AN APPROXIMATE PHYSICALLY BASED DIFFUSIVE WAVE CHANNEL ROUTING METHOD

Abstract

The present study aims to develop a simplified channel routing method based on the approximate diffusive wave equation for routing flood waves in different prismatic channels. This method is derived directly from the diffusive wave equation developed from the Saint-Venant equations without considering lateral inflow. To evaluate the routing capabilities of the developed method, a set of 25 types of channels with each set of channels characterized by trapezoidal, rectangular and triangular channel sections and each of these channels characterized by a unique slope selected from the range of So = 0.0001 to 0.002 and a unique roughness coefficient selected from the range of n0.01 to 0.06 are used for routing a given hypothetical inflow hydrograph using the proposed method. The benchmark solutions required for comparative evaluation of the proposed routing method were obtained using the well known software package HEC-RAS (version 4.1). The routed discharge hydrographs and the corresponding estimated stage hydrographs arrived at using the proposed method are compared with the respective benchmark solutions based on the reproduction of some pertinent characteristics of the benchmark discharge and stage hydrographs using appropriate evaluation measures. The solutions of the proposed method are also compared with the Variable Parameter McCarthy-Muskingum (VPMM) method proposed by Pérumal and Price (2013) and the Variable Parameter Muskingum-Cunge-Todini method proposed by Todini (2007) with and without considering the diffusion coefficient correction introduced by Cappelacre in 1997.It was concluded by Todini (2007) that the MCTc method has better accuracy in routing a given discharge hydrograph than the MCT method. It is inferred from the study that the proposed method has the same order of accuracy as that of the VPMM and MCTc methods in reproducing the benchmark discharge and stage hydrographs. This method is fully mass conservative