Application of a soil water hysteresis model to simple water retention curves

The Parlange hysteresis model is reformulated as a pair of recurrence relations to provide relationships between wetting and drying phases to any order. The model is applied to the classical van Genuchten model for soil water retention used as the main wetting curve. The nonphysical behaviour of these retention curves is related to the existence of a point of inflection in the van Genuchten model when it is used for the wetting boundary. Where the van Genuchten form is used as the main drying curve, the Parlange hysteresis model provides an ordinary differential equation describing the main wetting curve. A number of simple analytical solutions, relating to particular values of the parameters of the van Genuchten model, then provide forms for the main wetting curve. In general, a numerical integration is required to generate the main wetting curve, for general values of the parameters of the van Genuchten model. The recurrence relations for the hysteresis cycling are still applicable, even when the main wetting curve is only known numerically. The new main wetting curves do not have inflection points and there is no nonphysical behaviour. The model is then applied to the experimental data of Viaene et al. (1994).