Author(s)

A. Guadagnini & S.P. Neuman

Abstract

We consider the effect of measuring randomly varying hydraulic conductivities K(x) on the prediction of groundwater flow in a bounded porous domain under uncertainty. Hydraulic head is governed by a stochastic Poissbn equation subject to random source and boundary terms. We present a system of exact nonlocal deterministic equations for optimum unbiased predictors of these quantities and for measures of corresponding prediction errors. We then develop recursive approximations for these equations and solve them to leading order in the variance of In K(x) by nonlocal Galerkm finite elements. Our results compare well with Monte Carlo simulations of mean uniform and convergent flows in media with large variance and arbitrary correlation. 1 Introductio

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