where Tk is the transmissivity of layer k and ΣT is the sum of the transmissivities of all layers penetrated by the multilayer well Unfortunately as the first layer is unconfined we do not exactly know the saturated thickness and the transmissivity of this layer at 266 4 Tutorials the position of the well Equation 41 cannot be used unless we assume a saturated thickness for calculating the transmissivity Another possibility to simulate a multi layer well is to set a very large vertical hydraulic conductivity or vertical leakance eg 1 ms to all cells of the well The total pumping rate is assigned to the lowest cell of the well For the display purpose a very small pumping rate say 1 1010m3s can be assigned to other cells of the well In this way the exact extraction rate from each penetrated layer will be calculated by MODFLOW implicitly and the value can be obtained by using the Water Budget Calculator see below Since we do not know the required pumping rate for capturing the contaminated area shown in Fig 41 we will try a total pumping rate of 00012 m3s To specify the pumping well and the pumping rate 1 Select Models MODFLOW Well 2 Move the grid cursor to the cell 1 15 25 and press the Enter key or the right mouse button to display a Cell Value dialog box 3 Type 1E10 in the dialog box then click OK Note that a negative value is used to indicate a pumping well 4 Move the grid cursor to the cell 2 15 25 and press the Enter key or the right mouse button to display a Cell Value dialog box 5 Type 1E10 in the dialog box then click OK 6 Move the grid cursor to the cell 3 15 25 and press the Enter key or the right mouse button to display a Cell Value dialog box 7 Type 00012 in the dialog box then click OK 8 Select File Leave Editor or click the leave editor button 9 Now select Parameters Vertical Hydraulic Conductivity and change the vertical hydraulic conductivity value at the location of the well to 1 in all layers 4123 Step 3 Perform the Flow Simulation Before starting the computation a solver has to be chosen This example uses the de fault solver PCG2 with its default settings For details about the solvers see Section 26113 To perform the flow simulation 1 Select Models MODFLOW Run The Run Modflow dialog box appears Fig 47 2 Click OK to start the flow simulation Prior to running MODFLOW PM will use the userspecified data to generate input files for MODFLOW and optionally MODPATH as listed in the table of the Run 41 Your First Groundwater Model with PM 267 Fig 47 The Run Modflow dialog box Modflow dialog box An input file will be generated only if its generate flag is set to Normally the flags do not need to be changed since PM will take care of the settings automatically If necessary click on the check box to toggle the generate flag between and 4124 Step 4 Check Simulation Results During a flow simulation MODFLOW writes a detailed run record to pathOUT PUTDAT where path is the folder in which the model data are saved When a flow simulation is completed successfully MODFLOW saves the simulation results in var ious unformatted binary files as listed in Table 41 Prior to running MODFLOW the user may control the output of these unformatted binary files by choosing Models MODFLOW Output Control The output file pathINTERBEDDAT will only be generated if the Interbed Storage Package is activated see Chapter 2 for details about the Interbed Storage Package The system of equations of the finite difference model MODFLOW actually con sists of a flow continuity statement for each model cell Since MODFLOW uses iter ative equation solvers the accuracy of the simulation results need to be checked after each simulation run Continuity should exist for the total flows into and out of the en tire model or any subregion of the model This means that the difference between total 268 4 Tutorials Table 41 Output files from MODFLOW File Contents pathOUTPUTDAT Detailed run record and simulation report pathHEADSDAT Hydraulic heads pathDDOWNDAT Drawdowns the difference between the starting heads and the calculated hydraulic heads pathBUDGETDAT CellbyCell flow terms pathINTERBEDDAT Subsidence of the entire aquifer and compaction and precon solidation heads in individual layers pathMT3DFLO Interface file to MT3DMT3DMS This file is created by the LKMT package provided by MT3DMT3DMS Zheng 1990 1998 path is the folder in which the model data are saved Table 42 Volumetric budget for the entire model written by MODFLOW CUMULATIVE VOLUMES L3 RATES FOR THIS TIME STEP L3T IN IN CONSTANT HEAD 2099241410 CONSTANT HEAD 22174E03 WELLS 00000 WELLS 00000 RECHARGE 2541700160 RECHARGE 26848E03 TOTAL IN 4640941560 TOTAL IN 49022E03 OUT OUT CONSTANT HEAD 3504297810 CONSTANT HEAD 37016E03 WELLS 1136040160 WELLS 12000E03 RECHARGE 00000 RECHARGE 00000 TOTAL OUT 4640338130 TOTAL OUT 49016E03 IN OUT 603438 IN OUT 63796E07 PERCENT DISCREPANCY 001 PERCENT DISCREPANCY 001 inflow and total outflow should theoretically equal to 0 for a steadystate flow simu lation or equal to the total change in storage for a transient flow simulation To verify the accuracy of the results MODFLOW calculates a volumetric water budget for the entire model at the end of each time step and saves it in the listing file outputdat see Table 42 The water budget provides an indication of the overall acceptability of the numerical solution If the accuracy is insufficient a new run should be made using a smaller convergence criterion in the iterative solver see Section 26113 It is recom mended to check the listing file by selecting Models MODFLOW View Run Listing File This file contains other further essential information In case of difficulties this supplementary information could be very helpful 41 Your First Groundwater Model with PM 269 4125 Step 5 Calculate subregional water budget There are situations in which it is useful to calculate water budgets for various sub regions of the model To facilitate such calculations flow terms for individual cells are saved in the file pathBUDGETDAT These individual cell flows are referred to as cellbycell flow terms and are of four types 1 cellbycell stress flows or flows into or from an individual cell due to one of the external stresses excitations represented in the model eg pumping well or recharge 2 cellbycell storage terms which give the rate of accumulation or depletion of storage in an individual cell 3 cellbycell constanthead flow terms which give the net flow to or from individual fixedhead cells and 4 internal cellbycell flows which are the flows across individual cell facesthat is between adjacent model cells The Water Budget Calculator uses the cellby cell flow terms to compute water budgets for the entire model userspecified sub regions and flows between adjacent sub regions To calculate subregional water budget 1 Select Tools Water Budget The Water Budget dialog box appears Fig 48 2 Click Subregions PM displays the model grid Click the button if the display mode is not Grid View The water budget of each subregion will be calculated A subregion is in dicated by a number ranging from 0 to 50 A number must be assigned to each model cell The number 0 indicates that a cell is not associated with any subre gion Follow the steps below to assign subregion numbers 1 to the first and 2 to the second layer 3 Move the grid cursor to the first layer 4 Select Value Reset Matrix type 1 in the Reset Matrix dialog box then click OK 5 Move the grid cursor to the second layer by pressing the PgDn key 6 Select Value Reset Matrix type 2 in the Reset Matrix dialog box then click OK 7 Select File Leave Editor or click the leave editor button 8 Click OK in the Water Budget dialog box PM calculates and saves the flows in the file pathWATERBDGDAT as shown in Ta ble 43 The unit of the flows is L3T 1 Flows are calculated for each subregion in each layer and each time step Flows are considered as IN if they are entering a sub region Flows between subregions are given in a Flow Matrix HORIZ EXCHANGE gives the flow rate horizontally across the boundary of a zone EXCHANGE UPPER 270 4 Tutorials gives the flow rate coming from IN or going to OUT to the upper adjacent layer EXCHANGE LOWER gives the flow rate coming from IN or going to OUT to the lower adjacent layer For example the flow rate from the first layer to the second layer 26107365E03 m3s is saved in EXCHANGE LOWER of REGION 1 and LAYER 1 The percent discrepancy in Table 43 is calculated by 100 IN OUT IN OUT2 42 In this example the percent discrepancy of in and outflows for the model and each zone in each layer is acceptably small This means the model equations have been correctly solved To calculate the exact flow rates to the well we repeat the previous procedure for calculating subregional water budgets This time we only assign the cell 1 15 25 to zone 1 the cell 2 15 25 to zone 2 and the cell 3 15 25 to zone 3 All other cells are assigned to zone 0 The water budget is shown in Table 44 The pumping well is abstracting 78003708E05 m3s from the first layer 56002894E04 m3s from the second layer and 55900711E04 m3s from the third layer Almost all wa ter withdrawn comes from the second stratigraphic unit as can be expected from the configuration of the aquifer 4126 Step 6 Produce Output In addition to the water budget PM provides various possibilities for checking sim ulation results and creating graphical outputs The particletracking model PMPATH can display pathlines head and drawdown contours and velocity vectors Using the Results Extractor simulation results of any layer and time step can be read from the unformatted binary result files and saved in ASCII Matrix files An ASCII Matrix Fig 48 The Water Budget dialog box 41 Your First Groundwater Model with PM 271 Table 43 Output from the Water Budget Calculator WATER BUDGET OF SUBREGIONS WITHIN EACH INDIVIDUAL LAYER REGION 1 IN LAYER 1 FLOW TERM IN OUT INOUT STORAGE 00000000E00 00000000E00 00000000E00 CONSTANT HEAD 18595711E04 24354266E04 57585552E05 HORIZ EXCHANGE 00000000E00 00000000E00 00000000E00 EXCHANGE UPPER 00000000E00 00000000E00 00000000E00 EXCHANGE LOWER 00000000E00 26107365E03 26107365E03 WELLS 00000000E00 10000000E10 10000000E10 DRAINS 00000000E00 00000000E00 00000000E00 RECHARGE 26880163E03 00000000E00 26880163E03 SUM OF THE LAYER 28739735E03 28542792E03 19694213E05 DISCREPANCY 069 REGION 2 IN LAYER 2 FLOW TERM IN OUT INOUT STORAGE 00000000E00 00000000E00 00000000E00 CONSTANT HEAD 10105607E03 17374435E03 72688283E04 HORIZ EXCHANGE 00000000E00 00000000E00 00000000E00 EXCHANGE UPPER 26107365E03 00000000E00 26107365E03 EXCHANGE LOWER 00000000E00 19322647E03 19322647E03 WELLS 00000000E00 10000000E10 10000000E10 DRAINS 00000000E00 00000000E00 00000000E00 RECHARGE 00000000E00 00000000E00 00000000E00 SUM OF THE LAYER 36212972E03 36697080E03 48410846E05 DISCREPANCY 133 WATER BUDGET OF THE WHOLE MODEL DOMAIN STORAGE 00000000E00 00000000E00 00000000E00 CONSTANT HEAD 22167889E03 37117251E03 14949362E03 WELLS 00000000E00 12000003E03 12000003E03 DRAINS 00000000E00 00000000E00 00000000E00 RECHARGE 26880163E03 00000000E00 26880163E03 SUM 49048052E03 49117254E03 69201924E06 DISCREPANCY 014 FLOW RATES BETWEEN SUBREGIONS The value of the element ij of the following flow matrix gives the flow rate from the ith region to the jth region Where i is the column index and j is the row index FLOW MATRIX 1 2 3 1 0000 0000 0000 2 26107E03 0000 0000 3 0000 19323E03 0000 272 4 Tutorials Table 44 Output from the Water Budget Calculator for the pumping well FLOWS ARE CONSIDERED IN IF THEY ARE ENTERING A SUBREGION THE UNIT OF THE FLOWS IS Lˆ3T WATER BUDGET OF SUBREGIONS WITHIN EACH INDIVIDUAL LAYER REGION 1 IN LAYER 1 FLOW TERM IN OUT INOUT STORAGE 00000000E00 00000000E00 00000000E00 CONSTANT HEAD 00000000E00 00000000E00 00000000E00 HORIZ EXCHANGE 78003708E05 00000000E00 78003708E05 EXCHANGE UPPER 00000000E00 00000000E00 00000000E00 EXCHANGE LOWER 00000000E00 79934180E05 79934180E05 WELLS 00000000E00 10000000E10 10000000E10 DRAINS 00000000E00 00000000E00 00000000E00 RECHARGE 31999998E06 00000000E00 31999998E06 SUM OF THE LAYER 81203711E05 79934282E05 12694290E06 REGION 2 IN LAYER 2 FLOW TERM IN OUT INOUT STORAGE 00000000E00 00000000E00 00000000E00 CONSTANT HEAD 00000000E00 00000000E00 00000000E00 HORIZ EXCHANGE 56002894E04 00000000E00 56002894E04 EXCHANGE UPPER 79934180E05 00000000E00 79934180E05 EXCHANGE LOWER 00000000E00 63981197E04 63981197E04 WELLS 00000000E00 10000000E10 10000000E10 SUM OF THE LAYER 63996314E04 63981209E04 15104888E07 REGION 3 IN LAYER 3 FLOW TERM IN OUT INOUT STORAGE 00000000E00 00000000E00 00000000E00 CONSTANT HEAD 00000000E00 00000000E00 00000000E00 HORIZ EXCHANGE 55900711E04 00000000E00 55900711E04 EXCHANGE UPPER 63981197E04 00000000E00 63981197E04 EXCHANGE LOWER 00000000E00 00000000E00 00000000E00 WELLS 00000000E00 12000001E03 12000001E03 SUM OF THE LAYER 11988191E03 12000001E03 11809170E06 file contains a value for each model cell in a layer PM can load ASCII matrix files into a model grid The format of the ASCII Matrix file is described in Section 621 PM includes a builtin 2D visualization tool which can be used to display contours of almost all kind of model results including hydraulic heads drawdown concentration and other values We will carry out the following tasks in this step 1 Use the Results Extractor to read and save the calculated hydraulic heads 2 Create a contour map based on the calculated hydraulic heads 3 Use PMPATH to compute pathlines as well as the capture zone of the pumping well To read and save the calculated hydraulic heads 41 Your First Groundwater Model with PM 273 1 Select Tools Results Extractor The Results Extractor dialog box appears Fig 49 The options in the Results Extractor dialog box are grouped under six tabs MODFLOW MOC3D MT3D MT3DMS and RT3D In the MODFLOW tab you may choose a result type from the Result Type drop down box You may specify the layer stress period and time step from which the result should be read The spreadsheet displays a series of columns and rows The intersection of a row and column is a cell Each cell of the spreadsheet corresponds to a model cell in a layer Refer to Section 276 for details about the Results Extractor For the current sample problem follow steps 2 to 6 to save the hydraulic heads of each layer in three ASCII Matrix files 2 Choose Hydraulic Head from the Result Type drop down box 3 Type 1 in the Layer edit field For this example steadystate flow simulation with only one stress period and one time step the stress period and time step number should be 1 4 Click Read Hydraulic heads in the first layer at time step 1 and stress period 1 will be read and put into the spreadsheet You can scroll the spreadsheet by clicking on the scrolling bars next to the spreadsheet 5 Click Save A Save Matrix As dialog box appears By setting the Save as type option the result can be optionally saved as an ASCII matrix or a SURFER data file Specify the file name H1DAT and select a folder in which H1DAT should be saved Click OK when ready Fig 49 The Results Extractor dialog box 274 4 Tutorials 6 Repeat steps 3 4 and 5 to save the hydraulic heads of the second and third layer in the files H2DAT and H3DAT respectively 7 Click Close to close the dialog box To generate contour maps of the calculated heads 1 Select Tools 2D Visualization The Result Selection dialog box Fig 410 appears 2 Click OK to select the default result type Hydraulic Head PM displays the model grid and head contours Fig 411 By default PM sets 10 contour levels ranging from the minimum to the maximum value One can customize the appearance of the contour lines by using the Environment Options dialog box Refer to Section 292 for details about this dialog box 3 To save or print the graphics select File Save Plot As or File Print Plot 4 Select File Leave Editor or click the leave editor button To draw a pathline 1 Select Models PMPATH Pathlines and Contours if PMPATH is not yet started PM calls the advective transport model PMPATH which will load the current model automatically PMPATH uses a grid cursor to define the column and row for which the cross sectional plots should be displayed You can move the grid cursor by holding down the Ctrl key and click the left mouse button on the desired position Note If you subsequently modify and calculate a model within PM you must load the modified model into PMPATH again to ensure that the modifications can be recognized by PMPATH To load a model click and select a model file with the extension PM5 from the Open Model dialog box 2 Click the Set Particle button 3 Rightclick on a point within the model area to set a particle 4 Click to start the backward particle tracking 5 Click to start the forward particle tracking Each time you press one of the buttons or particles may move backward Fig 410 The Result Selection dialog box 41 Your First Groundwater Model with PM 275 Fig 411 Contours of the hydraulic heads in the first layer or forward for a defined time length Refer to Section 332 for the definition of the time length To delineate the capture zone of the pumping well 1 Select Models PMPATH Pathlines and Contours if PMPATH is not yet started 2 Click the Set Particle button 3 Move the mouse pointer to the model area The mouse pointer turns into crosshairs 4 Place the crosshairs at the upperleft corner of the pumping well as shown in Fig 412 5 Hold down the left mouse button and drag the crosshairs until the window covers the pumping well 6 Release the left mouse button An Add New Particles dialog box appears Assign the numbers of particles to the edit fields in the dialog box as shown in Fig 413 Click the Properties tab and click the colored button to select an appropriate color for the new particles When finished click OK 276 4 Tutorials 7 To set particles around the pumping well in the second and third layer press PgDn to move down a layer and repeat steps 4 through 6 Use other colors for the new particles in the second and third layers 8 Click to start the backward particle tracking PMPATH calculates and shows the projections of the pathlines as well as the cap ture zone of the pumping well Fig 414 To see the projection of the path lines on the cross section windows in greater details open an Environment Options dialog box by selecting Options Environment and setting a larger exaggeration value for the vertical scale in the Cross Sections tab Fig 415 shows the same path lines by setting the vertical exaggeration value to 10 Note that some path lines end up at the groundwater surface where recharge occurs This is one of the major differences between a threedimensional and a two dimensional model In twodimensional simulation models such as ASM for Windows 20 FINEM 70 or MOC 73 a vertical velocity term does not exist or always equals to zero This leads to the result that path lines can never be tracked back to the ground surface where the groundwater recharge from the precipitation occurs Note that pathlines can be drawn in 3 dimensions in PMPATH even if you build a 2D model See Section 511 for an example Fig 412 The model loaded in PMPATH 41 Your First Groundwater Model with PM 277 Fig 413 The Add New Particles dialog box PMPATH can create timerelated capture zones of pumping wells The 100days capture zone shown in Fig 416 is created using the settings in the Particle Tracking Time Properties dialog box Fig 417 and clicking To open this dialog box select Options Particle Tracking Time Refer to Section 332 for details about this dialog box Note that the capture zone in the first layer is smaller than those in the other layers due to lower hydraulic conductivity and thus lower flow velocity of the first layer 413 Simulation of Solute Transport Basically the transport of solutes in porous media can be described by three processes advection hydrodynamic dispersion and physical chemical or biochemical reactions The MT3DMS and MOC3D models use the methodofcharacteristics MOC to simu late the advective transport in which dissolved chemicals are represented by a number of particles and the particles are moving with the flowing groundwater Besides the MOC method the MT3DMS model provide several other methods for solving the ad vective term see Section 2623 for details The hydrodynamic dispersion can be expressed in terms of the dispersivity L and the coefficient of molecular diffusion L2T 1 for the solute in the porous medium The types of reactions incorporated into MOC3D are restricted to those that can be represented by a firstorder rate reaction such as radioactive decay or by a retarda tion factor such as instantaneous reversible sorptiondesorption reactions governed 278 4 Tutorials Fig 414 The capture zone of the pumping well vertical exaggeration 1 by a linear isotherm and constant distribution coefficient Kd In addition to the lin ear isotherm MT3DMS supports nonlinear isotherms ie Freundlich and Langmuir isotherms Prior to running MT3DMS or MOC3D you need to define the observation bore holes for which the breakthrough curves will be calculated To define observation boreholes 1 Select Models MT3DMS Concentration Observations or Models MOC3D Concentration Observations A Concentration Observation dialog box appears En ter the coordinates of the observation boreholes into the dialog box as shown in Fig 418 For boreholes 1 and 2 set the proportion value of the first layer to 1 and other layers to 0 This means that these two boreholes are screened at the first layer For boreholes 3 and 4 set the proportion value of the second layer to 1 and other layers to 0 For boreholes 5 and 6 set the proportion value of the third layer to 1 and other layers to 0 2 Click OK to close the dialog box 41 Your First Groundwater Model with PM 279 Fig 415 The capture zone of the pumping well vertical exaggeration 10 4131 Perform Transport Simulation with MT3DMS MT3DMS requires a cell status code for each model cell which indicates whether 1 solute concentration varies with time active concentration cell 2 the concentration is kept fixed at a constant value constantconcentration cell or 3 the cell is an inactive concentration cell Use 1 for an active concentration cell 1 for a constant concentration cell and 0 for an inactive concentration cell Active variablehead cells can be treated as inactive concentration cells to minimize the area needed for transport simulation as long as the solute concentration is insignificant near those cells Similar to the flow model you must specify the initial concentration for each model cell The initial concentration value at a constantconcentration cell will be kept con stant during a transport simulation The other concentration values are used as starting values in a transport simulation To assign the cell status to MT3DMS 1 Select Grid Cell Status ICBUND MT3DMT3DMS For the current example we accept the default value 1 for all cells 2 Select File Leave Editor or click the leave editor button 280 4 Tutorials Fig 416 The 100day capture zone calculated by PMPATH Fig 417 The Particle Tracking Time Properties dialog box 41 Your First Groundwater Model with PM 281 Since MT3DMS is capable of handling multiple species we need to define the number of species involved in the simulation This is done by defining the reaction types and species in the following steps To set reaction definition 1 Select Models MT3DMS Reaction Definition The Reaction Definition dialog box Fig 419 appears 2 In the Reaction Definition dialog box set the Type of Reaction to No kinetic reaction is simulated and activate the first species by checking the Active box of the first row of the table Modify the description of the species as needed 3 Click OK to close the dialog box To set the initial concentration 1 Select Models MT3DMS Initial Concentration For the current example we accept the default value 0 for all cells 2 Select File Leave Editor or click the leave editor button To assign the input rate of contaminants Fig 418 The Concentration Observation dialog box 282 4 Tutorials Fig 419 The Reaction Definition dialog box 1 Select Models MT3DMS SinkSource Concentration Recharge 2 Assign 12500 µgm3 to the cells within the contaminated area This value is the concentration associated with the recharge flux Since the recharge rate is 8 109 m3m2s and the dissolution rate is 1 104 µgsm2 the concentration associated with the recharge flux is 1 1048 109 12500 µgm3 3 Select File Leave Editor or click the leave editor button To assign the transport parameters to the Advection Package 1 Select Models MT3DMS Advection The Advection Package MT3DMS dialog box appears Enter the values shown in Fig 420 into the dialog box select Method of Characteristics MOC for the solution scheme and Firstorder Euler for the particletracking algorithm 2 Click OK to close the dialog box To assign the dispersion parameters 1 Select Models MT3DMS Dispersion The Dispersion Package MT3D dialog box appears Enter the ratios of the trans verse dispersivity to longitudinal dispersivity as shown in Fig 421 41 Your First Groundwater Model with PM 283 2 Click OK PM displays the model grid At this point you need to specify the lon gitudinal dispersivity to each cell of the grid 3 Click the button if the display mode is not Grid View 4 Select Value Reset Matrix or press CtrlR type 10 in the dialog box and select the option Apply to the entire model then click OK to assign the value of 10 to all model cells 5 Select File Leave Editor or click the leave editor button To assign the chemical reaction parameters 1 Select Models MT3DMS Chemical Reaction A Chemical Reaction Data MT3DMS dialog box appears 2 In the Chemical Reaction Data MT3DMS dialog box select the first species which is only one species in this example and click Edit to start the Data Editor 3 Select Value Reset Matrix or press CtrlR A Reset Matrix dialog box appears Fig 422 Set the Type of Sorption to Lin ear equilibrium isotherm and type 0000125 for the distribution coefficient then Click OK to assign the value to the first layer 4 Turn on layer copy by clicking the layer copy button 5 Move to the second layer and the third layer by pressing PgDn twice The cell values of the first layer are copied to the second and third layers 6 Select File Leave Editor or click the leave editor button Fig 420 The Advection Package MT3DMS dialog box 284 4 Tutorials Fig 421 The Dispersion Package MT3DMT3DMSRT3D dialog box 7 The Chemical Reaction Data MT3DMS dialog box appears again Click Close to close this dialog box Fig 422 The Reset Matrix dialog box for chemical reaction data of MT3DMS The last step before running the transport model is to specify the output times at which the calculated concentration should be saved To specify the output times 41 Your First Groundwater Model with PM 285 Fig 423 The Output Control MT3D Family dialog box 1 Select Models MT3DMS Output Control The Output Control MT3D Family dialog box appears Fig 423 The options in this dialog box are grouped under three tabs Output Terms Output Times and Misc 2 Click the Output Times tab then click the header Output Time of the empty table An Output Times dialog box appears Enter 3000000 to Interval Click OK to accept the other default values 3 Click OK to close the Output Control MT3D Family dialog box To perform the transport simulation 1 Select Models MT3DMS Run The Run MT3DMS dialog box appears Fig 424 2 Click OK to start the transport computation Prior to running MT3DMS PM will use userspecified data to generate input files for MT3DMS as listed in the table of the Run MT3DMS dialog box An input file will be generated only if the corre sponding Generate box is checked You can click on the box to check or uncheck Normally we do not need to worry about these boxes since PM will take care of the settings Check simulation results and produce output 286 4 Tutorials Fig 424 The Run MT3DMS dialog box During a transport simulation MT3DMS saves a detailed run record pathOUT PUTMTM where path is the folder in which the model data is saved In addition MT3DMS saves the simulation results in various files The output options are con trolled by selecting Models MT3DMS Output Control To check the quality of the simulation results MT3DMS calculates a mass budget at the end of each transport step and accumulated to provide summarized information on the total mass into or out of the groundwater flow system The discrepancy between the in and outflows of mass serves as an indicator of the accuracy of the simulation results It is highly recommended to check the record file or at least take a glance at it Follow the steps below to generate contour maps of the calculated concentration values at the end of the simulation To generate contour maps of the calculated concentration values 1 Select Tools 2D Visualization A Result Selection dialog box appears 2 Select the MT3DMS tab in the Result Selection dialog box 3 Click OK to accept the default result type Solute Concentration and species 1 PM displays the model grid sets the Simulation Time on the toolbar to the be ginning of the simulation and automatically loads the results pertained to the Sim ulation Time Contours are not visible at this stage since the initial concentration values are zero over the entire model domain 41 Your First Groundwater Model with PM 287 4 Click the Simulation Time dropdown list and set the simulation time to 9467E07 the end of the simulation By default PM sets 10 contour levels ranging from the minimum to the maximum concentration values of the selected simulation time Fig 425 One can customize the contour levels and the appearance of the contours by using the Environment Options dialog box Refer to Section 292 for details about this dialog box 5 To save or print the graphics select File Save Plot As or File Print Plot 6 Select File Leave Editor or click the leave editor button Follow the steps below to generate the concentrationtime series curves at the obser vation boreholes To generate the concentrationtime series curves at the observation boreholes 1 Select Models MT3DMS View ConcentrationTime Curves A Species dialog box appears 2 In the Species dialog box select the first species and click OK PM displays the Time Series Curves Concentration dialog box Fig 426 This dialog box has two tabs The Data tab displays the calculated and measurement data if any The Chart tab displays the timeseries curves Refer to Section 26120 for details about these tabs Fig 425 Contours of the concentration values at the end of the simulation 288 4 Tutorials Fig 426 The Time Series Curves Concentration dialog box 3 Click the Chart tab to display the curves Fig 427 4 Use the button Save Plot As to save the chart to a file or use Copy to Clipboard to copy the chart to the Windows Clipboard An image in the clipboard can be pasted into most word or graphicsprocessing software by using CtrlV 5 Click OK to close the Time Series Curves Concentration dialog box 4132 Perform Transport Simulation with MOC3D In MOC3D transport may be simulated within a subgrid which is a window within the primary model grid used to simulate flow Within the subgrid the row and column spacing must be uniform but the thickness can vary from cell to cell and layer to layer However the range in thickness values or product of thickness and effective porosity should be as small as possible The initial concentration must be specified throughout the subgrid within which solute transport occurs MOC3D assumes that the concentration outside of the subgrid is the same within each layer so only one value is specified for each layer within and adjacent to the subgrid The use of constantconcentration boundary condition has not been implemented in MOC3D To set the initial concentration 1 Select Models MOC3D Initial Concentration For the current example we accept the default value 0 for all cells 41 Your First Groundwater Model with PM 289 Fig 427 The Chart tab of the Time Series Curves Concentration dialog box 2 Select File Leave Editor or click the leave editor button To define the transport subgrid and the concentration outside of the subgrid 1 Select Models MOC3D Subgrid The Subgrid for Transport MOC3D dialog box appears Fig 428 The options in the dialog box are grouped under two tabs Subgrid and C Outside of Subgrid The default size of the subgrid is the same as the model grid used to simulate flow The default initial concentration outside of the subgrid is zero 2 Click OK to accept the default values and close the dialog box To assign the input rate of contaminants 1 Select Models MOC3D SinkSource Concentration Recharge 2 Assign 12500 µgm3 to the cells within the contaminated area This value is the concentration associated with the recharge flux Since the recharge rate is 8 109 m3m2s and the dissolution rate is 1 104 µgsm2 the concentration associated with the recharge flux is 1 1048 109 12500 µgm3 3 Select File Leave Editor or click the leave editor button To assign the parameters for the advective transport 290 4 Tutorials 1 Select Models MOC3D Advection to display a Parameters for Advection Trans port MOC3D dialog box 2 Enter the values as shown in Fig 429 into the dialog box 3 Select Bilinear X Y directions for the interpolation scheme for particle velocity As given by Konikow and others 74 if transmissivity within a layer is homoge neous or smoothly varying bilinear interpolation of velocity yields more realistic pathlines for a given discretization than does linear interpolation 4 Click OK to close the dialog box To assign the parameters for dispersion and chemical reaction 1 Select Models MOC3D Chemical Reaction to display a Dispersion Chemical Reaction MOC3D dialog box Check Simulate Dispersion and enter the values Fig 428 The Subgrid for Transport MOC3D dialog box Fig 429 The Parameters for Advective Transport MOC3D dialog box 41 Your First Groundwater Model with PM 291 Fig 430 The Dispersion Chemical Reaction MOC3D dialog box as shown in Fig 430 The retardation factor R 2 is calculated as follows R 1 ρb ne Kd 1 2000 025 0000125 2 43 Note that the parameters for dispersion and chemical reaction are the same for each layer 2 Click OK to close the dialog box To set StrongWeak Flag 1 Select Models MOC3D StrongWeak Flag 2 Move the grid cursor to the cell 1 15 25 3 Press the right mouse button once to open a Cell Value dialog box type 1 into the dialog box then click OK Note that a strong sink or source is indicated by the cell value of 1 When a fluid source is strong new particles are added to replace old particles as they are advected out of that cell Where a fluid sink is strong particles are removed after they enter that cell 4 Repeat steps 2 and 3 to assign the value 1 to the cells 2 15 25 and 3 15 25 5 Select File Leave Editor or click the leave editor button To specify the output terms and times 1 Select Models MOC3D Output Control An Output Control MOC3D dialog box appears The options in the dialog box are grouped under five tabs Concentration Velocity Particle Locations Disp Coeff and Misc 292 4 Tutorials Fig 431 The Output Control MOC3D dialog box 2 In the Concentration tab select the option These data will be printed or saved every Nth particle moves and enter N 20 3 Click OK to accept all other default values and close the Output Control MOC3D dialog box Fig 431 To perform the transport simulation 1 Select Models MOC3D Run The Run MOC3D dialog box appears Fig 432 2 Click OK to start the transport computation Prior to running MOC3D PM uses userspecified data to generate input files for MOC3D as listed in the table of the Run MOC3D dialog box An input file will be generated only if the corresponding Generate box is checked You can click on the box to check or uncheck Normally we do not need to worry about these boxes since PM will take care of the settings Check simulation results and produce output During a transport simulation MOC3D writes a detailed run record to the file pathMOC3DLST where path is the folder in which your model data are saved MOC3D saves the simu lation results in various files which can be controlled by selecting Models MOC3D Output Control To check the quality of the simulation results MOC3D calculates mass balance and saves the results in the run record file The mass in storage at any time is calculated from the concentrations at the nodes of the transport subgrid to provide summarized information on the total mass into or out of the groundwater flow system The mass 41 Your First Groundwater Model with PM 293 Fig 432 The Run Moc3d dialog box balance error will typically exhibit an oscillatory behavior over time because of the nature of the method of characteristics and the finitedifference approximation The oscillations reflect the fact that the mass balance calculation is itself just an approxi mation Follow the steps below to generate contour maps of the calculated concentration values at the end of the simulation To generate contour maps of the calculated concentration values 1 Select Tools 2D Visualization A Result Selection dialog box appears 2 Select the MOC3D tab in the Result Selection dialog box 3 Click OK to accept the default result type Solute Concentration PM displays the model grid sets the Simulation Time on the toolbar to the be ginning of the simulation and automatically loads the results pertained to the Sim ulation Time Contours are not visible at this stage since the initial concentration values are zero over the entire model domain 4 Click the Simulation Time dropdown list and set the simulation time to 9467E07 the end of the simulation By default PM sets 10 contour levels ranging from the minimum to the maximum concentration values of the selected simulation time Fig 433 One can customize the contour levels and the appearance of the 294 4 Tutorials contours by using the Environment Options dialog box Refer to Section 292 for details about this dialog box 5 To save or print the graphics select File Save Plot As or File Print Plot 6 Select File Leave Editor or click the leave editor button Follow the steps below to generate the concentrationtime series curves at the obser vation boreholes To generate the concentrationtime series curves at the observation boreholes 1 Select Models MOC3D View ConcentrationTime Curves pmp displays the Time Series Curves Concentration dialog box Fig 434 This dialog box has two tabs The Data tab displays the calculated and measurement data if any The Chart tab displays the timeseries curves Refer to Section 26120 for details about these tabs 2 Click the Chart tab to display the curves Fig 435 3 Use the button Save Plot As to save the chart to a file or use Copy to Clipboard to copy the chart to the Windows Clipboard An image in the clipboard can be pasted into most word or graphicsprocessing software by using CtrlV 4 Click OK to close the Time Series Curves Concentration dialog box Fig 433 Contours of the concentration values at the end of the simulation 41 Your First Groundwater Model with PM 295 414 Parameter Estimation The process of estimating unknown parameters is one of the most difficult and critical steps in the model application The parameter estimation often referred to as model calibration of a flow model is accomplished by finding a set of parameters hydrologic stresses or boundary conditions so that the simulated values match the measurement values to a reasonable degree Hill 62 gives methods and guidelines for model cali bration using inverse modeling To demonstrate the use of the parameter estimation program PEST within PM we assume that the hydraulic conductivity in the third layer is homogeneous but its value is unknown We want to find out this value through a model calibration by using the measured hydraulic heads at the observation boreholes listed in Table 45 Three steps are required for the parameter estimation 1 Define the region of each parameter Parameter estimation requires a subdivision of the model domain into a small num ber of reasonable regions A region is defined by using the Data Editor to assign a parameter number to the model cells 2 Specify the coordinates of the observation boreholes and the measured hydraulic head values 3 Specify the starting values upper and lower bounds for each parameter To define the region of horizontal hydraulic conductivity Fig 434 The Time Series Curves Concentration dialog box 296 4 Tutorials Fig 435 The Chart tab of the Time Series Curves Concentration dialog box 1 Select Parameters Horizontal Hydraulic Conductivity 2 Click the button if the display mode is not Grid View 3 Move to the third layer 4 Select Value Reset Matrix or press CtrlR A Reset Matrix dialog box appears 5 Enter 1 to the Parameter Number edit box then click OK The horizontal hydraulic conductivity of the third layer is set to the parameter 1 6 Select File Leave Editor or click the leave editor button To specify the coordinates of the observation boreholes and measured values 1 Select Head Observations from the MODFLOW MODFLOW2000 Parameter Estimation or PEST Parameter Estimation menu The Head Observation dialog box appears Fig 436 Table 45 Measured hydraulic head values for parameter estimation Borehole XCoordinate YCoordinate Layer Observation Time Hydraulic Head h1 130 200 3 946728E07 885 h2 200 400 3 946728E07 874 h3 480 250 3 946728E07 818 h4 460 450 3 946728E07 826 41 Your First Groundwater Model with PM 297 Fig 436 The Head Observation dialog box 2 Enter the coordinates of the observation boreholes into the Observation Borehole table as shown in Fig 436 3 For all boreholes set the proportion value of the third layer to 1 and other layers to 0 This means that all boreholes are screened in the third layer 4 In the Head Observatiions group enter the observation time and hydraulic head of each borehole to Time and HOBS Set the value for Weight to 1 5 Click OK to close the dialog box 4141 Parameter Estimation with PEST To specify the starting values for each parameter 1 Select Models PEST Parameter List The List of Parameters PEST dialog box Fig 437 appears The options of the dialog box are grouped under five tabs Parameters Group Definitions Prior Information Control Data and Options 2 In the Parameters tab enter values as shown in Fig 437 PARVAL is the initial guess of the parameter Minimum is the lower bound and Maximum is the upper bound of the parameter 3 Click OK to close the dialog box 298 4 Tutorials To perform Parameter Estimation with PEST 1 Select Models PEST Run The Run PEST dialog box appears Fig 438 2 Click OK to start PEST Prior to running PEST PM uses userspecified data to generate input files for PEST and MODFLOW as listed in the table of the Run PEST dialog box An input file will be generated only if the corresponding Generate box is checked You can click on the box to check or uncheck Normally we do not need to worry about these boxes since PM will take care of the settings Check the Parameter Estimation Results Several result files are created through the parameter estimation process During a parameter estimation process PEST prints the estimated parameter values to the run record file PESTCTLREC in the model folder and writes the estimated parameter val ues to the corresponding input files of MODFLOW BCFDAT WELDAT etc So after a parameter process the simulation results of MODFLOW are updated by using the most recently estimated parameter values PEST does not modify the orig inal model data This provides a greater security to the model data since a parameter estimation process does not necessarily lead to a success Follow the steps below if you want to operate on the estimated parameters Fig 437 The List of Parameters PEST dialog box 41 Your First Groundwater Model with PM 299 Fig 438 The Run PEST dialog box To operate on the estimated parameters 1 Select Models PEST Parameter List to open the List of Parameters PEST dialog box 2 Click the Update button to retrieve the estimated parameter values into the param eter list 3 Click the Options tab and set the Run Mode to Perform Forward Model Run using PARVAL values given in the Parameters tab 4 Click OK to close the List of Parameters PEST dialog box 5 Select Models PEST Run to run PEST in the forward model run mode Alternatively you can create a new model with the estimated parameters by using the Convert Models dialog box see Section 233 for details You can create a scatter diagram to present the parameter estimation result The observed head values are plotted on one axis against the corresponding calculated val ues on the other If there is an exact agreement between measurement and simulation all points lie on a 45 line The narrower the area of scatter around this line the better is the match To create a scatter diagram for head values 1 Select Models PEST View Head Scatter Diagram The Scatter Diagram Hydraulic Head dialog box appears Fig 439 This dialog 300 4 Tutorials Fig 439 The Scatter Diagram dialog box box has two tabs The Data tab displays the calculated and observed values The Chart tab displays the scatter diagram Refer to Section 26120 for details about these tabs 2 Click the Chart tab to display the scatter diagram Fig 440 3 Use the button Save Plot As to save the chart to a file or use Copy to Clipboard to copy the chart to the Windows Clipboard An image in the clipboard can be pasted into most word or graphicsprocessing software by using CtrlV 4 Click OK to close the Scatter Diagram Hydraulic Head dialog box 415 Animation You already learned how to use the 2D Visualization tool to create and print con tour maps of calculated head and concentration values The saved or printed im ages are static and ideal for paperbased reports or slidebased presentations In many cases however these static images cannot ideally illustrate the motion of concentra tion plumes or temporal variation of hydraulic heads or drawdowns PM provides an animation technique to display a sequence of the saved images in rapid succession Al though the animation process requires relatively large amount of computer resources to read process and display the data the effect of a motion picture is often very helpful The 2D Visualization tool is used to create animation sequences The following steps show how to use the Environment Options and Animation dialog boxes to create 41 Your First Groundwater Model with PM 301 Fig 440 The Chart tab of the Scatter Diagram dialog box an animation sequence for displaying the motion of the concentration plume in the third layer To create an animation sequence 1 Select Tools 2D Visualization 2 Select the MT3DMS tab in the Result Selection dialog box 3 Click OK to accept the default result type Solute Concentration and species 1 PM displays the model grid sets the Simulation Time on the toolbar to the be ginning of the simulation and automatically loads the results pertained to the Sim ulation Time 4 Click the Simulation Time dropdown list and set the simulation time to 9467E07 the end of the simulation By default PM sets 10 contour levels ranging from the minimum to the maximum concentration values of the selected simulation time Fig 425 One can customize the contour levels and the appearance of the contours by using the Environment Options dialog box 5 Click the button if the display mode is not Grid View 6 Move to the third layer 7 Select Options Environment 8 Click the Contours tab clear Display contour lines and check Visible and Fill Colors 302 4 Tutorials 9 Click the table header Level A Contour Levels dialog box appears Set the value for Minimum to 100 Maximum to 1600 and Interval to 100 When finished click OK to close the dialog box 10 Click the table header Fill A Color Spectrum dialog box appears Set an appropriate color range by clicking the Minimum color and Maximum color buttons When finished click OK to close the dialog box 11 Click OK to close the Environment Options dialog box 12 Select File Animation The Animation dialog box appears Fig 441 13 Click the button to display a Save File dialog box 14 Select an existing file or specify a new base file name without extension in the or specify a file name in Save File dialog box then click Open 15 In the Animation dialog box click OK to start the animation PM will create a frame image for each time point at which the simulation re sults here concentration are saved Each frame is saved in filenamennn where filename is the base file name specified in previous step and nnn is the serial num ber of the frame Note that if you have complex DXFbase maps the process will be slowed down considerably When all frames are created PM will repeat the animation indefinitely until the Esc key is pressed Once a sequence is created you can playback the animation at a later time by repeating steps 8 to 11 with the Create New Frames box cleared in step 10 Note Since the number and the size of the image files can be very large make sure that there is enough free space on your hard disk To reduce the file size you can change the size of the PM window before creating the frames You may also wish to turn off the display of the model grid in the Environment Options dialog box so that you dont have the grid cluttering the animation Fig 441 The Animation dialog box 42 Unconfined Aquifer System with Recharge 303 42 Unconfined Aquifer System with Recharge Folder pmdirexamples utorials utorial2 421 Overview of the Hypothetical Problem The model assumes a simple scenario which is designed to demonstrate the basic features of PMWIN and MODFLOW An unconfined aquifer Fig 442 is a coarse grained sand with a measured isotropic hydraulic conductivity of 160 mday the spe cific yield has been assessed as 006 Recharge to the aquifer only occurs throughout the 4 month wet season at a rate of 75 104mday outside the wet season there is no recharge to the aquifer The elevations of the aquifer top and bottom are 25 m and 0 m respectively The area of interest is 10000 m long and 6000 m wide and is bounded by no flow zones to the east and west There is also a volcanic mountain in the southeast corner of the model area To the north an area of constant hydraulic head existed with a value of 15 m The southern boundary is a specified flux boundary with an inflow rate of 00672 m3day per meter A total of nine wells in the area are pumped at 45 ls 3888 m3d each during the 8month dry season to supply water for irrigation and domestic purposes The task is to assess the water levels in the aquifer under the following conditions 1 Steadystate with the mean recharge rate 25 104mday no pumping 2 After 8 months pumping during the dry season and 3 The water levels by the end of the followed 4month wet season 422 Steadystate Flow Simulation Seven main steps need to be done in this tutorial 1 Create a new model 2 Generate the model grid 3 Refine the model grid 4 Assign the model data 5 Perform steadystate flow simulation 6 Extract and view results 7 Produce output from the steadystate simulation 4221 Step1 Create a New Model The first step in running a flow simulation is to create a new model To create a new model 304 4 Tutorials 1 Select File New Model A New Model dialog box appears Select a folder for saving the model data such as CModels utorial2 and type the file name TU TORIAL2 as the model name A model must always have the file extension PM5 All file names valid under MSWindows with up to 120 characters can be used It is a good idea to save every model in a separate folder where the model and its output data will be kept This will also allow PM to run several models simultane ously multitasking 2 Click OK PM takes a few seconds to create the new model The name of the new model name is shown in the title bar 4222 Step2 Generate the Model Grid To generate the model grid Fig 442 Configuration of the hypothetical model 42 Unconfined Aquifer System with Recharge 305 1 Select Grid Mesh Size A Model Grid and Coordinate System dialog box appears 2 Enter the values as shown in Fig 443 to the dialog box 3 Click OK to close the dialog box Fig 443 The Model Grid and Coordinate System dialog box You are now in the Grid Editor of PM To help visualize the model site we can overlay a DXF file as a site map which gives us the locations of the boundaries and the pump ing wells To load a map 1 Select Options Map to open the Map Options dialog box 2 Rightclick on the first DXF File field to bring up the Map Files dialog box and then select the file BASEMAPDXF from the folder examples utorials utorial2 3 Check the box at the front of the DXF File field The map will be displayed only if the box is checked 4 Click OK to close the Map Options dialog box 5 Select File Leave Editor or click the leave editor button 306 4 Tutorials 4223 Step 3 Refine the Model Grid It is a good practice to use a smaller grid in areas where the hydraulic gradient is expected to be large which are normally located around the wells In PM grid refine ment takes place within the Grid Editor and it is quite easy to add additional rows and columns to an existing model grid This is done by using a combination of holding down the CTRL key and using the arrow keys as follows CTRL Up arrow add a row CTRL Down arrow remove an added row CTRL Right arrow add a column CTRL Left arrow remove an added column It is also possible to specify the row and column spacing of individual cells by clicking the right mouse button within the cell of interest however we will not be doing that in this exercise To refine the model grid around the pumping wells 1 Select Grid Mesh Size to open the Grid Editor 2 Zoom in around Well 1 by clicking on the button and then dragging a box around the area of Well 1 3 Click the button and click on the cell containing Well 1 4 Divide this column into three by adding two additional columns with CTRL Right arrow followed by CTRL Right arrow 5 Divide the row also into three by adding two additional rows with CTRL Up arrow followed by CTRL Up arrow You should see dashed lines where the new rows and columns will be placed 6 Zoom out by pressing the button You will notice that the rows and columns added extend throughout the model domain and form part of the fine discretization around some of the other wells 7 Repeat the above refinement around Well 2 to Well 9 remember some of the dis cretization has already been done when you added rows and columns around Well 1 8 At this stage the model cells change from a size of 167 m to 500 m abruptly In order to have a more gradual size change we need to half the size of the following rows and columns again using the CTRL key and the arrow keys Columns 3 and 11 Rows 7 9 10 12 17 and 19 Upon completion of the refinement your grid should look like that in Fig 444 42 Unconfined Aquifer System with Recharge 307 9 Select File Leave Editor or click the leave editor button 4224 Step 4 Assign Model Data The Data Editor is accessed each time when spatial data such as recharge hydraulic conductivity etc need to be input to the model The format and commands of the Data Editor are the same for each parameter and once you become familiar with the commands and menus it is very easy to enter and change the model data The values of the particular data being edited or entered and the selected cell are displayed in the status bar on the bottom of the screen The model data for task 1 steadystate water level with recharge no pumping includes layer properties model boundaries aquifer geometry aquifer parameters ini Fig 444 Model grid after the refinement 308 4 Tutorials tial conditions time parameters and recharge rates To define the layer properties 1 Select Grid Layer Property A Layer Options dialog box appears 2 In the Layer Options dialog box click on Type and select Unconfined it is okay to browse through the rest of this dialog box but leave all the values as the default ones 3 Click OK to close the Layer Options dialog box To define the model boundaries 1 Select Grid Cell Status IBOUND Modflow MODFLOW uses a cell status array called the IBOUND array to determine if a particular cell is active inactive no flow or a constant head cell Cell values within IBOUND are as follows active 1 or other positive integers inactive 0 fixedhead 1 or other negative integers These values are assigned to cells as required in the Data Editor By default and convention the area outside the model domain is deemed to be a no flow zone and as such it is not necessary to set this area to inactive 2 Click the button if the display mode is not Grid View 3 Make sure the cell selected is 1 1 1 and press Enter or rightclick to open the Cell Value dialog box Since this is going to be a constant head boundary enter 1 and click OK to exit the dialog box The cell should now have a blue color signifying that it has been set as constant head To save doing this for the remaining constant head cells it is possible to copy the value in this case 1 to any other cell 4 Click on the Duplication button duplication is activated if the button is de pressed 5 Simply leftclick in any cell that you want to specify as a constant head cell If you make a mistake turn off Duplication by clicking the duplication button and right click in the cell where you have made a mistake and replace it with the desired value 6 Complete specification of the entire North boundary as constant head cells We will assign a head value to these cells a little later The outer grid boundaries are assigned as No Flow by default However the mountain area in the south corner of the domain which is impervious and still falls inside the model grid needs to be explicitly assigned as No Flow ie IBOUND0 42 Unconfined Aquifer System with Recharge 309 To specify the noflow zone 1 Ensure Duplication is off and then click in a cell within the No Flow zone 2 Press Enter or Rightclick the cell to open the Cell Value dialog box 3 Enter 0 as the value for IBOUND and click OK to exit the dialog box You will notice that the cell is now gray in color 4 Either repeat the above 3 steps for the remaining no flow cells or turn on the Duplication and copy the value of IBOUND 0 to the other cells In some cases you will notice that the boundary cuts through part of a cell In these cases you need to make a judgment as to whether the cell should remain active IBOUND1 or be specified as inactive IBOUND0 Generally you should choose the option which applies to more than 50 of the cell area If all the steps were completed correctly the grid should now look similar to that in Fig 445 5 Select File Leave Editor or click the leave editor button The next step in the modeling process is to specify the top and bottom elevations of the model layer To specify the elevation of the top of the model layer 1 Select Grid Top of Layers TOP 2 Since the aquifer top elevation is uniform throughout the model it is possible to set a single value to the entire grid by selecting Value Reset Matrix 3 Enter 25 in the Reset Matrix dialog box and click OK to exit 4 Select File Leave Editor or click the leave editor button Repeat the above process to set the elevation of the base of the aquifer to 0 m Although the default value in this model is zero we still have to enter the editor to let the model know that the parameter has been specified To specify the horizontal hydraulic conductivity 1 Select Parameters Horizontal Hydraulic Conductivity 2 Since the horizontal hydraulic conductivity is uniform throughout the model it is possible to set a single value to the entire grid by selecting Value Reset Matrix 3 Enter 160 in the Reset Matrix dialog box and click OK to exit 4 Select File Leave Editor or click the leave editor button MODFLOW requires initial hydraulic head conditions to enable it to perform the flow simulation The hydraulic head values of the constant head cells are important as these do not change throughout the simulation The values in the other cells serve as initial guesses for the iterative solvers In a transient simulation the hydraulic heads at the start of the simulation are the basis for determining the resulting head distribution after 310 4 Tutorials the aquifer is subject to some timedependent stresses It is usual to perform a steady state flow simulation first and use the resulting head distribution as the basis for the transient simulations which is what we shall do in this case To set the initial hydraulic heads 1 Select Parameters Initial Prescribed Hydraulic Heads 2 First set the entire grid to a uniform value by selecting Value Reset Matrix 3 Enter 16 in the Reset Matrix dialog box and click OK to exit 4 Now set hydraulic head of the northern constant head boundary to 15 meters by first selecting the top left cell 1 1 1 with the left mouse button and then assigning a value of 15 by pressing Enter or rightclicking and entering 15 in the Cell Value dialog box Fig 445 Model Boundaries 42 Unconfined Aquifer System with Recharge 311 5 Copy the value of 15 to the remainder of the northern boundary using the Dupli cation button and the left mouse button 6 Select File Leave Editor or click the leave editor button To specify the time parameters 1 Select Parameters Time 2 In the Time Parameters dialog box change the Simulation Time Unit to DAYS and check that Steady State is selected in the Simulation Flow Type box 3 Click OK to leave the Time Parameters dialog box To specify the recharge rate 1 Select Models MODFLOW Recharge 2 Set the entire grid to a uniform value by selecting Value Reset Matrix 3 In the Reset Matrix dialog box enter Recharge Flux LT 1 000025 this is the mean recharge rate of the two seasons Layer Indicator IRCH 0 Recharge Options Recharge is applied to the highest active cell 4 Click OK to exit the dialog box 5 Select File Leave Editor or click the leave editor button To specify the boundary flux 1 Select Models MODFLOW Well Since MODFLOW does not have a separate package for a specified flux boundary condition we use the Well package to simulate this boundary condition 2 Make sure the cell selected is 1 36 1 Since the width of this cell is 500 m the inflow rate through this cell is 500m 00672m3daym 336m3day Press Enter or rightclick to open the Cell Value dialog box enter 336 then click OK to exit the dialog box A positive value means that water enters the system 3 Specify the value 336 to the cell 1 36 2 the value 168 to the cells 1 36 3 and 1 36 4 and the value 112 to the rest of the South boundary 4 Select File Leave Editor or click the leave editor button 4225 Step 5 Perform steadystate flow simulation You are just about ready to run the flow model Quickly review the data that you have entered for each of the parameters by checking the values of various cells Correct any data that does not look right by redoing the appropriate sections above To run the flow simulation 312 4 Tutorials 1 Select Models Modflow Run 2 Click OK to accept the warning regarding the Effective Porosity 3 Click OK in the Run Modflow dialog box to generate the required data files and to run MODFLOW you will see a DOS window open and MODFLOW perform the iterations required to complete the flow simulation 4 Press any key to exit the DOS Window 4226 Step 6 Extract and view results It is now time to view the results of your efforts but first it is necessary to understand how the Results Extractor operates On occasions it is necessary to view some of the various sorts of output such as hydraulic heads and cellbycell flows generated by a MODFLOW simulation This layerwise data is accessed using 2D Visualization tool It is quite a simple procedure to load and save any of the output generated by MOD FLOW To generate contour maps of the calculated heads 1 Select Tools 2D Visualization to display a Result Selection dialog box 2 Click OK to select the default result type Hydraulic Head PM displays the model grid and head contours By default PM sets 10 contour levels ranging from the minimum to the maximum value You can customize the appearance of the contour lines by using the Environment Options dialog box 3 Select Options Environment to open the Environment Options dialog box to cus tomize the appearance of the contours Click the Contours tab and make sure the Visible box is checked Click on the header Level of the table to change the contour minimum to 125 maximum to 19 and the contour interval to 05 It is also possible to change contour color if you desire If Fill Contours is checked the contours will be filled with the colors given in the Fill column of the table Use the Label Format button to specify an appropriate format 4 Click OK to close the Environment Options dialog box Contours should now appear and if everything has gone well they will look similar to Fig 446 Note The display of the model grid is deactivated by using the Appearance tab of the Environment Options dialog box 5 To save or print the graphics select File Save Plot As or File Print Plot 6 You may save the calculated head values in ASCII Matrix files by selecting Value Matrix to open a Browse Matrix dialog box and then clicking the Save button 7 Select File Leave Editor or click the leave editor button 42 Unconfined Aquifer System with Recharge 313 Fig 446 Steady state head distribution 423 Transient Flow Simulation It is now time to perform the transient simulations with the wet season recharge 120 days and dry season pumping 240 days The hydraulic heads resulting from the steady state simulation are used as the starting heads for the transient analysis To set the steady state heads as the starting values for the simulation 1 Select Parameters Initial Prescribed Hydraulic Heads to start the Data Editor 2 Select Value Import Results to open an Import Results dialog box 3 Click OK to import the hydraulic head it is the default result type from the first time step of the first stress period 4 Select File Leave Editor or click the leave editor button 314 4 Tutorials We now need to change from a steady state simulation to a transient simulation In the transient simulation there are two stress periods one of 240 days when pumping is occurring and no recharge and the other of 120 days when there is recharge only It is possible to have different conditions for each stress period as will be demonstrated below To change to a transient simulation 1 Select Parameters Time to open the Time Parameters dialog box 2 Change the model to transient by clicking on Transient in the Simulation Flow Type box 3 Activate the second period by checking the Active box in the second row of the table 4 Change the length of periods and numbers of time steps such that For period 1 Period Length 240 Time Steps 12 For period 2 Period Length 120 Time Steps 6 5 Click OK to close the Time Parameters dialog box Now we need to set the pumping rate for each well during stress period 1 To set the pumping rate 1 Select Models MODFLOW Well 2 The status bar displays Period 1 indicating that you are entering data for stress period 1 3 At each of the wells marked by a little shaded box on the DXF Map leftclick to select the cell and then rightclick to set the pumping rate to 3888 m3d in the Cell Value dialog box This pumping rate is equivalent to 45 ls the negative sign means that water is being extracted from the system A recharge well would have a positive sign 4 Click the Change Stress Period button to open a Temporal Data dialog box this allows you to select and edit the data so that different values can apply during different Stress Periods 5 In the Temporal Data dialog box select Period 2 and click the Edit Data button The status bar displays Period 2 indicating that you are entering data for stress period 2 6 For each well in the system set the pumping rate to 0 7 Select File Leave Editor or click the leave editor button There are two recharge periods namely the dry season when recharge is zero and the wet season when recharge is 75 104mday 42 Unconfined Aquifer System with Recharge 315 To set the recharge rate 1 Select Models MODFLOW Recharge 2 The status bar displays Period 1 indicating that you are entering data for stress period 1 3 Set the entire grid to a uniform value for the first stress period by selecting Value Reset Matrix to open a Reset Matrix dialog box 4 In the Reset Matrix dialog box enter the following values then click OK to close the dialog box Recharge Flux LT 1 00 Layer Indicator IRCH 0 Recharge Options Recharge is applied to the highest active cell 5 Click the Change Stress Period button to open a Temporal Data dialog box select Period 2 then click the Edit Data button The status bar displays Period 2 indicating that you are entering data for stress period 2 6 Use the above procedure to change the recharge flux for the entire grid to 000075 the values for the layer indicator and recharge option remain the same 7 Select File Leave Editor or click the leave editor button Before running a transient simulation it is necessary to specify storage terms which account for the amount of water stored or released from aquifer matrix due to changes in hydraulic heads For an unconfined layer MODFLOW requires the storage term specific yield To specify the specific yield 1 Select Parameters Specific Yield 2 Select Value Reset Matrix to set the entire grid to 006 3 Select File Leave Editor or click the leave editor button To run the transient model 1 Select Models MODFLOW Run 2 Click OK to accept the warning regarding the Effective Porosity 3 Click OK in the Run Modflow dialog box to generate the required data files and to run MODFLOW you will see a DOS window open and MODFLOW performs the iterations required to complete the flow simulation By default the simulation results at the end of each time step are saved Refer to Section 26118 page 87 for more about Output Control 4 Press any key to exit the DOS Window 316 4 Tutorials To create head contours Using the 2D Visualization you can create contour plots for the water levels at the end of each time step The water level at the end of the pumping period dry season corresponds to the heads in time step 12 of period 1 Fig 447a The water level at the end of the recharge period wet season corresponds to the heads in time step 6 of period 2 Fig 447b Both figures use the contour interval of 05 m The minimum and maximum contour levels are 125 m and 19 m respectively Fig 447 a Head distribution after 240 days of pumping period 1 time step 12 b Head distribution after 120 days of recharge period 2 time step 6 43 Aquifer System with River 317 43 Aquifer System with River Folder pmdirexamples utorials utorial3 431 Overview of the Hypothetical Problem A river flows through a valley Fig 448 which is bounded to the north and south by impermeable granite intrusions The hydraulic heads at the upstream and down stream constant head boundaries are known which are saved in a data file The river forms part of a permeable unconfined aquifer system horizontal hydraulic conductiv ity HK 5 mday vertical hydraulic conductivity V K 05mday specific yield Sy 005 effective porosity ne 02 which overlies a confined aquifer of a vari able thickness HK 2 mday V K 1 mday specific storage Ss 5 105 ne 025 A silty layer thickness 2 m KH 05 mday V K 005 mday ne 025 separates the two aquifers The elevations of the aquifer tops and bot toms are known and saved in ASCII Matrix files Three pumping wells pumping at 500m3day each abstracts water from the confined aquifer The river has the following properties Fig 448 Configuration of the hypothetical model 318 4 Tutorials River stage 194 m on the upstream boundary River stage 17 m on the downstream boundary river width 100 m riverbed hydraulic conductivity 2 mday riverbed thickness 1 m Riverbed bottom elevation 174 m on the upstream boundary Riverbed bottom elevation 15 m on the downstream boundary The task is to construct a 3layer groundwater flow model of the area including the river and the pumping wells and to determine the capture zone of the wells Seven main steps need to be done in this tutorial 1 Create a new model 2 Generate the model grid 3 Refine the model grid 4 Assign the model data 5 Perform steadystate flow simulation 6 Extract and view results 4311 Step 1 Create a New Model The first step in running a flow simulation is to create a new model To create a new model 1 Select File New Model A New Model dialog box appears Select a folder for saving the model data such as CModels utorial3 and type the file name TU TORIAL3 as the model name A model must always have the file extension PM5 All file names valid under MSWindows with up to 120 characters can be used It is a good idea to save every model in a separate folder where the model and its output data will be kept This will also allow PM to run several models simultane ously multitasking 2 Click OK PM takes a few seconds to create the new model The name of the new model name is shown in the title bar 4312 Step 2 Generate the Model Grid To generate the model grid 1 Select Grid Mesh Size A Model Grid and Coordinate System dialog box appears 43 Aquifer System with River 319 2 Enter the values as shown in Fig 449 to the dialog box The values for the Model Thickness and Model Top Elevation are not relevant at this stage since we are going to import the elevations from disk files We will generate a model grid of 3 layers The unconfined aquifer is the layer 1 in the model The silty layer and the confined aquifer are represented by layer 2 and layer 3 respectively 3 Click OK to close the dialog box Fig 449 The Model Grid and Coordinate System dialog box You are now in the Grid Editor To help visualize the problem we can overlay a DXF file as a map which gives us the locations of the boundaries and the pumping wells To load a map 1 Select Options Map to open the Map Options dialog box 2 Rightclick on the first DXF File field to bring up the Map Files dialog box and then select the file BASEMAPDXF from the folder examples utorials utorial3 3 Check the box at the front of the DXF File field The map will be displayed only if the box is checked 4 Click OK to close the Map Options dialog box You will see that it does not match the grid that you have generated So we need to move the grid to the proper position To move the grid 320 4 Tutorials 1 Select Options Environment to open the Environment Options dialog box 2 In the Coordinate System tab enter Xo 200 and Yo 6000 then click OK to close the dialog box 3 Select File Leave Editor or click the leave editor button 4313 Step 3 Refine the Model Grid To refine the model grid 1 Select Grid Mesh Size to open the Grid Editor 2 Refine the grid around each of the three wells by halving the size of the following rows and columns Columns 8 through 14 Rows 7 through 12 The grid should now be refined around the wells and appear similar to Fig 450 3 Select File Leave Editor or click the leave editor button 4314 Step 4 Assign Model Data To define the layer properties 1 Select Grid Layer Property to open the Layer Property dialog box Fig 450 Model grid after the refinement 43 Aquifer System with River 321 2 Make sure that for layer 1 the type is set to 1unconfined and layers 2 and 3 are set to 3confinedunconfined Note that MODFLOW requires horizontal hydraulic conductivity for layers of type 1 or 3 and transmissivity for layers of type 0 or 2 Refer to Section 242 page 30 for details of the Layer Property dialog box 3 Click OK to close the Layer Property dialog box To define the model boundaries 1 Select Grid Cell Status IBOUND Modflow 2 Click the button if the display mode is not Grid View 3 Set noflow boundaries in the first layer in the areas defined by the Granite and South Granite Hills 4 Turn layer copy on by click the layer copy button Layer Copy is on if the layer copy button is sunk The cell values of the current layer will be copied another layer if you move to the other model layer while layer copy is on 5 Move to the second layer and the third layer by pressing PgDn twice 6 Set fixedhead boundaries IBOUND 1 in layer 3 at the west and east bound aries where the river enters and leaves the model area 7 Copy the fixedhead boundaries from layer 3 to layer 1 by clicking the Current Layer edit field in the tool bar typing in the layer number 1 and pressing the Enter key remember that layer copy is still on We do not need to specify fixed head cells in the second layer because the horizontal flow component in the silty layer is considered to be negligible The model grid in layers 1 and 3 should look like Fig 451 The model grid in layer 2 should look like Fig 452 8 Select File Leave Editor or click the leave editor button The top of each aquifer slopes gradually from west to east To save you entering this data the top elevation of each aquifer has been saved in ASCII Matrix file To specify the top elevation of each aquifer 1 Select Grid Top of Layers TOP PM will ask if you want to use the layer bottom elevations as the layer top elevations Click No 2 Click the button if the display mode is not Grid View 3 Select Value Matrix Load to import examples utorials utorial3aq1topdat as the elevation of the top of aquifer 1 4 Move to Layer 2 5 Select Value Matrix Load to import examples utorials utorial3aq2topdat as the elevation of the top of aquifer 1 322 4 Tutorials 6 Move to Layer 3 7 Select Value Matrix Load to import examples utorials utorial3aq3topdat as the elevation of the top of aquifer 1 8 Select File Leave Editor or click the leave editor button To specify the bottom elevation of each aquifer 1 Select Grid Bottom of Layers BOT PM will ask if you want to use the Top of Layer 2 as the Bottom of Layer 1 and Top of Layer 3 as the Bottom of Layer 2 We will accept this 2 Move to the layer 3 and select Value Reset Matrix to set the elevation of the bottom of the layer 3 to 00 m 3 Select File Leave Editor or click the leave editor button Specification of the geometry of the system is now complete all we need to do now is enter the physical parameters of the system To specify the time parameters 1 Select Parameters Time 2 In the Time Parameters dialog box change the Simulation Time Unit to DAYS and select Steady State in the Simulation Flow Type box Fig 451 Model grid of the 1st layer and 3rd layer 43 Aquifer System with River 323 Fig 452 Model grid of the 2nd layer 3 Click OK to close the Time Parameters dialog box The groundwater flows naturally under a gentle gradient towards the river from both sets of hills and also in an easterly direction The values of starting heads which in clude the required values for the fixedhead cells are saved in examples utorials u torial3 2shdat We will import this file to the initial hydraulic head To specify the initial prescribed hydraulic heads 1 Select Parameters Initial Prescribed Hydraulic Heads 2 Select Value Matrix to open the Browse Matrix dialog box 3 Click the button select the file examples utorials utorial3 2shdat and then click OK The data will appear in the Browse Matrix dialog box click OK to close this dialog box and return to the Data Editor The data is now loaded into layer 1 4 Turn on layer copy by pressing down the layer copy button 5 Move to the second layer and the third layer Now the data of layer 1 is copied to the second and third layers 6 Select File Leave Editor or click the leave editor button To specify the horizontal hydraulic conductivity 324 4 Tutorials 1 Select Parameters Horizontal Hydraulic Conductivity 2 Use Value Reset Matrix to enter the following data for each layer Layer 1 50 mday Layer 2 05 mday Layer 3 20 mday 3 Select File Leave Editor or click the leave editor button To specify the vertical hydraulic conductivity 1 Select Parameters Vertical Hydraulic Conductivity 2 Use Value Reset Matrix to enter the following data for each layer Layer 1 05 mday Layer 2 005 mday Layer 3 10 mday 3 Select File Leave Editor or click the leave editor button To specify the effective porosity 1 Select Parameters Effective Porosity The effective porosity is used in PMPATH which will be used to define the capture zones of the pumping wells 2 Use Value Reset Matrix to enter the following data for each layer Layer 1 02 Layer 2 025 Layer 3 025 3 Select File Leave Editor or click the leave editor button To specify the well data 1 Select Models Modflow Well 2 Click the button if the display mode is not Grid View 3 Switch to Layer 3 by pressing the PgDn key twice 4 Move the grid cursor to Well 1 press Enter or rightclick and set the pumping rate to 500 m3day 5 Repeat the above step with Well 2 and Well 3 6 Select File Leave Editor or click the leave editor button The last step before running the steadystate simulation in this tutorial is to specify river data which is a little difficult to set up MODFLOW requires that the river data ie river stage river bottom elevation and riverbed conductance be specified to each model cell The riverbed conductance is defined as 43 Aquifer System with River 325 Criv Kriv L Wriv Mriv 44 where Criv hydraulic conductance of the riverbed L2T 1 Kriv hydraulic conductivity of the riverbed sediment LT 1 L length of the river within a cell L Wriv width of the river within a cell L Mriv thickness of the riverbed within a cell L Entering the river data on a cellbycell basis is sometimes very cumbersome Fortu nately pmp provides a Polyline input method which dramatically facilitates the data input process We will use this input method to specify the river data To specify the river data 1 Select Models Modflow River to open the Data Editor 2 Click the button if the display mode is not Grid View 3 Click the button to switch to the Polyline input method 4 Leftclick on the upstream end of the river to anchor one end of the polyline 5 Move the mouse pointer along the trace of the river and leftclick to anchor another vertex of the polyline 6 Repeat steps 4 and 5 until the polyline looks similar to Fig 453 then click on the latest vertex again to complete to polyline While drawing the polyline you may press the right mouse button to abort 7 Rightclick on the first vertex of the polyline on the upstream side to open a River Parameters dialog box and enter the values as shown in Fig 454 then click OK to close the dialog box 8 Rightclick on the last vertex of the polyline on the downstream side to open a River Parameters dialog box and enter the values as shown in Fig 455 then click OK to close the dialog box The parameters specified to the vertices are used to calculated the cell properties along the trace of the polyline Refer to Section 2618 page 56 for details 9 Select File Leave Editor or click the leave editor button 4315 Step 5 Perform steadystate flow simulation To run the flow simulation 1 Select Models Modflow Run 326 4 Tutorials Fig 453 Define the river using a polyline Fig 454 Parameters of the upstream vertex 2 Click OK in the Run Modflow dialog box to generate the required data files and to run MODFLOW you will see a DOS window open and MODFLOW perform the iterations required to complete the flow simulation 43 Aquifer System with River 327 Fig 455 Parameters of the downstream vertex 3 Press any key to exit the DOS Window 4316 Step 6 Extract and view results To generate contour maps of the calculated heads 1 Select Tools 2D Visualization to display the Result Selection dialog box Fig 456 2 Click OK to select the default result type Hydraulic Head PM displays the model grid and sets 10 contour levels ranging from the lowest to the highest head value 3 Select Options Environment to customize the appearance of the contours The contour map for the first model layer should look similar to that in Fig 457 To delineate the capture zones of the pumping wells 1 Start PMPATH by selecting Models PMPATH Advective Transport PMPATH will load the current model automatically We will place particles around the pumping wells and examine their 10year capture zones 2 Move to Layer 3 by pressing the PgDn key twice 3 Click on the button and drag a small box around the cell containing Well 1 by holding down the left mouse button and moving the mouse 4 When you release the mouse button the Add New Particles dialog box appears In the Particles on circles group set the number of particles to 15 the radius R 80 and the number of planes NK 3 328 4 Tutorials Fig 456 The Result Selection dialog box Fig 457 Steady state hydraulic head distribution in the first model layer 5 Click the Properties tab and change the color of new particles to Blue 6 Click OK to close the Add New Particles dialog box 7 Use a similar procedure to add particles around Well 2 and Well 3 Assign a dif ferent color say Green and Black to each of these particle groups 8 Select Options Environment to open the Environment Options dialog box for setting up the display of the hydraulic heads contours and cross sections 9 Click the Contours tab check the Visible box and click the Restore Defaults button to get standard settings 10 Click the Cross Sections tab check the Visible and Show grid boxes and set Ex aggeration 25 Projection Row 15 and Projection Column 9 11 Click OK to close the Environment Options dialog box The hydraulic head contours for layer 3 and cross sections showing the location of 43 Aquifer System with River 329 the particles should appear 12 Select Options Particle Tracking Time to open the Particle Tracking Time Properties dialog box for setting up the particle tracking parameters In the Track ing Steps group change the time unit to years step length to 10 and maximum number of steps to 200 13 Click OK to close the Particle Tracking Time Properties dialog box 14 Start the backward particle tracking by clicking on the button You can easily see that the flowlines intersect with the river in numerous places Fig 458 Fig 458 Steady state hydraulic head distribution in the 3rd model layer and capture zones of the pumping wells To run forward particle tracking We will now introduce a contaminant source upstream of Well 2 and see how far the contamination moves through the steady state flow field after 75 100 and 125 years 330 4 Tutorials 1 Since the contamination is a surface source we need to place the particles in layer 1 If you arent already in Layer 1 change to it by using the PgUp key 2 To place the particles on the ground surface drag a box around the cell 1 5 6 3 In the Cell Faces tab of the Add New Particles dialog box you will notice that the figure defines the various faces of an individual cell since the contamination is a surface source we only want to place particles on cell face 5 4 Click the Particles tab and set the number of particles on Face 5 to NI4 and NJ4 and set all the other values to 0 5 Click OK to close the Add New Particles dialog box 6 Open the Particle Tracking Time Properties dialog box by selecting Options Particle Tracking Time 7 In the Tracking Steps group change the time unit to years step length to 1 and maximum number of steps to 75 When finished click OK to close the dialog box 8 Start the backward particle tracking by clicking on the button 9 Repeat the above for Maximum number of steps of 100 and 125 The plot gener ated after 125 steps should look similar to Fig 459 43 Aquifer System with River 331 Fig 459 125year streamlines particles are started at the cell 6 5 1 and flow to wards Well 2 5 Examples and Applications The examples contained in this chapter are intended to illustrate the use of PM and the supported programs The description of each problem is divided into three parts It starts out with Folder where you can find the readytorun model for example pmdirexamplesbasicbasic1 pmdir is the installation folder of PM Next youll find a discussion of the problem and finally you will find the simulation results 51 Basic Flow Problems 511 Determination of Catchment Areas Folder pmdirexamplesbasicbasic1 Overview of the Problem Fig 51 shows a part of an unconfined aquifer The extent of the aquifer to the North and South is assumed to be unlimited The aquifer is homogeneous and isotropic with a measured horizontal hydraulic conductivity of 00005 ms and an effective porosity of 01 The elevations of the aquifer top and bottom are 15 m and 0 m respectively The aquifer is bounded by a noflow zone to the west To the east exists a river which is in direct hydraulic connection with the aquifer and can be treated as fixedhead boundary The river width is 50 m and stage is 10 m The mean groundwater recharge rate is 8 109 ms A pumping well is located at a distance of 1000 m from the river The task is to calculate the catchment area of the well and the 365dayscapture zone under steadystate flow conditions 334 5 Examples and Applications Fig 51 Plan view of the model area Modeling Approach and Simulation Results The west boundary of the model is impervious and the river to the east is simulated by the fixedhead boundary condition IBOUND 1 with the initial hydraulic head at 10 m There are no natural boundaries to the South and North so we have to use streamlines as impervious boundaries The distance of the selected streamline from the well must be large enough so that the hydraulic head at these boundaries are not affected by the pumping well This is the case if the total recharge in the chosen strip is considerably larger than the pumping rate of the well Because of the symmetry of the system we could use onehalf of the model area only To show the whole catchment area we decided to use the entire model area The aquifer is simulated using a grid of one layer 50 rows and 51 columns A regu lar grid space of 50 m is used for each column and row The layer type is 1 unconfined Fig 52 shows the contours the catchment area and the 365daysisochrones of the pumping well using a 2Dapproach where the groundwater recharge is treated as a dis tributed source within the model cells and 50 particles are initially placed around the pumping well in the middle of the aquifer If the groundwater recharge is applied on the groundwater surface refer to RCHEVT Tab page 250 particles will be tracked back to the groundwater surface Fig 53 We can easily imagine that the size and form of 51 Basic Flow Problems 335 Fig 52 Catchment area and 365days isochrones of the pumping well 2Dapproach groundwater recharge is treated as distributed source within the model cells the calculated catchment area depend on the boundary condition recharge rate and the vertical position of the well screen if the well is only partially penetrating A discus sion about the determination of catchment areas in two and three spatial dimensions can be found in Kinzelbach and others 71 To delineate the catchment area of a pumping well in a 3D flow field we must place enough particles around and along the well screen Fig 54 shows the catchment area calculated by PMPATH First 425 particles are placed around the well by using the Add New Particles dialog box the settings are NI5 NJ5 on faces 5 and 6 and 25 particles on the circles with R25 and NK15 around the pumping well Then backward tracking is applied for a 100years duration Finally the end points of the particles are saved by selecting File Save Particles As in PMPATH This file can be reloaded into PMPATH by selecting File Load Particles to display the catchment area 336 5 Examples and Applications Fig 53 Particles are tracked back to the groundwater surface by applying the ground water recharge on the groundwater surface 3Dapproach Fig 54 Catchment area of the pumping well 3Dapproach 51 Basic Flow Problems 337 512 Use of the GeneralHead Boundary Condition Folder pmdirexamplesbasicbasic2 Overview of the Problem This simple example Kinzelbach and Rausch 72 demonstrates the use of the generalhead boundary package of MODFLOW A confined homogeneous and isotropic aquifer is shown in Fig 55 The aquifer is bounded by noflow zones to the north and south The hydraulic heads at the west and east boundaries are 12 m and 10 m respec tively The transmissivity of the aquifer is T 001 m2s The aquifer has a constant thickness of 10 m The task is to calculate the head contours for the case that only the west part of the aquifer is modeled The east boundary of the modeled part should be approached by using the generalhead boundary Modeling Approach and Simulation Results Fig 55 Plan view of the model area 338 5 Examples and Applications The aquifer is simulated using a grid containing 1 layer 10 rows and 16 columns A regular grid spacing of 100 m is used for each column and row The layer type is 0 confined and the Transmissivity flag in the Layer Options dialog box is Userspecified The initial hydraulic head is 12 m everywhere While the west model boundary is simulated by the fixedhead boundary condition IBOUND 1 with the initial head at 12 m the east boundary is simulated by the generalhead boundary GHB condition with the head h 10 m Analogous to the riverbed hydraulic conductance equation 219 the hydraulic conductance term of each GHB cell is CGHB KGHB AL where KGHB is the horizontal hydraulic conductivity L is the distance from the actual fixedhead boundary to the modeled GHB cell and A is the area of the cell face which is perpendicular to the groundwater flow in the unmodeled area For this example CGHB T10 100 101000 0001 m2s Fig 56 shows the calculated contours For comparison the entire aquifer is mod eled with the east and west fixedhead boundaries and the result is shown in Fig 57 The model is saved in the folder pmdirexamplesbasicbasic2a Fig 56 Calculated head contours for the west part of the aquifer 51 Basic Flow Problems 339 Fig 57 Calculated head contours for the entire aquifer 513 Twolayer Aquifer System in which the Top layer Converts between Wet and Dry Folder pmdirexamplesbasicbasic3 Overview of the Problem This example is adapted from the the first test problem of the BCF2 package Mc Donald and others 86 In an aquifer system where two aquifers are separated by a confining bed large pumping rates from the bottom aquifer can desaturate parts of the upper aquifer If the pumping is discontinued resaturation of the upper aquifer can occur Fig 58 shows two aquifers separated by a confining unit No flow boundaries surround the system on all sides except that the lower aquifer discharges to a stream along the right side of the area Recharge from precipitation is applied evenly over the entire area The stream penetrates the lower aquifer in the region above the stream the upper aquifer and confining unit are missing Under natural conditions recharge flows through the system to the stream Under stressed conditions two wells withdraw water from the lower aquifer If enough water is pumped cells in the upper aquifer will desaturate Removal of the stresses will then cause the desaturated areas to resaturate The task is to construct a model to compute the natural steadystate head distri bution and then calculate the head distribution under the stressed condition When solving for natural conditions the top aquifer initially is specified as being entirely dry and many cells must convert to wet When solving for pumping condition the top aquifer is initially specified to be under natural conditions and many cells must convert to dry 340 5 Examples and Applications Fig 58 Configuration of the hypothetical model after McDonald and others 86 51 Basic Flow Problems 341 Modeling Approach and Simulation Results The model consists of two layers one for each aquifer Since horizontal flow in the confining bed is small compared to horizontal flow in the aquifers and storage is not a factor in steady state simulations the confining bed is not treated as a separate model layer The effect of the confining bed is incorporated in the value for vertical leakance Note that if storage in the confining bed were significant transient simulations would require that the confining layer be simulated using one or more layers The confining layer must also be simulated if you intend to calculate pathlines with PMPATH or to simulate solute transport A uniform horizontal grid of 10 rows and 15 columns is used Aquifer parameters are specified as shown in Fig 58 Two steady state solutions were obtained to simulate natural conditions and pump ing conditions The steady state solutions were obtained through a single simulation consisting of two stress periods The first stress period simulates natural conditions and the second period simulates the addition of pumping wells with extraction rates of 30000 ft3d 850 m3d The simulation is declared to be steady state so no storage values are specified and each stress period requires only a single time step to produce a steady state result The PCG2 Package is used to solve the flow equations for the simulations Determination of the wetting threshold THRESH see Modflow Wetting Capa bility often requires considerable effort The user may have to make multiple test runs trying different values in different areas of the model In many cases positive THRESH values may lead to numerical instability and therefore the user should try negative THRESH values first 342 5 Examples and Applications 514 WaterTable Mount resulting from Local Recharge Folder pmdirexamplesbasicbasic4 Overview of the Problem This example is adapted from the the first test problem of the BCF2 package McDon ald and others 86 Localized recharge to a water table aquifer results in formation of a ground water mound For example a ground water mound may form in response to recharge from infiltration ponds commonly used to artificially replenish aquifers or to remove contamination by filtration through a soil column If the aquifer has low vertical hydraulic conductivity or contains interspersed zones of low hydraulic con ductivity it may be necessary to simulate the aquifer using multiple model layers in which the mound crosses more than one layer The conceptual model consists of a rectangular unconfined aquifer overlain by a thick unsaturated zone Fig 59 The horizontal hydraulic conductivity is 5 feet per day and vertical hydraulic conductivity is 025 feet per day 00762 md A leaking pond recharges the aquifer resulting in the formation of a ground water mound The pond covers approximately 6 acres 23225m2 and pond leakage is 12500 cubic feet per day 354 m3d The specific yield is 20 percent The water table is flat prior to the creation of the recharge pond The flat water table is the result of a uniform fixed head boundary that surrounds the aquifer The task is to calculate the water table under the steadystate condition and the formation of the groundwater mound over time Modeling Approach and Simulation Results Because of the symmetry heads are identical in each quadrant of the aquifer and there is no flow between quadrants therefore only one quarter of the system needs to be simulated The problem is simulated using a grid of 40 rows 40 columns and 14 layers Fig 59 A uniform horizontal grid spacing of 125 feet 381 m is used and each layer is 5 feet 152 m thick The pond is in the upper left corner of the grid The boundaries along row 1 and column 1 are no flow as a result of the symmetry A fixed head boundary of 25 feet 762 m is specified along row 40 and column 40 for layers 10 14 a no flow boundary is assigned along row 40 and column 40 for layers 1 9 Without the recharge from the pond layers 1 9 are dry and the head in all the cells of layers 10 14 is 25 feet Recharge from the pond is applied to the horizontal area encompassed by rows 1 through 2 and columns 1 through 2 The recharge option Recharge is applied to the highest active cell is used so that recharge will penetrate through inactive cells down to the water table The specific recharge rate of 005 foot per day 00152 md simulates leakage of 3125 cubic feet per day 51 Basic Flow Problems 343 Fig 59 Hydrogeology and model grid configuration 885 m3d through one quarter of the pond bottom a simulated area of 62500 square feet 5806m2 Reasonable solutions to the ground water mounding problem can be obtained in two steady state simulations by using the PCG2 solver In the first simulation dry cells are converted to wet by comparison of the wetting threshold THRESH to heads in underlying cells only which is indicated by a negative value of THRESH The wetting 344 5 Examples and Applications iteration interval is 1 and THRESH is 05 foot which means that the wetting threshold is 10 percent of the thickness of a cell In the second simulation wetting of cells is based on comparison to heads both in horizontally adjacent and underlying cells THRESH is positive A wetting iteration interval of 2 and a THRESH of 15 feet are used in order to prevent continued oscillation between wet and dry for some cells Due to the steepness of the head gradient and the grid discretization the head difference between adjacent horizontal cells is generally much larger than the head difference between adjacent vertical cells along the mound For example the cell at layer 4 row 3 and column 4 is supposed to be dry even though the head in the horizontally adjacent cell in column 3 is 14 feet above the bottom of the layer The vertical head difference between cells in this part of the model is much less the difference between the head at the cell in layer 4 row 3 column 3 and the cell below is only 005 foot Thus the neighboring cell to the right is repeatedly and incorrectly converted to wet during the solution process if horizontal wetting is used with a wetting threshold of 05 foot The larger wetting threshold and wetting iteration interval used in the second simulation allow convergence to occur but only after many iterations In this simulation head in adjacent vertical cells is the best indicator of when a dry cell should become wet The formation of the groundwater mound over time can be obtained with a tran sient simulation The transient simulation is run for one stress period with a length of 500000 days The stress period is divided into 50 time steps with a time step multi plier of 13 The first time step is 03 days and the last time step is 115385 days The specific yield is 20 percent and the confined storage coefficient is 0001 The PCG2 solver is used and cells are activated by comparison of the wetting threshold to heads in underlying cells The head change criterion for closure is 0001 foot and the resid ual change criterion is 10000 cubic feet the wetting threshold is 05 foot the wetting factor is 05 and the wetting iteration interval is 1 Fig 510 shows simulated water table heads along row 1 at several times during the transient simulation Steady state conditions were reached at the 44th time step of the transient simulation as indicated by storage flow terms being zero see the simulation listing file OUTPUTDAT 51 Basic Flow Problems 345 Fig 510 Simulated watertable along row 1 beneath a leaking pond after 190 708 2630 days and steady state conditions 515 Perched Water Table Folder pmdirexamplesbasicbasic5 Overview of the Problem This example is adapted from the the third test problem of the BCF2 package McDon ald and others 86 Contrasts in vertical hydraulic conductivity within the unsaturated zone can provide a mechanism for the formation of perched ground water tables The conceptual model is rectangular and consists of three geohydrologic units The upper and lower units have higher hydraulic conductivities than the middle unit Fig 511 There is a regional water table in which the head is below the bottom of the middle unit Natural recharge occurs over the entire area at a rate of 0001 foot per day This recharge can percolate through the two upper units without the formation of a water table above the middle because the vertical hydraulic conductivity of this unit is 0002 foot per day Recharge at a rate of 001 foot per day from a pond covering 6 acres 23225 m2 will cause a perched ground water body to form in the top two units The total pond leakage is about 2360 cubic feet per day 668 m3d The perched water table spreads out over an area much larger than the area covered by the pond This has an impact on the distribution of recharge to the lower unit 346 5 Examples and Applications Fig 511 Hydrogeology and model grid configuration 51 Basic Flow Problems 347 The task is to calculate the long term head distribution resulting from the pond recharge Modeling Approach and Simulation Results Because of the rectangular symmetry of the system there is no flow between quadrants Therefore only one quarter of the system must be simulated The problem is simulated using a grid of 50 rows 50 columns and 2 model layers A uniform grid spacing of 16 feet is used The recharge pond is in the upper left corner of the grid the quarter of the pond that is simulated occupies a square area that is 16 rows long and 16 columns wide The boundaries along row 1 and along column 1 are no flow boundaries as a result of the symmetry Model layer 1 simulates the upper geohydrologic unit and is assigned a hydraulic conductivity of 5 feet per day The bottom of layer 1 is at an elevation of 20 feet The lower geohydrologic unit is simulated as model layer 2 This layer is simulated as a confinedunconfined layer with constant transmissivity layer type 2 The top and bottom elevations of layer 2 are set at 10 and 0 feet respectively Because the head in this layer is always below the layer top the flow from above is limited as described by McDonald and Harbaugh 85 p 5 19 Thus there is no direct hydraulic connection between the perched layer and the lower layer but the perched heads have a direct impact on the recharge into the lower layer All cells in layer 2 are assigned a constant head of 1 foot because there is no need to simulate heads in this layer for the purpose of estimating recharge The middle geohydrologic unit is not simulated as a separate model layer because it is assumed that horizontal flow and storage effects are negligible This unit is represented by the value for vertical leakance between model layers 1 and 2 The vertical leakance is assumed to be 00002 per day In areas not covered by the pond recharge is applied areally at a rate of 0001 foot per day to simulate natural recharge The recharge option Recharge is applied to the highest active cell is used so that recharge will penetrate through inactive cells to the water table A recharge rate of 001 foot per day is applied to the area covered by the pond A steady state simulation is performed to simulate the formation of a perched water table Solution of the flow equation is obtained using the SIP solver Starting hydraulic head in layer 1 under the pond is set at 21 feet All other cells in layer 1 initially are specified as no flow cells The wetting iteration interval THRESH and wetting factor are set at 2 iterations 10 foot and 05 foot respectively see MODFLOW Wetting Capability A positive value of THRESH indicates that horizontally adjacent cells can cause dry cells to become wet This is the only way for cells in layer 1 to become wet because heads in layer 2 are always below the bottom of layer 1 348 5 Examples and Applications Fig 512 Simulated steady state head distribution in layer 1 516 An Aquifer System with Irregular Recharge and a Stream Folder pmdirexamplesbasicbasic6 Overview of the Problem This example is adapted from the first test problem of the Streamflow Routing STR1 package 100 Results from the STR1 Package were compared to results from an analytical solution developed by Oakes and Wilkinson 92 An idealized aquifer with a river flowing through the middle was chosen and is shown in Fig 513 The width of the aquifer perpendicular to the river was 4000 ft on each side while the length parallel to the river was 13000 ft Assumptions used in both the analytical solution and the model simulation include 1 The lateral boundaries of the aquifer are impermeable no flow is allowed 2 The rocks beneath the aquifer are impermeable 3 The river penetrates the entire depth of the aquifer and has vertical banks 4 The river is not separated from the aquifer by any confining material 5 The transmissivity and storage coefficient are constant throughout the aquifer and remain constant in time 6 The aquifer is confined and Darcys Law is valid 7 The flow of groundwater is horizontal 8 The water level in the river is constant along its length and with time 51 Basic Flow Problems 349 9 The infiltration of recharge to the aquifer is instantaneous no delay between the time precipitation infiltrates the surface until it reaches the water table 10 The discharge from the aquifer is only to the river Transmissivity of the aquifer used for both the analytical solution and in the model simulation was 3200 ft2d 345 103 m2s The storage coefficient is 020 Be cause the river is assumed to be fully penetrating and the aquifer is not separated from the river by any confining material the streambed conductance value was assumed equal to the transmissivity of the aquifer in this example the width of the river is assumed equal to the depth of the aquifer times the length of the river in each cell 1000 ft divided by an assumed l foot thickness of the riverbed Actually any large streambed conductance value can be used as long as the head value in the model cell containing the river remains constant during the simulation Varying the streambed conductance value shows that for this problem streambed conductance values greater Fig 513 Configuration of the model grid and the location of the observation well 350 5 Examples and Applications than 10 ft2d produce nearly the same results Annual recharge to the aquifer is 15 ft However the daily recharge rate varied according to a sinusoidal distribution for the first 180 days while no recharge was allowed for the following 180 days The distribution of the recharge over time is shown in Fig 514 Fig 514 Distribution of recharge used for analytical solution and the model after Prudic 100 51 Basic Flow Problems 351 Modeling Approach and Simulation Results The aquifer is simulated using one model layer Specification of the elevations of layer top and bottom are not necessary because the layer is confined and transmissivity and confined storage coefficient are specified directly as defined in the Layer Property dialog box The sinusoidal distribution of the recharge rate was divided into 15 day intervals for the model simulation and the rate for the middle of each interval was used as input value The distribution used in the simulation is also shown in Fig 514 A total of six 360 day infiltration periods 144 stress periods each with a length of 15 days was used in the simulation The first five 360day infiltration periods were computed to allow the model to reach a stable yearly cycle because the starting water level for each model cell was not known Results of the model simulation from the sixth infiltration period are compared to the results from the analytical solution for an observation well 2000 ft from the river Fig 515 The coordinates of the observation well are given in the Head Observation dialog box The Streamflow Routing package is not really needed to simulate this condition as the river could have been represented using fixed head or river cells The same results can be obtained using the River package The simulation was done to determine whether the STR1 package correctly accumulates flow from the aquifer into the stream 352 5 Examples and Applications Fig 515 Comparison of simulation results to analytical solution developed by Oakes and Wilkinson 92 517 Flood in a River Folder pmdirexamplesbasicbasic7 Overview of the Problem This example is adapted from the second test problem of the STR1 package 100 The function of the STR1 package that computes the head in the stream as well as changes in flows to and from the aquifer was compared to an analytical solution developed by Cooper and Rorabaugh 28 The model grid used in the previous example was also used in this model The aquifer properties and assumptions are the same as those used in the previous example except for assumptions 8 10 which are replaced with the following assumptions 1 The recharge to the aquifer is only from the river as river stage increases with time and 2 The discharge from the aquifer is only to the river as river stage decreases with time The analytical solution from Cooper and Rorabaugh 28 pp 355 358 is appli cable for the case where the lateral boundary is at infinity referred to by Cooper and Rorabaugh as semiinfinite The impermeable boundary assigned at 4000 ft for this 51 Basic Flow Problems 353 model is of sufficient distance from the river in order not to interfere with the results A flood in the river was simulated for a 30 day period The procedure used to calculate the distribution of streamflow for the 30 day period and for 60 days following the flood was first to calculate a distribution of river stage using equation 71 in Cooper and Rorabaugh 28 p 355 assuming a maximum flood stage of 4 ft above the initial river stage The streamflow distribution Fig 516 was calculated from the river stage distribution The river has a width of 100 ft a dimensionless roughness coefficient of 002377 and a slope of 00001 A constant C 1486 should be used for the simulation see Equation 226 Fig 516 Distribution of streamflow for a 30day flood event used for the simulation after Prudic 100 Modeling Approach and Simulation Results Streamflow for the first 30 days was divided into l day periods for simulation Fig 517 shows the computed river stage The simulation results are the same as the manually calculated river stage values using equation 71 of Cooper and Rorabaugh 28 p 355 354 5 Examples and Applications Detailed discussion on the analytical and numerical results can be found in Prudic 100 Results of varying both the number of columns and the length of stress periods used to simulate the flood wave indicate that both the number of columns and the length of the time step are important in exactly duplicating the analytical solution Fig 517 Model calculated river stage A groundwater flow model with the Streamflow Routing package has an advan tage over analytical solutions because it can be used to simulate complex systems An example Folder pmdirexamplesbasicbasic7a containing a stream system Fig 518 is used to illustrate most of the features of the Streamflow Routing package The example assumes that an aquifer of 6000 ft wide by 6000 ft long is divided into six equally spaced rows and columns The transmissivity of the aquifer is 008 ft2s Recharge to the aquifer occurs only from stream leakage The example includes 7 stream segments with totally 16 reaches There is one diversion segment 2 and two places where streams join segments 2 and 4 join to make segment 5 and segments 3 5 and 6 join to make segment 7 Stream stages are also computed for each reach The streams range in width from 5 to 10 ft Streambed conductance values also vary depending on the length and width of each stream reach The hydraulic conductivity of the streambed is 4 104fts 51 Basic Flow Problems 355 Fig 518 Numbering system of streams and diversions after Prudic 100 518 Simulation of Lakes Folder pmdirexamplesbasicbasic8 Overview of the Problem Fig 519 shows an unconfined aquifer with the boundary conditions and the loca tion of a planned opencast mining site The aquifer is bounded by a noflow zone to the north and to the south To the west and east exist fixedhead boundaries with the hydraulic heads h 100 m and 95 m the elevations of the aquifer top and bottom are 100 and 0 m respectively The aquifer is homogeneous and isotropic with a measured horizontal hydraulic conductivity of 00001 ms and vertical hydraulic conductivity of 000001 ms The specific yield and effective porosity are assumed to be 025 The specific storage coef ficient is 00001 In the final mining phase the hydraulic head beneath the mining pit must be drawn down to the level of h 21 m Afterwards the mining pit will be filled with water to form an artificial lake 356 5 Examples and Applications Fig 519 Plan and crosssectional views of the model area The task is to 1 Construct a steadystate flow model and calculate the necessary abstraction rate inflow into the mining site for holding the head at 21 m and 2 Use the calculated steadystate head as the initial hydraulic head and calculate the temporal development curve of the water level head vs time in the artificial lake for the case that the abstraction within the mining site is turned off Modeling Approach and Simulation Results The aquifer is simulated using five model layers 21 rows and 25 columns The thick ness of each model layer is 20 m The elevation of the top of the first model layer is 100 m A regular grid spacing of 100 m is used for each column and row The layer type 3 confinedunconfined transmissivity varies is used for every layer 51 Basic Flow Problems 357 For task 1 the cells within the mining pit in the 4th model layer are set as fixed head cells with the initial hydraulic head of 21 m The cells of all 5 layers at the west boundary are fixedhead cells with the initial head h 100 m The cells of the layers 3 to 5 at the east boundary are fixedhead cells with the initial head h 95 m The initial hydraulic head values at all other cells have been set at 100 m To ensure that there is no resistance to the groundwater flow within the mining pit a very high value say 1 ms is used for the vertical and horizontal hydraulic conductivities of the cells within the pit A steadystate flow simulation was performed Fig 520 shows the two cross sections and the head contours of layer 4 It is obvious that the cells above the ground water surface went dry To calculate inflow into the mining pit we select Tools Water Budget to calculate the water budget by assigning zone 1 to the fixedheads cells within the mining pit The water budget for zone 1 in layer 4 should look like Table 518 The inflow rate to the constant head cells mining pit is 19428713E00 m3s For task 2 all cells within the mining pit are set as active cells The wetting capa bility of MODFLOW is turned on by selecting Models Modflow Wetting Capability The wettingiteration interval is 1 wetting factor is 05 and THRESH is 1 for all cells The specific yield and effective porosity of all cells within the mining pit lake are set to 1 Compared to the specific yield the influence of the elastic storage coefficient within the lake is insignificant Therefore the specific storage coefficient Ss 00001 is assigned to all cells A transient flow simulation is performed for a stress period with the length of 315576E08 seconds 100 time steps and a timestep multiplier of 10 The temporal development curve of the water table at a measurement point located in the fourth layer within the lake is shown in Fig 521 The final stage in the lake is about 971 m Table 51 Volumetric budget for the entire model written by MODFLOW Flow Term In Out InOut STORAGE 00000000E00 00000000E00 00000000E00 CONSTANT HEAD 00000000E00 19428709E00 19428709E00 HORIZ EXCHANGE 11840475E00 00000000E00 11840475E00 EXCHANGE UPPER 00000000E00 00000000E00 00000000E00 EXCHANGE LOWER 75882387E01 00000000E00 75882387E01 WELLS 00000000E00 00000000E00 00000000E00 DRAINS 00000000E00 00000000E00 00000000E00 RECHARGE 00000000E00 00000000E00 00000000E00 ET 00000000E00 00000000E00 00000000E00 358 5 Examples and Applications Fig 520 Steadystate hydraulic head contours in layer 4 Fig 521 Timeseries curve of the water stage in the lake 52 EPA Instructional Problems 359 52 EPA Instructional Problems Folder pmdirexamplesEPA Instructional Problems Overview of the Problem The manual of instructional problems for MODFLOW Andersen 5 is intended to allow the student to have handson experience with the practical application of mod els Twenty documented problems complete with problem statements input data sets and discussion of results are presented in that manual The problems are designed to cover modeling principles specifics of inputoutput options available to the modeler rules of thumb and common modeling mistakes You can find an electronic version of this manual in the folder DocumentInstructional Problems for MODFLOW EPA on the companion CDROM Modeling Approach and Simulation Results Most of the models described in the manual of instructional problems have been re built by using PM You can find the models in subfolders under pathexamplesEPA Instructional Problems Although these models are readytorun it is suggested to construct the models by yourself because you will learn more through exercises and mistakes 360 5 Examples and Applications 53 Parameter Estimation and Pumping Test 531 Basic Parameter Estimation Skill Folder pmdirexamplescalibrationcalibration1 Overview of the Problem Groundwater models are usually applied to conceptualize and understand a hydrologic system or to predict the outcome of a future change to the system In order to provide some assurance that the model reflects the behavior or appearance of the flow system it must be calibrated prior to use as a predictive tool Model Calibration is accomplished by finding a set of model parameters boundary conditions and excitations or stresses that produce simulated heads or drawdowns and fluxes that match measurement val ues within an acceptable range of error Model calibration can be performed by the handoperated trialanderror adjustment of aquifer parameters or by inverse models such as PEST MODINV 32 MODFLOWP 61 or MODFLOW2000 56 63 This example provides an exercise in model calibration with PEST Specific details of this example are from Andersen 5 Fig 522 shows the idealized flow system and locations of observation boreholes The flow system is a small confined aquifer which is strongly controlled by the river flowing across it The aquifer is approximately 100 ft thick and is composed primarily of silty sand The river is not in direct hydraulic connection with the aquifer but acts as a leaky boundary condition which can gain or lose water to the aquifer Stage data for the river and riverbed elevation are listed in Table 52 Other boundary conditions are noflow which surround the square and define the areal extent of the aquifer Given constraints of uniform transmissivity and recharge and additional data be low the task is to obtain a steady state calibration based on the measurements listed in Table 53 Initial hydraulic head 1000 ft Grid size 15 15 x y 500 ft River base flow at western model boundary 10 cfs River base flow at eastern model boundary 11125 cfs Riverbed conductance 001 ft2s 53 Parameter Estimation and Pumping Test 361 Fig 522 Configuration of the aquifer system 362 5 Examples and Applications Table 52 River data Row Column Stage ft Riverbed Elevation ft 4 1 1000 900 4 2 1000 900 4 3 1000 900 4 4 990 890 4 5 990 890 5 6 980 880 6 7 970 860 7 8 960 860 8 9 950 850 9 10 940 840 9 11 940 840 9 12 940 840 9 13 940 840 9 14 930 830 9 15 930 830 Table 53 Measurement data Borehole X Y Head ft Borehole X Y Head ft 1 250 750 1240 7 4750 2250 1085 2 1750 2250 1199 8 4750 2250 1117 3 6250 1250 1139 9 6750 4250 1076 4 250 3750 1161 10 3750 6250 1113 5 5750 5750 1130 11 7250 6750 1156 6 2750 3250 1140 Modeling Approach and Simulation Results The aquifer is simulated using a grid of one layer 15 columns and 15 rows A regular grid spacing 500 ft is used for each column and row The layer type is 0confined and the Transmissivity flag in the Layer Property dialog box is userspecified Transmis sivity and recharge are defined as estimated parameters Note that the names of these two parameters are t 1 and rch 2 The optimized parameter values and the correlation coefficient matrix calculated by PEST are listed below Parameter Estimated 95 percent confidence limits value lower limit upper limit t1 1000282E02 9902461E03 1010419E02 53 Parameter Estimation and Pumping Test 363 rch2 1996080E08 1983990E08 2008169E08 Note confidence limits provide only an indication of parameter uncertainty They rely on a linearity assumption which may not extend as far in parameter space as the confidence limits themselves see PEST manual Parameter correlation coefficient matrix t1 rch2 t1 1000 09870 rch2 09870 1000 The diagonal elements of the correlation coefficient matrix are always unity The offdiagonal elements are always between 1 and 1 The closer an offdiagonal element is to 1 or 1 the more highly correlated are the parameters corresponding to the row and column numbers of that element For this example transmissivity parameter t 1 and recharge parameter rch 2 are highly correlated as is indicated by the value 0987 of the correlation coefficient matrix This means that these parameters are determined with a high degree of uncertainty in the parameter estimation process A sensitivity analysis could be used to quantify the uncertainty in the calibrated model caused by uncertainty in the estimates of the aquifer parameters For our example the only discharge is to the river and the only source is recharge To be in steady state these two must balance Recharge must therefore be equal to 1125 cfs the river gain equals 11125 cfs 10 cfs Spreading over the modeled area RECHARGE 1125 ft3s 15 15 500 ft 500 ft 2 108fts 51 The estimated parameter values are acceptable A better procedure would have been to compute the recharge right away from Equation 51 and estimate only transmissivity 364 5 Examples and Applications 532 Estimation of Pumping Rates Folder pmdirexamplescalibrationcalibration2 Overview of the Problem This example involves the encapsulation of a highly contaminated area The aquifer in which the contaminated area is buried is unconfined isotropic and of infinite areal extent The extent of the contamination area is about 65 m65 m The hydraulic head in the center of this area is about 945 m The elevation of the aquifer top is 10 m and the aquifer bottom is at 0 m The hydraulic conductivity is uniformly 3 104 ms The unconfined storage coefficient specific yield is 02 Recharge is assumed to be zero The groundwater flow is directed from west to east with a hydraulic gradient of 005 To prevent contaminated water flow out of the area a remedial measure is re quired Different types and combinations of measures can be introduced for this pur pose including a cutoff wall around the area drains and pumping wells All measures are directed towards the same goal a reduction of the hydraulic head in the con taminated area itself such that groundwater flows towards the contaminated area To achieve this objective a cutoff wall around this area and four pumping wells have been chosen The cutoff wall is 05 m thick and the hydraulic conductivity of the material is 5 108 ms The task is to estimate the required pumping rate of the wells such that the steady state piezometric head in the center of the contaminated area is 8 m Furthermore the duration until the steady state is reached should be calculated Modeling Approach and Simulation Results The condition is simulated using a grid of one layer 31 columns and 31 rows The layer type is 1unconfined Fig 523 shows the model grid and the selected boundary conditions The extent of the model is fairly large to ensure that the changes in hy draulic heads at the boundaries are not affected by the remedial measure To obtain the hydraulic gradient of 005 the west and east sides of the model are assumed to be fixedhead boundaries with hydraulic head values of 98925 m and 9 m respectively The steadystate condition is simulated using one stress period and one time step Al though the length of the stress period is not relevant for a steadystate solution we set the length to 1 so the computed head values can be compared with observed values For this example an observation borehole is set at the center of the contaminated area The observed head at time 1 is set at 8 m the objective using the Head Observation dialog box see Section 26114 53 Parameter Estimation and Pumping Test 365 Fig 523 Plan view of the model The configuration of the remedial measures is shown in Fig 524 The pumping rates of the wells are defined as an estimated parameter by assigning the parameter number 1 to all four wells Using PEST the pumping rate of each well is estimated at about 79 105 m3s To calculate the required time to reach the steadystate condition the estimated pumping rate of 79 105 m3s is specified to each well A transient simulation with one stress period subdivided into 25 equal time steps is carried out The total simulation time is set at 1 108 seconds The calculated headtime curve Fig 525 shows that the steady state is reached at t 4 107 s 366 5 Examples and Applications Fig 524 Location of the cutoff wall and pumping wells Fig 525 Time series curve of the calculated hydraulic head at the center of the con taminated area 53 Parameter Estimation and Pumping Test 367 533 The Theis Solution Transient Flow to a Well in a Confined Aquifer Folder pmdirexamplescalibrationcalibration3 Overview of the Problem This example gives an approximation of the Theis solution with a numerical model Given the aquifer properties transmissivity and confined storage coefficient the Theis solution predicts drawdown in a confined aquifer at any distance from a well at any time since the start of pumping The assumptions inherent in the Theis solution in clude 1 The aquifer is homogeneous isotropic and of uniform thickness 2 The aquifer is confined between impermeable formations on top and bottom and of infinite areal extent 3 The initial piezometric surface is horizontal and uniform 4 The pumping rate of the well is constant with time 5 The well penetrates the entire aquifer and the well diameter is small 6 Water is removed from storage instantaneously with decline in head A numerical model can represent all of these assumptions with the exception of infinite areal extent In this example a fully penetrating well is located at the center of the model do main and withdraws water at a constant rate The drawdown of the hydraulic head is monitored with time at a borehole 55 m from the pumping well The task is to construct a numerical model calculate the drawdown curve at the borehole and compare it with the analytical Theis solution The model parameters are given below Initial hydraulic head 00 m Transmissivity 00023 m2s Storage coefficient 000075 Pumping rate 4 103 m3s Total simulation time 86400 s Number of time steps 20 Time step multiplier 13 Number of SIP iteration parameters 5 Convergence criterion of head change 00001 m Maximum number of iterations 50 368 5 Examples and Applications Modeling Approach and Simulation Results To meet the requirement of an infinite areal extent the modeled domain is chosen fairly large The boundary could alternatively be moved even further from the pumping well by using the General Head Boundary see Section 512 A single layer model simulates the aquifer An increasing grid spacing expansion is used to extend the model boundaries Fig 526 The layer type is 0confined In the Layer Property dialog box the flags of Transmissivity and Storage Coefficient are set to Userspecified The top and bottom elevations of the model layer are not required in this example since the geometrical information is included in Transmissivity and Storage Coefficient The analytical drawdown values at the borehole are specified in the Drawdown Observation dialog box Models Modflow Drawdown Observation Both the ana lytical and calculated drawdown curves are shown in Fig 527 An exact comparison is not attained because of the approximations made in the numerical model These in clude 1 use of a discrete rather than continuous spatial domain 2 use of a discrete rather than continuous time domain 3 use of an iterative solution with a convergence tolerance 4 artificial placement of boundaries In practice we can use this model to estimate transmissivity and confined storage coefficient by specifying the real observation time and data in the Drawdown Observa Fig 526 Plan view of the model 53 Parameter Estimation and Pumping Test 369 tion dialog box By defining transmissivity and storage coefficient as estimated param eters the parameter estimation program PEST can estimate the parameters automat ically Select Models PEST Parameter Estimation Run to see how the parameter estimation programs work Since the analytical drawdown values were used as the ob servations the results from the parameter estimation programs must be transmissivity 00023 m2s and storage coefficient 000075 Fig 527 Timeseries curves of the calculated and observed drawdown values 370 5 Examples and Applications 534 The Hantush and Jacob Solution Transient Flow to a Well in a Leaky Confined Aquifer Folder pmdirexamplescalibrationcalibration4 Overview of the Problem This example demonstrates how to approach leaky confined aquifers A leaky confined aquifer is overlaid andor underlaid by geologic formations which are not completely impermeable and can transmit water at a sufficient rate Fig 528 Hantush and Jacob 52 give an analytical solution to describe the drawdown with time during pumping with a well in a leaky confined aquifer In addition to the assumptions in the Theis solu tion the analytical solution requires two assumptions the hydraulic head in the over lying or underlying aquifer is constant during pumping in the leaky confined aquifer and the rate of leakage into the pumped aquifer is proportional to drawdown In this example a pumping well withdraws water at a constant rate from the leaky confined aquifer The drawdown of the hydraulic head is monitored with time at a bore hole 55 m from the pumping well The borehole is located in the leaky confined aquifer Fig 528 Configuration of the leaky aquifer system and the aquifer parameters 53 Parameter Estimation and Pumping Test 371 The initial hydraulic head is 8 m everywhere Specific yield and effective porosity are 01 The other aquifer parameters are given in Fig 528 The analytical solution for this case is given in Table 54 The task is to construct a numerical model calculate the drawdown curve at the borehole and compare it with the HantushJacob solution Note that the parameters for the confined leaky aquifer are the same as in the previous example so we can compare the results of these two examples Modeling Approach and Simulation Results The modeled domain is the same as in the previous example Three model layers are used to simulate the system The layer type of all three layers is 3confinedunconfined transmissivity varies In the Layer Property dialog box the Storage Coefficient flag is set to userspecified and the Transmissivity flag is calculated All model cells in the first model layer are fixedhead cells and all other cells are specified as active cells A transient flow simulation is performed for a stress period with the length of 49320 seconds 20 time steps and a timestep multiplier of 13 For comparison the analytical solution is entered in the Drawdown Observation dialog box Fig 529 shows the numerical and analytical drawdowntime curves at the observation borehole which is at a distance of 55 m from the pumping well The match of these two curves is very good While the use of the analytical solution is limited to the primary assumptions the numerical model can be used to evaluate pumping tests even if the confining aquitard Fig 528 has a higher value of the vertical hydraulic conductivity and the hydraulic head in the overlying aquifer is not constant during the pumping To do this simply specify all model cells as active cells This is allowed because the simulation time is normally very short and the extent of the model domain is relative large so that at the end of a transient flow simulation the drawdown values at the model boundaries are acceptable low Table 54 Analytical solution for the drawdown with time Time seconds Drawdown m Time seconds Drawdown m 123 00067 4932 0336 247 003 12330 0449 352 0052 24660 0529 493 0077 35228 0564 1233 0168 49320 0595 2466 025 123300 0652 3523 0294 372 5 Examples and Applications Fig 529 Configuration of the leaky aquifer system and the aquifer parameters If the vertical hydraulic conductivity of the aquitard is known we can use PEST to estimate the horizontal hydraulic conductivity and storage coefficient of the leaky aquifer by defining them as estimated parameters Click Models PEST Run to see how the parameter estimation programs work Because the analytical drawdown values were used as the observations the results from the parameter estimation programs must be horizontal hydraulic conductivity 23 104 ms and storage coefficient 000075 If the vertical hydraulic conductivity is unknown and needs to be estimated we will need additional drawdown values in the overlying aquifer during the pumping test 53 Parameter Estimation and Pumping Test 373 535 Parameter Estimation with MODFLOW2000 Test Case 1 Folder pmdirexamplescalibrationcalibration5 Overview of the Problem This example model is adapted from Hill and others 63 The physical system for this example is shown in Fig 530 The synthetic system consists of two confined aquifers separated by a confining unit Each aquifer is 50 m thick and the confining unit is 10 m thick The river is hydraulically connected to aquifer 1 Groundwater flow from the hillside adjoining the system is connected to aquifers 1 and 2 at the boundary farthest from the river The parameters that define aquifer properties are shown in Fig 530 and listed in Table 55 The observations of head and riverflow gain used in the parameter esti mation were generated by running the model with the given parameter values and the parameter multiplier PARVAL 1 for all parameters the actual parameter values used in the simulation are calculated as the product of the parameter values and the pa rameter multiplier PARVAL Different starting values are used for PARVAL and the estimated PARVAL values are expected to be close to 1 Fig 530 Physical system for test case 1 Adapted from Hill and others 63 374 5 Examples and Applications The hydraulic conductivity of the second aquifer is known to increase with distance from the river The variation is defined by a step function with the value 10 HK 3 in columns 1 and 2 20 HK 3 in columns 3 and 4 and so on to the value 90 HK 3 in columns 17 and 18 Stresses on the system include 1 areal recharge to aquifer 1 in the area near the stream zone 1 and in the area farther from the stream zone 2 and 2 groundwater abstraction from wells in each of the two layers The pumping rates from aquifers 1 and 2 are assumed to be the same Modeling Approach and Simulation Results For the finitedifference method the system is discretized into square 1000 m by 1000 m cells so that the grid has 18 rows and 18 columns Three model layers are used Lay ers 1 and 3 represent aquifers 1 and 2 respectively Layer 2 represents the confining unit A fairly small value of 1 109 ms is assigned to horizontal hydraulic conduc tivity of layer 2 so that the groundwater flows vertically through the confining unit Time discretization for the model run is specified to simulate a period of steady state conditions with no pumping followed by a transientstate period with a constant rate of pumping The steadystate period is simulated with one stress period having one time step The transient period is simulated with four stress periods the first three are 87162 261486 and 522972 seconds long and each has one time step the fourth is 2356745 107 seconds long and has 9 time steps and each timestep length is 12 times the length of the previous timestep length Groundwater flow into the system from the adjoining hillside is represented us ing the GeneralHead Boundary Package Thirtysix generalheadboundary cells are specified in column 18 of layers 1 and 3 each having an external head of 350 m and a hydraulic conductance of 1 107 m2s The river is treated as a headdependent boundary which is simulated using the River Package to designate 18 river cells in column 1 of layer 1 the head in the river is 100 m The parameter RIV 1 specifies the conductance of the riverbed for each cell Recharge in zone 1 RCH 1 applies to cells in columns 1 through 9 recharge in zone 2 RCH 2 applies to cells in columns 10 through 18 The pumpage is simulated using the Well Package Wells are located at the center of the cells at row 9 column 10 there is one well is in each of layer 1 and 3 Both wells have the same pumping rate The parameter WEL 1 specifies the pumping rate for each of the wells As shown in Table 55 the estimated values of PARVAL are as expected close to 1 The final parameter values are obtained by multiplying the estimated PARVAL with the parameters initial cellvalues 53 Parameter Estimation and Pumping Test 375 Table 55 Parameters defined for MODFLOW2000 test case 1 parameter values start ing and estimated PARVAL PARNAM Description Parameter values Starting PARVAL Estimated PARVAL HK 1 Hydraulic conductivity of layer1 4 104 ms 075 100000 HK 3 Hydraulic conductivity of layer 3 under the river 44 105 ms 09 100013 RCH 1 Recharge rate in zone 1 1 108 ms 20 099997 RCH 2 Recharge rate in zone 2 15 108 ms 066 100005 RIV 1 Hydraulic conductance of the riverbed 12 m2s 12 100036 SS 1 Specific storage of layer 1 4 105 1m 065 100006 SS 3 Specific storage of layer 3 2 106 1m 20 0999274 WEL 1 Pumping rate in each of layers 1 and 3 10 m3s 11 100003 VK 2 Vertical hydraulic conductivity of layer 2 2 107 ms 050 100017 376 5 Examples and Applications 536 Parameter Estimation with MODFLOW2000 Test Case 2 Folder pmdirexamplescalibrationcalibration6 Overview of the Problem This example model is adapted from Hill and others 63 The model grid shown in Fig 531 has a uniform grid spacing of 1500 m in the horizontal and has 247 active cells in each of three layers Layers 1 2 and 3 have a constant thickness of 500 m 750 m and 1500 m respectively Hydraulic conductivity is divided into four zones each of which is present in the middle layer and three of which are present in the top and bottom layers Constanthead boundaries comprise portions of the western and eastern boundaries with no flow across the remaining boundaries Headdependent boundaries representing springs are simulated using both the Drain and GeneralHead Boundary Packages Wells are present at selected cells with pumpage at rates ranging from 100 to 200 m3d Modeling Approach and Simulation Results Ten parameters were identified for inclusion in the parameter estimation and are de scribed in Table 56 along with their true assigned values The observations used in the parameter estimation were generated by running the model with the true parameter values and the parameter multiplier PARVAL 1 for all parameters the actual param eter values used in the simulation are calculated as the product of the parameter values and the parameter multiplier PARVAL The locations of the 42 observed hydraulic heads are shown in Fig 531 The flows simulated at the headdependent boundaries also were used as observations for the parameter estimation In this ideal situation the estimated values of the parameter multiplier PARVAL are expected to be close to 1 If this is accomplished it suggests that the observation sensitivities are calculated correctly and that the regression is performing correctly The final parameter values are obtained by multiplying the estimated PARVAL with the parameters initial values 53 Parameter Estimation and Pumping Test 377 Fig 531 Test case 2 model grid boundary conditions observation locations and hy draulic conductivity zonation used in parameter estimation Adapted from Hill and others 63 378 5 Examples and Applications Table 56 Parameters defined for MODFLOW2000 test case 2 parameter values start ing and estimated PARVAL PARNAM Description Parameter values Starting PARVAL Estimated PARVAL HK 1 Hydraulic conductivity of zone 1 see Fig 531 10 md 15 0999990 HK 2 Hydraulic conductivity of zone 2 see Fig 531 001 md 05 0999989 HK 3 Hydraulic conductivity of zone 3 see Fig 531 1 104 md 12 0999987 HK 4 Hydraulic conductivity of zone 4 see Fig 531 1 106 md 20 1000330 VANI 12 Vertical anisotropy of layers 1 and 2 4 025 1000010 VANI 3 Vertical anisotropy of layer 3 1 100 1000040 RCH 1 Areal recharge rate applied to the area shown in Fig 531 31 104 md 142 0999988 EVT 1 Maximum evapotranspiration rate applied to area shown in Fig 531 4 104 md 075 0999968 GHB 1 Conductance of headdependent boundaries represented using the GeneralHead Boundary package G in Fig 531 10 m2d 05 0999988 DRN 1 Conductance of headdependent boundaries represented using the Drain package D in Fig 531 10 m2d 20 0999990 54 Geotechnical Problems 379 54 Geotechnical Problems 541 Inflow of Water into an Excavation Pit Folder pmdirexamplesgeotechniquesgeo1 Overview of the Problem This example is adapted from Kinzelbach and Rausch 72 Fig 532 shows the plan view and a cross section through a shallow aquifer situated in a valley In the north the aquifer is bounded by the outcrop of the sediments in the valley while the south boundary is a river which is in contact with the aquifer The aquifer extends several kilometers to the west and east it is unconfined homogeneous and isotropic The top and bottom elevations of the aquifer are 7 m and 0 m respectively The average horizontal hydraulic conductivity of the sandy sediments is 0001 ms the effective porosity is 015 The groundwater recharge from precipitation is 6 109 m3sm2 The water stage in the river is 5 m above the flat aquifer bottom which is the reference level for the simulation At a distance of 200 m from the river there is an excavation pit The length of the pit is 200 m the width 100 m The bottom of the excavation is 3 m above the aquifer bottom The task is to calculate the inflow into the pit and show head contours and catch ment area of the pit Modeling Approach and Simulation Results The aquifer is simulated using a grid of one layer 40 columns and 19 rows A regular grid spacing of 50 m is used for each column and row The layer type is 1unconfined To simplify the simulation use of symmetry is made by modeling only half the domain The river and the pit are modeled as fixedhead boundaries with hydraulic heads of h 5 m and 3 m respectively All other boundaries are noflow boundaries The distance between the eastern noflow boundary and the pit is not known a priori and must be selected large enough so that the pit does not influence it Whether the choice was adequate can be easily checked by increasing the sizes of the last few columns and calculating again If the results do not change appreciably the first computation was fine Fig 533 shows the head contours the catchment area of the excavation and two crosssections Using the Water budget calculator the inflow into the pit is calculated at 2 00129 m3s 00258 m3s 380 5 Examples and Applications Fig 532 Configuration of the physical system 54 Geotechnical Problems 381 Fig 533 Simulated head distribution and catchment area of the excavation pit 382 5 Examples and Applications 542 Flow Net and Seepage under a Weir Folder pmdirexamplesgeotechniquesgeo2 Overview of the Problem This example is adapted from Kinzelbach and Rausch 72 An impervious weir is par tially embedded in a confined aquifer The aquifer is assumed to be homogeneous with a hydraulic conductivity of the aquifer of 00005 ms and a thickness of 9 m The effective porosity of the aquifer is 015 The boundary conditions are shown in Fig 534 Calculate the flow net and the flux through the aquifer for the cases that 1 the aquifer is isotropic and 2 the aquifer is anisotropic with an anisotropy factor of 02 Modeling Approach and Simulation Results To compute the head distribution and the corresponding flowlines it is sufficient to consider a vertical crosssection of the aquifer with a uniform thickness of 1 m In this example the vertical crosssection is represented by a model with a grid of one layer 65 columns and 9 rows A regular grid spacing of 1 m is used for each column and row The layer type is 0confined Fig 535 shows the cross section the selected model grid and the boundary conditions The boundaries at the upstream and downstream of the weir are modeled as fixedhead boundaries with h 12 m and h 10 m above reference level respectively The aquifer bottom and the weir itself are modeled as noflow boundaries Fig 536 shows the flow net for the isotropic case The head values range from 10 to 12 m with a head increment of 01 m The flux through the aquifer per meter width of the weir is 365 104 m3sm 3156 m3daym Fig 537 shows the flow net for the aquifer in the anisotropic case The flux through the aquifer is now only 25 104 m3sm 216 m3daym Note that in a homogeneous and anisotropic medium flowlines intersect head contours at right angle only where flow is parallel to one of the principal directions of hydraulic conductivity 54 Geotechnical Problems 383 Fig 534 Configuration of the physical system Fig 535 Model grid and the boundary conditions Fig 536 Flowlines and calculated head contours for isotropic medium Fig 537 Flowlines and calculated head contours for anisotropic medium 384 5 Examples and Applications 543 Seepage Surface through a Dam Folder pmdirexamplesgeotechniquesgeo3 Overview of the Problem This example is adapted from Kinzelbach and Rausch 72 It demonstrates how to calculate the seepage surface using a vertical crosssectional model As shown in Fig 538 the length of the dam is 100 m the thickness and height are 10 m The water table is 10 m at the upstream side of the dam and 2 m at the downstream side The material of the dam is homogeneous and isotropic with a hydraulic conductivity of 1 105 ms The unrealistic bank slope is used here to simplify the data input The task is to calculate the seepage surface and the seepage rate by using a vertical crosssectional numerical model Compare the seepage rate with an analytical solution after Dupuit Modeling Approach and Simulation Results To compute the head distribution and the seepage surface it is sufficient to consider a vertical crosssection of the aquifer with a uniform thickness of 1 m The aquifer is simulated using a grid of one layer 21 columns and 20 rows A regular grid spacing of 05 m is used for each column The layer type is 0confined The boundary at the upstream side of the dam is modeled as fixedhead boundary with the hydraulic head h 10 m On the righthand side of the dam there are four fixedhead cells with h 2 m The other cells on this boundary are modeled as drain cells with a high drain hydraulic conductance L2T 1 value The elevation of the drain is set the same as the bottom elevation of each cell for example the 20 m for the cell 1 16 21 and 25 m for the cell 1 15 21 The drain cells are activated only if water table is higher than the level of the drain The selected model grid and the boundary conditions are shown in Fig 539 Except the four fixedhead cells at the righthand side of the dam the initial hydraulic head for all cells are 10 m The first step in solving this problem is to carry out a steadystate flow simula tion with these data Fig 540 shows the calculated hydraulic heads By comparing the calculated heads with the elevation of the cell bottom we can easily find that the hydraulic heads of some of the cells at the upperright corner of the model are lower than the cell bottom This means that these cells went dry In the second step these dry cells will be defined as inactive cells by setting IBOUND 0 and a steadystate flow simulation will be carried out again Now it is possible that some of the calculated heads are higher than the top elevation of the highest active cell In this case these cells will be defined as active and a steadystate flow simulation will be performed again This iterative solution will be repeated until the water table remains unchanged 386 5 Examples and Applications Fig 538 Seepage surface through a dam 54 Geotechnical Problems 387 Fig 539 Model grid and the boundary conditions Fig 540 Calculated hydraulic heads after one iteration step 388 5 Examples and Applications Fig 541 Calculated hydraulic heads distribution and the form of the seepage surface 54 Geotechnical Problems 389 544 Cutoff Wall Folder pmdirexamplesgeotechniquesgeo4 Overview of the Problem As shown in Fig 542 a highly contaminated area is located in the first stratigraphic unit of an unconfined aquifer To the west and east of the aquifer exist fixedhead boundaries with the hydraulic head h 04 m and 05 m The aquifer consists of five stratigraphic units Each unit is horizontally isotropic with uniform thickness The ele vations and horizontal hydraulic conductivities are illustrated in Fig 542 The vertical hydraulic conductivities are assumed to be a tenth of the horizontal hydraulic conduc tivities The effective porosity of the aquifer is 015 The recharge rate is 1108 ms Because of the high cost the contaminants cannot be removed The task is to de velop a strategy to isolate the contamination There are four subtasks to be done 1 Construct a groundwater flow model and perform a steadystate flow simulation by using the data given above and the model grid given in Fig 542 2 Geotechnical measures such as cutoff wall impervious cover drain etc can be considered as an alternative Calculate flowlines for the case that a cutoff wall has been built to a depth of 8m and the recharge rate within the cutoff wall is reduced to zero by an impervious cover The location of the cutoff wall is given in Fig 542 When calculating the flowlines particles should be started from the contaminated area 3 Repeat previous step for the case that the cutoff wall reaches the depth 10m 4 Use a pumping well located in the cell row column 12 6 to capture the contaminants Calculate the required pumping rate and penetration depth Modeling Approach and Simulation Results The aquifer is simulated using a grid of 5 layers 23 rows and 23 columns All layers have the same layer type 3 confinedunconfined Transmissivity varies The cutoff wall is modeled by using the HorizontalFlow Barriers package An impervious cover can be easily simulated by reducing the recharge rate Figures 543 and 544 show the flowlines by performing forward and backward particletracking with PMPATH The particles are initially placed in the center of each cell which is located in the first model layer and within the cutoff wall It is obvious that the contaminants will be washed out even if the cutoff wall is going deeper The contaminated area can be captured by using a pumping well located in the cell row column 12 6 penetrating in the first model layer with a pumping rate of 390 5 Examples and Applications 00025 m3s This low pumping rate is possible because of the low groundwater flow velocity within the zone around the contaminated area Fig 542 Model grid and boundary conditions 54 Geotechnical Problems 391 Fig 543 Plan and crosssectional views of flowlines Particles are started from the contaminated area The depth of the cutoff wall is 8 m 392 5 Examples and Applications Fig 544 Plan and crosssectional views of flowlines Particles are started from the contaminated area The depth of the cutoff wall is 10 m 54 Geotechnical Problems 393 545 Compaction and Subsidence Folder pmdirexamplesgeotechniquesgeo5 Overview of the Problem Fig 545 shows a plan view and a cross section through an aquifer which consists of three stratigraphic units of uniform thickness The first unit of the aquifer is unconfined and the other units are confined The initial hydraulic head is 43 m everywhere The areal extent of the aquifer is assumed to be infinite large Except a confining bed clay in the second unit the sandy sediments of the aquifer are homogeneous horizontally isotropic with an average horizontal hydraulic conductivity of 00001 ms and vertical hydraulic conductivity of 000001 ms The specific yield of the first stratigraphic unit is 015 The specific storage of the aquifer is assumed to be 00001 1m The proper ties of the confining bed are Horizontal hydraulic conductivity 1 106 ms Vertical hydraulic conductivity 1 107 ms Elastic specific storage 0002 1m Inelastic specific storage 0006 1m To construct a new building an excavation pit with the size 200 m 100 m is required The bottom elevation of the pit is 40 m The pit must be held dry for one year The task is to calculate the required withdrawal rate for keeping the pit dry and the delineate the distribution of subsidence after one year Modeling Approach and Simulation Results The aquifer is simulated using a grid of 3 layers 36 columns and 36 rows The extent of the model grid is fairly large Each model layer represents a stratigraphic unit The layer type 3 confinedunconfined Transmissivity varies can be used for all layers as layers of this type switch between confined and unconfined automatically In the Layer Property dialog box the Interbed storage flag for the second layer is checked The pit is modeled as fixedhead boundary with the hydraulic head h 40 m The compaction and thus the land surface subsidence of the confining bed is modeled using the Interbed Storage package A transient flow simulation with one stress period and 30 time steps has been car ried out The length of the stress period is one year 31536 107 seconds The required withdrawal rate changes with time and can be calculated by using the water budget calculator by assigning the subregion number 1 to the pit For the first time step the required withdrawal rate is 00134 m3s 482 m3h For the last time step it is reduced to 00066m3s 2376m3h The distribution of the subsidence caused 394 5 Examples and Applications by this withdrawal rate can be obtained by using the Results Extractor tool Fig 546 shows the contours of the land surface subsidence for the last time step The maximum subsidence is about 011 m For detailed description of the Interbed Storage package and the calculation of compaction and subsidence refer to Leake and Prudic 78 which includes two test cases We have rebuilt the test cases and saved them in pmdirexamplesgeotechniquesgeo5a and pmdirexamplesgeotechniquesgeo5b 54 Geotechnical Problems 395 Fig 545 Model grid and boundary conditions 396 5 Examples and Applications Fig 546 Distribution of the land surface subsidence maximum 011 m 55 Solute Transport 397 55 Solute Transport 551 Onedimensional Dispersive Transport Folder pmdirexamples ransport ransport1 Overview of the Problem This example demonstrates the use of the numerical transport model and compares the numerical results with an analytical solution A uniform flow with a hydraulic gradient of 02 exists in a sand column The hydraulic conductivity of the sand column is 100 md The effective porosity is 02 The longitudinal dispersivity is 1 m A pollutant mass of 1 gram is injected into the sand column instantaneously The task is to construct a onedimensional numerical model and calculate the breakthrough curve time series curve of concentration at 20 m downstream of the injection point Calculate the breakthrough curve by using a longitudinal dispersivity of 4 m and compare these two curves Will the peak arrival time of the concentration be changed if only the longitudinal dispersivity is changed Modeling Approach and Simulation Results The numerical model of this example consists of one layer one row and 51 columns The thickness of the layer and the width of the row and column is 1 m To obtain a hydraulic gradient of 02 the first cell and the last cell of the model are specified as fixedhead cells with initial hydraulic heads of 11 m and 10 m respectively The initial head of all other cells is 10 m A steady state flow simulation is carried out for a stress period length of 100 days The injected mass of 1 g is simulated by assigning an initial concentration of 5 gm3 to the cell 1 1 10 Using the Concentration Observation dialog box an observation borehole is set in the center of the cell 1 1 30 The breakthrough curves for the dispersivity values of 1 m and 4 m are shown in Fig 547 It is interesting to see that the concentration peak arrives earlier with a lower concentration value when the value of dispersivity is higher At the first glance this result is somewhat confusing because the center of mass should travel with the same velocity regardless of the value of dispersivity Because of a higher dispersivity the front of the concentration plume travels faster and at the same time the intensity of the concentration drops faster This combination causes this phenomenon Analytical solutions for solute transport involving advection dispersion and first order irreversible decay in a steadystate uniform flow field are available in many text books for example Javandel and others 68 Kinzelbach 69 or Sun 112 A 398 5 Examples and Applications computer program for the analytical solutions of 1D and 2D solute transport for pointlike pollutant injections is provided by Rausch 101 and included in the folder Sourceanalytical solution of the companion CDROM This program is written in BASIC Try to use this program to compare the analytical and numerical solutions Fig 547 Comparison of the calculated breakthrough curves with different dispersivity values 55 Solute Transport 399 552 Twodimensional Transport in a Uniform Flow Field Folder pmdirexamples ransport ransport2 Overview of the Problem In this example transport of solute injected continuously from a point source in a steady state uniform flow field should be simulated The available parameters are listed below Layer thickness 10 m Groundwater seepage velocity l3 mday Effective porosity 03 Longitudinal dispersivity 10 m Ratio of transverse to longitudinal dispersivity 03 Volumetric injection rate 1 m3day Concentration of the injected water 1000 ppm The task is to construct a 2Dmodel and use MT3DMS to calculate the concentra tion distribution at the end of a 365 day simulation period Modeling Approach and Simulation Results A numerical model consisting of 1 layer 31 rows and 46 columns and was con structed to simulate the problem A regular grid spacing of 10 m is used for each column and row The configuration of the model is shown in Fig 548 The model layer is simulated as a confined layer The top and bottom of the model layer are at an elevation of 10 m and 0 m respectively To simulate the groundwater seepage velocity of 13 mday fixedhead boundaries with h 11 m and h 10 m are assigned to the west and east side of the model The horizontal hydraulic conductivity is 45 mday The flow field was first calculated by MODFLOW The third order TVD scheme was used in the simulation for the advection term and the GCG solver is used to solve the system equations The contour map of the concentration field at the end of the 365 day simulation period obtained for this example is shown in Fig 549 An analytical solution for this problem is given by Wilson and Miller 118 The analytical solution is applicable only under the assumption that 1 the aquifer is relatively thin so that instantaneous vertical mixing can be assumed 2 the injection rate is insignificant compared with the ambient uniform flow Fig 550 shows the breakthrough curves at an observation well located 60 m down stream of the injection well The analytical solution is obtained by using the computer 400 5 Examples and Applications program by Rausch 101 included in the folder Sourceanalytical solution of the companion CDROM Fig 551 compares the analytical solution with the numerical solution obtained by using the upstream finite difference method The numerical dis persion is significant when the upstream finite difference method is used to solve the advection term Fig 548 Configuration of the model and the location of an observation borehole 55 Solute Transport 401 Fig 549 Calculated concentration distribution Fig 550 Comparison of the breakthrough curves at the observation borehole The numerical solution is obtained by using the 3rd order TVD scheme 402 5 Examples and Applications Fig 551 Comparison of the breakthrough curves at the observation borehole The numerical solution is obtained by using the upstream finite difference method 55 Solute Transport 403 553 Monod Kinetics Folder pmdirexamples ransport ransport3 Overview of the Problem The example problem considered in this section is adapted from Zheng 124 It in volves onedimensional transport from a constant source in a uniform flow field The model parameters used in the simulation are given below Cell width along columns Idirection 1 m Cell width along rows Jdirection 10 m Layer thickness Kdirection 1 m Longitudinal dispersivity 10 m Groundwater seepage velocity 024 mday Effective Porosity 025 Simulation time length 2000 days Three simulations using different parameters for the Monod kinetics as given below need to be carried out Note that these reaction parameters are intended for demonstra tion purposes only and have no particular physical relevance Case 1 Mt µmax 2 mgliterday Ks 1000 mgliter Case 2 Mt µmax 2 103 mgliterday Ks 1 mgliter Case 3 Mt µmax 2 103 mgliterday Ks 0001 mgliter Modeling Approach and Simulation Results The model grid consists of 1 layer 1 row and 101 columns In the flow model the first and last columns are constanthead boundaries To establish the required uniform hydraulic gradient the initial hydraulic head values of 70 m and 10 m are assigned to the first and last columns respectively In the transport model the first column is a constantconcentration boundary with a concentration value of 10 mgliter The last column is sufficiently far away from the source to approximate a semiinfinite onedimensional flow domain Fig 552 shows the simulation results For Case 1 the Monod kinetics should approach a firstorder reaction since Ks is three orders greater than the maximum con centration in the aquifer Indeed the calculated concentration profile with the Monod kinetics is nearly identical to the solution for the same transport problem but assuming 404 5 Examples and Applications a firstorder reaction with the rate coefficient λ Mt µmaxKs 2 103 day1 Case 2 with Ks in the same order as the aquifer concentrations shows the mixed order characteristics of the Monod kinetics In Case 3 the Monod kinetics approaches a zeroorder reaction ie Ct Mt µmax since Ks is negligible compared to the concentrations in the aquifer Fig 552 Calculated concentration values for onedimensional transport from a con stant source in a uniform flow field 55 Solute Transport 405 554 Instantaneous Aerobic Biodegradation Folder pmdirexamples ransport ransport4 Overview of the Problem The example problem considered in this section is adapted from Zheng 124 and is similar to the model described in Section 552 The problem involves twodimensional transport from a continuous point source in a uniform flow field The point source has a volumetric injection rate of 1 m3day and the injected water contains hydrocarbon species 1 with a constant concentration of 1000 ppm The background concentration of oxygen species 2 in the aquifer is 9 ppm Hydrocarbon and oxygen are assumed to react instantaneously the stoichiometric ratio for the reaction is approximately 30 ie one mass unit of hydrocarbon reacts with three mass unit of oxygen The other model parameters used in the simulation are given below Cell width along columns Idirection 10 m Cell width along rows Jdirection 10 m Layer thickness Kdirection 10 m Groundwater seepage velocity 03333 mday Effective Porosity 03 Longitudinal dispersivity 10 m Ratio of transverse to longitudinal dispersivity 03 Volumetric injection rate 1 m3day Simulation time 730 days The concentration distributions of hydrocarbon and oxygen after a simulation pe riod of 730 days 2 years need to be calculated Modeling Approach and Simulation Results The model grid is aligned with the flow direction along the xaxis and consists of 1 layer 31 rows and 46 columns The flow model is surrounded by constanthead boundaries on the east and west borders and noflow boundaries on the north and south borders To establish the required uniform hydraulic gradient the head values 11 m and 10 m are assigned to the first and last columns respectively The point source is simulated using an injection well located at column 11 and row 16 The injection rate is sufficiently small so that the flow field remains approximately uniform The background oxygen concentration is modeled by setting the initial con centration of species 2 to 9 ppm in all model cells and by assigning 9 ppm to the species 2 concentration of the inflow from the constanthead boundary 406 5 Examples and Applications The concentrations for hydrocarbon and oxygen at the end of the twoyear simula tion period are calculated by RT3D and shown in Figures 553 and 554 The maximum concentration of hydrocarbon is approximately 50 ppm at the injection point Fig 553 The oxygen plume is depleted where the concentration of hydrocarbon is above zero Fig 554 For this example the TVD scheme is chosen for solving the advection term while all other terms are solved by the explicit finitedifference option The mass balance discrepancies for both species are less than 104 The calculated hydrocar bon and oxygen plumes are nearly identical to those calculated using MT3D99 124 Fig 553 Calculated concentration values of hydrocarbon 55 Solute Transport 407 Fig 554 Calculated concentration values of oxygen 408 5 Examples and Applications 555 FirstOrder ParentDaughter Chain Reactions Folder pmdirexamples ransport ransport5 Overview of the Problem The example problem is adapted from Zheng 124 It involves onedimensional trans port of three species in a uniform flow field undergoing firstorder sequential trans formation The model parameters used in this example are identical to those used in Clement 25 for the PCETCEDCEVC sequential transformation and are given below Cell width along columns Idirection 1 cm Cell width along rows Jdirection 05 cm Layer thickness Kdirection 1 cm Longitudinal dispersivity 18 cm Groundwater seepage velocity 01 cmhr Firstorder reaction rate for PCE species 1 005 hr1 Firstorder reaction rate for TCE species 2 003 hr1 Firstorder reaction rate for DCE species 3 002 hr1 Firstorder reaction rate for VC species 4 001 hr1 Retardation factor for PCE species 1 2 Yield coefficient between PCE and TCE Y12 0792 Yield coefficient between TCE and DCE Y23 0738 Yield coefficient between DCE and VC Y34 0644 Simulation time 200 hours Modeling Approach and Simulation Results The model grid consists of 1 layer 1 row and 101 columns In the flow model the first and last columns are constanthead boundaries To establish the required uniform hydraulic gradient the head values 05 cm and 0 cm are assigned to the first and last columns respectively In the transport model the first column is a constantconcentration boundary for all species with the concentration values equal to 10 mgliter for PCE species 1 and zero for other species The last column is sufficiently far away from the source to approximate a semiinfinite onedimensional flow domain The initial concentration values for all species are assumed to be zero The retardation factor of 2 is simulated by assigning ne 01 bulk density ρb 1000kgm3 and distribution coefficient Kd 00001m3kg as the retardation factor R is calculated by 55 Solute Transport 409 R 1 ρb ne Kd 53 Fig 555 shows the concentration distributions calculated by RT3D for all four species at the end of the 200hour simulation period The calculated values agree closely with the solutions of MT3D99 124 which are not shown in the figure since the curves are nearly identical It can be seen that as PCE species 1 is transported from the source its mass lost to decay becomes the source for TCE species 2 some of which is in turn transformed into DCE species 3 and then VC species 4 Fig 555 Comparison of calculated concentration values of four species in a uniform flow field undergoing firstorder sequential transformation 410 5 Examples and Applications 556 Benchmark Problems and Application Examples from Literature Folder pmdirexamples ransport Overview of the Problem To test the accuracy and performance of the MT3DMT3DMS and MOC3D codes sev eral benchmark problems and application examples are introduced in the users guides of MT3D 119 MT3DMS 123 and MOC3D 74 You can find these documents on the folders documentmt3d documentmt3dms and documentmoc3d of the companion CDROM Modeling Approach and Simulation Results We have rebuilt most of the benchmark problems of MT3DMT3DMS and MOC3D by using PM These models are saved in the subfolders under pathexamples rans port listed below All these models are readytorun It is recommended that the users try these test problems first to become familiarized with the various options before applying MT3DMT3DMS or MOC3D to solve their own problems Folder Description ransport6 This model is described in Section 75 of the manual of MT3DMS A numerical model consisting of 1 layer 31 rows and 31 columns is used to simulate the twodimensional transport in a radial flow field numerical results were compared with the analytical solution of Moench and Ogata 88 ransport7 This model is described in Section 76 of the manual of MT3DMS A numerical model consisting of 1 layer 31 rows and 31 columns is used to simulate the concentration change at the injectionabstraction well numerical results were compared with the approximate analyt ical solution of Gelhar and Collins 48 ransport8 This model is described in Section 77 of the manual of MT3DMS A numerical model consisting of 8 layers 15 rows and 21 columns is used to solve threedimensional transport in a uniform flow field The point source was simulated at layer 7 row 8 and column 3 Nu merical results were compared with the analytical solution of Hunt 67 ransport9 This model is described in Section 79 of the manual of MT3DMS This example illustrates the application of MODFLOW and MT3DMT3DMS to a problem involving transport of contaminants in a twodimensional heterogeneous aquifer 55 Solute Transport 411 Folder Description ransport10 This model is described in Section 710 of the manual of MT3DMS This example illustrates the application of MT3DMT3DMS to an actual field problem involving the evaluation of the effectiveness of proposed groundwater remediation schemes ransport11 This model is described in the section MODEL TESTING AND EVALUATION OneDimensional Steady Flow of the users guide of MOC3D A numerical model consisting of 1 layer 1 row and 122 columns is used to simulate onedimensional transport having a thirdtype source boundary condition in a steadystate flow field nu merical results were compared with the analytical solution of Wexler 116 ransport12 This model is described in the section MODEL TESTING AND EVALUATION ThreeDimensional Steady Flow of the users guide of MOC3D A numerical model consisting of 40 layers 32 rows and 12 columns is used to simulate threedimensional trans port having a permanent point source in a steadystate flow field nu merical results were compared with the analytical solution of Wexler 116 ransport13 This model is described in the section MODEL TESTING AND EVALUATION TwoDimensional Radial Flow and Dispersion of the users guide of MOC3D A numerical model consisting of 1 layer 30 rows and 30 columns is used to simulate twodimensional trans port having a permanent point source in a steadystate radial flow field numerical results were compared with the analytical solution given by Hsieh 65 ransport14 This model is described in the section MODEL TESTING AND EVALUATION Point Initial Condition in Uniform Flow of the users guide of MOC3D A numerical model consisting of 26 lay ers 26 rows and 26 columns is used to simulate threedimensional transport having an initial point source in a parallel steadystate flow at 45 degrees to the xdirection numerical results were compared with the analytical solution given by 116 The point source was simulated at layer 12 row 4 column 4 412 5 Examples and Applications 56 PHT3D Examples Folder pmdirexamplesPHT3D Overview of the Problem Twelve documented examples complete with problem statements input data sets and discussion of results are presented in the users guide of PHT3D 99 Those examples are designed to use as benchmark problems as well as to demonstrate the application of PHT3D A complete list of the examples is given in Table 57 Modeling Approach and Simulation Results Most of the models described in the users guide of PHT3D were created or recreated by using the present version of PM You can find the models in subfolders under pathexamplesPHT3D Table 57 PHT3D Examples Example Description EX01 Single Species Transport with Monod Kinetics EX02 Transport and mineral precipitationdissolution EX03 Migration of precipitationdissolution fronts EX04 Cation exchange flushing of a sodiumpotassium nitrate solution with calcium chloride EX05 Cation exchange during artificial recharge EX06 Cation exchange and precipitationdissolution during tenside injection EX07 Kinetic sequentialparallel degradation of multiple species EX08 Kinetic sequential degradation of chlorinated hydrocarbons EX09 Kinetic degradation of BTEX using multiple electron acceptors EX10 Dissolution degradation and geochemical response EX11 Transport and surface complexation of uranium EX12 Modelling of an oxidation experiment with pyritecalciteexchangersorganic matter containing sand 57 SEAWAT Examples 413 57 SEAWAT Examples Folder pmdirexamplesSEAWAT Overview of the Problem The examples presented here are based on the example problem described in the users guide of SEAWAT V4 77 The example problem consists of a twodimensional cross section of a confined coastal aquifer initially saturated with relatively cold seawater at a temperature of 5 C Warmer freshwater with a temperature of 25 C is injected into the coastal aquifer along the left boundary to represent flow from inland areas The warmer freshwater flows to the right where it discharges into a vertical ocean bound ary The ocean boundary is represented with hydrostatic conditions based on a fluid density calculated from seawater salinities at 5 C Noflow conditions are assigned to the top and bottom boundaries A complete list of the input values used for the prob lem is given in table 5 of the SEAWAT V4 users guide This problem is a simplified representation of what might occur in a coastal carbonate platform Modeling Approach and Simulation Results Five cases of the example problem described in the users guide of SEAWAT V4 were recreated by using the present version of PM and are given in Table 58 You can find the models in subfolders under pathexamplesSEAWAT Table 58 SEAWAT Examples Example Description CASE1 Variabledensity simulation in which the fluid density is a function only of salinity CASE2 Variabledensity simulation in which the fluid density is a function of salinity and temperature CASE3 Variabledensity simulation in which the fluid density is a function of salinity and temperature while considering heat conduction in the simulation CASE4 Variabledensity simulation in which the fluid density is a function of salinity and temperature while considering heat conduction and thermal equlibration between the fluid and the solid matrix CASE5 Variabledensity simulation in which the fluid density is a function of salinity and temperature while considering heat conduction and thermal equlibration between the fluid and the solid matrix as well as heat conduction at the seawater boundary 414 5 Examples and Applications 58 Miscellaneous Topics 581 Using the Field Interpolator Folder pmdirexamplesmiscmisc1 Overview of the Problem This example illustrates the use of the Field Interpolator Fig 556 shows the plan view of the model area the model grid and the locations of measurement points The model grid consists of 1 layer 70 rows and 60 columns The measured hydraulic heads and the coordinates of the measurement points are saved in pmdirexamplesmiscmisc1measuredat To obtain the starting head distribution of a flow simulation the measured hydraulic heads should be interpolated to each model cell Modeling Approach and Simulation Results The starting heads are interpolated to model cells using the four interpolation methods provided by the Field Interpolator The interpolation results are shown in the form of contours in Figures 557 560 The octant search method with Data Per Sector 1 Fig 556 Model domain and the measured hydraulic head values 58 Miscellaneous Topics 415 is used by all gridding methods A weighting exponent of F 2 is used by Shepards inverse distance method The Kriging method uses the linear variogram model with c0 0 and α 1 There is no significant difference observed in these figures when sufficient data points are available The major difference is observed in the southern part of the model area where only one measurement point is found and the system is not well conditioned Fig 557 Contours produced by Shepards inverse distance method 416 5 Examples and Applications Fig 558 Contours produced by the Kriging method 58 Miscellaneous Topics 417 Fig 559 Contours produced by Akimas bivariate interpolation Fig 560 Contours produced by Renkas triangulation algorithm 418 5 Examples and Applications 582 An Example of Stochastic Modeling Folder pmdirexamplesmiscmisc2 Overview of the Problem Aquifer remedial measures are often designed by means of groundwater models Model results are usually uncertain due to the imperfect knowledge of aquifer parame ters We are uncertain about whether the calibrated values of parameters represent the real aquifer system We never know the actual smallscale distribution of some param eters eg hydraulic conductivity or recharge Thus all groundwater models involve uncertainty Stochastic models are often employed to take into account uncertainty In the stochastic modeling approach the model parameters appear in the form of proba bility distributions of values rather than as deterministic sets We use the aquifer described in Section 41 to illustrate the concept of stochas tic modeling Using a twodimensional approach to model the aquifer we may use the Field Generator to create lognormal correlated distributions of the horizontal hy draulic conductivity The mean horizontal hydraulic conductivity of the aquifer is equal to 40000160000510 34104 ms The standard deviation is assumed to be σ 05 A correlation length of 60 m is used In Section 41 the pumping rate of the well was determined such that the contam inated area lies within the capture zone of the well When different realizations of the heterogeneous distribution of hydraulic conductivity are introduced it is obvious that the capture zone not always covers the entire contaminated area The safety criterion for the measure can be defined as the percentage of the covered area in relation to the entire contaminated area The expected value of the safety criterion can be obtained from stochastic simulation Modeling Approach and Simulation Results Using the Field Generator lognormal distributions of the horizontal hydraulic conduc tivity are generated and stored in ASCII Matrix files First each generated realization is imported into the horizontal hydraulic conductivity matrix then a flow simulation is performed The capture zone of the pumping well as well as pathlines are computed with PMPATH The resulting safety criterion is obtained by a Monte Carlo simulation This implies that many realizations of the parameter field are produced and used in the flow simulation Fig 561 shows results of five realizations and the calculated mean safety criterion The mean safety criterion is the sum of safety criteria divided by the number of real izations A large number of realizations may be required for the mean safety criterion to converge 58 Miscellaneous Topics 419 Fig 561 Calculation of the mean safety criterion by the Monte Carlo method 6 Supplementary Information 61 Limitation of PM This section gives the size limitation of PM Refer to the documentation of individual packages for their assumptions applicability and limitations 611 Data Editor Maximum number of layers 300 Maximum number of stress periods 1000 Maximum number of cells along rows or columns 2000 Maximum number of cells in a layer 1000000 Maximum number of polygons in a layer 20 Maximum number of vertex nodes of a polygon 40 Maximum number of stream segments 1000 Maximum number of tributary segments of each stream segment 10 Maximum number of reservoirs 20 Maximum number of observed stages of each reservoir 200 Maximum number of estimated parameters 500 Maximum number of species 60 There is no limit to the polylines and number of wells generalhead boundary cells rivers drains and horizontalflowbarrier cells 422 6 Supplementary Information 612 Boreholes and Observations No limit to the maximum number of boreholes Maximum number of observations for each borehole 4000 613 Digitizer Maximum number of digitized points 50000 614 Field Interpolator Maximum number of cells in a layer 1000000 Maximum number of cells along rows or columns 5000 Maximum number of input data points 5000 615 Field Generator Maximum number of cells in a layer 250000 Maximum number of cells along rows or columns 500 616 Water Budget Calculator Maximum number of subregions 50 62 File Formats 621 ASCII Matrix File An ASCII Matrix file can be saved or loaded by the Browse Matrix dialog box see Section 281 of the Data Editor The Results Extractor Field Interpolator and Field Generator save their generated data in this format File Format 1 Data NCOL NROW 2 Data MATRIX NCOL NROW Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space 62 File Formats 423 NCOL is the number of model columns NROW is the number of model rows MATRIX is a twodimensional data matrix saved row by row Matrix can be saved in free format If the wrap from is used to save the matrix each line of the matrix contains up to 20 values Example If NCOL6 and NROW5 an ASCII Matrix file would be 6 5 121 152 133 144 315 516 221 252 233 244 215 216 321 352 333 344 315 316 421 452 433 444 415 416 521 552 533 544 515 516 Or 6 5 121 152 133 144 315 516 221 252 233 244 215 216 321 352 333 344 315 316 421 452 433 444 415 416 521 552 533 544 515 516 622 Contour Table File A contour table file can be saved or loaded by the Environment Options dialog box see Section 292 File Format 1 Data LABEL 2 Data NL XXX XXX XXX XXX The following data repeats NB times 3 Data LEVEL COLOR FILL LVISIBLE LSIZE LDIS XXX XXX XXX Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space 424 6 Supplementary Information LABEL is the file label It must be PMWIN5000 CONTOUR FILE The file for mat has been changed since PMWIN 50 NL is the number of contour levels XXX reserved LEVEL is the Contour level COLOR is the color used to draw the contour line The color is defined by a long integer using the equation color red green 256 blue 65536 where red green and blue are the color components ranging from 0 to 255 FILL is the color used to fill the space between the current contour and the next contour level LVISIBLE controls the visibility of the corresponding contour The contour is visible if LVISIBLE is TRUE LSIZE is the appearance height of the label text in the same unit as the model LDIS is the distance between two contour labels in the same unit as the model 623 Grid Specification File The grid specification file provides the grid geometry and location details File Format 1 Data NROW NCOL 2 Data X Y ANGLE 3 Data DELRNCOL 4 Data DELCNROW 5 Data X1 Y1 6 Data X2 Y2 7 Data NLAY The following data contains the top elevations of each layer This data record repeats NLAY times if the layer top elevation has been specified 8 Data TOP The following data contains the bottom elevations of each layer This data record re peats NLAY times if the layer bottom elevation has been specified 9 Data BOTTOM Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space 62 File Formats 425 NROW is the number of model rows NCOL is the number of model columns X is the xcoordinate of the topleft corner of the model grid Y is the ycoordinate of the topleft corner of the model grid ANGLE is the rotation angle expressed in degrees and measured counterclockwise from the positive xaxis DELR is the cell width along rows Read one value for each of the NCOL columns This is a single array with one value for each column DELC is the cell width along columns Read one value for each of the NROW rows This is a single array with one value for each row X1 Y1 are the coordinates of the lower left corner of the model worksheet see Coordinate System for details X2 Y2 are the coordinates of the upper right corner of the model worksheet see Coordinate System for details NLAY is the number of model layers TOP is a 2D matrix contains the top elevation of each model cell of a model layer BOTTOM is a 2D matrix contains the bottom elevation of each model cell of a model layer 624 Line Map File A line map file contains a series of polylines each polyline is defined by the number of vertices and a series of coordinate pairs File Format Repeat Data 1 and 2 for each polyline 1 Data NVERTEX The following data repeats NVERTEX times 2 Data X Y Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space NVERTEX is the number of vertices of a polyline X is the xcoordinate of the ith vertex Y is the ycoordinate of the ith vertex 426 6 Supplementary Information 625 ASCII Time Parameter File An ASCII time parameter file can be saved or loaded by the Time Parameters dialog box see Section 251 File Format 1 Data LABEL 2 Data NPER ITMUNI 3 Data Reserved Reserved Reserved Reserved 4 Data Reserved Reserved Reserved Reserved 5 Data Reserved Reserved Reserved Reserved The following data repeat NPER times 6 Data ACTIVE PERLEN NSTP TSMULT DT0 MXSTRN TTSMULT TRANS 7 Data Reserved Reserved Reserved Reserved Reserved Reserved Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space LABEL is the file label It must be PMWIN TIME FILE NPER is the number of stress periods in the simulation ITMUNI indicates the time unit of model data The time unit must be consistent for all data values that involve time For example if years is the chosen time unit stress period length time step length transmissivity etc must all be expressed using years for their time units Likewise the length unit must also be consistent 0 undefined 3 hours 1 seconds 4 days 2 minutes 5 years ACTIVE A stress period is active if ACTIVE 1 Set ACTIVE0 if a stress period is inactive PERLEN is the length of a stress period It is specified for each stress period NSTP is the number of time steps in a stress period TSMULT is the multiplier for the length of successive time steps The length of the first time step DELT1 is related to PERLEN NSTP and TSMULT by the relation DELT1 PERLEN1 TSMULT1 TSMULTNSTP DT0 is the length of transport steps If DT00 the length of transport steps will be determined by an automatic stepsize control procedure in MT3D MXSTRN is the maximum number of transport steps 62 File Formats 427 TTSMULT is the multiplier for the length of successive transport steps within a flow time step if the Generalized Conjugate Gradient GCG solver is used and the solution option for the advection term is the upstream finite difference method TRANS is used by MODFLOW2000 only A stress period is simulated in transient state is TRANS 1 otherwise a steadystate solution will be calculated for the stress period Reserved Reserved for future use Enter 0 in the file 626 HeadDrawdownConcentration Observation Files The Head or Drawdown or Concentration Observation dialog box uses the following four formats for saving and loading data The formats are described in the following sections Observation Boreholes obs borehole contains names and coordinates of ob servation boreholes Layer Proportions layer prop contains the proportion values of each layer Using the Head Observation dialog box a Layer Proportions file can be loaded to an observation borehole at a time Observations observation contains observation times observed values and weights Using the Head Observation dialog box an Observations file can be loaded to an observation borehole at a time Complete Information complete obs contains all information mentioned above for all boreholes 6261 Observation Boreholes File 1 Data NBOREHOLES The following data repeat for each borehole ie NBOREHOLES times 2 Data OBSNAM Active x y Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space NBOREHOLES is the number of observation boreholes Active A borehole is active if Active 1 A borehole is inactive if Active 0 x x coordinate of the borehole y y coordinate of the borehole 428 6 Supplementary Information 6262 Layer Proportions File 1 Data NLAYERS 2 Data PR1 PR2 PRNLAYERS Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space NLAYERS Number of layers in the model PRi layer proportion values for layer i 6263 Observations File 1 Data NHOBS The following data repeat for each observation ie NHOBS times 2 Data Time HOBS STWT Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space NHOBS number of observations Time Observation time HOBS observed value at Time STWT For MODFLOW2000 STWT is the statistic value for the observation For PEST STWT is the weighting factor for the observation 6264 Complete Information File 1 Data PMWIN OBSERVATION FILE 2 Data NBOREHOLES EVH 3 Data Reserved Reserved Reserved Reserved 4 Data ITT STAT FLAG 5 Data Reserved Reserved Reserved Reserved The following data repeat for each borehole ie NBOREHOLES times 62 File Formats 429 6 Data OBSNAM Active x y NHOBS 7 Data PR1 PR2 PRNLAYERS The following data repeat NHOBS times for each borehole 8 Data Time HOBS statistic weight Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space The text string PMWIN OBSERVATION FILE must be entered literally NBOREHOLES is the number of observation boreholes EVH default 1 for MODFLOW2000 not used by PEST ITT default 1 for MODFLOW2000 not used by PEST STAT FLAG default 0 for MODFLOW2000 not used by PEST OBSNAM name of the observation borehole max 8 characters blank and special characters are not allowed Active A borehole is active if Active 1 A borehole is inactive if Active 0 x x coordinate of the borehole y y coordinate of the borehole NHOBS number of observations of a borehole PRi layer proportion values for layer i NLAYERS Number of layers in the model Time Observation time HOBS observed value at Time Statistic statistic value for the observation used by MODFLOW2000 weight weighting factor for the observation used by PEST Reserved Reserved for future use Enter 0 in the file 627 Flow Observation Files The Flow Observation dialog box uses the following three formats for saving and load ing data The formats are described in the following sections Cell Group cell group contains the data of the Cell Group table of the Flow Observation dialog box 277 Flow Observations Data Flow observations contains observation times ob served values and weights of a cell group Using the Flow Observation dialog box a Flow Observations Data file can be loaded to associate with a cell group at a time Complete Information complete flow obs contains all cell groups and their observation data 430 6 Supplementary Information 6271 Cell Group File 1 Data NCELLGROUPS The following data repeat for each cell group ie NCELLGROUPS times 2 Data OBSNAM GroupNumber Active Description Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space NCELLGROUPS is the number of cell groups OBSNAM is the name of the cell group max 8 characters blank and special char acters are not allowed GroupNumber is the number associated with the cell group Active A cell group is active if Active 1 A cell group is inactive if Active 0 Description Description of the cell group 6272 Flow Observations Data File 1 Data NFOBS The following data repeat for each observation ie NFOBS times 2 Data Time FOBS STWT Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space NFOBS number of flow observations Time Observation time FOBS observed value at Time STWT STWT is the statistic value for the observation 6273 Complete Information File 1 Data PMWIN6000 FLOW OBSERVATION 2 Data NCELLGROUPS EVF 3 Data Reserved Reserved Reserved Reserved Reserved 62 File Formats 431 4 Data STAT FLAG 5 Data Reserved Reserved Reserved Reserved The following data repeat for each cell group ie NCELLGROUPS times 6 Data OBSNAM GroupNumber Active NFOBS 7 Data Description The following data repeat NHOBS times for each cell group 8 Data Time FOBS statistic Reserved Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space The text string PMWIN OBSERVATION FILE must be entered literally NCELLGROUPS is the number of cell groups EVF default 1 STAT FLAG default 0 OBSNAM is the name of the cell group max 8 characters blank and special characters are not allowed GroupNumber is the unique group number associated with the cell group Active A cell group is active if Active 1 A cell group is inactive if Active 0 Description Description of the cell group NFOBS number of flow observations of a cell group Time observation time FOBS observed value at Time Statistic statistic value for the observation Reserved reserved for future use Enter 0 in the file 628 Trace File A Trace file can be saved or loaded by the Search and Modify dialog box see Section 285 File Format 1 Data LABEL The following data repeats 50 times one record for each search range 432 6 Supplementary Information 2 Data ACTIVE COLOR MIN MAX VALUE OPTION Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space LABEL is the file label It must be PMWIN TRACEFILE ACTIVE Set ACTIVE 1 to activate a search range see MIN MAX below COLOR is the fill color The color is defined by a long integer using the equation color red green 256 blue 65536 where red green and blue are the color components ranging from 0 to 255 COLOR is assigned to the finitedifference cells that have a value located within the search range see MIN MAX below MIN MAX define the lower limit and upper limit of the search range VALUE According to OPTION see below you can easily modify the cell values OPTION defines the actions OPTION 0 Display only OPTION 1 Replace The cell values are replaced by VALUE OPTION 2 Add VALUE is added to the cell values OPTION 3 Multiply The cell values are multiplied by VALUE 629 Polygon File A polygon file can be saved or loaded by the Data Editor by selecting Value Polygon File Format 1 Data LABEL 2 Data NZONES XXX XXX XXX XXX Data 36 repeat NZONES times 3 Data NP 4 Data PARNO 5 Data Value1 Value2 Value3 ValueI Value16 The following data repeats NP times 62 File Formats 433 6 Data XJ YJ Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space LABEL is the file label It must be PMWIN4000 ASCII ZONEFILE or PMWIN ASCII POLYGONFILE NZONES is the number of polygons Maximum is 20 XXX reserved NP is the number of vertices of each polygon The first and the last vertices must overlap The maximum number of NP is 41 PARNO is the parameter number see Sections 267 268 for how to define an estimated parameter ValueI I 1 to 16 ValueI are the polygon values For aquifer parameters such as porosity or transmissivity only the first value or two values if a parameter num ber can be defined is used For MODFLOW packages such as Drain Package as many values as required by the package are used For example two values Hy draulic conductance and the elevation of the drain required for defining a drain will be saved in Value1 and Value2 Other values that are not used must be specified as zero Table 61 gives the assignment of the parameters in the ValueI vector XJYJ are the xy coordinates of the Jth vertex of the polygon The first and the last vertices must overlap 434 6 Supplementary Information Table 61 Assignment of parameters in the ValueI vector Package Value1 Value2 Value3 Value4 WEL Recharge rate XXX XXX XXX DRN Hydraulic conductance Elevation XXX XXX RIV Hydraulic conductance Head in river Elevation XXX EVT Max ET rate ET Surface Extinction Depth Layer Indicator GHB Hydraulic conductance Head at boundary XXX XXX RCH Recharge Flux Layer Indicator XXX XXX HFB Barrier Direction KThickness XXX XXX IBS Preconsolidation head Elastic storage Inelastic storage Starting compaction CHD Flag Start head End head XXX The values used by the STR1 package are Value1 Segment Value2 Reach Value3 Streamflow Value4 Stream stage Value5 Hydraulic conductance Value6 Elevation of the streambed top Value7 Elevation of the streambed bottom Value8 Stream width Value9 Stream slope Value10 nC Mannings roughness coefficient divided by C 6210 XYZ File An XYZ file must be saved as ASCII text using the following format N X1 Y1 Z1 X2 Y2 Z2 Xi Yi Zi XN YN ZN Where N is the number of points Xi and Yi are the x y coordinate values and Zi is the data value associated with the point i All values are are separated by at least one space 6211 Pathline File 62111 PMPATH Format A pathline file in the PMPATH format is a text file that begins with the header of the form 62 File Formats 435 PMPATH Version 600 The user may add any number of comment lines following the header line and before the particle data records Comment lines must contain the symbol in col umn 1 Comment lines may not be interspersed with the particle data records The header and comment lines are followed by a sequence of lines Each line contains the following data items in the order specified 1 Particle index number The index number is positive if the forward particle tracking scheme is used A negative index number indicates that the backward particletracking scheme is used 2 Global coordinate in the xdirection 3 Global coordinate in the ydirection 4 Local coordinate in the zdirection within the cell 5 Global coordinate in the zdirection 6 Cumulative tracking time 7 J index of cell containing the point 8 I index of cell containing the point 9 K index of cell containing the point 10 RGBColor of the pathline 62112 MODPATH Format The standard text pathline file of MODPATH Pollock 9597 is a text file that be gins with the header of the form MODPATH Version 300 V3 Release 1 994 TREF 0000000E00 The user may add any number of comment lines following the header line and be fore the particle data records Comment lines must contain the symbol in column 1 Comment lines may not be interspersed with the particle data records The header and comment lines are followed by a sequence lines Each line contains the following data items in the order specified 1 Particle index number 2 Global coordinate in the xdirection 3 Global coordinate in the ydirection 4 Local coordinate in the zdirection within the cell 5 Global coordinate in the zdirection 6 Cumulative tracking time 7 J index of cell containing the point 436 6 Supplementary Information 8 I index of cell containing the point 9 K index of cell containing the point 10 Cumulative MODFLOW time step number 6212 Particles File A Particles File is a a text file that begins with the header of the form 1 Data PMPATHV100PARTICLES 2 Data NP The following data repeats NP times 3 Data LI LJ LK I J K Z C R Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space The text string PMPATH V100 PARTICLES must be entered literally NP is the number of particles LI Local coordinate in the row direction LJ Local coordinate in the column direction LK Local coordinate in the layer direction I Row index of cell containing the particle J Column index of cell containing the particle K Layer index of cell containing the particle Z global vertical coordinate of the particle C Color of the particle R Retardation factor associated with the particle The particle locations within the cell J I K are specified using local coordinates LJ LI LK Local coordinates vary within a cell from zero to one as shown in Fig 61 63 Input Data Files of the supported Model 631 Name File The name file contains the names of most input and output files used in a model sim ulation and controls the parts of the model program that are active The format of the 63 Input Data Files of the supported Model 437 Fig 61 Local coordinates within a cell name file for MODFLOW 8896 is identical to that of MODFLOW2000 except the latter has some additional file types marked with the character see Ftype below The name file contains one record similar to the following line for each input and output file used in a MODFLOW model simulation All variables are free format The length of each record must be 199 characters or less Ftype Nunit Fname Explanation of Fields Used in Input Instructions All data in the same record are separated by at least one space Ftype is the file type which must be one of the following character values Ftype may be entered in all uppercase all lowercase or mixed case LIST for the simulation listing file BAS for the Basic Package of MODFLOW BCF for the BlockCentered Flow Package of MODFLOW CHD for the TimeVariant SpecifiedHead Package DE4 for the Direct Solver Package DRN for the Drain Package EVT for the Evapotranspiration Package HFB for the Horizontal Flow Barrier Package of MODFLOW GHB for the GeneralHead Boundary Package 438 6 Supplementary Information IBS for the Interbed Storage package OC for the Output Control Option PCG for the Preconditioned Conjugate Gradient 2 Package RCH for the Recharge Package RIV for the River Package SIP for the Strongly Implicit Procedure Package SOR for the SliceSuccessive OverRelaxation Package STR for the Streamflow Routing Package WEL for the Well Package DIS for the discretization file BAS6 for the Basic Package of MODFLOW2000 BCF6 for the BlockCentered Flow Package of MODFLOW20002005 LPF for the Layer Property Flow package of MODFLOW20002005 HFB6 for the Horizontal Flow Barrier Package of MODFLOW20002005 LMG for the Link Algebraic Multigrid Solver Package of MODFLOW 20002005 OBS for the main input file to the Observation Process of MODFLOW2000 HOB for the Head Observation Package of MODFLOW2000 DROB contains the observed flows to features represented by the Drain pack age This file is used by the Observation Process of MODFLOW2000 GBOB contains the observed flows to features represented by the General Head Boundary package This file is used by the Observation Process of MODFLOW2000 RVOB contains the observed flows to features represented by the River pack age This file is used by the Observation Process of MODFLOW2000 STOB contains the observed flows to features represented by the Streamflow Routing package This file is used by the Observation Process of MODFLOW 2000 CHOB contains the observed flows to features represented by the Time Variant SpecifiedHead package This file is used by the Observation Process of MODFLOW2000 SEN for the Sensitivity Process of MODFLOW2000 PES for the Parameter Estimation Process of MODFLOW2000 ZONE for the Zone Array file of MODFLOW2000 MULT for the Multiplier Array file of MODFLOW2000 DATABINARY for binary unformatted files such as those used to save cell bycell budget data and binary unformatted head and drawdown data DATA for formatted text files such as those used for input of data from files that are separate from the primary package input files 63 Input Data Files of the supported Model 439 Nunit is the Fortran unit to be used when reading from or writing to the file Any legal unit number on the computer being used can be specified except units 9699 Fname is the name of the file The path names may be specified as part of Fname Example of a Name File LIST 6 outputdat BAS 1 basdat BCF 11 bcfdat OC 22 ocdat WEL 12 weldat RCH 18 rchdat PCG 23 pcg2dat DATABINARY 50 budgetdat DATABINARY 51 headsdat DATABINARY 52 ddowndat DATABINARY 32 mt3dflo 632 MODFLOW96 Basic Package BASDAT BlockCentered Flow Package BCFDAT Density Package DEN1 DEN1DAT Direct Solution Package DE45 DE45DAT Drain Package DRNDAT Evapotranspiration Package EVTDAT GeneralHead Boundary Package GHBDAT HorizontalFlow Barrier Package HFB1DAT InterbedStorage Package IBS1DAT Output Control OCDAT Preconditioned Conjugate Gradient 2 Package PCG2 PCG2DAT River Package RIVDAT Recharge Package RCHDAT Reservoir Package RES1DAT Strongly Implicit Procedure Package SIPDAT SliceSuccessive Overrelaxation Package SORDAT StreamRouting Flow Package STR1DAT Time Variant Specified Head CHD1DAT Well Package WELDAT 440 6 Supplementary Information 633 MODFLOW20002005 Discretization File DISCRETDAT Basic Package BAS6DAT Zone Array File ZONEDAT Multiplier Array File MULTIPLEDAT LayerProperty Flow Package LPF6DAT BlockCentered Flow Package BCF6DAT Drain Package DRN6DAT Evapotranspiration Package EVT6DAT GeneralHead Boundary Package GHB6DAT HorizontalFlow Barrier Package HFB6DAT InterbedStorage Package IBS1DAT Recharge Package RCH6DAT StreamRouting Flow Package STR6DAT Reservoir Package RES1DAT River Package RIV6DAT Time Variant Specified Head CHD6DAT Well Package WEL6DAT Strongly Implicit Procedure Package SIPDAT SliceSuccessive Overrelaxation Package SORDAT Direct Solution Package DE45 DE45DAT Link Algebraic Multigrid Solver Package LMGDAT Preconditioned Conjugate Gradient 2 Package PCG2 PCG2DAT Output Control OCDAT Observation Process OBS MAINDAT Sensitivity Process SENDAT Parameter Estimation Process PESDAT Head Observation Package HOBDAT Observed flows to features represented by the Drain package DROBDAT Observed flows to features represented by the GeneralHead Boundary package GBOBDAT Observed flows to features represented by the River package RVOBDAT Observed flows to features represented by the Streamflow Routing package STOBDAT Observed flows to features represented by the TimeVariant SpecifiedHead package CHOBDAT 63 Input Data Files of the supported Model 441 634 MODPATH and MODPATHPLOT version 1x Main data file MAINDAT Other files required by MODPATH such as RIVDAT or WELDAT are the same as those of MODFLOW 8896 635 MODPATH and MODPATHPLOT version 3x Main data file MAIN30DAT Other files required by MODPATH such as RIVDAT or WELDAT are the same as those of MODFLOW 8896 636 MOC3D Main MOC3D Package MOCMAINDAT Source Concentration in Recharge MOCCRCHDAT Observation Well File MOCOBSDAT Other files required by the flow simulation such as RIVDAT or WELDAT are the same as those of MODFLOW 8896 637 MT3D Advection Package MTADV1DAT Basic Transport Package MTBTN1DAT Chemical Reaction Package MTRCT1DAT Dispersion Package MTDSP1DAT Sink Source Mixing Package MTSSM1DAT 442 6 Supplementary Information 638 MT3DMSSEAWAT Advection Package MTMSADV1DAT Basic Transport Package MTMSBTN1DAT Chemical Reaction Package MTMSRCT1DAT Dispersion Package MTMSDSP1DAT Generalized Conjugate Gradient Solver MSMSGSG1DAT Sink Source Mixing Package MTMSSSM1DAT Variable Density Flow Package SEAWAT Only SW2KVDF1dat 639 RT3D Advection Package MTMSADV1DAT Basic Transport Package MTMSBTN1DAT Chemical Reaction Package MTMSRCT1DAT Dispersion Package MTMSDSP1DAT Generalized Conjugate Gradient Solver MSMSGSG1DAT Sink Source Mixing Package MTMSSSM1DAT 6310 PHT3D Advection Package PHT3DADVDAT Basic Transport Package PHT3DBTNDAT Chemical Reaction Package PHT3DRCTDAT Dispersion Package PHT3DDSPDAT Generalized Conjugate Gradient Solver PHT3DGCGDAT Sink Source Mixing Package PHT3DSSMDAT PHREEQC Interface File PHT3D PHDAT PHREEQCStyle Database File PHT3D DATABDAT 64 Using MODPATH with PM 443 6311 PEST Instruction File INSTRUCTDAT Control File PESTCTLDAT BlockCentered Flow Package Template File BCFTPLDAT Drain Package Template File DRNTPLDAT Evapotranspiration Package Template File EVTTPLDAT GeneralHead Boundary Package Template File GHBTPLDAT Recharge Package Template File RCHTPLDAT River Package Template File RIVTPLDAT Well Package Template File WELTPLDAT StreamRouting Flow Package Template File STRTPLDAT InterbedStorage Package Template File IBSTPLDAT Grid Specification File used by MODBOREEXE filenameGRD Borehole Listing File used by MODBOREEXE BORELISTDAT Borehole Coordinates File used by MODBOREEXE BORECOORDAT filename is the name of the model 64 Using MODPATH with PM PM supports two versions version 1x and 3x of MODPATH and MODPATH PLOT Since MODPATH and MODPATHPLOT reads the binary model result files from MODFLOW these programs needed to be compiled with the same Fortran Compiler to ensure the binary compatibility between them The MODFLOW pro grams which come with pmp are compiled with LaheyFortran 95 To run MODPATH or MODPATHPLOT with PM these programs need to be compiled the same com piler too The users can however use their own compiler to compile the MODFLOW MODPATH and MODPATHPLOT for using with pmp See Section 12 for details MODPATH or MODPATHPLOT must be started within a DOSBox of Win dows or in the DOSEnvironment When using MODPATH version 1x released prior to September 1994 type pathPATHFILE at the prompt ENTER NAME OF FILE CONTAINING NAMES AND UNITS OF DATA FILES Where path is the path to the directory of your model data PATHFILE contains the IUNIT assignments and paths and names of input data files generated by PMWIN The names of the input files for MODFLOW and MOD PATH are given in Sections 632 634 and 635 444 6 Supplementary Information When using MODPATH or MODPATHPLOT version 3x follow the steps below TO READ INPUT FROM AN EXISTING RESPONSE FILE ENTER FILE NAME CR ENTER DATA INTERACTIVELY Help WHAT TO DO Just press ENTER here When running MODPATH or MODPATH PLOT at the first time a response file does not exist and the user has to enter data in teractively The userspecified data will be saved by MODPATH or MODPATHPLOT in the response files MPATHRSP or MPLOTRSP respectively Using a response file it is not necessary to go through the input procedures unless the data for MODPATH or MODPATHPLOT need to be changed Only for MODPATHPLOT TO REDEFINE SETTINGS ENTER NAME OF FILE WITH SETTINGS DATA CR USE DEFAULT SETTINGS FOR DEVICE Help WHAT TO DO Just press ENTER here unless the settings need to be changed ENTER THE NAME FILE Help WHAT TO DO Type pathMPATH30 at this prompt Where path is the path to the di rectory of your model data For example if model data are saved in CPMWINDATA type CPMWINDATAMPATH30 at this prompt After this prompt the user enters the interactive input procedure of MODPATH or MODPATHPLOT Just follow the prompts of the programs 65 Define PHT3D Reaction Module Before creating a new userdefined reaction module a basic knowledge of PHREEQC 2 must be obtained and at least for more complex cases it is strongly recommended to first test and debug reaction definitions in batchmode ie by setting up a PHREEQC 2 batchtype simulation To add a userdefined PHT3D reaction module for PM you need to complete the following three steps 65 Define PHT3D Reaction Module 445 1 Create a database file analogous to the original PHREEQC2 database files You can find a number of examples such as pht3d databex1 pht3d databex2 etc in the pmdirpht3dDatabase folder where pmdir is the installation folder of PM 2 Create a module file that contains information about the number names and types of chemical and reaction rate constants that are used in the corresponding database file created in the first step You can find a number of examples and templates in the pht3dDatabase For example pmwin pht3dv2standard contains information corresponding to the standard PHREEQC2 database file pht3d databstandard 3 Add module definition to the pmdirpht3dDatabasepht3d module definitiontxt file To add a module definition you need to modify the number of modules in the pht3d module definitiontxt file and then add the four lines containing the follow ing information to the end of the pht3d module definitiontxt file Name of the module Description of the module Name of the PHREEQC database file created in step 1 Name of the module file created in step 2 LOCATION CREATE YOUR GAME MODE Campaign Battles Custom Store Bestiary Collection Adventure Map EXIT Menu BACK PLAY Next mission 4 minutes 59 seconds 72 28 min Campaign Completed The future of Albion lies in your hands Assemble a team of heroes train and level up your troops and defeat mages and warlords to bring peace back to the realm QUIT MISSION YES NO References 1 Akima H 1978a A method of bivariate interpolation and smooth surface fitting for irreg ularly distributed data points ACM Transactions on Mathematical Software 4 148159 2 Akima H 1978b Algorithm 526 Bivariate interpolation and smooth surface fitting for irregularly distributed data points ACM Transactions on Mathematical Software 4 160 164 3 Akin H and Siemes H 1988 Praktische Geostatistik Springer Berlin Heidelberg New York 4 Alexander M 1994 Biodegradation and Bioremediation Academic Press San Diego Calif 302 pp 5 Andersen PF 1993 A manual of instructional problems for the USGS MODFLOW model Center for Subsurface Modeling Support EPA600R93010 6 Anderson MP 1979 Using models to simulate the movement of contaminants through ground water flow systems Critical Reviews in Environmental Control 92 97156 7 Anderson MP 1984 Movement of contaminants in groundwater groundwater transport advection and dispersion Groundwater Contamination 3745 National Academy Press Washington DC 8 Anderson MP and Woessner WW 1991 Applied groundwater modeling simulation of flow and advective transport 381 pp Academic Press San Diego CA 9 Ashcraft CC and Grimes RG 1988 On vectorizing incomplete factorization and SSOR preconditioners SIAM Journal of Scientific and Statistical Computing 91 122151 10 Axelsson O and Lindskog G 1986 On the eigenvalue distribution of a class of precondi tioning methods Numerical Mathematics 48 479498 11 Baetsle LH 1967 Computational methods for the prediction of underground movement of radionuclides J Nuclear Safety 86 576588 12 Bear J 1972 Dynamics of fluids in porous media American Elsevier Pub Co New York 13 Bear J 1979 Hydraulics of Groundwater McGrawHill NY 569 pp 14 Behie A and Forsyth Jr P 1983 Comparison of fast iterative methods for symmetric systems IMA J of Numerical Analysis 3 4163 448 References 15 Borden RC and Bedient PB 1984 Transport of dissolved hydrocarbons influenced by oxygenlimited biodegradation 1 theoretical development Water Resour Res 20 1973 1982 16 Cheng X and Anderson MP 1993 Numerical simulation of ground water interaction with lakes allowing for fluctuating lake levels Ground Water 316 929933 17 Chiang WH and Kinzelbach W 1991 1993 Processing Modflow PM Pre and postpro cessors for the simulation of flow and contaminant transport in groundwater system with MODFLOW MODPATH and MT3D Distributed by Scientific Software Group Washing ton DC 18 Chiang WH 1993 Water Budget Calculator A computer code for calculating global and subregional water budget using results from MODFLOW Kassel University Germany 19 Chiang WH and Kinzelbach W 1994 PMPATH An advective transport model for Pro cessing Modflow and Modflow Geological Survey of Hamburg Germany 20 Chiang WH Kinzelbach W and Rausch R 1998 Aquifer Simulation Model for Windows Groundwater flow and transport modeling an integrated program Gebrder Borntraeger Berlin Stuttgart ISBN 3443010393 21 Chiang WH Bekker M and Kinzelbach W 2001 User guide for three dimensional vi sualization for MODFLOWrelated groundwater flow and transport models Institute for Groundwater Studies University of the Free State South Africa 22 Chiang WH and Kinzelbach W 2001 3DGroundwater Modeling with PMWIN First Edition Springer Berlin Heidelberg New York ISBN 3540 677445 346 pp 23 Chiang WH Chen J and Lin J 2002 3D Master A computer program for 3D visualiza tion and realtime animation of enviromental data Excel Info Tech Inc 146 pp 24 Chiang WH 2005 3DGroundwater Modeling with PMWIN Second Edition Springer Berlin Heidelberg New York 25 Clement TP 1997 RT3D A modular computer code for simulating reactive multi species transport in 3dimensional groundwater systems Battelle Pacific Northwest Na tional Laboratory Richland Washington 99352 26 Clement TP 2000 RT3D Version 20 A modular computer code for simulating reactive multispecies transport in 3dimensional groundwater systems 27 Clement TP 2002 RT3D Version 25 A modular computer code for simulating reactive multispecies transport in 3dimensional groundwater systems 28 Cooper Jr HH and Rorabaugh MJ 1963 Groundwater movements and bank storage due to flood stages in surface streams U S Geological Survey WaterSupply Paper 1536J 343366 29 Council GW 1999 A lake package for MODFLOW LAK2 Documentation and users manual HSI Geotrans 30 Davis JC 1973 Statistics and data analysis in geology John Wiley Sons New York 31 Deutsch CV and Journel AG 1998 GSLIB Geostatistical Software Library and Users Guide Second Edition Oxford University Press ISBN 0195100158 32 Doherty J 1990 MODINV Suite of software for MODFLOW preprocessing post processing and parameter optimization Users manual Australian Centre for Tropical Freshwater Research 33 Doherty J Brebber L and Whyte P 1994 PEST Modelindependent parameter estima tion Users manual Watermark Computing Australia References 449 34 Doherty J 2000 PEST Modelindependent parameter estimation Users manual Wa termark Computing Australia 35 Doherty J 2001a MODFLOWASP Using MODFLOW2000 with PESTASP Water mark Computing Australia 36 Doherty J 2001b PESTASP upgrade notes Watermark Computing Australia 37 Doherty J 2004 ModelIndependent Parameter Estimation User Manual 5th Edition Watermark Computing Australia Downloaded from httpwwwpesthomepageorg 38 Doherty J 2010 PEST Modelindependent parameter estimation Version 12 Water mark Computing Australia Downloaded from httpwwwpesthomepageorg 39 Doherty J 2010 Addendum to the PEST Manual Watermark Computing Australia Downloaded from httpwwwpesthomepageorg 40 Domenico PA 1972 Concepts and Models in Groundwater Hydrology McGrawHill New York 405 pp 41 Domenico PA and Schwartz FW 1990 Physical and Chemical Hydrogeology John Wi ley Sons New York 709 pp 42 Englund E and Sparks A 1991 Users guide of GEOEAS Geostatistical environmental assessment software EPA 600891008 43 Fenske J P Leake SA and Prudic DE 1996 Documentation of a computer program RES1 to simulate leakage from reservoirs using the modular finitedifference ground water flow model MODFLOW U S Geological Survey OpenFile Report 96364 44 Fetter CW 1994 Applied Hydrogeology 3rd Edition Macmillan College New York 691 pp 45 Franke R 1982 Scattered data interpolation Tests of some methods Mathematics of computation 38157 181200 46 Freeze RA and Cherry JA 1979 Groundwater PrenticeHall Inc Englewood Cliffs New Jersey 47 Frenzel H 1995 A field generator based on Mejias algorithm Institut fr Umweltphysik University of Heidelberg Germany 48 Gelhar LW and Collins MA 1971 General analysis of longitudinal dispersion in nonuni form flow Water Resour Res 76 15111521 49 Gelhar LW Mantaglou A Welty C and Rehfeldt KR 1985 A review of fieldscale phys ical solute transport processes in saturated and unsaturated porous media EPRI Report EA4190 Electric Power Research Institute Palo Alto CA 50 Gelhar LW Welty C and Rehfeldt KR 1992 A critical review of data on fieldscale dispersion in aquifers Water Resour Res 287 19551974 51 Guo Weixing and Langevin CD 2002 Users guide to SEAWAT A computer program for simulation of threedimensional variabledensity groundwater flow US Geological Survey Techniques of WaterResources Investigations book 6 chap A7 77 p 52 Hantush MS and Jacob CE 1955 Nonsteady radial flow in an infinite leaky aquifer Trans Am Geophys Un 3611 95100 53 Harbaugh AW 1995 Direct solution package based on alternating diagonal ordering for the US Geological Survey modular finite difference ground water flow model US Geo logical Survey Open File Report 95 288 46 pp 450 References 54 Harbaugh AW and McDonald MG 1996a Users documentation for MODFLOW96 an update to the US Geological Survey modular finitedifference groundwater flow model USGS OpenFile Report 96485 55 Harbaugh AW and McDonald MG 1996b Programmers documentation for MODFLOW96 an update to the US Geological Survey modular finitedifference groundwater flow model USGS OpenFile Report 96486 56 Harbaugh AW Banta ER Hill MC and McDonald MG 2000 MODFLOW2000 The US Geological Survey modular groundwater model User guide to modularization con cepts and the groundwater flow process U S Geological Survey Openfile report 0092 57 Harbaugh AW 2005 MODFLOW2005 the US Geological Survey modular ground water model the GroundWater Flow Process US Geological Survey Techniques and Methods 6A16 58 Higgins GH 1959 Evaluation of the groundwater contamination hazard from under ground nuclear explosives J Geophys Res 64 15091519 59 Hill MC 1990a Preconditioned ConjugateGradient 2 PCG2 A computer program for solving groundwater flow equations U S Geological Survey Denver 60 Hill MC 1990b Solving groundwater flow problems by conjugategradient methods and the strongly implicit procedure Water Resour Res 269 19611969 61 Hill MC 1992 MODFLOWP A computer program for estimating parameters of a tran sient threedimensional groundwater flow model using nonlinear regression US Geo logical Survey Openfile report 91484 62 Hill MC 1998 Methods and guidelines for effective model calibration US Geological Survey WaterResources Investigations Report 984005 63 Hill MC Banta ER Harbaugh AW and Anderman ER 2000 MODFLOW2000 The US Geological Survey modular groundwater model User guide to the observation sensitivity and parameterestimation processes and three postprocessing programs U S Geological Survey Openfile report 00184 64 Hoschek J and Lasser D 1992 Grundlagen der geometrischen Datenverarbeitung B G Teubner Stuttgart Germany 65 Hsieh PA 1986 A new formula for the analytical solution of the radial dispersion prob lem Water Resour Res 2211 15971605 66 Hsieh PA and Freckleton JR 1993 Documentation of a computer program to simulate horizontalflow barriers using the U S Geological Surveys modular threedimensional finitedifference groundwater flow model US Geological Survey OpenFile Report 92 477 67 Hunt BW 1978 Dispersive sources in uniform groundwater flow ASCE Journal of the Hydraulics Division 104HY1 p7585 68 Javandel I Doughty C and Tsang CF 1984 Groundwater transport Handbook of math ematical models 228 pp American Geophysical Union 69 Kinzelbach W 1986 Groundwater Modelling An introduction with sample programs in BASIC Elsevier ISBN 0444425829 70 Kinzelbach W Ackerer P Kauffmann C Kohane B and Mller B 1990 FINEM Nu merische Modellierung des zweidimensionalen Strmungs und Transportproblems mit Hilfe der Methode der finiten Elemente Programmdokumentation Nr 8923 HG 111 Institut fr Wasserbau Universitt Stuttgart References 451 71 Kinzelbach W Marburger M and Chiang WH 1992 Determination of catchment areas in two and three spatial dimensions J Hydrol 134 221246 72 Kinzelbach W and Rausch R 1995 Grundwassermodellierung Einfhrung mit bungen Gebrder Borntraeger Berlin Stuttgart ISBN 3443010326 73 Konikow LF and Bredehoeft JD 1978 Computer model of twodimensional solute trans port and dispersion in ground water U S Geological Survey Water Resources Investiga tion Book 7 Chapter C2 90 pp 74 Konikow LF Goode DJ and Homberger GZ 1996 A threedimensional methodof characteristics solutetransport model U S Geological Survey Water Resources Inves tigations report 964267 75 Kuiper LK 1981 A comparison of the incomplete Cholesky conjugate gradient method with the strongly implicit method as applied to the solution of twodimensional ground water flow equations Water Resour Res 174 10821086 76 Langevin CD Shoemaker WB and Guo W 2003 MODFLOW2000 the US Geolog ical Survey modular groundwater modelDocumentation of the SEAWAT2000 Version with the variabledensity flow process VDF and the integrated MT3DMS transport pro cess IMT US Geological Survey OpenFile Report 03426 43 p 77 Langevin CD Thorne Jr DT Dausman AM Sukop MC and Guo W 2008 SEAWAT Version 4 A Computer Program for Simulation of MultiSpecies Solute and Heat Trans port Techniques and Methods Book 6 Chapter A22 US Geological Survey 78 Leake SA and Prudic DE 1991 Documentation of a computer program to simulate aquifersystem compaction using the modular finitedifference groundwater flow model US Geological Survey 79 Leonard BP 1979 A stable and accurate convective modeling procedure based on quadratic upstream interpolation Computer Methods Appl Mech Engng 19 80 Leonard BP 1988 Universal Limiter for transient interpolation modeling of the advec tive transport equations the ULTIMATE conservative difference scheme NASA Technical Memorandum 100916 ICOMP8811 81 Leonard BP and Niknafs HS 1990 Costeffective accurate coarsegrid method for highly convective multidimensional unsteady flows NASA Conference Publication 3078 Com putational Fluid Dynamics Symposium on Aeropropulsion April 1990 82 Leonard BP and Niknafs HS 1991 Sharp monotonic resolution of discontinuities without clipping of narrow extrema Computer Fluids 191 141154 83 Li YH and Gregory S 1974 Diffusion of ions in seawater and in deepsea sediments Pergamon Press 84 Matheron G 1963 Principles of geostatistics Economic Geology 58 12461266 85 McDonald MG and Harbaugh AW 1988 MODFLOW A modular threedimensional finite difference groundwater flow model U S Geological Survey Openfile report 83 875 Chapter A1 86 McDonald MG Harbaugh AW Orr BR and Ackerman DJ 1991 BCF2 A method of converting noflow cells to variablehead cells for the US Geological Survey Modular FiniteDifference Groundwater Flow Model US Geological Survey OpenFile Report 91536 Denver 452 References 87 Mehl SW and Hill MC 2001 User guide to the LinkAMG LMG package for solving matrix equations using an algebraic multigrid solverUS Geological Survey OpenFile Report 01177 88 Moench AF and Ogata A 1981 A numerical inversion of the Laplace transform solution to radial dispersion in a porous medium Water Resour Res 171 250253 89 Neumann SP 1984 Adaptive EulerianLagrangian finite element method for advection dispersion Int J Numerical Method in Engineering 20 321337 90 Naff RL and Banta ER 2008 The US Geological Survey Modular GroundWater Mod elXPCGN A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Con trol OpenFile Report 20081331 US Geological Survey 91 Niswonger RG Panday S and Ibaraki M 2011 MODFLOWNWT A Newton Formu lation for MODFLOW2005 Chapter 37 of Section A Groundwater Book 6 Modeling Techniques US Geological Survey 92 Oakes BD and Wilkinson WB 1972 Modeling of ground water and surface water sys tems I Theoretical relationships between ground water abstraction and base flow Read ing Great Britain Reading Bridge House Water Resources Board 16 37 pp 93 Parkhurst DL and Appelo C 2000 PHREEQC Version 2 A computer program for spe ciation batchreaction onedimensional transport and inverse geochemical calculations U S Geological Survey Water Resources Investigations report 994259 94 Pannatier Y 1996 Variowin Software for spatial data analysis in 2D Springer Berlin Heidelberg New York ISBN 0387946799 95 Pollock DW 1988 Semianalytical computation of path lines for finite difference models Ground Water 266 743750 96 Pollock DW 1989 MODPATH version 1x Documentation of computer programs to compute and display pathlines using results from the U S Geological Survey modular threedimensional finitedifference groundwater model U S Geological Survey Open file report 89381 97 Pollock DW 1994 Users Guide for MODPATHMODPATHPLOT Version 3 A parti cle tracking postprocessing package for MODFLOW the U S Geological Survey finite difference groundwater flow model U S Geological Survey Openfile report 94464 98 Prommer H 2002 PHT3D A multicomponent transport model for three dimensional reactive transport in saturated porous media Personal communication 99 Prommer H and Vincent P 2010 PHT3D Version 2 A Reactive Multicomponent Trans port Model for Saturated Porous Media WWWPHT3DORG 183 p 100 Prudic DE 1988 Documentation of a computer program to simulate streamaquifer rela tions using a modular finitedifference groundwater flow model US Geological Survey OpenFile Report 88729 Carson City Nevada 101 Rausch R 1998 Computer program for the calculation of 1D and 2D concentration distribution Personal communication 102 Renka RJ 1984a Interpolation of the data on the surface of a sphere ACM Transactions on Mathematical Software 10 417436 103 Renka RJ 1984b Algorithm 624 Triangulation and interpolation at arbitrarily distributed points in the plane ACM Transactions on Mathematical Software 10 440442 104 Rifai HS Bedient PB Borden RC and Haasbeek JF 1987 BIOPLUME II Computer model of twodimensional contaminant transport under the influence of oxygen limited References 453 biodegradation in ground water National Center for Ground Water Research Rice Uni versity 105 Rifai HS Newell CJ Gonzales JR Dendrou S Kennedy L and Wilson J 1997 BIO PLUME III Natural attenuation decision support system version 1 Users Manual Air Force Center for Environmental Excellence Brooks AFB San Antonio Texas 106 Robinson RA and Stokes RH 1965 Electrolyte Solutions 2nd ed Butterworth London 107 Saad Y 1985 Practical use of polynomial preconditionings for the conjugate gradient method SIAM Journal of Scientific and Statistical Computing 64 865881 108 Scandrett C 1989 Comparison of several iterative techniques in the solution of symmetric banded equations on a two pipe Cyber 205 Appl Math Comput 342 95112 109 Seber GAF and Wild CJ 1989 Nonlinear Regression John Wiley Sons NY 768 pp 110 Shepard D 1968 A two dimensional interpolation function for irregularly spaced data Proceedings 23rd ACM126 National Conference 517524 111 Spitz K and Moreno J 1996 A practical guide to groundwater and solute transport mod eling 461 pp John Wiley Sons New York ISBN 0471136875 112 Sun NZ 1995 Mathematical modeling of groundwater pollution 377 pp Springer Berlin Heidelberg New York 113 Theil H 1963 On the use of incomplete prior information in regression analysis Ameri can Statistical Association Journal 58 302 401414 114 Trescott PC and Larson SP 1977 Comparison of iterative methods of solving two dimensional groundwater flow equations Water Resour Res 131 125136 115 Watson DF 1992 Contouring A guide to the analysis and display of spatial data with programs on diskette Pergamon ISBN 0080402860 116 Wexler EJ 1992 Analytical solutions for one two and threedimensional solute trans port in groundwater systems with uniform flow U S Geological Survey Techniques of Water Resources Investigations Book 3 Chapter B7 190 pp 117 Wilson JD and Naff RL 2004 The US Geological Survey modular groundwater model GMG linear equation solver package documentation US Geogolical Survey OpenFile Report 20041261 118 Wilson JL and Miller PJ 1978 Twodimensional plume in uniform groundwater flow J Hyd Div ASCE4 503514 119 Zheng C 1990 MT3D a modular threedimensional transport model SS Papadopulos Associates Inc Rockville Maryland 120 Zheng C and Bennett GD 1995 Applied contaminant transport modeling Theory and practice 440 pp Van Nostrand Reinhold New York 121 Zhang Y Zheng C Neville CJ and Andrews CB 1995 ModIME An integrated modeling environment for MODFLOW PATH3D and MT3D SS Papadopulos Associates Inc Bethesda Maryland 122 Zheng C 1996 MT3D Version DoD 15 a modular threedimensional transport model The Hydrogeology Group University of Alabama 123 Zheng C and Wang PP 1999 MT3DMS A modular threedimensional multispecies model for simulation of advection dispersion and chemical reactions of contaminants in groundwater systems Documentation and Users Guide Contract Report SERDP991 US Army Engineer Research and Development Center Vicksburg MS 454 References 124 Zheng C 1999 MT3D99 A modular 3D multispecies transport simulator SS Papadop ulos and Associates Inc Bethesda Maryland 125 Zheng C 2006 MT3DMS 52 Supplemental Users Guide The University of Alabama Alabama 126 Zheng C and Wang PP 2002 MGO A Modular Groundwater Optimizer The University of Alabama Alabama Index 2D Visualization 27 184 3D Visualization 25 184 adjustable parameter define 135 149 advection MOC3D 119 MT3D 126 MT3DMSSEAWAT 89 RT3D 114 advective transport 176 advective transport model 203 aerobic biodegradation 361 animation 27 anisotropy 36 horizontal 29 vertical 29 artificial oscillation 91 127 ASCII Matrix File 376 average pore velocity 205 213 biodegradation 131 bivariate interpolation 179 Block Centered Flow 24 BMP 26 224 bottom of layers 32 BTEX 113 bulk density 38 catchment area 297 Cell Status 31 cellbycell data modify 16 cellbycell flow terms 75 CellbyCell Input Method 16 chain reactions 363 chemical reaction MT3D 130 MT3DMSSEAWAT 97 columns delete 10 insert 10 compaction 351 compaction observations 73 compaction scatter diagram MODFLOW 81 Compatibility Issues 5 concentration observation MOC3D 124 MT3D 131 MT3DMSSEAWAT 104 RT3D 116 concentration scatter diagram MT3D 134 MT3DMS 108 RT3D 118 concentrationtime curves MOC3D 126 456 Index MT3D 134 MT3DMSSEAWAT 108 RT3D 118 contour table file 377 contours 184 200 217 color 201 217 label 201 218 level 200 217 Control Data MODFLOW2000 140 convert model 21 coordinate system 196 198 Courant number 121 criterion parameterestimation 140 171 crosssections 215 CSA 140 cutoff wall 348 Data Editor 13 DE45 solver package 63 decay rate 228 DERINC 156 DERINCLB 156 DERINCMUL 157 DERMTHD 157 Digitizer 176 dispersion 94 MOC3D 121 MT3D 130 RT3D 114 dispersive transport 354 dispersivity 122 horizontal transverse 122 longitudinal 122 vertical transverse 122 distribution coefficient 99 Double Monod model 114 Drain package 39 drawdown observations 73 drawdown scatter diagram MODFLOW 81 PEST 175 drawdowntime curves PEST 176 dualdomain mass transfer 99 DXF 26 224 effective porosity 37 EPA instructional problems 320 estimated parameter values MODFLOW2000 147 PEST 175 estimation of pumping rates 325 Evapotranspiration package 41 excavation pit 340 FACORIG 170 FACPARMAX 169 FCONV 140 Field Generator 183 Field Interpolator 177 field interpolator 369 file formats 376 firstorder decay rate 122 firstorder Euler algorithm 91 128 firstorder irreversible reaction 86 100 firstorder kinetic sorption 98 firstorder parentdaughter chain reactions 86 101 firstorder rate reaction 121 flow net 342 Flow Package 24 flow velocity 225 flowlines 220 FORCEN 156 format 376 ASCII Matrix file 376 cell group file 383 complete information file of flow observation 384 complete information file of head observation 382 contour table file 377 flow observations file 383 grid specification file 378 line map file 379 MODPATH 388 observation boreholes file 381 Index 457 observation file 380 382 observations file 381 particles file 388 pathline file 387 PMPATH 387 polygon file 385 time parameter file 379 trace file 384 transparent 5 unformatted sequential 5 XYZ file 387 Fortran compiler 5 fourthorder RungeKutta method 91 128 Freundlich isotherm 98 GCG solver 103 generalhead boundary 301 Generalhead boundary package 42 georeference 196 GEOKRIG 177 GMG solver package 68 Grid Editor 8 Grid Menu 27 grid specification file 378 GRIDZO 177 Groundwater Flow Process 1 GSLIB 177 halflife 122 Hantush and Jacob Solution 331 head observations 70 head scatter diagram MODFLOW 78 PEST 175 headtime curves MODFLOW 81 PEST 176 heat transport 4 horizontal anisotropy 29 36 hydraulic conductivity 36 transverse dispersivity 96 horizontal transverse dispersivity 95 Horizontalflow barrier package 44 Hybrid method of characteristics 126 hydrodynamic dispersion 95 IBOUND 31 ICBUND 32 import DXF map 223 DXFmap 195 matrix 188 raster graphics 195 results 193 INCTYP 156 initial prescribed hydraulic heads 36 initial concentration MOC3D 119 MT3D 126 MT3DMSSEAWAT 89 rt3d 114 Input Method CellbyCell 16 Polygon 17 Polyline 19 instantaneous reaction among species 86 interbed storage 31 Interbed storage package 45 interface file to mt3d 75 interpolation methods 177 inverse distance 179 Kriging 177 label format 201 Langmuir isotherm 98 layer bottom 32 property 27 top 32 Layer Proportions 71 LayerProperty Flow 24 Leakance 29 Limitation of PM 375 line map file 379 linear equilibrium isotherm 98 Logtransform 138 longitudinal dispersivity 95 96 458 Index massloading 103 matrix 188 import 188 reset 191 MAXCHANGE 140 MAXITER 140 mesh size 27 Method of characteristics 126 MOC3D 2 25 118 394 advection 119 concentration observation 124 concentrationtime curves 126 dispersion 121 observation wells 122 output control 123 run 125 scatter diagram 126 sinksource concentration 123 strongweak flag 122 model data checked 77 modeling environment 7 PMPATH 208 MODFLOW 1 25 39 compaction scatter diagram 81 drawdown scatter diagram 81 head scatter diagram 78 headtime curves 81 run 75 subsidence scatter diagram 81 MODFLOW2000 1 25 393 forward model run 141 parameter estimation 135 334 337 perform parameter estimation 141 perform sensitivity analysis 141 run 144 scatter diagram 148 timeseries curves 149 MODFLOW2005 393 MODFLOW88 1 MODFLOW96 1 392 MODFLOWASP 2 MODFLOWVersion 23 Modified method of characteristics 126 MODPATH 2 393 396 MODPATH format 388 MODPATHPLOT 393 molecular diffusion coefficient 122 228 Monod kinetics 86 100 359 MT3D 3 25 126 394 chemical reaction 130 concentration observation 131 concentration scatter diagram 134 concentrationtime curves 134 dispersion 130 sinksource concentration 131 transport step size 97 MT3D99 3 MT3DMS 3 25 84 394 MT3DMSSEAWAT advection 89 chemical reaction 97 concentration observation 104 concentration scatter diagram 108 concentrationtime curves 108 Diffusion species dependent 97 MassLoading 103 sinksource concentration 102 Species dependent diffusion 97 MT3DMSSEAWAT Simulation Settings 85 MT3DMSSEAWAT2000 dispersion 94 Multigrid 68 name file 389 New Model 21 nonequilibrium sorption 130 NOPTMAX 170 NPHINORED 171 NPHISTP 170 NRELPAR 171 numerical dispersion 91 127 NUMLAM 169 observation borehole 71 observation data 71 observation file Drawdown 380 Index 459 flow 382 head 380 Observation Process 1 observations compaction 73 drawdown 73 head 70 subsidence 73 OFFSET 154 Open Model 21 output control MOC3D 123 MODFLOW 74 MT3D 131 MT3DMSSEAWAT 104 RT3D 117 output frequency 75 packages DE45 solver 63 Drain 39 Evapotranspiration 41 Generalhead boundary 42 GMG solver 68 Horizontalflow barrier 44 Interbed storage 45 modflow solvers 61 PCG2 solver 65 Recharge 47 Reservoir 48 river 51 SIP solver 67 SSOR solver 67 Streamflowrouting 53 Timevariant specifiedhead 58 Well 59 Wetting capability 59 parameter anisotropy 36 bulk density 38 effective porosity 37 horizontal anisotropy 36 horizontal hydraulic conductivity 36 initial prescribed hydraulic heads 36 specific storage 38 specific yield 38 storage coefficient 38 time 33 vertical hydraulic conductivity 37 vertical leakance 37 parameter estimation MODFLOW2000 135 PEST 149 Parameters MODFLOW2000 136 Parameters Menu 33 PARCHGLIM 154 parentdaughter chain reactions 363 PARGP 154 PARLBND 154 PARNAM 137 PEST 153 particle location 124 particle tracking 203 219 particle tracking algorithm 91 128 particle velocity 119 Particles file format 388 PARTIED 154 PARTRANS 154 PARUBND 154 PARVAL 138 PARVAL1 PEST 153 pathline file format 387 pathlines 220 Paths to Simulation Program File 26 PCE sequential degradation of 114 PCG2 solver package 65 Peclet number 91 127 Perchloroethene sequential degradation of 114 PEST 2 25 395 Control Data 167 drawdown scatter diagram 175 drawdowntime curves 176 estimated parameter values 175 460 Index head scatter diagram 175 headtime curves 176 Output Options 171 parameter estimation 149 Parameter Groups 155 Parameters 152 Prior Information 157 Regularization 159 run 172 SVD 162 SVDAssist 162 PHIRATSUF 168 PHIREDSTP 170 PHIREDSWH 170 PHT3D 4 25 109 395 Define Reaction Module 397 Examples 367 PMPATH 2 25 176 203 polygon assign value 18 delete 18 modify 19 polygon file format 385 Polygon Input Method 17 polygons 191 polyline assign value 20 delete 19 modify 20 Polyline Input Method 19 polylines 10 preconditioning method 103 preconsolidation head 75 Preferences 23 Prescribed Fluid Density SEAWAT 102 Print Plot 26 Prior Information MODFLOW2000 138 radioactive decay 121 131 raster graphic 195 import 195 reaction among species 86 reaction parameters RT3D 115 recharge 271 Recharge package 47 refine 12 refinement 22 RELPARMAX 169 RELPARSTP 171 Reservoir package 48 Results extractor 184 retardation 122 retardation factor 96 121 212 river 284 River package 51 RLAMBDA1 167 RLAMFAC 168 RMAR 140 RMARM 140 rows delete 10 insert 10 RT3D 3 25 113 395 advection 114 concentration observation 116 concentration scatter diagram 118 concentrationtime curves 118 dispersion 114 output control 117 run 117 Simulation Settings 113 sinksource concentration 116 run MOC3D 125 MODFLOW 75 MODFLOW2000 144 MT3D 133 MT3DMSSEAWAT 105 PEST 172 RT3D 117 run listing file MOC3D 126 MODFLOW 78 Index 461 MODFLOW2000 147 MT3D 134 MT3DMSSEAWAT 108 pest 174 rt3d 118 Save Plot As 26 SCALE 154 scatter diagram MOC3D 126 MODFLOW 78 MODFLOW2000 148 MT3D 134 MT3DMSSEAWAT 108 PEST 175 RT3D 118 SEAWAT 4 26 84 Examples 368 Prescribed Fluid Density 102 seepage 342 344 semianalytical particle tracking method 204 semivariance 180 sensitivity composite observation 175 composite parameter 175 composite scaled 148 dimensionless scaled 147 onepercent scaled 148 sensitivity analysis MODFLOW2000 141 sensitivity arrays onepercent scaled 148 Sensitivity Process 1 Simulation Settings MODFLOW2000 136 MT3DMSSEAWAT 85 PEST 151 PHT3D 109 113 sinksource concentration MT3D 131 MT3DMSSEAWAT 102 RT3D 116 SIP solver package 67 solution methods comparison 62 solvers 61 DE45 63 GCG 103 GMG 68 PCG2 65 SIP 67 SSOR 67 sorption distribution coefficient 99 firstorder kinetic 98 Freundlich isotherm 98 Langmuir isotherm 98 linear equilibrium isotherm 98 SOSC 140 specific storage 38 specific yield 38 SSOR solver package 67 stochastic modeling 372 stoichiometry 87 storage coefficient 30 38 Streamflowrouting package 53 subgrid 118 subsidence 75 351 subsidence observations 73 subsidence scatter diagram MODFLOW 81 SURFER 177 TECKONEM 177 telescoping flow model 22 Theis Solution 328 time 33 time parameter file 379 timeseries curves MOODFLOW2000 149 Timevariant specifiedhead package 58 TOL 140 toolbar buttons Data Editor 15 Grid Editor 12 PMPATH 211 top of layers 32 trace file 462 Index format 384 Transient Simulation Specifying Data 20 transmissivity 29 36 triangulation 180 tutorials 227 Type of Reaction 86 unconfined aquifer system 271 units 7 Upstream finite difference method 127 variable density 87 Variable Density Flow 85 variogram 180 VCONT 37 vector graphic 194 scaling 195 velocity 124 velocity vectors 216 vertical anisotropy 29 37 hydraulic conductivity 37 leakance 29 37 transverse dispersivity 95 96 Water Budget 187 Water Budget Calculator 4 Well package 59 XYZ file format 387