Conditional Analysis of Unsaturated Flow in Randomly Heterogeneous Soils Without Monte Carlo Simulation or Upscaling

Abstract

This study focused on flow in the unsaturated or vadose zone, which forms a major hydrologic link between the ground surface and underlying groundwater aquifers. To properly understand its role in protecting groundwater from surface and near surface sources of contamination, one must be able to analyze quantitatively fluid flow in unsaturated soils. The difficulty is that such soils are ubiquitously heterogeneous, with hydraulic properties that fluctuate from point to point in a seemingly erratic manner. The common approach has been to delineate this variation, and analyze unsaturated flow in randomly heterogeneous soils, deterministically. Yet with increasing frequency, the popular deterministic approach is proving to be inadequate. Our project aimed at developing theoretical and computational methods to predict, in an optimum fashion, unsaturated flow in randomly heterogeneous soils under the action of uncertain forcing terms and to assess the corresponding prediction errors. Previously, such predictions and assessments required the conduct of numerous Monte Carlo simulations on a fine grid, which was computationally demanding and therefore seldom used in practice. An alternative is to conduct Monte Carlo simulations on a coarse grid, which is still computationally intensive (due to the need for many repetitions) and leads to a loss of accuracy due to the need to average (upscale) the flow equations over relatively large grid cells. Our objective was to avoid the need for either Monte Carlo simulation or upscaling by developing ways to render predictions and uncertainty assessments directly, in a computationally efficient and accurate manner. This final technical report describes our accomplishment in the development of two novel approaches, one based on the Kirchhoff transformation and the other on a Gaussian method of approximation. The report also describes some initial ideas about how to extend the applicability of these two approaches to multidimensional and transient flows in a broader class of soils than we have considered previously. The report cites publications based on research supported in part by this ARO grant.