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MODAC Manual - MODAC A Hydrology

1. Maximum MODFLOW Iteration 5 OK Cancel You will see each window is updating three times for each calibration step following a sequence of Layer 3 Layer 2 and Layer 1 In the top left window the RMSE pnt value is also changing with time because a file with observed head values is placed in the same directory with a name of target dat thus comparison between simulated head and observed head is available In the bottom left window you will also see that Layer 1 is dry in some areas in the early calibration steps However the dry area gradually reduces and disappears with increased calibration steps This is because that the target water levels are higher than the bottom elevation not dry and the parameter adjustment is working toward the direction to make the simulated water levels match the MODAC Version 1 15 target levels Thus when you see such initial dry conditions do not turn on the rewetting function in MODFLOW just let MODAC work When MODAC operation is done select Save Result to continue you will be back to Run Dialog T In Run Dialog e Set Number of calibration step 10 or more e Increase Maximum MODFLOW Iteration 100 to let solution converge Repeat step 7 as many times as you like until you satisfy your results 8 Import the results into a GUI to review water budgets and calibration statistics Most of MODAC files such as K Vcont and upper and lower limits for K can b
2. Ideally all color zones should disappear gradually implying all the residuals are below a predefined residual value head residual criteria for screen plot If color spots in certain area persist you may need to either adjust the methods or go back to original model to check the conceptual model and numerical model setup Screen plot of residual zone depends on selected criteria i e predefined residual value for plotting The criteria can vary depending on your problem A default value for residual plotting criteria is 1 0 feet When MODAC finishes the run select Save Result to continue you will be back to Model Run Dialog 8 In Model Run Dialog e Set Number of calibration step 10 or more e Increase Maxinum MODFLOW iteration 40 to let solution converge MODAC Version 1 12 After repeating step 7 for a few times you should see match of the simulated and target water tables reasonably well in the bottom left window and residuals in bottom right window disappearing 9 Review Results You may review the results under Graphic after run or at any time or import the results to any groundwater model graphic user interface GUI The true hydraulic conductivity distribution of Case 1 is provided in Appendix B The calibrated one should be fairy close to the true distribution Be sure to check water budget for the final results However in the early stage of parameter adjustment as long as the solution is not isolating fewer i
3. Nalt 2 1 111 All layers require K estimation Layers 2 and 3 support layer 1 96 1 0 10f12 4 0 5 0000e 03 5 0000e 03 5 0000e 03 step size for each layer 96 1 0 10f12 4 0 2 0000e 02 2 0000e 02 2 0000e 02 Maximum step size for each layer 96 1 0 10f12 4 0 1 1500e 00 1 1000e 00 1 1000e 00 Upper smooth factor for each layer 96 1 0 10f12 4 0 8 5000e 01 9 5000e 01 9 5000e 01 Lower smooth factor for each layer 96 1 0 10f12 4 0 1 0000e 08 1 0000e 08 Lower limit for vertical conductance OPEN CLOSE layerl vrt 1 0 FREE 1 Vertical Ratio for Layer 1 OPEN CLOSE LAYER 01 UPL 1 0 FREE 1 Upper Limit of Layer 01 0000e 01 0 Lower limit of Layer 1 OPEN CLOSE layer2 vrt 1 0 FREE 1 Vertical Ratio for Layer 2 0 1000 000 0 Upper limit of Layer 2 01 0000e 01 0 Lower limit of Layer 2 OPEN CLOSE layer3 vrt 1 0 FREE 1 Vertical Ratio for Layer 3 0 1000 000 0 Upper limit of Layer 3 01 0000e 01 0 Lower limit of Layer 3 1 00 Head residual criteria for screen plot MODAC Version 1 3 1 4 2 4 Constraints Constraints on hydraulic parameters for most of real world problems are necessary Constraints on hydraulic conductivity transmissivity and conductance of head dependent boundary are in two different formats 4 2 4 1 Constraints on Hydraulic Conductivity or Transmissivity Upper and lower constraints on hydraulic conductivity transmissivity can be specified as constant for an entire model domain for each layer or as distributed values using ar
4. couples the widely used three dimensional groundwater flow model MODFLOW 1996 version and the inverse hydraulic parameter estimation procedures developed by Guo and Zhang 1994 2000 MODAC is an indirect inverse solution procedure The numerical procedure is an iterative process that performs MODFLOW simulation and parameter adjustment alternatively It starts from a set of initial estimates of hydraulic parameters and improves the estimates according to the derived optimality condition Appendix A The iterative process gradually reduces the differences between the simulated and interpreted hydraulic gradient and hydraulic head as well as between the simulated and estimated boundary fluxes MODAC has been used for extensive applications on various real world groundwater model calibrations Results of these applications have demonstrated that MODAC can significantly improve quality and efficiency of model calibration 1 2 Role of MODAC in Model Calibration Groundwater model calibration involves estimation of hydraulic parameters and hydrology parameters and verification of conceptual model The hydraulic parameters hereafter refer to the parameters that reflect the hydraulic characteristics of a groundwater flow system They include hydraulic conductivity transmissivity head dependent boundary conductance vertical conductance and storage coefficient or specific yields Hydrologic parameters hereafter refer to sink and source such as gr
5. 01 120 00 1 142 190 89 300 237 83 88 80 162 00 2590 00 0 01 120 00 In this example AUX CLW Lower limit for conductance AUX CUP Upper limit for conductance AUX FLW Lower limit for target flux AUX FUP Upper limit for target flux In second line 7 80E 04 and 8 50E 04 are specified lower limit and upper limit of total flux out of all river boundary cells In each model cell the values in the very last two columns are specified flux targets and the values in the two columns second to the last two columns are specified constraints on conductance Note after modifying these files be sure to save them in the format as csv file in Microsoft Excel When browsing the file in the MODAC dialog window searching for the corresponding csv file The estimated range of flux for constant head boundary is specified in the CHD file 4 2 6 Observed Data File Observed hydraulic heads at monitoring wells can be input directly during MODAC calibration This data file should be located in the same folder used for calibration The name of the file should be Target dat The format of the file can be free or formatted but should follow the sequence as follows MODAC Version 1 33 Head line Well name X coordinate Y coordinate Water level Layer An example is provided as follows Name X Y Water level Layer Well 1 4659 1 6662 7 62 16 1 Well 2 4592 2 6776 4 61 81 1 Well 3 8307 6 10455 2 122 57 1 Well 4 7847 5 10262 8 117 36 1 Wel
6. 80E 04 Click one of these boundary conditions you will see a dialog window for each of the boundary fluxes as above The upper portion of the window is used to specify total fluxes and the lower portion for distributed fluxes Negative value means fluxes out of an aquifer and positive value means fluxes into an aquifer For Case2flx we specified the ranges of distributed fluxes for the river cells and the ranges of total fluxes for GHB River and CHD We have prepared a csv file Riverflx csv for distributed range for river fluxes for every river cell You may browse this file by clicking browse in the lower portion of the dialog window Note the specified lower and upper limit for each river cell was assumed with a wider range because lack of specific information However this provides you an example so that when you need and have data you may specify the range for certain section For the sections where you do not have data you may simply specify a broad range as dummy ranges The river input file may be prepared in the form of csv file by Microsoft Exel As the result of browse you will see a dialog window as follows MODAC Version 1 19 8 50E 04 7 80E 04 D MODAC MODAC_CASES Cas2flx 5 Go to File and chose Save Then chose Open MODAC NFL file and browse for Case2flx nfl 6 Go to Run and specify a few number of runs and specify other parameters accordingly This time you will see a DOS window as follows
7. difficult part of a groundwater flow model development Quality of model predictions is highly dependent on the quality of model calibrations To date there is no standard protocol for groundwater flow model calibration because site conditions and modeling objectives are highly variable Level of calibration and process of calibration often depend on modeling objectives and data availability Here we present our understanding about concept of model calibration and propose a process of performing model calibration using MODAC We often have two concerns regarding to model calibration e Should calibration be performed for hydraulic parameters e g hydraulic conductivity and stresses e g pumping rate groundwater recharge at the same time e Should calibration results be only compared to spot wise measurements or also compared to overall flow pattern The discussions in the following text present our understanding about the above concerns focusing on e Calibration of hydraulic parameters versus stresses e Targets of model calibration 2 1 Calibration of Hydraulic Parameters versus Stresses Ideally model calibration is to perform a quantitative physical characterization for an aquifer or a groundwater flow system given known stresses and observed aquifer responses The physical characteristics of an aquifer usually comprise of Dimension and geometry of hydrogeologic units Hydraulic conductivity or transmissivity distributi
8. iterations and the secondary method for 1 iteration o If NALT 3 MODAC uses the primary method for 3 iterations and secondary method for 1 iteration MODAC Version 1 28 A4 Array Format A5 Array Reader A6 Array Reader A7 Array Reader MODAC Version 1 e COMB combined method of gradient comparison and head comparison e GRAD hydraulic gradient comparison method e HEAD hydraulic head comparison method Layer Match NLAY 40D e Layer Match is a 1D integer array with double indications 1 specifying whether the hydraulic conductivity of the layer needs to be calibrated and 2 if the K values of the layer need to be calibrated specifying which target will be used for calibration The position of Layer Match in the array corresponds to sequence of model layers e Layer Match 0 No calibration for the layer e Layer Match 0 Horizontal hydraulic conductivity of this layer needs to be estimated e Layer Match Layer sequential number The potentiometric surface of this layer will be used as a direct target in parameter estimation e Layer Match Other layer number The potentiometric surface of the other layer will be used as indirect target The hydraulic conductivity of this layer will be estimated to support the other layer in matching the corresponding target Step Size NLAY UIDREL e Step Size is a 1D real array defining the step size a for parameter adjustment Appendix A Each val
9. screnn plot E D Save MAC Cancel 24 MODAC Version 1 Layer Match Layer Match 0 no calibration for this layer Layer Match Layer number parameter estimation will directly match the head information of this layer Case 2 selected this option for all three layers Layer Match gt 0 and Other layer number parameter estimation of the layer will support matching the head information of the other layer This option is often selected when the layer is hydraulically connected with the other layer that has potentiometric surface while the data in the layer itself are not adequate to generate a representative potentiometric surface This option was designed considering that potentiometric surface may only be available for uppermost layer in most practical problems In Case 2 this option can be chosen for layer 2 and layer 3 because the three layers are hydraulically connected Users are encouraged to try this option You will see the calibrated results of choosing this option are somewhat close to the results of choosing all layers matching their potentiometric surfaces When using MODAC to set or modify Layer Match you can double click and specify according to your need Parameter Adjustment Step Size Step Size Step size is the value of scaling factor amp used to determine the step size of parameter adjustment as shown in Equation 10 in Appendix A The greater the step size the faster the change of parameter value Ad
10. using hypothetical cases 3 1 Running MODAC with Hypothetical Case 1 Hypothetical Case 1 assumes an unconfined and heterogeneous groundwater flow system The specified hydraulic conductivity distribution ranges from 0 1 ft day to 10 0 ft day The bottom elevation of the aquifer is variable A one layer finite difference grid consisting of 100 rows and 100 columns with a uniform cell dimension of 100 ft by 100 ft is superimposed on the flow system Boundary conditions consist of general head boundary prescribed flux and no flow The conductance of the general head boundary is constant and specified as 250 ft day Several source sink terms exist within the model domain including two pumping wells two injection wells and areal positive and negative ground water recharge The hydraulic head distribution was generated using MODFLOW input file data under steady state condition In the parameter estimation process the hydraulic conductivity distribution and general head boundary conductance are assumed unknown The generated hydraulic head distribution is assumed to be the interpreted potentiometric surface and is used as the calibration target for parameter estimation In total 10 000 hydraulic conductivity values and 100 conductance values need to be estimated given 10 000 known hydraulic head values specified boundary conditions and other parameters Parameter estimation is an iterative forward process which follows the numerical proc
11. 1 ft day to 10 0 ft day as shown in Figure 1 a The bottom elevation of the aquifer is variable A one layer finite difference grid consisting of 100 rows and 100 columns with a uniform cell dimension of 30 5 m 100 ft by 30 5 m 100 ft is superimposed on the flow system Boundary conditions consist of general head boundary prescribed flux and no flow The conductance of the general head boundary is constant and specified as 23 2 m day 250 ft day Several source sink terms exist within the model domain including two pumping wells two injection wells and areal positive and negative ground water recharge The hydraulic head distribution solid line in Figure 2 was generated using MODFLOW input file data under steady state condition Parameter Estimation Processes In the parameter estimation process the hydraulic conductivity distribution and general head boundary conductance are assumed unknown The generated hydraulic head distribution in Figure 2 was assumed to be the interpreted potentiometric surface and is used as the calibration target for parameter estimation In total 10 000 hydraulic conductivity values and 100 river conductance values need to be estimated given 10 000 known hydraulic head values specified boundary conditions and other parameters Parameter estimation is an iterative forward process which follows the numerical procedure as described in Section 2 The initial hydraulic conductivity distribution is assu
12. 18 26 17 8 1 699 9 900 18 26 20 S 1 808 9 900 18 26 22 10 1 325 9 900 18 26 25 MAAAR S ex RMSE vs CALIBRATION STEPS N iy Map for Residual gt 1 00 B Sim gt Target R Sim lt Target Save Results and Continue iffstart des 3yb AMobaciMobac 7 MODAC 1 06 U MO RI bocumentt Microso fi MODAC_Manualt 2 amp mMODAC LC MIEJVS 6 26PM TOP LEFT WINDOW N RMSE map RMSE pnt Time Layer Where N Number of calibration steps RMSE map Root mean squared error between simulated and target head values over entire model domain of the layer RMSE pnt Root mean squared error between simulated and observed head values at measurement points Time Operation time Layer Layer number During MODAC operation you should see the RMSE map is progressively decreasing with time if the program works well In Casel observed values are not inputted thus RMSE pnt is a default value of 9 900 TOP RIGHT WINDOW A dynamic curve of RMSE vs calibration steps is displayed to show the trend of root mean squared error which is consistent with what is displayed in the top left window If 11 MODAC Version 1 the curve moves down the parameter estimation works well and towards convergence If the curve moves up the parameter estimation is having difficulty either the internal constraints e g upper or lower limit of hydraulic conducti
13. MODAC Version 1 A Hydrogeology Based Parameter Estimation Program for Groundwater Flow Model Developed by Xiaoniu Guo Chuan Mian Zhang Copyright 2002 2004 by Xiaoniu Guo and Chuan Mian Zhang Contact Information Chuan Mian Zhang or Xiaoniu Guo 9241 Bauer CT Lone Tree CO 80124 Chuan Mian_Zhang urscorp com http www groundwater modac com TABLE OF CONTENTS 1 INTRODUCE TION PEDI T 1 Lp Whats MODAG minnannona nonn eunas hEDD heeded ected tye hed ttc 1 1 2 Role of MODAC in Model Calibration een 1 1 3 Features of MOD AQ ise aee a teet ve eer eed datas acts sac EP EE EM ace eed Qo 1 Luo Wise MODAC usi eot pe Eb tate E RP hup DEM PE Med E HE PM Ns 2 1 5 Installation and Uninstallation of MODAC esee eene 2 L6 Obtaming d Security Cole espe te ERR pae IR HIREN ER eoa fes ie roe M aca ISI iii 3 1 7 Technical Support t HIR REEL OR ERE RUE SC oases Ganda eden RARE EUM Voas 3 1 8 How to Use This Manual eeeeeeeeeeeeeee eene ne i anat PariS LaSi nean 3 2 CONCEPT OF MODAC TO SUPPORT GROUNDWATER FLOW MODEL CALIBRATION e T aises isee t es oeieo oosa 5 2 1 Calibration of Hydraulic Parameters versus Stresses ccssscccccceeeeeeeeenteeeeeeees 5 2 2 Targets for Model Calibration isi oer eor t hae eosam e PRI TAS EMT EET 7 3 TUTORIAL WITH HYPOTHETICAL CASE DEMONSTRATION 9 3 Running MODAC with Hypothetical Case 1 eee eeesneeeeeeeeeeeeeen
14. MODAC Version 1 20 5 MODAC BIS x 66 645 769691 5 6 927281 269691 Qeeoeaoaod m Go co c 8 8 5 5 a s 6 8 au m 2 4 9289356 Four columns are shown in this window The first column is the type of boundary In this window only GHB and River are present This means that the calculated flux for CHD is already in the range The second column is the calculated flux at the corresponding calibration step The third column is the specified value for either lower limit or upper limit The fourth column is the coefficient calculated by MODAC to adjust the corresponding boundary flux In this window the calculated GHB flux is 669 645 initially which is greater than the specified upper limit so the corresponding coefficient is 0 909091 In line 9 the GHB flux drops to 604 467 which is close to the specified value of 600 000 After that GHB disappears indicating the calculated GHB flux is within the range of specification The River flux initially 91665 8 which is much greater than the specified upper limit of 85000 0 thus the corresponding coefficient is always less than 1 0 By iteration of 10 or last line in the window the River flux drops to 85914 4 During model calibration this DOS window can be minimized or moved to different location if it covers the area you want to see It should be noted that when specifying boundary fluxes you should consider mass balance under steady state co
15. SEQUANTIALLY Enter A10 only if there is more than one layer in model A10 Record A11 Record MODAC Version 1 INCODE Vertical anisotropy ratio Coefficient Form If vertical anisotropy ratio is a constant for a layer e NCODE 0 e Vertical anisotropy Kx Kz e Format 110 F10 2 If vertical anisotropy ratio is an array for a layer e NCODE OPEN CLOSE e Vertical anisotropy ratio file name of the array e Coefficient e Form Format of the array e Format Free format INCODE Upper limit of K for the layer Coefficient Form IF upper limit is a constant for a layer e INCODE 0 e Upper limit constant e Format I10 F10 2 IF upper limit is an array for a layer e INCODE OPEN CLOSE Upper limit file name of the array Coefficient Form Format of the array Format Free format 30 A12 Record INCODE Lower limit of K for the layer Coefficient Form e IF lower limit is a constant for a layer e INCODE 0 Lower limit constant e Format I10 F10 2 e IF lower limit is an array for a layer e INCODE OPEN CLOSE e Lower limit file name of the array e Coefficient e Form Format of the array e Format Free format GENERAL A 3 Record Head residual criteria for screen plot Format F10 2 For illustration purpose an example is provided as follows EXAMPLE 1 HYK RIV hydraulic conductivity and river conductance are estimated HYK COMB HEAD 1 Primary combined secondary head
16. acteristics of a groundwater flow system are inherent and supposed not to change over time under normal conditions in an average field scale sense Model calibration refers to a process that estimates the physical characteristics of a groundwater flow system given stresses and responses while model prediction refers to a process that estimates aquifer responses given a calibrated flow system and potential stresses If the physical characteristics are calibrated well the prediction results should be representative when stresses to a groundwater system are changed The calibration process described above is an ideal process that may only be found in a laboratory or in a hypothetical case In real world modeling a lot of information is only known at sparsely distributed points or known with some uncertainty including both hydraulic parameters and stresses Therefore model calibration has to deal with estimation of both hydraulic parameters and stresses However because hydraulic parameters and stresses are highly correlated in a model calibration MODAC does not deal with them at the same time Facing the practical complexity we propose to decompose the model calibration process into separate steps and then integrate these steps together through an iterative process Hydraulic parameter estimation and stress estimation can be decomposed into separate steps using different approaches Stresses can be estimated independently prior to groundwater
17. arameter identification a practical and efficient automated procedure In Proceeding of the 1994 Groundwater Modeling Conference Fort Collins Colorado page 111 118 1994 Guo Xiaoniu and Chuan Mian Zhang 2000 Hydraulic gradient comparison method to estimate aquifer hydraulic parameters under steady state conditions Ground Water 38 No 6 815 826 Harbaugh A W and M G McDonald 1996 Programmer s documents for MODFLOW 96 an update to the U S Geologic Survey modular finite difference ground water flow model USGS Open File Report 96 486 Harbaugh A W E R Banta M C Hill and M G McDonald 2000 MODFLOW 2000 The U S Geologic Survey modular ground water model user guide to modularization concept and the ground water flow processes USGS Open File Report 00 92 Hill M C 1992 A computer program MODFLOWP for estimating parameters of a transient three dimensional groundwater flow model using nonlinear regression USGS Open File Report 91 484 McDonald M G and A W Harbaugh 1988 A modular three dimensional finite difference groundwater flow model USGS Open File Report 83 875 Morel Seytoux H J and Xiaoniu Guo Application of Constrained Calculus of Variations to the Inverse Problem in Groundwater Report No 90 5 Hydrowar Reports Division Hydrology Days Publications 57 Selby Lane Atherton CA 94027 1990 Yeh W W G Review of Parameter Identification Procedures in Groundwater Hydr
18. ase combined method or head method could be used alternatively either as the primary method or the secondary method Alternating Interval The alternating interval is the number of steps using primary method If the alternating interval equals 1 adjustment will use one step for primary method and one step for secondary method If the alternating interval is equal to or greater than 2 adjustment will use two or more steps for primary method and one step for secondary method ial x i MODAC MAC SETUP r Selecting Parameter for Calibration Selecting Method v Hydraulic Conductivity or Transmissivity Primary Method Secondary Method Alternating Interval IV General Head Conductance Combined ho Drain Conductance Head Head PETI ate eat ie Gradient m Storage Woenicient Layer Match Calibration of Layer 1 for Heads Match in Layer lt 1 gt Parameter Adjustment Step Size 0 020 0 10 Step Size Maxium Step Size Smooth Factor Upper Ratio 21 0 E 15 Lower Ratio lt 1 0 fo 95 Vertical Anisotropy Ratio of Kh Kv Minimum V cont Value Select Layer o o000001 Layer 1 Use File lt LAYER 01 VAT gt Layer 2 Uniform alue 100 E m Upper Limits of K Select Layer Layer 1 Use File lt LAYER 01 UPL gt Layer 2 Uniform Value 100 hd Lower Limits of K Select Layer Layer 1 Uniform Value 0 0001 Layer 2 Uniform Value 0 009 Residual criteria for
19. aulic conductivity Smooth will not happen across the boundary of different zones of K constraints Vertical Anisotropy Ratio of Kh Kv The vertical anisotropy ratio is used in calculation of vertical conductance between layers Vertical anisotropy ratio of Kh Kv can be set as a constant for each layer or distributed values using a matrix file The matrix file can be generated using groundwater model GUI with specified format or free format When using MODAC to set or modify the vertical anisotropy ratio you may double click the layer then you will see a dialog window as follows im Set up Vertical Ratio of Layer 1 F Gap initial evel ETE Corstrarnts MODAC Version 1 26 You have two choices e Input a uniform value e Input an existing matrix file if you need to you can modify it Upper Limits of K Upper limits of hydraulic conductivity can be set as a constant for each layer or distributed using a matrix file The matrix file can be generated using groundwater model GUI with specified format or free format In practical problems it is important to set constraints on hydraulic conductivity based on field aquifer test results or other supporting data The uncertainty associated with interpretation of potentiometric surface can be somewhat controlled by interpreted aquifer test results if they are representative When using MODAC to set upper limits you may double click the layer under Upper Limits of K A set up dialog will
20. aulic conductivity and Vcont matrix from the BCF file 4 2 2 Interpreted Potentiometric Surface as Direct Target MODAC uses interpreted potentiometric surface as direct target for hydraulic parameter estimation although in an entire model calibration process a global calibration target is required as discussed in Section 2 Requirement for interpreted potentiometric surface includes e Interpreted potentiometric surface should honor observed points e Interpreted potentiometric surface should cover an entire active model domain e Interpreted potentiometric surface should not be conflict with specified model boundary conditions e g a no flow boundary should be perpendicular to equal potential line e Potentiometric surface is better to be interpreted by hydrogeologist based on hydrogeologic understanding but not simply by contour software MODAC Version 1 22 Interpreted potentiometric surface for an entire model domain should be read as the initial conditions for MODFLOW in a MODFLOW BAS file or attached to a BAS file for the layer which hydraulic conductivity distribution needs to be calibrated Input of initial conditions can be directly prepared as matrix or prepared by a GUI However caution should be taken to check if the specified initial conditions are reserved on prescribed head boundaries in the ASCH MODFLOW BAS input file 4 2 35 MAC File The only additional input file required by MODAC is a MAC file which contains speci
21. ayer 1 Use File lt LAYER 01 UPL gt Layer 2 Uniform Value 100 T Layer 1 Uniform Value 0 0001 Layer 2 Uniform Value 0 009 x Residual criteria for screnn plot fi n Save MAC Cancel You may review the MODAC MAC setup window and click Save MAC 5 Go to File again click Open MODAC NFL file browse for Case2 nfl You may review the setup under Graphic including initial hydraulic conductivity upper and lower limits on hydraulic conductivity You will see the upper limits on hydraulic conductivity of layer 1 is distributed while the constraints for others are constant 6 Go to Run in Run Dialog e Set Number of calibration step 100 e Check Smooth MODAC Version 1 14 e Select Calculate leakance e Set Maximum MODFLOW iteration 5 for Case 2 it is the PCG external iteration number e Click OK and let MODAC to run ia Model Run Dialog x Number of Calibration Step 100 Selecting Method Primary Method Secondary Method Altemating Interval E Combined 2 Head Head Gradient Selecting Parameter for Calibration Iv Hydraulic Conductivity or Transmissivity General Head Conductance Drain Conductance IV River Conductance Storage Coefficient I Zone Average E Emo Vertical Conductance Smooth Factor Keep Leakance J Uniform for all layer Calibrate Leakance PATER Calculate Leakance Upper Ratio gt 1 0 fi 15 z Lower Ratio lt 1 0 fo 85 X
22. bject to the boundary conditions h h on B 2a MODAC Version 1 35 T Vh nzq on Bz 2b T Vh n t h h on B3 2c where V gradient operator T transmissivity tensor h hydraulic head q source sink term R flow domain Bi boundary of domain R for prescribed head condition B2 boundary of domain R for prescribed flux condition B3 boundary of domain R for head dependent condition n unit vector normal to boundary hy prescribed head at prescribed head boundary qi prescribed flux at prescribed flux boundary h prescribed head at a general head boundary T conductance of the general head boundary From the literature the common approach to identification of distributed hydraulic parameters e g transmissivity is to define an objective function OBJ that minimizes the differences between observed and simulated hydraulic heads h and h If a classical least square error criterion is used the objective function to be minimized is OBJ Y h h 3 i l where N is the total number of hydraulic head observations This is often used as the general performance criteria in inverse models to describe how good that fit head observations Equation 3 is a typical multi dimensional optimization problem which is often solved using the Gauss Newton algorithm Cooley 1977 1979 Several currently available automated calibration computer codes including MODINV Doherty 1990 MODFLOWP Hill 1991 and PEST Doherty 1994 we
23. ces for parameter estimation One is to assume the target potentiometric surface is known for all the three layers The other choice is to assume that the target potentiometric surface is only available for first layer The second choice is fairly common in actual conditions Let us introduce the first choice now and you may try second choice by yourself Please follow the steps below 1 Unzip Case2 zip in a new folder 2 Click MODAC icon to start the program MODAC Version 1 13 3 Go to File and click NEW MODFLOW NAM file browse for Case2 nam 4 Go to Setup and click Import MAC file then import Initial mac You will see a MODAC MAC Setup window as follow ia MODAC MAC SETUP m Selecting Parameter for Calibration v Hydraulic Conductivity or Transmissivity v General Head Conductance ial x Selecting Method Primary Method Secondary Method Alternating Interval Combined E Drain Conductance EE Head i Gradient Layer Match Calibration of Layer 1 for Heads Match in Layer lt 1 gt Y Parameter Adjustment Step Size Step Size Maxium Step Size 0 020 0 10 Smooth Factor Upper Ratio gt 1 0 E 16 Lower Ratio lt 1 0 fo 95 Vertical Anisotropy Ratio of Kh Ky Minimum V cont Value Select Layer 0 000001 Layer 1 Use File lt LAYER 01 VAT gt Layer 2 Uniform Value 100 Lower Limits of K m Upper Limits of K Select Layer Select Layer L
24. chnique plays a role to overcome potential over parameterization However sometimes smoothing could limit variation of parameters at a local area which would limit continuation of parameter estimation In this case you may turn off the smooth function let MODAC to work in a more flexible environment If the results are improved you may turn on the smooth factor again When you click Smooth in Run Dialog you may specify the upper ratio and lower ratio You can change these ratios any time during MODAC operation Vertical Conductance You have three options depending on need and data availability e Keep leakance e Calibrate leakance e Calculate leakance Keep leakance Vertical conductance will not change during parameter adjustment This is used only for limited conditions Calibrate leakance Vertical conductance will be calibrated based on comparison of vertical hydraulic gradient between layers This is only used when representative potentiometric surfaces are available for both upper and lower layers Calculate leakance Vertical conductance will be calculated at every calibration step according to estimated hydraulic conductivity with specified vertical anisotropy ratios This is a commonly used option Maximum MODFLOW Iteration The maximum MODFLOW iteration here refers to the number of MODFLOW solver iterations The MODFLOW solver package requires specification of maximum calculation iterations In MODAC o
25. e conveniently reviewed or modified under Graphic in MODAC or exchanged with GV as matrix files You can review or modify them either in GUI or in MODAC 3 3 Model Run Dialog Instruction Number of Calibration Step Each calibration step includes a MODFLOW simulation and a MODAC parameter adjustment When you start a problem you may try a small number first like 5 to 20 No limit on number of calibration steps Alternating Interval Alternating interval is the number of steps using primary method If alternating interval equals 1 adjustment will use one step of primary method and one step of secondary method If alternating interval is equal to or greater than 2 adjustment will use two or more steps of primary method and one step of secondary method Selecting Parameter for Calibration The parameters that you can use MODAC to estimate include Hydraulic conductivity General head conductance River conductance Drain conductance Storage coefficient not applicable yet Zone Average MODAC Version 1 16 If clicking this button the distributed K within a specified zone will be averaged You may click this button after your calibration results are generally acceptable depending on your need Smooth Smooth technique should be applied during parameter estimation It tends to minimize spatial variation of parameter values when MODAC tends to vary parameter values to meet the optimality conditions Therefore smooth te
26. edure as described in Appendix A The initial hydraulic conductivity distribution is assumed to be constant over the entire model domain The upper limit and lower limit on hydraulic conductivity is set as constant as 100 ft day and 0 001 ft day respectively To run MODAC on Case 1 please follow the steps below 1 Unzip Casel zip in a new folder you will see standard MODFLOW files with root name as Casel 2 Click MODAC icon to start the program 3 Go to File and click NEW MODFLOW NAM file browse for Casel nam 4 Go to Setup and click Import MAC file then import file Initial mac After reviewing the content of the MAC file click Save MAC You may review the initial setup of Case 1 under Graphic including bottom elevation water table thickness hydraulic conductivity upper limits on hydraulic conductivity and lower limits on hydraulic conductivity 5 Go to File again click Open MODAC NFL file browse for Casel nfl 6 Go to Run you will see Model Run Dialog MODAC Version 1 9 ia Model Run Dialog EE Gradient storage belfictent 7 In Model Run Dialog e Set Number of calibration step 50 e Check Smooth e Set Maximum MODFLOW iteration 5 for Case 1 it is the PCG external iteration number e Click OK You will see the target potentiometric surface first and then four windows on screen MODAC Version 1 10 J MODAC N RMSE map RMSE pnt Time 6 2 787 9 900 18 26 15 7 2 470 9 900
27. f MODAC is similar to other Windows products as following steps e Unzip the MODAC package in a separate folder e Click setup exe installation will automatically start If this is the first time to install MODAC you may see a note This is a demo version results cannot be saved This means that without registration to get a security code you may try the examples or play with your cases but you will not be able to save the results Uninstallation Uninstallation of MODAC is similar to other Windows program as following steps e Double click My Computer in the upper left corner of the desktop Double click Control Panel and then double click the Add Remove Programs icon e Select MODAC from the list of programs and click the Add Remove button on the dialog Then follow the prompts from the uninstall wizard from there 1 6 Obtaining a Security Code MODAC package is protected by a security code that is tied with your computer If you want to obtain a standard version you must obtain a security code to complete installation To obtain a security code please do the following Goto File and select Register e A code registration dialog displays the System Code Copy the System Code then send it via an email to Chuan Mian Zhang urscorp com including your name affiliation and email address You will get an email back and receive a Security Code If you obtain the code from Groundwater Vistas please send the information to support g
28. fications for parameters used in parameter estimation and various constraints The MAC file can be created and modified on screen or prepared by a groundwater model GUI prior to starting MODAC This MAC file should be included in the NFL file as DATA 96 XXXXXXXX MAC When using MODAC to generate a NFL file the above line is included automatically Explanation of MAC File Parameters The parameters as shown in the following MODAC MAC Setup window are explained as follows Selecting Parameters for Calibration The parameters that you can use MODAC to estimate include Hydraulic conductivity General head conductance River conductance Drain conductance Storage coefficient not applicable yet You may choose appropriate parameter s according to your problem Selecting Method Three parameter adjustment methods are included in the MODAC package for estimation of hydraulic conductivity e Gradient hydraulic gradient comparison method e Head hydraulic head comparison method e Combined hybrid of gradient and head comparison methods MODAC Version 1 23 In general conditions the gradient method is the most powerful one However the gradient method alone has some limitation When boundary conditions are complicated or constraints on K in certain area have limited a good match of hydraulic head in that area gradient method may not be flexible enough to allow match of the heads in the rest of area In this c
29. for hydraulic conductivity K can be derived by simple substitution The resulting optimality conditions for an unconfined aquifer are oL 1 2 042 2 s Vh V h Vh 1 2 N 8 JK ral j VOY Why dedy j 8 DL cl f y nya Hs 1 1 2 M_ PT p lb Hydrology Concept in the Optimality Conditions An important feature implied in Equation 6 is that the optimality condition is consistent with Darcy s law From mathematical point of view to make the partial derivative L T approach the optimality condition according to Equation 6 if Vh Vh Vh gt 0 the value of transmissivity T needs to be increased Conversely if Vh Vh Vh lt 0 the value of T for the partial derivative must be decreased to approach the optimality condition This concept is consistent with Darcy s law Spatial Independence of Optimality Conditions Another important feature that is implied in Equation 6 is the spatial independence of the optimality conditions The partial derivative of the objective function with respect to transmissivity is solely a function of local hydraulic conductivity and local hydraulic gradient It is not related to hydraulic conductivity or hydraulic gradient at other locations In other words under steady state conditions adjustment of a hydraulic parameter using the hydraulic gradient comparison method is spatially independent of adjustment of that parameter at other locations Equation 7 implies the simi
30. istribution can approach the true values of the specified hydraulic conductivity field and hydraulic conductance of the boundary The criterion for the test was specified as the average relative percent error of K MRPEK calculated as 2 meres jE 00 1 n K where K estimated hydraulic conductivity Ki true hydraulic conductivity n total number of parameters The estimated K distribution Figure 1 b is plotted in comparison to the specified K distribution in Figure 1 a which shows the difference between the estimated and specified K distributions is minimal The estimated boundary conductance ranging from 21 m day to 25 9 m day and with a mean of 23 3 m day is also close to the specified conductance of 23 2 m day Parameter estimation was conducted four times using different initial values of uniform K which are 0 3 m day 0 9 m day 1 8 m day and 2 7 m day respectively and an initial conductance of 3 6 m day The initial MRPEK was as high as 1600 percent During the estimation processes values of MRPEK were smoothly reduced to less than 7 percent Figure 4 after 40 iterations for all cases using different initial values of K Indication of Hypothetical Case Results The hypothetical case study results indicate that the hydraulic gradient comparison method is correct mathematically Simultaneously solving many one dimensional optimization MODAC Version 1 42 problems over an entire model domain can lead t
31. justment of the step size is problem dependent and needs to be cautious Maximum Step Size Maximum value of step size which limits big change of parameter value that may cause unstable solution Smooth Factor Smooth factor is used to control spatial variation of parameter values At the early stage you may or may not turn on this function In the later stage it is encouraged to turn on this function to force a smooth spatial variation of parameters The use of smooth factor is problem dependent Users are encouraged to try under different conditions Upper Ratio Upper smooth factor is used to control the ratio of hydraulic conductivity values in neighboring cells The value should be greater than or equal to 1 0 The smaller the value the smoother the K distribution The value can be changed during MODAC operation in the Model Run Dialog window When both upper and lower smooth factors are equal to 1 0 the smooth effect is maximized MODAC Version 1 25 Lower Ratio Lower smooth factor is also used to control the ratio of the hydraulic conductivity values in neighboring cells The value should be greater than 0 0 and less than or equal to 1 0 The greater the value the smoother the K distribution The value can be changed during MODAC operation in the Model Run Dialog window When both upper and lower smooth factors are equal to 1 0 the smooth effect is maximized Smooth factors work within each specified zone of constraint on hydr
32. l 5 7237 1 10001 6 107 02 1 Well 6 7248 1 10006 2 106 94 3 Well 7 7242 2 10005 106 94 2 4 2 7 Culture Lines MODAC also prepares a culture lines file for user with a name as CULTURE BLN If your site coordinates are different from the model coordinates you need to provide the X and Y site coordinates for your model origin offset You may also introduce background culture lines with the standard format of the SURFER BLN file in this file MODAC Version 1 34 APPENDIX A THE INVERSE METHOD MODAC is a package that includes two parts MODFLOW and the inverse methods that perform parameter adjustment There are three inverse methods used in the package The primary inverse method is the hydraulic gradient comparison method Guo and Zhang 1994 Guo and Zhang 2000 The other two methods are the hydraulic head comparison method and the combined methods hybrid of hydraulic gradient and hydraulic head comparison methods These two methods are approximation of the hydraulic gradient comparison method The inverse methods can be used independently with any groundwater flow model package either based on finite difference method or finite element method MODAC couples these methods with MODFLOW for user s convenience To introduce the concept of the inverse method here we only discuss the hydraulic gradient comparison method The hydraulic gradient comparison method is an inverse method for estimation of aquifer hydraulic conductivity or tra
33. lar feature Because of the spatial independence of the optimality conditions a multi dimensional optimization problem can be solved by many one dimensional optimization procedures As stated by Yeh 1986 because of the spatial dependence of hydraulic head on distributed hydraulic parameters an inverse problem is usually formulated as a multi dimensional optimization problem which requires solution of a system of equations simultaneously When the number of parameters increases the computational time increases exponentially In contrast to the traditional inverse technique the spatial independence of the optimality conditions for the hydraulic gradient comparison method allows a multi dimensional optimization problem to be solved by many one dimensional optimization procedures simultaneously Therefore the solution procedures based on the hydraulic gradient comparison method are much simpler and the dimension of the estimated parameters is not limited This is one of the major reasons that the hydraulic gradient comparison method can MODAC Version 1 38 be easily applied to field projects while the traditional inverse technique encounters difficulty when it is applied to complex real world problems Numerical Procedure The numerical procedure to implement the hydraulic gradient comparison method is an iterative process The procedure starts from a set of initial estimates of hydraulic conductivity values At each iteration a model simula
34. med to be constant over the entire model domain The initial RMSE map can be as high as about 6 feet or more while after a number of iterations of alternating model simulation and parameter adjustment the RMSE map could reach a level lower than 0 1 feet depending on MODAC Version 1 41 number of calibration steps method selected and or smooth factor chosen Eventually the simulated hydraulic head contours red color will closely match the target contours blue color in all areas and residuals will disappear from the right bottom window Because there is no uncertainty associated with model boundary conditions potentiometric surface and other parameters the simulated head contours can perfectly match the observed head in theory This RMSE map defined as the root mean squared error of head RMSEH is the average of the squared differences in simulated and interpreted heads For the purpose of testing the numerical procedure we also calculated the average of the squared differences in simulated and interpreted hydraulic gradients referred to as the root mean squared error of gradient RMSEG Comparison of RMSEH and RMSEG is displayed in Figure 3 Both error curves have the same trend which demonstrates that minimizing the differences in hydraulic gradients has the same effect as minimizing the differences in hydraulic heads One important goal of the hypothetical case study was to test if the estimated hydraulic conductivity d
35. model calibration Groundwater recharge can be estimated using various hydrology methods and source sink can be estimated based on field investigations water use records and water budget analysis Based on the independently estimated stresses hydraulic parameters can be estimated using the groundwater flow model inverse procedures such as MODAC In this way we could sufficiently use as much information as possible Uncertainty related to correlation of hydraulic parameters and stresses can be controlled to a relatively low level In a groundwater flow model calibration the role of MODAC version 1 is only to automatically estimate aquifer hydraulic parameters This is only one of the components MODAC Version 1 6 of a complete model calibration However it is usually the most time consuming and most difficult task in a model calibration MODAC can significantly speed up this process and to improve model calibration result 2 2 Targets for Model Calibration Targets for model calibration are those available aquifer responses including measured hydraulic heads or fluxes It is common that a model calibration is only evaluated by comparing simulated hydraulic head to measured head at sparsely distributed points using statistics Based on our practical modeling experiences it is important to have a global calibration target for model calibration A global target includes not only point wise measured heads but an entire flow pattern hydraulic g
36. nditions If specified boundary fluxes do not follow rule of mass balance the specification range cannot be approached MODAC Version 1 21 4 DATA PRPARATION AND INPUT INSTRUCTION 4 1 Data Requirement Data requirement for using MODAC includes two parts The basic files are the standard MODFLOW input files that should be consistent with the MODFLOW 1996 version Specific dada requirement for parameter estimation using MODAC includes e Interpreted potentiometric surface as direct model calibration target which should be used as initial head for MODFLOW in the BAS file e Hydraulic conductivity or transmissivity constraints e Constraints on conductance of head dependent boundaries if they are required to be estimated e Estimated boundary fluxes as a secondary model calibration target If information is not available this can be considered as an optional data requirement or applied in later stage of model calibration based on professional judgment 4 2 Input Instructions 4 2 1 Standard MODFLOW Input Files and NFL File Basic files are standard MODFLOW input files However the hydraulic conductivity matrix and Vcont matrix need to be separated from the BCF file so the values of these matrix can be quickly replaced by the newly estimated values You may use a groundwater model GUI to generate standard MODFLOW files first Then run MODAC to open a NEW MODFLOW NAM File MODAC will generate a NFL file for you and separate the hydr
37. nnneeeeeeees 9 3 2 Running MODAC with Hypothetical Case 2 sse 13 3 3 Model Run Dialog Instruction asts 3isq scdisscisgpaniesedusacadsiseazegesaadeacecpasgeaeisaactesees 16 34 Running MODAC with Hypothetical Case 2 Plus cece cece eee ene 15 4 DATA PREPARATION AND INPUT INSTRUCT ION sccccccssssssceeees 19 41 Data Requirement ccce er tete eee centre dte dad adder 22 4 2 Input struc HOTSCs oi otio ATI Edi etd or e Eis dxa IQuR e d LOTO PAD DS RUE 22 4 2 Standard MODFLOW Input Files and NFL File esses 22 4 2 2 Interpreted Potentiometric Surface as Direct Target eessssss 22 423 MACBIle orte oie ret reet eee tessa uto code eet e ue toot reet aou eed 23 4274 CONStEAINS c i aere e eh eee eoe delve ded eee poco done de bade ve eo ve eE eene Pe edie 32 425 Flux Targets on Boundary eee teo to I Ro NR GE Pret RP BI E Rer I RI eds 30 4 2 6 Observed Data File cc a aa a a a a a aa a aa aa ana e aeaa 32 42 QUIture TINE Sienne na a eee br e a e Poe ie 34 APPENDIXES Appendix A The Inverse Method Appendix B Discussion of Hypothetical Case 1 REFERENCES MODAC Version 1 i INTRODUCTION This document serves as the user s manual of MODAC a hydrogeology based parameter estimation package for groundwater flow model calibration 11 What is MODAC MODAC is a parameter estimation package for groundwater flow model calibration It
38. nsmissivity and head dependent boundary conductance for a groundwater flow model under steady state conditions or transient conditions This method following formal optimization techniques defines its objective function to minimize differences between interpreted observed and simulated hydraulic gradients which leads to minimization of differences between observed and simulated hydraulic heads without additional specification of boundary conditions There are two key features in this method The first one is that the derived optimality conditions have an explicit form with a clear hydrogeology concept that is consistent with Darcy s law The second one is that the derived optimality conditions are spatially independent as they are a function of only local hydraulic conductivity and local hydraulic gradient therefore a multi dimensional optimization problem can be solved by many one dimensional optimization procedures simultaneously which results in substantial reduction of computation time No preconceived zonation of parameter is required estimation of hydraulic conductivity distribution is performed on a cell by cell basis A brief summary of the hydraulic gradient comparison method and the numerical procedure are presented in the following sections Objective Function Conventionally the governing equation for groundwater flow in a heterogeneous confined aquifer under steady state conditions is defined as V T Vh 2q in R 1 su
39. o minimization of the differences between simulated and interpreted hydraulic gradients and heads over the entire model domain In other words if the optimality condition at every model cell is approached the objective function for the entire model domain is approached The results of the hypothetical case study also indicate that 1 Where the hydrogeologic conditions are completely known 1 e the problem is not ill posed it is mathematically possible to estimate hydraulic conductivity and conductance to a level that is close to true values 2 Using different initial values of K the method can lead to same parameter estimation results However it should be noted in a practical problem because we cannot avoid uncertainty in conceptual model development boundary conditions and hydrologic parameters estimation of hydraulic parameters cannot avoid certain uncertainty The only way to reduce such uncertainties is to apply MODAC in an iterative calibration procedure with a global calibration target Section 2 Successful application of MODAC relies on good conceptual model development MODAC Version 1 43 in 4 a Generated Hydraulic Conductivity Distribution in d b Calibrated Hydraulic Conductivity Distribution unit m day Figure 1 Comparison of specified and estimated hydraulic conductivity distributions MODAC Version 1 44 Generated hydraulic head contour in mete
40. ology Inverse Problem Water Resour Res 22 2 pp 95 108 1986 MODAC Version 1 47
41. ons Types of boundary conditions and related hydraulic conductance Storage coefficient or specific yield The physical characteristics of a groundwater flow system are usually measured in field at discrete points by geologic borings and aquifer tests and then interpreted qualitatively through conceptual model development MODAC Version 1 5 Among the physical characteristics the dimension and geometry of hydrogeologic units are often represented by model configuration including layers thickness and bottom elevations These are considered as numerical model structure which are designed prior to parameter adjustment and are usually not to be changed unless it is necessary The type of boundary conditions is also specified prior to parameter estimation The other three items i e hydraulic conductivity or transmissivity head dependent boundary conductance and storage coefficient are conventionally considered as hydraulic parameters They need to be intensively adjusted during model calibration This hydraulic parameter estimation process is often referred to as the inverse process in the inverse technique literature Stresses usually are referred to as groundwater recharge evapotranspiration and source sink which are placed at the right hand side of a groundwater governing equation Aquifer responses are usually referred to as groundwater hydraulic heads and fluxes Both stresses and responses can vary over time while the physical char
42. oundwater recharge evaporation and extraction or injection rates The current version of MODAC only automatically estimates hydraulic parameters under steady state conditions including e Hydraulic conductivity transmissivity e Head dependent boundary conductance e Vertical conductance The hydrologic parameters sink and source need to be estimated independently prior to model calibration and to be adjusted during iterative model calibration processes 13 Features of MODAC MODAC is a hydrology based parameter estimation package The concept that guides parameter adjustment is consistent with Darcy s law Appendix A which in essence is MODAC Version 1 1 different from those parameter estimation packages based on non linear regression method The general features of MODAC are listed as follows and explained in detail in the main text e MODAC is specifically developed for groundwater flow model calibration thus only applicable to groundwater flow model e Effective use of MODAC for model calibration requires rigorous conceptual model development with a global calibration target and to be implemented with an iterative calibration procedure e Interpreted groundwater potentiometric surface based on measured hydraulic heads is used as direct calibration target e Estimated or measured fluxes are used as secondary calibration target e Constraints on hydraulic conductivity and conductance are directly applied in parameter estima
43. peration as long as your MODFLOW solution is stable in early stage of parameter adjustment you may chose a number that is smaller than the number of iteration specified in the MODFLOW solver package to speed up the parameter estimation process Please be cautious when selecting the maximum MODFLOW iteration For final results you must select a proper number of iteration to meet a predetermined converge criteria MODAC Version 1 17 3 4 Running MODAC with Hypothetical Case 2 Plus As an important model calibration target boundary fluxes should be introduced during parameter estimation process MODAC provides you opportunities to specify a range of estimated fluxes as a secondary calibration target During the process MODAC tries to adjust parameters so that the calculated fluxes to stay within the specified range or to approach the specified range You may specify lower limit and upper limit for one type of boundary condition by e Either total inflow flux or total outflow flux but not the net of both fluxes e Distributed fluxes at boundary cells depending on your need Let us illustrate Case 2 plus by following the steps below 1 Unzip Case2flx zip in a new folder 2 Click MODAC icon to start the program 3 Go to File and click NEW MODFLOW NAM file browse for Case2flx nam 4 Go to Setup and Boundary Constraints you will see options as e GHB e River e Drain e Constant head CHD MODAC Version 1 1 8 8 50E 04 7
44. r Calibrated hydraulic head contour in meter Figure 2 Comparison of generated and calibrated hydraulic head distributions e RMSEH X RMSEGx10 SERS AAG EN 1 4 7 10 13 16 19 22 25 28 31 34 37 40 Number of iterartions Figure 3 The root mean squared error of head RMSEH and the root mean squared error of gradient RMSEG versus calibration iterations MODAC Version 1 45 o Ki 0 3 m day o Ki 0 9 m day A Ki 1 8 m day Ki 2 2 7 m day Average Relative Percent Error of MRPEK No of Iterations Figure 4 The average relative percent error of hydraulic conductivity MRPEK versus calibration iterations using different initial values of hydraulic conductivity MODAC Version 1 46 REFERENCES Cooley R L 1979 A method of estimating parameters and assessing reliability for models of steady state groundwater flow 2 Application of statistical analysis Water Resources Research 15 no 3 603 617 Doherty J 1990 MODINV Australian Center for Tropical Fresh water Resources Townsville Australia 278 pp Doherty J 1994 PEST Watermark Computing Corinda Australia 122 pp DuChateau Paul and David Zachmann 1989 Applied Partial Differential Equations Harpper amp Row Publishers New York 620 pages Guo Xiaoniu and Chuan Mian Zhang 1994 Use of the physical feature of groundwater flow system to reduce the mathematical complexity in p
45. r partial differential equation in hydraulic head is given which defines the hydraulic gradient of a flow field the head distribution is also unique given the same set of boundary conditions as for the governing equation Therefore minimization of hydraulic gradient differences can achieve the same results as minimization of head differences In summary this method does not require additional specification of boundary condition other than the well posed problem defined by the governing equation When the boundary conductance for head dependent type boundary needs to be estimated at the same time when hydraulic conductivity is estimated the objective function of Equation 4 is expanded as OBJ Vh Vh Vh Vh dxdy h h ds 5 Optimality Conditions Based on the objective function Equation 5 the optimality condition was derived Guo and Zhang 2000 using the constrained calculus of variations method Morel Seytoux and Guo 1990 as follows oL 2 j Sr pa Ve Vh dxdy j212 N 6 J J rj Equation 6 can be considered as the optimality condition for parameter T when it approaches zero Similarly the partial derivative of the objective function with respect to t can be obtained oL 2 o 2 h h h h d 1 1 2 M 7 OT Ti Jo nm pe When Equation 7 approaches zero it approaches the optimality condition MODAC Version 1 37 For an unconfined aquifer the optimality conditions
46. radient flow pathways fluxes seep locations and flow rates water budget and field aquifer test results as well as groundwater contaminant migration information if it is relevant To meet such a global calibration target we propose to include an interpreted potentiometric surface map as one of the calibration targets A representative potentiometric surface will include flow pattern hydraulic gradient and flow pathways It is a common practice for a site hydrogeologic characterization to prepare a groundwater potentiometric surface which should be interpreted based on measured hydraulic heads and understanding of hydrogeologic conditions Using potentiometric surface as a calibration target is a special requirement using MODAC Advantages of using potentiometric surface as one of calibration targets are e From a conceptual model development point of view a potentiometric surface is a key component of conceptual model development which contains qualitative and quantitative geologic and hydrogeologic information including flow directions hydraulic gradient and flow path which may not be fully reflected from only point wise head measurements e Based on Darcy s law a steady state potentiometric surface may reflect a subsurface hydraulic parameter distribution pattern or an equivalent subsurface hydraulic parameter distribution pattern Thus preconceived zonation for parameter structure may not be necessary e From a numerical poin
47. ray with the concept of zonation Zonation of upper and lower constraints can be generated using GUI and be modified in MODAC during model calibration Format of distributed constraints should be consistent with user s specification in MAC file If the constraints are set as zones the smooth function will be applied within each zone but not across boundary between zones Zone Average also applies within each zone following the zones specified for constraints 4 2 4 2 Constraints on Conductance of Head Dependent Boundary Constraints on conductance for head dependent boundary conditions such as River General Head and Drain are set within MODFLOW input files for the corresponding head dependent boundaries In each of these head dependent boundary input files an auxiliary parameter specified as xyz can be used to specify upper and lower limits for each conductance corresponding to each model cell If user did not specify upper and lower limits on conductance for user s convenience MODAC sets the default upper and lower limits automatically for user The format follows the standard MODFLOW 1996 input files for any head dependent boundary input files The default upper limit is four times of your specified conductance and the default lower limit is one fourth of your specified conductance The following is an example of a river input file with specified upper and lower limits Example River Package Input file with specified constraint
48. re developed based on this nonlinear least squares regression approach Like the conventional approach to the inverse problem described earlier the hydraulic gradient comparison method for parameter estimation is also formulated as a mathematical optimization problem However the objective function is defined differently than in Equation 3 In this method the objective function is to minimize the differences between simulated and interpreted observed hydraulic gradients as shown in Equation 4 rather than to minimize the differences between observed and simulated hydraulic heads The objective function for the hydraulic gradient comparison method is defined as MODAC Version 1 36 OBJ Vh Vh Vh Vh lxdy 4 where Vh and Vh are simulated and interpreted observed hydraulic gradients In Equation 4 minimization of hydraulic gradient differences under given boundary conditions is equivalent to minimization of hydraulic head differences using Equation 3 As we know the governing equation for groundwater flow is a second order partial differential equation in hydraulic head that when solved yields a unique hydraulic head distribution for a given set of boundary conditions that should satisfy a well posed problem in partial differential equations Du Chateau and Zachmann 1989 Simply stated a well posed problem requires that flux boundary conditions should not be specified for all boundaries Similarly if the first orde
49. roundwatermodels com e Enter this Security Code then click Register your are registered and complete the installation If the security code is invalid or expired MODAC will run as a demo version no results can be saved 1 7 Technical Support For questions you may send an email to Chuan Mian Zhang urscorp com 1 8 How to Use This Manual MODAC Version 1 3 This manual describes the general concept of MODAC and detailed instruction of how to use MODAC Section 2 discusses the concept of using MODAC in model calibration Section 3 provides a tutorial for first time users with demonstration of hypothetical cases Section 4 includes descriptions of data preparation and input instruction Appendixes include theoretical background for the inverse method numerical procedures and discussion for hypothetical case Electronic files for three hypothetical cases are included for users to understand how MODAC works and how to use MODAC MODAC Version 1 4 2 CONCEPT OF MODAC TO SUPPORT GROUNDWATER FLOW MODEL CALIBRATION A groundwater flow model development involves understanding of site hydrogeology conceptual model development conversion of conceptual model to appropriate numerical model design estimation of hydrologic and hydraulic parameters and evaluation of calibration results comparing to observations The last two steps are often referred to as model calibration Model calibration is the most important and perhaps the most
50. s 8 51 AUX CLW AUX CUP 8 1 9 12 6139 040 134 17 6138 54 20 00 2000 00 1 9 13 6140 710 20 00 6140 21 20 00 2000 00 T 9 14 6140 500 20 00 6140 00 20 00 2000 00 i 9 15 6140 860 20 00 6140 36 20 00 2000 00 I 9 21 6139 350 10 00 6139 85 10 00 1000 00 1 9 22 6138 950 27 01 6138 45 10 00 1000 00 E 9 23 61921 370 135 44 6136 87 10 00 1000 00 1 9 24 6137 350 Tee 6136 85 10 00 1000 00 4 2 5 Flux Targets on Boundary MODAC Version 1 32 Two types of flux targets can be used in model calibration One is total flux through one given boundary condition and the other is distributed flux at individual model cells For total flux either total inflow or total outflow should be specified but not the net flux of the sum of inflow and outflow A range of estimated flux rates as upper limit and lower limit can be specified or reviewed within the MODAC dialog window page 19 20 A negative sign means aquifer looses water to boundary while a positive sign means aquifer gains water from boundary The range of total fluxes for the GHB River Drain boundaries are written in the second line of each corresponding input files You may review or modify them in the ASCII input files see example as follows too Example River Package Input file with specified constraints and flux targets 686 50 AUX CLW AUX CUP AUX FLW AUX FUP 686 7 80E 04 8 50E 04 1 142 192 89 040 82 17 8854 55 80 893 00 0 01 120 00 1 142 191 89 500 521 46 89 00 243 00 3890 00 0
51. show as follows w Set up Upper Limit of of Layer2 You have three choices e Use a uniform value e Input an existing matrix e Modify initial K value as constraint by using multipliers MODAC Version 1 27 You can click on one of these options and follow the sequential prompt to finish your upper limit setup Lower Limits of K Lower limits of hydraulic conductivity can be set as a constant for each layer or distributed using a matrix file The matrix file can be generated using groundwater model GUI Lower limits can be set as same as upper limits if a user does not want the K values to be changed in certain area Residual Criteria for Screen Plot Residual criteria for screen plot on the bottom right window can be determined by user according to your conditions Input Instruction of MAC file in ASCII Format GENERAL Al Record Parameters selected for estimation Format free format with space delimited e HYK hydraulic conductivity e GHB general head boundary conductance e DRN drain conductance e RIV river conductance For GHB DRN RIV if not selected they will not be estimated HYK will always be estimated A2 Record HEADNG Format A80 e HEADNG HYK in the current version A3 Record MTHD1 MTHD2 NALT Format AS AS I5 e MTHDI primary method e MTHD2 secondary method e NALT number of alternating iterations using primary or secondary method e g o IfNALT 2 MODAC uses the primary method for 2
52. t of view a potentiometric surface provides measured or estimated hydraulic heads for all model cells which mitigates the so called ill posed problem in inverse technology e The process of matching the potentiometric surface in a model calibration would warrant matching calculated hydraulic heads with measured hydraulic heads at well locations if the interpretation of potentiometric surface honor observations e Using an interpreted potentiometric surface as calibration target will avoid dry cell problems that are attributable to numerical isolation which is a commonly accounted problem in the inverse procedure using non linear least squares methods MODAC Version 1 7 It should be noted that targets of model calibration using MODAC are not limited to potentiometric surface Application of MODAC in model calibration requires using a global target which should include all the following components if it is possible Potentiometric surface and measured hydraulic heads Measured or estimated fluxes Water budget analyses Field aquifer test results Groundwater contaminant migration direction pathways and velocity Meeting such a comprehensive global calibration target can only be accomplished through an iterative calibration process that comprise of several decomposed steps as mentioned in Section 2 1 MODAC Version 1 8 3 TUTORIAL WITH HYPOTHETICAL CASE DEMONSTRATION This section illustrates how MODAC works through demonstration
53. teration steps can be used to speed up the process and the early results do not have to meet the converge discrepancy criteria The decision is often problem specific and depending on experiences 32 Running MODAC with Hypothetical Case 2 Hypothetical Case 2 is a three layer model case The three model layers are assumed hydraulically connected The hydraulic conductivity values range between 0 005 ft day to 50 ft day A river running through the center of the model domain is one of the main groundwater discharge zone The primary source of water to the groundwater flow system is areal groundwater recharge The external boundary conditions include prescribed head general head and no flow boundaries Similar to Case 1 the MODFLOW simulated hydraulic head distributions are assumed as the target potentiometric surface for hydraulic parameter estimation while the hydraulic conductivity distribution the river conductance and the conductance for the general head boundary are assumed unknown Case 2 is illustrated through two conditions e Case 2 Potentiometric surfaces are used as calibration target while boundary fluxes are evaluated and adjusted by users externally This is usually the case when you just start a model calibration and do not have a good sense about boundary fluxes e Case 2 plus Both potentiometric surfaces and estimated boundary fluxes are used as calibration targets Section 3 4 To run MODAC on Case 2 you have two choi
54. thing technique is implemented within prior specified constraints on hydraulic parameters The minimization of hydraulic gradient differences is performed simultaneously with a minimization of spatial variation of parameter values Thus estimated hydraulic parameters can vary smoothly within each zone to reflect the continuity and heterogeneity of the geologic properties potential over parameterization is controlled MODAC Version 1 40 APPENDIX B DISSCUTION OF HYPOTHETICAL CASE 1 In order to show how MODAC works hypothetical case 1 and the associated electronic files are included for discussion and screen demonstration This section discusses Purpose of the hypothetical case study How the hypothetical case was generated How to understand the process of parameter estimation of the hypothetical case What the results of hypothetical case indicate Purpose of Hypothetical Case Study The original purpose of the hypothetical case study was to test the numerical performance of the hydraulic gradient comparison method Guo and Zhang 2000 The specific purpose of including the case study in this package is to discuss the concept via an example and to provide an on line demonstration for users to understand the MODAC working process Development of Hypothetical Case The hypothetical case assumes an unconfined and heterogeneous groundwater flow system The specified hydraulic conductivity distribution ranges from 0 03 m day to 3 05 m day 0
55. tion is performed then hydraulic conductivity values at each model cell are adjusted simultaneously based on Equations 8 and 9 for unconfined conditions or Equations 6 and 7 for confined conditions The adjustment of hydraulic conductivity follows the following gradient search method j L K Kj a A i 1 2 N 10 OK subject to Ku lt K lt K naxi and j GST EE 1 1 2 M 11 oT subject to 7 min lt T lt T max where K hydraulic conductivity T conductance of the head dependent boundary i cell index l boundary section index for boundary B3 j iteration index L K partial derivative of the objective function with respect to the hydraulic conductivity at cell i dL oq partial derivative of the objective function with respect to the conductance at section The values of OL OK and 0L 0t are calculated using Equations 8 and 9 or 6 and 7 Coefficients a and D are scaling factors to determine the step size of parameter adjustment This numerical procedure has been implemented to MODAC a computer code that performs an iterative procedure of the USGS MODFLOW McDonald and Harbaugh 1988 Harbaugh and McDonald 1996 simulation and hydraulic parameter adjustment as described above In an iterative process about 95 percent or more computer time is used by MODFLOW simulation and only 5 percent or less is used for parameter adjustment MODAC Version 1 39 Smooth Technique In the numerical procedure a smoo
56. tion process e No zonation of parameters is required parameter adjustment is performed based on cell by cell basis e Smoothing technique is used to minimize spatial variation of parameter e The current version of MODAC is only for steady state condition Transient condition will be included in the later version 1 4 Why Use MODAC e Calibration results not only match observed heads at measurement points but also match hydraulic gradients general flow pattern flow paths and measured estimated fluxes e Computation time is significantly less than the time required by nonlinear least squares methods because multiple optimization problem is solved by many one dimensional problems simultaneously Appendix A e Particularly powerful and efficient in calibrating highly heterogeneous aquifer and matching large quantity of observations with small residuals The more the data the more the confident of calibration e No limit on number of hydraulic parameters to be estimated thus highly heterogeneous aquifer can be easily calibrated e Calibration procedure does not cause dry cell problem attributable to numerical isolation e Easy to understand easy to use and easy to identify problems associated with conceptual model 1 5 Installation and Uninstallation of MODAC If you have old version of MODAC please uninstall the package following the instruction under Uninstallation first Installation MODAC Version 1 2 Installation o
57. ue in the array corresponds to one modellayer Step size is generally less than 0 1 usually varies between 0 001 to 0 01 Maximum Step Size NLAY UIDREL e Maximum Step Size is the maximum value of Each value in the array corresponds to one model layer Upper Smooth Factor NLAY UIDREL e Upper smooth factor is used to control the ratio of the hydraulic conductivity values in neighboring cells The value should be greater than or equal to 1 0 The value can be changed during MODAC operation in the Model Run Dialog window When both upper and lower smooth factors are equal to 1 0 the smooth effect is maximized 29 A8 Array Reader Lower Smooth Factor UIDREL Lower smooth factor is also used to control the ratio of the hydraulic conductivity values in neighboring cells The value should be greater than 0 0 and less than or equal to 1 0 The smaller the value the less the smooth effect The value can be changed during MODAC operation in the Model Run Dialog window When both upper and lower smooth factors are equal to 1 0 the smooth effect is maximized Each value in the array corresponding to one model layer Enter A9 only if there is more than one layer in model Lower limit of vertical conductance NLAY 1 UIDREL A9 Array Reader Lower limit of vertical conductance is set to prevent calculated Vcont approach to zero The default value for the lower limit of vertical conductance is 0 000001 FOR EVERY LAYER
58. vity have been exhausted or the estimation is being locked or bounded in local areas In these cases you may need to try different methods as primary method or secondary method and or choose different alternating interval number You may also turn on or turn off Smooth to either limit the spatial variation or do not limit the spatial variation during parameter estimation When the curve approaches flat i e no improvement in matching the gradient or head and if the RMSE is acceptable you may accept the estimation results and save the results If the RMSE is still pretty large you may try to adjust the methods and the smooth factors If all these adjustments do not help you may go back to check your model setup and conceptual model BOTTOM LEFT WINDOW This window shows comparison of target and calculated potentiometric surfaces at every calibration step Target potentiometric surface is in blue and does not change with iterations Calculated potentiometric surface is in red and changes with iterations If MODAC works smoothly red contour lines should gradually match blue contour lines BOTTOM RIGHT WINDOW This window displays residual map showing residuals between target head and simulated head at every calibration step Blue color indicates calculated head is higher than target head and red color means calculated head is lower than target head If both blue and red color spots reduce with time parameter estimation is working well

MODAC Manual - MODAC A Hydrology

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