Numerical Modeling of Rainfall-Generated Overland Flow Using Nonlinear Shallow-Water Equations

Abstract

This paper presents a physics-based two-dimensional (2D) numerical model to simulate overland flows typically generated by rainfall of a storm event or multiple events in natural terrain with complex topography, landform, soil characteristics, and land use. The model is based on the 2D fully nonlinear shallow-water equations (SWEs) in which tempospatial variations of rainfall intensity and infiltration are taken into account as source and sink terms, respectively. The Green-Ampt equation is used to simulate infiltration. Due to strong nonlinearity of the coupled dynamic processes in overland flow and stormwater runoff, special efforts were made to solve this coupled-flow system under the conditions of unsteady rainfall intensity and natural terrain. To attain the modeling capabilities for multiple flow regimes including subcritical, supercritical, and the transitions, a second-order central-upwind shock-capturing scheme, which is well balanced and depth-positivity preserving, is used to solve the governing equations. The model is capable of simulating the Hortonian overland flows resulting from the complex rainfall storm events recorded by multiple rain gauges. Model verification was achieved by comparing numerical results with corresponding analytical solutions. The model was validated by reproducing the field-scale rainfall-runoff experiments conducted in Niger, West Africa, in 1994. It was further applied to simulate historical storm events in the Goodwin Creek watershed in Mississippi. Verification and validation indicate that the developed numerical model is capable of simulating hydraulic and hydrological processes in rainfall-generated overland flows over a watershed with natural terrain by considering land use and soil characteristics.