Nonstationary stochastic analysis of flow in a heterogeneous semiconfined aquifer

[1] In this study, we investigate two-dimensional flow through a heterogeneous, semiconfined aquifer. In the presence of leakage the mean flow varies in space and the fluctuations of the flow become nonstationary spatially. Such a situation calls for a nonstationary stochastic approach since the classical stationary stochastic approaches are no longer appropriate. We make use of a nonstationary spectral method to account for such nonstationarities in finite semiconfined aquifers. Analytical expressions are obtained for head and specific discharge covariances that account for the spatial variability in the mean flow but neglect the contributions of the finite boundaries. Closed-form analytical expressions for the variances of hydraulic head and specific discharge are derived. The statistical structures of the head and specific discharge fields are investigated in terms of the leakage factor and the spatial structure of hydraulic conductivity field. Results based on the nonstationary approach show that the stationary assumption is inappropriate even for a small leakage.