Analytical models of infiltration and redistribution for unsaturated flow in soils with vertically non-uniform saturated hydraulic conductivity

Abstract

The Richards equation describes unsaturated water movement in soils. However, analytical solutions to the nonlinear Richards equation are possible only for simple and idealized conditions. In this paper, sharp front (SF) models are developed for vertically non-uniform soils, with the saturated hydraulic conductivity continuously decreasing with depth according to a power-law function. Analytical expressions for evolutions of water content profiles and fluxes past a control plane are developed for the three surface boundary conditions of constant saturation, applied surface flux, and redistribution that are applicable during and after rainfall events. Comparisons of model results with infiltrometer experimental data from Purdue University are provided for the special case of falling head conditions at the soil surface. Subsequently, model results are compared with numerical solutions of the Richards equation for different levels of vertical heterogeneity for rainfall events of finite duration so that all the three boundary conditions are employed. Results show that soil moisture fronts are steeper with increasing non-uniformity, making sharp front approximations more accurate for pre- and post-ponding conditions, but less so for redistribution. The developed model results are found to provide reasonable approximations to numerical solutions of the Richards equation for vertically non-uniform soils.