Use of similarity profiles for computing surface runoff over small watersheds

This study investigated the use of similarity profiles in space for analyzing surface-runoff hydrographs occurring at the outlet of small watersheds. The spatial behavior of the flow depth over each element (overland region or stream reach) was approximated by a sine function, so that the partial differential equations governing water movement were reduced to ordinary differential equations. Solutions of these reduced equations were obtained at a smaller computational cost, with analytical solutions available in some cases. These solutions then were extended to study surface water movement over small watersheds that could be represented as a sequence of cascading overland flow planes and streams. The performance of this model was studied by comparing with results from another physically based model, KINEROS, and experimental observations. It was concluded that the similarity solutions are robust and almost as accurate as numerical solutions that were obtained from physically based models, when used within their range of applicability explicitly defined in the paper. Some guidelines for spatial discretization of the watershed for appropriate use of the similarity solutions have been provided.