Approximate analytical solution of the flood routing equation in reservoirs

Flood routing through storage reservoirs is one of the simplest problems of hydrology. However, until now, the equation that describes the phenomenon has no known analytical solution, it is solved by numerical methods. The development of an approximate analytic solution to the problem, which has been reached through a perturbation approach, is presented in this paper General equations for arbitrary inflow hydrographs are shown. The proposed method has been applied to the design flood routing for the El Molinito dam (Sonora. Mexico) with good results. It is concluded that, for practical purposes, a oerturbatory first order solution and even the zero order solution are good approximations to the problem, and that the proposed method could represent the basis for further studies regarding the behavior of dams related to arbitrary inflow hydrographs.