Scaling Water Retention Curves for Soils with Lognormal Pore‐Size Distribution

Abstract

The scaling theory approach has been widely used as an effective method to describe the variation of soil hydraulic properties. In conventional scaling, reference retention curves and scaling factors are determined from minimization of residuals. Most previous studies have shown that scaling factors are lognormally distributed. In this study, we derived physically based scaling factors, assuming that soils are characterized by a lognormal pore-size distribution function. The theory was tested for three sets of retention data. Two data sets included samples of a sandy loam soil, and one set included samples of a loamy sand soil. Individual soil water retention data were fitted to the retention model proposed by Kosugi (1996). The parameters of the model are the mean and variance of the log-transformed poreradius distribution. Scaling factors and parameters of the reference curve were computed directly from the parameters of individual soil water retention functions. Assuming that (i) the soil pore radius of a study area is lognormally distributed and (ii) soil samples are obtained from random sampling of effective soil pore volume from the study area, we have proposed a theoretical interpretation of the lognormal scaling factor distribution. Scaling results for all three data sets compared well with those obtained using the conventional scaling method. D ESCRIBING WATER FLOW in soils requires knowledge of the soil hydraulic properties. The hydraulic properties of unsaturated soil are represented by the water retention characteristic (the relationship between the volumetric soil water content, 6, and the capillary pressure head, h, and the unsaturated hydraulic conductivity, K, function. Both properties are variable in het

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