Improved four-point solution of the kinematic equations

Abstract

In finite difference solutions of the kinematic equations for overland flow, uncontrolled numerical diffusion can be introduced into a system by the finite difference scheme. A formulation for overland flow based on the Muskingum-Cunge routing procedure [4] incorporating a four-point numerical scheme is described and the results of numerical experiments are presented, comparing the method with other kinematic routing methods. The experiments verify the dependence of kinematic routing accuracy on grid spacing and on the position of the space derivative, and show that the Muskingum-Cunge results are independent of grid spacing. By comparing the conventional kinematic routing formulation with the Muskingum-Cunge formulation, it is shown that a centred scheme is the most appropriate for overland flow routing if a fixed grid formulation of the kinematic equations is employed.