A Simple Model to Predict Hydraulic Conductivity in Medium to Dry Soil From the Water Retention Curve

Abstract

The mathematical representation of the soil hydraulic properties is of central importance for modeling water, solute and energy transport in soils. The established models of the water retention and hydraulic conductivity curves account for capillary water retention and conductivity, but neglect water adsorption and water flow in films and pore corners. They are therefore suited for modeling flow and transport processes in the medium to wet moisture range, but are susceptible to failure in dry soil. The model system developed by Peters (2013, https://doi.org/10.1002/wrcr.20548; 2014, https://doi.org/10.1002/2014wr016107) and Iden and Durner (2014, https://doi.org/10.1002/2014wr015937) (PDI in the following) is a simple parametric framework that overcomes these structural shortcomings. However, it requires one additional parameter to scale the hydraulic conductivity curve in the moisture range where non-capillary flow dominates. Measured conductivity data are required to determine this scaling parameter and to compute the hydraulic conductivity over the complete moisture range. In this contribution, we first show that the original PDI model is in close agreement with a comprehensive model for film conductivity in porous media. We then derive a physically-based approach to predict the film conductivity from the water retention curve. This improved PDI model has the same number of parameters as established models and provides a complete prediction of the hydraulic conductivity curve including non-capillary flow if water retention data and the saturated conductivity are known. Application to literature data covering a broad range of textures shows an improvement of the conductivity prediction by the factor five if compared to the van Genuchten/Mualem model.