Kinematic Wave Theory of Overland Flow
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© 2017, Springer Science+Business Media Dordrecht. Kinematic wave (KW) theory is widely applied for modeling overland flow. The theory is comprised of (1) continuous waves, (2) formation of shocks, and (3) propagation of shocks. This paper revisits the KW concept for overland flow from fluid mechanical and mathematical points of view. Then, it develops mathematical formulations of overland flow, based on the classification of overland flow problems and the influence of storm movement and areal coverage. Depending on the class of overland flow problems, the mathematical formulation involves free boundary problems that are not known beforehand and must be solved for along with the solution of the problem. Finally, the validity of the KW concept is revisited and the accuracy of the KW approximation can be expressed by Riccati equation that describes the error for the whole hydrograph.
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