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.

}, url = {http://pubs.water.usgs.gov/ofr20051072 }, author = {D. P. Ahlfeld and Barlow, Paul M. and Mulligan, Ann E.} } @inbook {13067, title = {Optimal Plume Capture Design in Unconfined Aquifers}, booktitle = {Physicochemical Groundwater Remediation}, year = {2002}, pages = {23-44}, publisher = {Springer, US}, organization = {Springer, US}, edition = {1}, chapter = {2}, isbn = {978-0-306-46928-2}, issn = {978-0-306-46569-7}, doi = {10.1007/b118279}, author = {Mulligan, Ann E. and D. P. Ahlfeld} } @book {13069, title = {Optimal Management of Flow in Groundwater Systems}, year = {2000}, pages = {185}, publisher = {Academic Press}, organization = {Academic Press}, abstract = {
In the decades ahead population increases are expected to place increased stress on water resources. A substantial portion of the world\&$\#$39;s fresh water is derived from groundwater.\ Optimal Hydraulic Control of Groundwater Systems\ will provide a practical guide for implementing mathematical and computer-based

tools to aid in the management of groundwater. Drawn from the operations research literature, this book combines methods for optimization techniques to numerical models for the simulation of groundwater flow. The resulting management model provides a valuable tool for optimizing performance of groundwater systems. This volume will fill a significant gap in the technical literature on groundwater modeling and management.

* Provides a thorough description of the mathematics underlying the method and a step-by-step introduction to practical application\

* Introduces key concepts using an example continued throughout the book

* Contains MODOFC software package and associated documentation that implements many of the methods described in the book\

* Details advanced topics, including nonlinear and integer problem elements and interpretation of management model results\

* Each chapter ends with a summary of selected references and brief histories of the methodologies presented in the book