STATISTICAL-ANALYSIS OF SPATIAL VARIABILITY IN UNSATURATED FLOW PARAMETERS

Core scale estimates of soil parameters of the Gardner-Russo and van Genuchten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench (20 m long, 2.5 m deep), using a a procedure based on inverse problem methodology. These estimates were used to evaluate the first two statistical moments of the underlying random space functions (RSFs), using the restricted maximum likelihood estimation procedure, coupled with the weighted least squares procedure, to estimate parameters of models of the covariance and the drift functions of the pertinent RSFs. The fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations. Covariance functions of log-saturated conductivity (log K(s)) and the "shape" parameters of the Gardner-Russo and van Genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4. Correlation scales of log K(s) were larger than those of the "shape" parameters. Consequently, the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation. The implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly.