A new sigmoidal but non-asymptotic soil water retention curve for the entire soil water content range brings together the van Genuchten and Brooks-Corey models

The most important parameterizations of the soil water retention curve do not perform very well in either the wet or the dry end. Rossi and Nimmo (WRR 1994) therefore gave the Brooks-Corey (1966) power-law model of the soil water retention curve a non-asymptotic dry range. Ippisch et al. (Adv. Water Resour., 2006) added an air-entry value to the sigmoidal retention model of van Genuchten (SSSAJ 1980). The models of Rossi and Nimmo and Ippisch et al. were Adapted by de Rooij (HESS 2021) to arrive at a sigmoidal, non-asymptotic soil water retention curve with an air-entry value, dubbed RIA. In RIA, the matric potential at oven-dryness, h_d, appeared as a derived parameter.

Bittelli and Flury (SSSAJ 2009) showed that dry-range soil water retention data points often are unreliable. In order to make RIA robust when this is the case, this presentation explains how h_d was made a fitting parameter that can be fixed if needed. This modification was complicated by the peculiar behavior of shape parameter α that made adequate parameter fitting impossible. The presentation elucidates this behavior and explains how this problem was solved by a reformulated model (de Rooij, HESS 2022). It then shows how earlier fits (when the problem had not yet been discovered) corroborate the reformulated model.

The work also offers support for a theoretical value for h_d proposed by Schneider and Goss (Geoderma 2012), which is very helpful if dry-range data are lacking or of poor quality. The mathematical structure of RIA is such that, for α → ∞, Rossi and Nimmo’s model arises as a special case of RIA, and, by implication, Brooks-Corey as a special case of Ippisch et al.

A public-domain code to fit the parameters using shuffled complex evolution (SCE) is available on Zenodo (de Rooij, 2022). It has features that help the user identify issues with local minima and overparameterization, and provides more information than most codes to offer better insight into the fitting process for those familiar with the SCE algorithm. These features may be useful for other parameter identification problems, so they will be discussed as well.