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Scientific Investigations Report 2007–5257

Prepared in cooperation with the Impact Area Groundwater Study Program of the National Guard Bureau and U.S. Army Environmental Command

Use of Inverse-Modeling Methods to Improve Ground-Water-Model Calibration and Evaluate Model-Prediction Uncertainty, Camp Edwards, Cape Cod, Massachusetts

By Donald A. Walter and Denis R. LeBlanc

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Historical weapons testing and disposal activities at Camp Edwards, which is located on the Massachusetts Military Reservation, western Cape Cod, have resulted in the release of contaminants into an underlying sand and gravel aquifer that is the sole source of potable water to surrounding communities. Ground-water models have been used at the site to simulate advective transport in the aquifer in support of field investigations. Reasonable models developed by different groups and calibrated by trial and error often yield different predictions of advective transport, and the predictions lack quantitative measures of uncertainty. A recently (2004) developed regional model of western Cape Cod, modified to include the sensitivity and parameter-estimation capabilities of MODFLOW-2000, was used in this report to evaluate the utility of inverse (statistical) methods to (1) improve model calibration and (2) assess model-prediction uncertainty.

Simulated heads and flows were most sensitive to recharge and to the horizontal hydraulic conductivity of the Buzzards Bay and Sandwich Moraines and the Buzzards Bay and northern parts of the Mashpee outwash plains. Conversely, simulated heads and flows were much less sensitive to vertical hydraulic conductivity. Parameter estimation (inverse calibration) improved the match to observed heads and flows; the absolute mean residual for heads improved by 0.32 feet and the absolute mean residual for streamflows improved by about 0.2 cubic feet per second. Advective-transport predictions in Camp Edwards generally were most sensitive to the parameters with the highest precision (lowest coefficients of variation), indicating that the numerical model is adequate for evaluating prediction uncertainties in and around Camp Edwards. The incorporation of an advective-transport observation, representing the leading edge of a contaminant plume that had been difficult to match by using trial-and-error calibration, improved the match between an observed and simulated plume path; however, a modified representation of local geology was needed to simultaneously maintain a reasonable calibration to heads and flows and to the plume path.

Advective-transport uncertainties were expressed as about 68-, 95-, and 99-percent confidence intervals on three dimensional simulated particle positions. The confidence intervals can be graphically represented as ellipses around individual particle positions in the X-Y (geographic) plane and in the X-Z or Y-Z (vertical) planes. The merging of individual ellipses allows uncertainties on forward particle tracks to be displayed in map or cross-sectional view as a cone of uncertainty around a simulated particle path; uncertainties on reverse particle-track endpoints—representing simulated recharge locations—can be geographically displayed as areas at the water table around the discrete particle endpoints. This information gives decisionmakers insight into the level of confidence they can have in particle-tracking results and can assist them in the efficient use of available field resources.

For additional information contact:
U.S. Geological Survey
Massachusetts-Rhode Island Water Science Center
10 Bearfoot Road
Northborough, MA 01532

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Suggested citation:

Walter, D.A., and LeBlanc, D.R., 2008, Use of inverse-modeling methods to improve ground-water-model calibration and evaluate model-prediction uncertainty, Camp Edwards, Cape Cod, Massachusetts: U.S. Geological Survey Scientific Investigations Report 2007–5257, 57 p., available online at




Purpose and Scope

Site Description and History

Hydrogeology of the Camp Edwards Area

Geologic Setting

Hydrologic Setting

Methods of Analysis

Numerical Ground-Water-Flow Model

Regional Model Design

Modifications to the Regional Model

Representation of Parameters

Incorporation of Observed Heads and Flows

Use of Inverse Methods to Improve Model Calibration

Evaluation of Model Sensitivity

Formulation of the Least-Squares Objective Function

Heads and Flows

Improvement in Calibration

Optimal Parameter Estimates

Precision of Parameter Estimates

Modification to the Model Framework

Advective-Transport Observations

Limitations of Analysis

Evaluation of Model-Prediction Uncertainty

Forward Particle Tracking

Reverse Particle Tracking

Summary and Conclusions


References Cited

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