Modeling of Conjunctive Two-Dimensional Surface-Three-Dimensional Subsurface Flows

Abstract

In the rainfall-runoff process, interaction between surface and subsurface flow components plays an important role, especially in rainwater abstraction and overland flow initiation at the early stage of rainfall events. Coupling of surface and subsurface flow submodels, therefore, is necessary for advanced comprehensive and sophisticated rainfall-runoff simulation. This article presents a conjunctive two-dimensional (2D) surface and three-dimensional (3D) subsurface flow model, which uses the noninertia approximation of the Saint-Venant equations for 2D unsteady surface flow and a modified version of the Richards equation for 3D unsteady unsaturated and saturated subsurface flows. The equations are written in the form of 2D and 3D heat diffusion equations, respectively, and solved numerically. The surface and subsurface flow components are coupled interactively using the common boundary condition of infiltration through the ground surface. The conjunctive model is verified with Smith and Woolhiser’s experimental data (reported in 1971) of initially dry and initially wet soil. Subsequently the model is applied to a hypothetical soil plot of clay or sand to simulate the overland flow, infiltration, and subsurface flow for four different rainfalls. The conjunctive model contributes as a tool for improved detailed simulation of 2D surface and 3D subsurface flows and their interaction.