[1] Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one-and two-dimensional test problems. When the system is illconditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

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Several field experiments have been performed by To provide data for more rigorous model testing, a third scientists from the University of Arizona and New Mexico Las Cruces Trench experiment (denoted the Plot 2b State University at the Las Cruces Trench Site to provide experiment) was designed by scientists from the University data to test deterministic and stochastic models for water of Arizona and New Mexico State University. Modelers flow and solute transport. These experiments were from the Center for Nuclear Waste Regulatory Analysis, performed in collaboration with INTRAVAL, which is an Massachusetts Institute of Technology, New Mexico State international effort toward the validation of geosphere University, Pacific Northwest Laboratory,and the models for the transport of radionuclides. During Phase I of University of Texas provided predictions for water flow INTRAVAL, qualitative comparisons between and tritium transport to New Mexico State University for experimental data from two experiments (denoted Plot 1 analysis. The corresponding models assumed soil and 2a experiments) and model predictions were made characterizations that ranged from uniform and isotropic, to using contour plots of water contents and solute two-dimensional heterogeneous, to stochastic. This report concentrations. Detailed quantitative comparisons between presents detailed qualitative and quantitative comparisons the predictions and field observations and between the between the model predictions and field observations for predictions of all of the models were not made. the Plot 2b experiment.

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