Water Resources Applications Software

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Summary of GWM-2000



ABSTRACT
GWM-2000 is a Groundwater Management Process for the U.S. Geological Survey modular three-dimensional groundwater model, MODFLOW-2000. GWM-2005 uses a response-matrix approach to solve several types of linear, nonlinear, and mixed-binary linear groundwater management formulations. Each management formulation consists of a set of decision variables, an objective function, and a set of constraints. Three types of decision variables are supported by GWM-2000: flow-rate decision variables, which are withdrawal or injection rates at well sites; external decision variables, which are sources or sinks of water that are external to the flow model and do not directly affect the state variables of the simulated groundwater system (heads, streamflows, and so forth); and binary variables, which have values of 0 or 1 and are used to define the status of flow-rate or external decision variables. Flow-rate decision variables can represent wells that extend over one or more model cells and be active during one or more model stress periods; external variables also can be active during one or more stress periods. A single objective function is supported by GWM-2000, which can be specified to either minimize or maximize the weighted sum of the three types of decision variables. Four types of constraints can be specified in a GWM-2000 formulation: upper and lower bounds on the flow-rate and external decision variables; linear summations of the three types of decision variables; hydraulic-head based constraints including drawdowns, head differences, and head gradients; and streamflow and streamflow-depletion constraints.

The Response Matrix Solution (RMS) Package of GWM-2000 uses the Groundwater Flow Process of MODFLOW to calculate the change in head at each constraint location that results from a perturbation of a flow-rate variable; these changes are used to calculate the response coefficients. For linear management formulations, the resulting matrix of response coefficients is then combined with other components of the linear management formulation to form a complete linear formulation; the formulation is then solved by use of the simplex algorithm, which is incorporated into the RMS Package. Nonlinear formulations arise for simulated conditions that include water-table (unconfined) aquifers or head-dependent boundary conditions (such as streams, drains, or evapotranspiration from the water table). Nonlinear formulations are solved by sequential linear programming; that is, repeated linearization of the nonlinear features of the management problem. In this approach, response coefficients are recalculated for each iteration of the solution process. Mixed-binary linear (or mildly nonlinear) formulations are solved by use of the branch and bound algorithm, which is also incorporated into the RMS Package.


HISTORY
Version 1.1.4 2011/6 – correct bug that may affect problems with both binary variables and external variables.

Version 1.1.3 2009/12 – MF2000-GWM is renamed GWM-2000.

Version 1.1.2 2009/06 – Bug fix that caused code failure when equality summation constraints were imposed on binary variables. Bug fix to correct output for SLP runs.

Version 1.1.1 2007/03 – Reconstructed from MODFLOW-2000 Version 1.17.02 so that the GMG solver can be used. Bug fixed that caused improper reading of response matrix when both head and stream constraints are present.

Version 1.1 2006/08 – New features added to output the response coefficients in a formatted file, the optimal values of the flow variables in a file formatted similarly to a MODFLOW WEL file, the solution at each iteration of the SLP algorithm, the status of summation constraints and additional screen and file output reporting on algorithm progress. Additional controls on SLP algorithm added. Several minor clean-ups and improvements. Many of these features are described in the online PDF called "GWM Addendum."

Version 1.0.3 2006/01/21 Correct a bug that caused incorrect reading of flow process files when certain combinations of variables are read using the parameter input structure.  Correct several bugs related to proper input when non-zero base and/or reference flows are specified and when the response matrix file is written or read.  New features added to SLP to check for dry cells at wells and to better control iterations.

Version 1.0.2 2005/09/24 Correct a compiler setting in the Version 1.0.1 executable that prevented opening of binary files.  Add ability to comment lines in GWM file.  Several minor improvements to output.

Version 1.0.1 2005/07/29 Fix a bug that caused incomplete checking for feasibility of binary-only summation constraints.  Fix an output bug that caused improper reporting of range analysis for stream depletion and drawdown constraints.  Several minor improvements to output appearance and input checking.

Version 1.0.0 2005/02 - Initial release, built from MODFLOW-2000 Version 1.13
    

PROCESSES
     This version of MF2K-GWM includes the following processes:

         GWF1 -- Ground-Water Flow Process
         GWM1 -- Ground-Water Management Process
         SEN1 -- Limited capability to read Sensitivity Process files


PACKAGES
     In addition to all of the packages included with Version 1.13 of MODFLOW-2000, this version of MF2K-GWM includes the following packages:

         DCV1 -- Decision Variable Package
         OBJ1 -- Objective Function Package
         HDC1 -- Head Constraints Package
         STC1 -- StreamFlow Constraints Package
         SMC1 -- Summation Constraints Package
         DCC1 -- Decision-Variable Constraints Package
         RMS1 -- Response Matrix Solution Package
         BAS1-GWM -- Basic Package for GWM



DOCUMENTATION

Ahlfeld, D.P., Barlow, P.M., and Mulligan, A.E., 2005, GWM-A ground-water management process for the U.S. Geological Survey modular ground-water model (MODFLOW-2000): U.S. Geological Survey Open-File Report 2005-1072, 124 p.


Addendum to GWM, version 1.1.1: A new input requirement; new capabilities added to increase output options; revised Supply sample problem (supply2). – March 2007.

Barlow, P.M., 2005, Use of Simulation-Optimization Modeling to Assess Regional Ground-Water Systems: U.S. Geological Survey Fact Sheet 2005-3095, 4 p.