SOIL SCIENCE SOCIETY OF AMERICA JOURNAL, vol.54, no.6, pp.1537-1547, 1990 (SCI-Expanded)
The knowledge of the statistical parameters of the variance, sigma-2, and the correlation scale, lambda, characterizing the spatial structures of the log of the saturated hydraulic conductivity, lnK(s), pore size distribution parameter alpha, and the specific water capacity, C, is required in stochastic modeling in order to understand the overall response of large-scale heterogenous unsaturated flow systems. These parameters are estimated assuming second-order stationarity and an exponential semivariogram model with nugget effect. Methods of ordinary least squares (OLS), maximum likelihood (ML), and restricted maximum likelihood (RML) are used for estimating sigma-2 and lambda, while methods of cross-validation (kriging) and uncorrelated residuals are used to validate the semivariogram model with estimated sigma-2 and lambda. The objectives of this study were to evaluate the sensitivity of sigma-2 and lambda to the estimation methods and to discuss the implications of the analysis in view of the stochastic modeling. The significance of the results of parameter estimation and model validation in relation to the stochastic modeling of large-scale transient unsaturated flow is demonstrated with two examples involving the variance of soil-water pressure head, sigma-h2, and the vertical component of effective hydraulic conductivity, K11*. Results show that the estimated values of sigma-2 and lambda are highly dependent on the estimation method. Although the majority of the estimated parameters pass the validation tests, the RML estimates of sigma-2 and lambda used in estimating sigma-h2 and K11* significantly reduce the prediction uncertainties.