A Comparative Study of Various Optimality Criteria for Experimental Design in Groundwater Modeling Model

Abstract:

In general, the goal of optimal experimental design is to select the observation locations and sampling frequency such that a specified criterion is optimized subject to a set of constraints. The constraints frequently encountered are cost, reliability of the estimated parameters, and time and duration of the experiments. In groundwater modeling, if one assumes that observations are taken from the beginning of the pumping test to the end, the experimental design problem is simplified to the determination of observation locations. The commonly used design criteria are: A-optimality – a design that minimizes the trace of the covariance matrix of the estimated parameters; D-optimality – a design that minimizes the determinant of the covariance matrix of the estimated parameters; E-optimality – a design that minimizes the maximal eigenvalue of the covariance matrix of the estimated parameters; and G-optimality – a design that minimizes the maximal variance of the estimated response, where the maximum is taken over all possible predictor variables.

We examine the A, D, E, and G - efficiencies of various observation well network designs for determining unknown hydrologic properties in a confined, anisotropic groundwater aquifer. Since solving for the optimal observation well network design is non-convex and contains integer variables, Genetic Algorithms (GAs) are used to search for optimal designs for the various optimality criterions. Proper Orthogonal Decomposition (POD) is used to reduce the computational burden of the repeated model calls necessitated by using a GA. The robustness with respect to other optimality criterion of the optimal designs is also investigated.