Open Access

William A. Jury, David Russo, Garrison Sposito, Hesham Elabd

• We analyzed the possibility of introducing a single stochastic scaling parameter a to describe the spatial variability of soil hydraulic properties, using the soil hydraulic properties of the Hamra field (Russo and Bresler 1981) and the Panache field (Nielsen, Biggar, and Erh 1973). In the traditional approach (Peck, Luxmoore, and Stolzy 1977; Russo and Bresler 1980; Warrick, Mullen, and Nielsen 1977), sets of scaling factors are estimated from the h(s) and K(s) functions. For "perfectly similar media," the two sets of a should be identical. Even though the sets of a in these studies were found to be correlated (table 2), they possessed different statistical properties, and were not identical. Results of structural analyses of the sets of a from the two fields suggested that the spatial structures of the two a-sets are quite distinct, reflecting the different spadal behavior of the h(θ) and the K(θ) functions. Moreover, there was poor correlation between the uncorrelated residuals of the a-sets, indicating that part of the high correlation between the a-sets found in earlier work must stem from the presence of an undetected drift and from correlation between nearby measurements. Under field conditions, the saturated hydraulic conductivity is controlled by the flow of water through large structural voids (macropores), which drain at very small negative values of water pressure. Because of this, we tried eliminating Ks by using relative hydraulic properties instead of the hydraulic properties themselves to estimate the scaling factor sets. For the Hamra field, for which we assumed that the hydraulic properties could be described by the model of Brooks and Corey (1964), we found the resultant sets of scaling factors to be highly correlated (R2 = 0.996) with the same spatial structure, but with slightly different variance. By examining the relationships between the two a-sets implied by the Brooks and Corey (1964) model we saw that (1) in general, both sets will be functions of the range of water saturation values used to estimate them, (2) the correlation between the two sets can be improved for media with broad pore-size distributions, and (3) the two sets will be identical if and only if the relative hydraulic conductivity function K,.(hr) is described by the deterministic function Kr(hr) = hy -2 ("strictly similar media"). This analysis suggests that, for media that are not well described by Kr = hr -2, a scaling factor would be required in addition to a in order to achieve agreement between scaled values of hr(θ) and Kr(θ) at all points. A general model Kr = hr -η was proposed, with η as a second stochastic scaling factor for media that do not obey the restrictive assumptions of macroscopic Miller similitude. In the Hamra field, this modified scaling procedure produced perfect agreement between the scaling hydraulic properties. In the Panache field, with values of η determined from linear regression analysis of the logarithmic transformations of Kr and h,., agreement was improved considerably between the scaled hydraulic properties as compared to the more restrictive scaling procedure. In contrast to the Hamra field, however, there remained some significant differences between the scaled properties. These differences may have been artifacts of the different methods used to estimate the hIs) and the K(s) functions for the Panache field. The results of our analysis suggest that in any transient transport problem involving both K(s) and h(s), the description of their spatial variability requires the use of at least three stochastic variates-Ks , α, and η-not a alone.