Numerical investigation of surface runoff in hillslopes with variably saturated flows

During heavy rainfall episodes, subsurface flow can saturate the soil in various regions near the surface and, therefore, contribute to the production of overland flow. This paper investigates numerically watertable dynamics in partially saturated porous media and the coupling mechanisms between the hydraulic state of the soil and the genesis of surface runoff. Variably saturated flows are modeled using Richards' equation discretized using a finite element method (P₁-conforming) on unstructured, non-uniform triangulations. Two strategies are considered to model the coupling between the subsurface water table and surface runoff. The first strategy neglects the height of the overland flow as well as re-infiltration processes. The water table position being an unknown of the problem, its intersection with the ground surface yields an unsteady obstacle-type problem. A more detailed approach consists of modeling the overland flow using a simplified form of the Saint-Venant equations, yielding the so-called diffusive wave approximation. Numerical results are presented to compare both approaches.