Simulation Capabilities of MODFLOW

Application of MODFLOW

Model Input

Model Output

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.

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Figure 3. Example comparison of computed and measured water levels.

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 for detailed analysis of the simulated ground-water system.

Inverse Modeling with MODFLOWP

Inverse modeling is a more formal approach to model calibration that includes automatic parameter adjustment in order to match field data. Program MODFLOWP (pronounced MOD^.FLOW^.P) is the USGS version of MODFLOW that includes automatic parameter estimation (Hill, 1992). MODFLOWP uses a weighted least-squares objective function as a measure of how well model results agree with field measurements. Weights are used to reflect reliability of individual measurements. Parameters that can be estimated by MODFLOWP include transmissivity; hydraulic conductivity; storage coefficient; vertical leakance; vertical and horizontal anisotropy; hydraulic conductance between aquifer systems and rivers, drains and other features; areal recharge; maximum evapotranspiration; pumping; and water levels at constant-head boundaries. Measured or externally estimated information on parameters also can be included. Parameter values that minimize the objective function (fig. 5) are calculated by MODFLOWP using the modified Gauss-Newton method or the conjugate-direction method. The resulting parameter values are "best-fit" in that they provide the closest match between measured and simulated heads and flows, as measured by the objective function. The task of the modeler is to evaluate how well these calculated values represent the physical system being simulated.

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Figure 4. Forward and inverse approaches to modeling.

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Figure 5. Example of an objective function and "best-fit" parameter values for a linear problem with two parameters.

Model output includes estimates of parameters and statistics relating to the parameter estimates. The statistics can be used to quantify the reliability of the resulting model, suggest changes in model construction, and compare results of models constructed in different ways. Post-processors can be used to calculate confidence intervals on predicted heads and flows to depict prediction uncertainty. To effectively use MODFLOWP, an understanding of principles of ground-water flow and basic statistics is needed.

Particle Tracking with MODPATH

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Figure 6. Flow paths of particles discharging at two wells. Pathlines were computed by MODPATH and are denoted by red and green lines. Blue squares are river cells and light blue lines are contours of water levels, in feet above sea level, computed by MODFLOW.

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Figure 7. Application of particle tracking to estimate ground-water travel time.

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.

Solute Transport with MOC3D

MOC3D is a solute-transport program that is integrated with MODFLOW and has the capability to calculate changes in concentration (fig. 8) of a single solute as affected by processes of advection, dispersion, diffusion, fluid sources, decay, and retardation. In addition to input data requirements for MODFLOW, the user must also define porosity, thickness, dispersivity, initial concentrations, and source-fluid concentrations. Model output includes the calculated concentration distribution in space and time.

MOC3D is based on a particle-tracking method coupled with an explicit finite-difference procedure. This numerical technique is optimal for advection-dominated problems. Alternative numerical methods are planned to broaden the range of types of field problems for accurate and efficient application of the model.

How to Obtain Ground-Water Model Programs, Documentation, and Additional Information

The MODFLOW program obtained from the USGS includes most simulation capabilities currently documented by the USGS. Added features for MODFLOW have been documented in separate reports. A bibliography of the documentation reports is included with copies of MODFLOW distributed by the USGS.

U.S. Geological Survey
Branch of Information Services
Box 25286
Denver, CO 80225-0286

For information on local USGS studies and research applications of the MODFLOW family of computer programs, contact the USGS state representative for the area of interest. A list of state representatives is available from the World Wide Web site

--S.A. Leake

References

Harbaugh, A.W., and McDonald, M.G., 1996, User's documentation for MODFLOW-96, an update to the U.S. Geological Survey modular finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 96Ð485, 56 p.

Hill, M.C., 1992, A computer program (MODFLOWP) for estimating parameters of a transient, three-dimensional, ground-water flow model using nonlinear regression: U.S. Geological Survey Open-File Report 91Ð484, 358 p.

McDonald, M.C., and Harbaugh, A.W., 1988, A modular three-dimensional finite-difference ground-water flow model: U.S. Geological Survey Techniques of Water-Resources Investigations, book 6, chap. A1, 586 p.

Pollock, D.W., 1994, User's guide for MODPATH/MODPATH-PLOT, version 3: a particle tracking post-processing package for MODFLOW, the U.S. Geological Survey finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 94Ð464, 234 p.