Simultaneous scaling of soil water retention and unsaturated hydraulic conductivity functions assuming lognormal pore-size distribution

Using simultaneous scaling, soil spatial variability of hydraulic functions can be described from a single set of scaling factors. The conventional scaling approach is based on empirical curve fitting, without paying much attention to the physical significance of the scaling factors. In this study, the concept of simultaneous scaling of the soil water retention and unsaturated hydraulic conductivity functions is applied to a physically based scaling theory. In this approach, it is assumed that soils are characterized by a lognormal pore-size distribution, which leads directly to lognormally distributed scaling factors. To test this concept, a total of 143 undisturbed soil samples were collected from two soil depths (25 and 50 cm), with each depth divided into two subsets based on the median soil capillary pressure head value, as determined from the lognormal pore-size distribution assumption. Moreover, the theory was compared with the conventional simultaneous scaling method. Both the conventional and physically based simultaneous scaling method performed equally well for all four subsets, as determined from the reduction in weighted root mean squared residual (WRMSR) values after scaling. We showed that the theoretical interpretation of the lognormal scaling factor distribution was applicable to simultaneous scaling of soil hydraulic functions.