A mathematical model for the coupled simulation of surface runoff and infiltration

The simulation of the unsteady free-surface flow on infiltrating surfaces h as many hydrological applications, including the study of overland flow, so il erosion and conservation, surface irrigation and contaminant transportat ion. The surface runoff is strictly connected to the infiltration through t he soil surface; so, an independent simulation of the two processes, althou gh very often adopted, may be unrealistic. This paper presents a mathematic al model for simulating these interdependent surface and subsurface process es. The model is based on the two-dimensional shallow water equations, coup led with the one-dimensional Richards equation. These equations are integra ted jointly, following the MacCormack scheme, which is an explicit, finite- difference scheme, accurate to the second order. The model can simulate ini tially dry surface conditions and variable initial soil water content, and can deal with space-variable characteristics (slope, roughness and soil hyd raulic properties). The accuracy of the model is tested by comparing its re sults with analytical solutions and with experimental data. Finally, a nume rical experiment carried out on a simple hypothetical catchment, both using the complete model and a simplified version, in which the Richards equatio n and the shallow water equations are solved in cascade, is discussed. (C) 2000 Silsoe Research Institute.