Scaling of Soil Hydraulic Functions: Revisiting the Miller and Miller Similar Media Theory.

The Miller and Miller similar media theory is widely applied to characterize the spatial variability of soil hydraulic properties. Assuming that two porous media are “similar” in their microscopic geometry, the theory suggests that transformation of hydraulic properties from one medium to another is possible by means of a scaling factor. It is common practice to derive a single scaling factor from either the soil water characteristic h(S) or the hydraulic conductivity K(S) function (expressed based on relative saturation S). It is generally assumed that the microscopic similarity leads to similarity in the shape of h(S) and K(S) (i.e. macroscopic similarity) and thus the Miller and Miller theory is valid when the macroscopic similarity assumption holds. In this paper, it is reiterated that the macroscopic similarity assumption is a necessary condition for validity of the Miller and Miller theory, but is not the only condition that needs to be satisfied. An interrelation of the h(S) and K(S) scale parameters is also required. The validity of the latter relies on several other assumptions besides the macroscopic similarity assumption such as the invariance of the contact angle and the negligibility of film flow contributions. A dimensionless parameter termed “joint scaling factor” was defined and applied to evaluate the soundness of the h(S) and K(S) scale parameters interrelation (SPI) for 26 soils from the UNSODA database that were grouped into 6 classes of macroscopically-similar soils. Obtained results clearly reveal that simultaneous scaling of h(S) and K(S) with a single scaling factor derived from either h(S) or K(S) data fails when there is no SPI. For such cases a weighted average scaling factor calculated from h(S) and K(S) resulted in significantly improved scaling performance.