An Effective Approach for Contaminant Source Location and
Release History Recovery, 20-R9530

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Principal Investigators
Alexander Y. Sun
Scott Painter
Gordon Wittmeyer

Inclusive Dates:  01/01/05 – 07/01/06

Background - Groundwater is a vital component of the potable water supply. Because of constantly expanding human development, groundwater is vulnerable to contamination from both industrial and domestic wastes. In the United States, the average annual spending on groundwater remediation is greater than $6 billion. A critical step in any environmental remediation project is to identify locations and release histories of contaminant sources so that a cost-effective remediation strategy can be designed and clean-up costs can be partitioned between liable parties. Site historical records kept by relevant agencies are often insufficient to establish source locations and release histories. As a result, the spatiotemporal evolution of a contaminant plume has to be reconstructed through numerical inversion techniques. Existing strategies for contaminant source identification have important practical limitations. In many cases, analytical solutions for point sources are used; the problem is often formulated and solved via nonlinear optimization, and model uncertainty is rarely considered. In practice, model uncertainty can be significant because of the uncertainty in model structure and parameters.

Approach - We developed a contaminant source identification framework based on robust optimization techniques. The contaminant source identification problem was formulated as a system of uncertain linear equations. Our formulation is general and applicable to any porous media flow and transport solvers. Two different estimators — Constrained Robust Least Squares (CRLS) and Robust Geostatistical Approach (RGS) — were formulated to solve the uncertain linear equations. CRLS is a deterministic estimator, whereas RGS is based on the Bayesian theorem. Both estimators directly incorporate the modeler's prior knowledge of model and data uncertainties and utilize the information to find estimates that are robust to the uncertainties.

Accomplishments - We successfully demonstrated the performance of our robust framework for source identification through one- and two-dimensional examples. CRLS and RGS were found to be more robust than other methods for ill-conditioned systems. CRLS was subsequently combined with a global optimization solver for solving a more difficult problem of automatic source location recovery. Our results indicate that the robustness of CRLS can be crucial in solving a nonlinear optimization problem like this. The following illustration demonstrates the performance of CRLS as compared to a nonrobust estimator.

A comparison between the CRLS and the nonnegative least squares (NNLS) for determining source release history in a confined groundwater aquifer. The results are based on 100 Monte Carlo realizations. The dashed line corresponds to the true source release history, the o's correspond to the mean CRLS solution, and the 's correspond to the mean NNLS solution. The minimum and maximum estimates obtained by each method are also shown in the figure.

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