Indicator Generalized Parameterization for Interpolation Point Selection in Groundwater Inverse Modeling

Abstract

This study developed an indicator generalized parameterization (IGP) method to cope with the problem of selecting interpolation points in estimating hydraulic conductivity fields. The IGP method introduced data indicators and d-neighborhoods to describe the actual contribution of sample data to unsampled locations. Moreover, the IGP method was applied to nonkriging basis functions to characterize spatially correlated hydraulic conductivity. This study used probabilistic data indicators to take into consideration the randomness and heterogeneity of hydraulic conductivity. The groundwater inverse method, along with an adjoint state method, was adopted to estimate the indicator probabilities. Then a cutoff was applied to determine the values of the data indicators for the IGP to estimate hydraulic conductivity. The numerical example validated the IGP and illustrated the significance of selecting interpolation points for hydraulic conductivity distributions. Further, the study demonstrated the IGP applicability to estimating hydraulic conductivity in the Alamitos Gap area, Calif. It was concluded that increasing the amount of data selected for interpolation results in smaller conditional variances, but causes the ensuing distribution to be smoother. However, smooth distributions of hydraulic conductivity may not be preferred. Proper selection of interpolation points can result in better hydraulic conductivity distributions for groundwater modeling purposes.