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Ground water in the Great Lakes Basin: the case of southeastern Wisconsin

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The following is modified from U.S. Geological Survey Fact Sheet FS-121-97

The modular finite-difference ground-water flow model (MODFLOW) was used to simulate the ground-water and surface water systems in Southeastern Wisconsin. MODFLOW, developed by the U.S. Geological Survey, is a computer program for simulating common features in ground-water systems (McDonald and Harbaugh, 1988; Harbaugh and McDonald, 1996). The program was constructed in the early 1980's and has continually evolved since then with development of many new packages and related programs for ground- water studies. Currently, MODFLOW is the most widely used computer program in the world for simulating ground-water flow.

MODFLOW is designed to simulate aquifer systems in which (1) saturated-flow conditions exist, (2) Darcy's Law applies, (3) the density of ground water is constant, and (4) the principal directions of horizontal hydraulic conductivity or transmissivity do not vary within the system. These conditions are met for many ground-water flow systems, at least at a regional scale. For these systems, MODFLOW can simulate a wide variety of hydrologic features and processes. Steady-state and transient flow can be simulated in unconfined aquifers, confined aquifers, and confining units. A variety of features and processes such as rivers, streams, drains, springs, reservoirs, wells, evapotranspiration, and recharge from precipitation and irrigation also can be simulated. Different solution methods are available for solving the finite-difference equations that MODFLOW constructs, allowing model users to select the most efficient method for their problem.

Application of MODFLOW

MODFLOW simulates ground-water flow in aquifer systems using the finite-difference method. In this method, an aquifer system is divided into rectangular blocks by a grid. The grid of blocks is organized, by rows, columns, and layers, and each block is commonly called a "cell."

Model Input
For each cell within the volume of the aquifer system, the user must specify aquifer properties. Also, the user specifies information relating to wells, rivers, and other inflow and outflow features for cells corresponding to the location of the features. For example, if the interaction between a river and an aquifer system is simulated, then for each cell traversed by the river, input information includes layer, row, and column indices, river stage, and hydraulic properties of the riverbed.

Model Output
MODFLOW uses the input to construct and solve equations of ground-water flow in the aquifer system. The solution consists of head (ground-water level) at every cell in the aquifer system (except for cells where head was specified as known in the input data sets) at intervals called "time steps." The head can be printed and/or saved on a computer storage device for any time step. Hydrologists commonly use water levels from a model layer to construct contour maps for comparison with similar maps drawn from field data. They also compare computed water levels at individual cells with measured water levels from wells at corresponding locations to determine model error. The process of adjusting the model input values to reduce the model error is referred to as model calibration. In addition to water levels, MODFLOW prints a water budget for the entire aquifer system. The budget lists inflow to and outflow from the aquifer system for all hydrologic features that add or remove water. Other program output consists of flow rates for each model cell. MODFLOW can write the flow rates onto a computer storage device for any hydrologic feature in a simulation. These cell-by-cell flow rates commonly are read by post-processing programs such as MODPATH for detailed analysis of the simulated ground-water system.

Particle Tracking with MODPATH
Many studies require information such as the average rate of movement of ground water and contaminants. Also, information often is needed on the recharge or capture areas for water discharging to wells, springs, stream reaches, and other features. Although MODFLOW does not compute this information directly, simulation with MODFLOW provides basic information needed for such analyses. The particle-tracking program, MODPATH, is a post-processing program for MODFLOW to estimate flow paths and times of travel in ground-water systems. MODPATH can be used for studies of steady-state and transient flows. Common applications include studies of paths and time of travel of contaminant movement; and source (recharge) areas of wells, springs, rivers, and other features. MODPATH can place particles at specified locations or generate starting locations of arrays of particles in selected regions. Particles can be tracked forward from starting locations to calculate where water is going or backwards to map where it came from. Multiple particle-release times can be used to simulate "plumes" of contamination.

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