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# GWM-a ground-water management process for the U.S. Geological Survey modular ground-water model (MODFLOW-2000)

April 25, 2005

GWM is a Ground?Water Management Process for the U.S. Geological Survey modular three?dimensional ground?water model, MODFLOW?2000. GWM uses a response?matrix approach to solve several types of linear, nonlinear, and mixed?binary linear ground?water 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: 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 ground?water 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, 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 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 uses the Ground?Water 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.

Three sample problems are provided to demonstrate the use of GWM for typical ground?water flow management problems. These sample problems provide examples of how GWM input files are constructed to specify the decision variables, objective function, constraints, and solution process for a GWM run. The GWM Process runs with the MODFLOW?2000 Global and Ground?Water Flow Processes, but in its current form GWM cannot be used with the Observation, Sensitivity, Parameter?Estimation, or Ground?Water Transport Processes. The GWM Process is written with a modular structure so that new objective functions, constraint types, and solution algorithms can be added.

Publication Year 2005 GWM-a ground-water management process for the U.S. Geological Survey modular ground-water model (MODFLOW-2000) 10.3133/ofr20051072 David P. Ahlfeld, Paul M. Barlow, Anne E. Mulligan Report USGS Numbered Series Open-File Report 2005-1072 ofr20051072 USGS Publications Warehouse