A Mathematical Model for the Coupled Simulation of Surface Runoff and Infiltration

The simulation of the unsteady free-surface flow on infiltrating surfaces has many hydrological applications, including the study of overland flow, soil erosion and conservation, surface irrigation and contaminant transportation. The surface runoff is strictly connected to the infiltration through the soil surface; so, an independent simulation of the two processes, although very often adopted, may be unrealistic. This paper presents a mathematical model for simulating these interdependent surface and subsurface processes. The model is based on the two-dimensional shallow water equations, coupled with the one-dimensional Richards equation. These equations are integrated jointly, following the MacCormack scheme, which is an explicit, finite-difference scheme, accurate to the second order. The model can simulate initially dry surface conditions and variable initial soil water content, and can deal with space-variable characteristics (slope, roughness and soil hydraulic properties). The accuracy of the model is tested by comparing its results with analytical solutions and with experimental data. Finally, a numerical experiment carried out on a simple hypothetical catchment, both using the complete model and a simplified version, in which the Richards equation and the shallow water equations are solved in cascade, is discussed.