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On Probability Distribution of Hydraulic Conductivity in Variably Saturated Bimodal Heterogeneous Formations

Dep. of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences, Agricultural Research Organization, The Volcani Center, Bet Dagan 50250, Israel

Correspondence: ^* Corresponding author (vwrosd{at}agri.gov.il).

Received for publication 27 July 2008. First-order analysis was used to analyze the probability density function (PDF) of the logarithm of conductivity, log K, in variably saturated, bimodal, heterogeneous formations, and to investigate the implications of the results with respect to solute transport. The bimodal formations were viewed as mixtures of two populations (background soil and embedded soil) of differing spatial structures. Two distinct cases were considered: in the first case, the texture of the embedded soil is finer than that of the background soil, while the second case is the reverse situation. Results of this study suggest that, because for a given volume fraction of the embedded soil, both the mean and the variance of log K depend on the mean pressure head, H, in a manner that depends on the texture of the embedded soil relative to that of the background soil, so does the log K PDF. Furthermore, because of the inherent concave behavior of the log K variance–pressure head relationships in these formations, the shape of the bimodal log K PDF may change with increasing H, such that at a certain critical mean pressure head it may degenerate into an "equivalent," unimodal PDF. One of the main findings of this study suggests that even when the two subdomains of the formation are characterized by mild heterogeneity, a relatively small volume fraction of coarse-textured embedded soil may lead to a highly skewed log K PDF, which, in turn, may exhibit an exceedingly large tail associated with the small K values, particularly when the contrast between mean conductivities of the two subdomains of the formation at saturation is relatively large and when the formation is relatively dry.

Abbreviations: MSE, mean square error • MVN, multivariate normal • PDF, probability density function • RSF, random space function