Similarity solutions for overland and stream flows to study watershed runoff

This study investigates the use of similarity profiles for analyzing surface flows-specifically those occurring on overland and stream sections. The spatial behaviour of the flow depth is approximated by a sine function, so that the partial differential equations reduce to ordinary differential equations. Solutions of these reduced equations are obtained at a much smaller computational effort, with analytical solutions available in some cases. These solutions were then extended to study surface water movement over small watersheds. These watersheds can be represented as a sequence of cascading overland flow planes and streams. The performance of the similarity solutions was studied by comparing with results from other physically-based models and experimental observations. It was concluded that the similarity solutions are more robust, and almost as accurate as numerical solutions that are obtained from physically-based models. Good agreement with experimental results was found. The potential application of such solutions for surface flow modeling over watersheds will be discussed.