Stochastic analysis and prioritization of the influence of parameter uncertainty on the predicted pressure profile in heterogeneous, unsaturated soils

Abstract

This article utilizes a Monte Carlo stochastic framework to investigate the influence on the mean and variance of the predicted mean pressure head profile of statistical assumptions regarding the parameters that enter the mathematical description of the problem of infiltration in unsaturated, heterogeneous layers. The parameters are treated as random functions with an exponential auto-covariance function expressing their spatial continuity. Four different truncated distributions are taken to describe the parameters according to field observations and various phases of site characterization campaigns. The exponential distribution is seen to produce the largest (in absolute value) mean and variance in the pressure head profile. For all distributions the variance in pressure head increases with increasing mean pressure. A second topic of this article is to investigate, the relative importance of each parameter, in terms of the mean and the variance of the predicted pressure. For uniformly or triangularly distributed parameters the saturated hydraulic conductivity appears to dominate the mean-behavior and the uncertainty in the system's solution. For lognormally or exponentially distributed parameters another parameter, the van Genuchten pore-size distribution index, is the dominant factor.