Three‐parameter lognormal distribution model for soil water retention

Abstract

Many models for soil water retention have been proposed. However, most of these models are curve‐fitting equations and do not emphasize the physical significance of their empirical parameters. A new retention model that exhibits increased flexibility was developed by applying three‐parameter lognormal distribution laws to the pore radius distribution function ƒ(r) and to the water capacity function, which was taken to be the pore capillary pressure distribution function ƒ(ψ). This model contains three parameters that are closely related to the statistics of ƒ(ψ): the bubbling pressure ψc, the mode ψ 0 of ƒ(ψ) and the standard deviation σ of transformed ƒ(ψ). By comparison of this model with three existing models (the van Genuchten model, the Brooks‐Corey model, and the modified Tani model), it was shown that ψc, ψ 0, and σ are all essential for a general retention model.