A Family of Soil Water Retention Models Based on Sigmoid Functions

The soil water retention curve is the fundamental soil hydraulic property to characterize soil water movement and solute transport. Many efforts have been devoted in the past decades to developing models to describe soil water retention curves. However, most of them are empirical equations or assume that soil pore size distributions conform to a lognormal distribution. Yet, few effects have been undertaken to systematically propose and compare a series of possible alternative probability density functions to describe the sigmoid retention curves with parameters physically explainable. Here, we proposed a family of five soil water retention models based on sigmoid functions with parameters of clear physical implications coinciding with the statistical measures of soil pore size distribution. Compared with the widely used models (i.e., Brooks & Corey, 1964; Kosugi, 1996; van Genuchten, 1980), the proposed models have somewhat improved performances to characterize water retention data for a wide range of soil textures without introducing additional model parameters. Two of the proposed models are capable of characterizing the observed two local extrema in the moisture capacity curves. The associated unsaturated hydraulic conductivity models of the proposed soil water retention models are also derived, which show superior performance in characterizing the observed hydraulic conductivities compared with competing models, especially in macropore regimes. Additionally, we analyzed the parameter-equivalent conversion between the proposed and the existing models, and a simple linear regression equation can be used to derive the parameters of the proposed models from the existing and other alternative different proposed models.