Submitted to: American Geophysical Union
Publication Type: Abstract only
Publication Acceptance Date: 9/9/1996
Publication Date: N/A
Citation: Interpretive Summary:
Technical Abstract: In previous studies the first-order reliability method (FORM) has been used to estimate the probability that chemical concentrations in groundwater will exceed some specified level. Most of these studies considered only simple analytical models of solute transport in homogeneous soils. Studies that examined more complex, heterogeneous systems found the computational requirements of FORM to be excessive and were inconclusive as to the accuracy of the method. We show that FORM cannot be used with all mathematical formulations of the transport problem because of inconsistencies with the underlying assumptions of the methodology. For a general solute source function, FORM may be applied in a consistent manner only when the problem is formulated in terms of the cumulative solute mass flux. As a demonstration, we used FORM to approximate the cumulative mass flux ccdf (complimentary) cumulative distribution function) in two-dimensional, random porous media. The computed ccdf is an estimate of the probability that the cumulative solute mass crossing a specified surface will exceed a particular level. An adjoint sensitivity method is used to minimize computational costs and FORM is found to require 8 times less CPU time than Monte Carlo simulation to generate the results presented. The accuracy of FORM is not affected significantly by the size of the initial solute body and the length of the solute travel distance. However, the accuracy is influenced by the degree of heterogeneity, with FORM providing an accurate estimate of the ccdf when there is a mild heterogeneity but a less accurate estimate when there is stronger heterogeneity.