William A. Jury

David Russo

Garrison Sposito

In this paper, we examine the possibility of introducing a single stochastic scaling factor α, derived from macroscopic Miller similitude, to describe the spatial variability of soil hydraulic properties. Most of the information available allowed only a conventional statistical analysis of the scaling factors derived from different soil properties. The field studies of (Nielsen, Biggar, and Erh (1973)) and (Russo and Bresler (1981)) were suitable also for more detailed structural analyses. Results of these analyses suggested that the spatial structure of the α-set derived from the hydraulic conductivity function *K*(?) is different from that of the α-set derived from the water retentivity function *h*(?), reflecting the different spatial structures of the *K*(?) and the *h*(?) functions. Consequently, the statistical relationship between the uncorrelated residuals of the two α-sets was rather weak. For the Hamra field of (Russo and Bresler (1981)), the use of relative hydraulic properties to estimate the scaling factor sets considerably improved the correlation between the α-sets, which had essentially the same spatial structure but slightly different variances.

In this study, where the soil hydraulic properties are assumed to be described by the model of (Brooks and Corey (1964)), analytical expressions for the variances of the two different α-sets indicated that (1) both α-sets are dependent on the range of water saturation that is used to estimate them, (2) the correlation between the two sets will improve in media with a wide pore-size distribution, and (3) the two sets will be identical if and only if the relative hydraulic conductivity function *K _{r}(h_{r})* is described by a deterministic function,

A more general *K _{r}(h_{r})* relation, defined by

The spatial variability of water and solute transport properties in unsaturated soil: II. Scaling models of water transport

55

William A. Jury

David Russo

Garrison Sposito

The spatial variability of water and solute transport properties in unsaturated soil: II. Scaling models of water transport

In this paper, we examine the possibility of introducing a single stochastic scaling factor α, derived from macroscopic Miller similitude, to describe the spatial variability of soil hydraulic properties. Most of the information available allowed only a conventional statistical analysis of the scaling factors derived from different soil properties. The field studies of (Nielsen, Biggar, and Erh (1973)) and (Russo and Bresler (1981)) were suitable also for more detailed structural analyses. Results of these analyses suggested that the spatial structure of the α-set derived from the hydraulic conductivity function *K*(?) is different from that of the α-set derived from the water retentivity function *h*(?), reflecting the different spatial structures of the *K*(?) and the *h*(?) functions. Consequently, the statistical relationship between the uncorrelated residuals of the two α-sets was rather weak. For the Hamra field of (Russo and Bresler (1981)), the use of relative hydraulic properties to estimate the scaling factor sets considerably improved the correlation between the α-sets, which had essentially the same spatial structure but slightly different variances.

In this study, where the soil hydraulic properties are assumed to be described by the model of (Brooks and Corey (1964)), analytical expressions for the variances of the two different α-sets indicated that (1) both α-sets are dependent on the range of water saturation that is used to estimate them, (2) the correlation between the two sets will improve in media with a wide pore-size distribution, and (3) the two sets will be identical if and only if the relative hydraulic conductivity function *K _{r}(h_{r})* is described by a deterministic function,

A more general *K _{r}(h_{r})* relation, defined by

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