Uncertainty Analysis of Linear and Nonlinear Groundwater Flow in a Heterogeneous Aquifer

Abstract

The two-dimensional linear and nonlinear stochastic groundwater flow equations in an unconfined heterogeneous aquifer with Dupuit assumptions and mixed boundary conditions is solved using analytical decomposition, which does not require perturbation, linearization, discretization, or knowledge of a particular probability distribution. New simple analytical expressions for the mean of the hydraulic head and its variance distribution are given for two common sets of field boundary conditions and recharge. This procedure allows the calculation of the head mean and error bounds in practical situations when only a limited sample allows the estimation of the mean and correlation structure of the transmissivity or the hydraulic conductivity. The results indicate that the head statistics are not only dependent on the transmissivity or the conductivity statistics (i.e., mean, variance parameter, and correlation structure), but also on the magnitude and type of boundary conditions, recharge, and other hydrogeologic...