Inverse groundwater modeling with emphasis on model parameterization

Abstract

This study develops an inverse method aiming to circumvent the subjective decision regarding model parameterization and complexity in inverse groundwater modeling. The number of parameters is included as a decision variable along with parameter values. A parameterization based on B‐spline surfaces (BSS) is selected to approximate transmissivity, and genetic algorithms were selected to perform error minimization. A transform based on linear least squares (LLS) is developed, so that different parameterizations may be combined by standard genetic algorithm operators. First, three applications, with isotropic, anisotropic, and zoned aquifer parameters, are examined in a single objective optimization problem and the estimated transmissivity is found to be near the true one. Interestingly, in the anisotropic case, the algorithm converged to a solution with an anisotropic distribution of control points. Next, a single objective optimization with regularization, penalizing complex models, is considered, and last, the problem is expressed in a multiobjective optimization framework (MOO), where the goals are simultaneous minimization of calibration error and model complexity. The result of MOO is a Pareto set of potential solutions where the user can examine the tradeoffs between calibration error and model complexity and select the most suitable model. By comparing calibration with prediction errors, it appears, that the most promising models are the ones near a region where the rate of decrease of calibration error as model complexity increases drops (bend of error curve). This is a useful result of practical interest in real inverse modeling applications.