Statistical Parameters Characterizing the Spatial Variability of Selected Soil Hydraulic Properties

Abstract

The knowledge of the statistical parameters of the variance, σ2, and the correlation scale, λ, characterizing the spatial structures of the log of the saturated hydraulic conductivity, lnKs, pore size distribution parameter α, and the specific water capacity, C, is required in stochastic modeling in order to understand the overall response of large‐scale heterogeneous 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 σ2 and λ, while methods of cross‐validation (kriging) and uncorrelated residuals are used to validate the semivariogram model with estimated σ2 and λ. The objectives of this study were to evaluate the sensitivity of σ2 and λ 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, σ2h, and the vertical component of effective hydraulic conductivity, K*11. Results show that the estimated values of σ2 and λ are highly dependent on the estimation method. Although the majority of the estimated parameters pass the validation tests, the RML estimates of σ2 and λ used in estimating σ2h and K*11 significantly reduce the prediction uncertainties.

On the effective hydraulic conductivity in mean vertical unsaturated steady flows

“…The variance of f can be either larger or smaller than that of Y. For example, [43] reported the f-variance in the range 0.045-0.112, and the variance of Y in the range 0.391-0.960, while [38] found r 2 f ¼ 0.425, compared to r 2 Y ¼ 1.242. Instead, White and Sully [46], and Russo and Bouton [35] found the variances of f and Y to be of similar order, whereas [28,29] observed the variance of f to exceed that of Y.…”

Application and Validation of an Upscaling Method for Unsaturated Water Flow Processes in Heterogeneous Soils

“…As is well known, the multiscale nature of the porous media flow problem often comes from the spatial heterogeneity of the saturated hydraulic conductivity ( K s ) and the pore size distribution parameter α G in the Gardner–Basha model or α v in the Mualem–van Genuchten model. Much experimental evidence indicates that the K s and α G (or α v ) of many soils follow a lognormal distribution (Byers and Stephens, 1983; Sudicky, 1986; Hopmans et al, 1988; Ünlü et al, 1990; Russo and Bouton, 1992; White and Sully, 1992), and such lognormal distributions have been widely used in the literature. In all examples below, we assume that K s and α G (or α v ) follow lognormal distributions and use the turning bands method (Mantoglou and Wilson, 1982; Tompson et al, 1989) with the exponential covariance model to generate realizations of K s and α G (or α v ) fields of the study domain.…”

An alternative deterministic method for the spatial interpolation of water retention parameters

“…This confirms the importance of analyzing the spatial distribution of water retention curves at this site. Among many available retention curve models, the Brooks and Corey (BC) model (Brooks and Corey, 1964), the van Genuchten (VG) model (van Genuchten, 1980), and the Kosugi (KSG) model based on the lognormal pore size distribution (Kosugi, 1996) are the most widely used analytical expressions for representing the dependence of the water content on the capillary pressure head for unimodal pore systems. Detailed discussions of the commonly used soil hydraulic models can be found in Leij et al (1997).…”

“…In this study, only water retention curve data will be analyzed, since we have assumed that only this information is available, while information about unsaturated hydraulic conductivities is lacking. The water retention parameters for a particular soil are usually obtained by first measuring a series of pressure head and water content data pairs from core samples in a laboratory and then by fitting the constructed discrete curve using a simple analytical model, such as the well-known van Genuchten model (van Genuchten, 1980). Water flow in soils is then usually obtained using a numerical model that simulates variably-saturated water flow, and uses analytical models of soil hydraulic properties.…”