An Effective Approach for Contaminant Source Location and
Inclusive Dates: 01/01/05 Current
Background - Groundwater is a vital component of the freshwater 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 so that clean-up costs can be partitioned between liable parties. In most cases, site historical records kept by relevant agencies are insufficient to establish source locations and release histories. Thus, the spatiotemporal evolution of a contaminant plume often has to be reconstructed through inversion. Existing strategies for contaminant source identification have important practical limitations. In many studies, 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 devised a robust framework for contaminant source identification. The contaminant source identification problem was first cast into one of solving uncertain linear equations, where the response matrix was constructed using a superposition technique. Our formulation is general and is applicable to any porous media flow and transport solvers. A Constrained Robust Least Squares (CRLS) estimator was then formulated to solve the uncertain linear equations. CRLS directly incorporates prior knowledge about model and data uncertainty, and uses the information to determine a regularization parameter that is optimal for robustness. CRLS does not require probability distributions of model parameters; instead it assumes that the worst-case scenario can be identified and the associated worst system perturbation is bounded. Because of its robustness, CRLS is perfectly suited for solving ill-conditioned systems resulting from, for example, poor sampling design.
Accomplishments - We successfully demonstrated the performance of our robust framework for source identification through one- and two-dimensional examples. CRLS was found to be more robust than other methods for ill-conditioned systems. A journal paper was submitted to Water Resources Research based on our initial findings. 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. We documented our more recent findings in another journal paper that is to be submitted for review. Finally, our framework is being used to reconstruct source release history at a Canadian landfill site, as part of an applied case study.
Comparison of the estimates obtained by CRLS and nonnegative least squares (NNLS) for source identification in a two-dimensional domain. The results are based on 100 Monte Carlo realizations. The dashed line corresponds to the true source release history, o corresponds to the mean CRLS solution, and x corresponds to the mean NNLS solution. The minimum and maximum estimates obtained by each method are also shown in the figure.