On the diffusion wave model for overland flow: 1. Solution for steep slopes

Abstract

A new solution technique for analyzing the overland flows on lands adjacent to stream networks is presented. Some of the practical short‐comings of the state‐of‐the‐art kinematic wave model are discussed and the more comprehensive diffusion wave model is adopted. As boundary conditions for steep slopes, homogeneous end conditions of zero depth at the upstream and zero‐depth gradient at the downstream are found to represent the physical situation adequately. A weighted residual method is used to develop an approximate solution to the problem. The trial functions are taken to be the spatial eigenfunctions of the corresponding homogeneous problem. It is demonstrated that the resulting approximation converges rapidly and the results agree well with the full Saint Venant solution and the kinematic wave approximation. It is also shown that the numerical solution to the diffusion wave approximation agrees very well with the weighted residual approximation for only a small number of terms. Both the rising and recession phases of the outflow hydrograph have been considered. The approximation can easily accommodate time and space variation in rainfall.