Improving prediction of hydraulic conductivity by constraining capillary bundle models to a maximum pore size

Abstract

The prediction of unsaturated hydraulic conductivity from the soil water retention curve by pore-bundle models is a cost-effective and widely applied technique. One problem for conductivity predictions from retention functions with continuous derivatives, i.e. continuous water capacity functions, is that the hydraulic conductivity curve exhibits a sharp drop close to water saturation if the pore-size distribution is wide. So far this artifact has been ignored or removed by introducing an explicit air-entry value into the capillary saturation function. However, this correction leads to a retention function which is not continuously differentiable. We present a new parameterization of the hydraulic properties which uses the original saturation function (e.g. of van Genuchten) and introduces a maximum pore radius only in the pore-bundle model. In contrast to models using an explicit air entry, the resulting conductivity function is smooth and increases monotonically close to saturation. The model concept can easily be applied to any combination of retention curve and pore-bundle model. We derive closed-form expressions for the unimodal and multimodal van Genuchten–Mualem models and apply the model concept to curve fitting and inverse modeling of a transient outflow experiment. Since the new model retains the smoothness and continuous differentiability of the retention model and eliminates the sharp drop in conductivity close to saturation, the resulting hydraulic functions are physically more reasonable and ideal for numerical simulations with the Richards equation or multiphase flow models.