APPROXIMATE ANALYTICAL SOLUTIONS FOR OVERLAND FLOWS

Following the study of Govindaraju et al. (1988), approximate analytical solutions are presented to the diffusion and kinematic wave models subject to space and time‐varying rainfall. An approximation in the form of the first term of an infinite sine series has been considered. This converts the partial differential equation to an ordinary differential equation, and analytical solutions for both rising and recession phases of the hydrograph can be developed. Time variation in rainfall is found to play a key role. Comparisons with full Saint‐Venant solutions, the kinematic wave approximation and experimental results are presented for validating the proposed solution methodology. The one‐term analytical solution is shown to perform well in some cases of physical interest. It is concluded that the analytical solution is useful for estimating runoff from steep overland flow sections. Copyright 1990 by the American Geophysical Union.