Stochastic subsurface hydrology from theory to applications

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Abstract
Research on stochastic analysis of subsurface flow has developed rapidly in the last decade, but applications of this approach have been very limited. The purpose of this paper is to illustrate how currently available techniques and results can be used to answer important questions about the large‐scale behavior of naturally heterogeneous aquifers. Perturbation‐based spectral theory, which presumes local statistical homogeneity, provides generic theoretical results for the head variance, effective conductivity tensor, and macrodispersivity tensor in a field. These results emphasize the key role of the variance and spatial correlation scales of the log hydraulic conductivity field. Field information of variances and correlation scales of natural materials is summarized. The validity of some of the generic stochastic results is evaluated through comparisons with Monte Carlo simulations and field observations. A specific field application example is developed to illustrate how the stochastic results are used to estimate large‐scale parameters and determine the reliability of three‐dimensional numerical simulations. Using typical log conductivity covariance parameters, the effective hydraulic conductivity tensor, and the macrodispersivity tensor are estimated. The calculated head variance, based on the simulated mean hydraulic gradient, is used as a measure of the adequacy of the calculation of the steady state flow model. Discussion emphasizes limitations and extensions of this approach, and ongoing field evaluations of the results.