Nonstationary stochastic analysis of flow in a heterogeneous unconfined aquifer subject to spatially-random periodic recharge

The problem of two-dimensional groundwater flow in a heterogeneous unconfined aquifer under periodic random forcing in time is analyzed from a stochastic point of view. It is assumed that the periodic random forcing, namely random recharge, can be represented by a sinusoidal function in time. Analytical solutions are developed through the nonstationary spectral approach in conjunction with the principle of superposition. The results, namely the variances of hydraulic head and specific discharge, are expressed in terms of statistical properties of hydraulic parameters and recharge field. It can be concluded from the analytical results that the mean recharge rate and integral scale of spatially random recharge fluctuations play essential roles in enhancing the variability of hydraulic head and specific discharges.