Modified Richards equation and its exact solutions for soil water dynamics on eroding hillslopes

Abstract

The modified Richards equation (MRE) is presented by using a rotated coordinate system to accommodate the geometry of a hillslope and a moving boundary to represent an eroding surface on a hillslope. Exact analytical solutions of MRE are developed subject to Fujita's [1952] diffusivity and Sander et al.'s [1988] unsaturated hydraulic conductivity. The mathematical analysis presented here for soil water dynamics and infiltration in particular on an eroding hillslope deviates from the traditional way in which infiltration has been investigated since Green and Ampt's [1911] pioneering work. The MRE clearly improves mathematical representation of physical reality. Field data are used to derive parameters in a solution of MRE to illustrate the effect of erosion rates on soil moisture profiles in a moving boundary.