A fully mass conservative variable parameter McCarthy-Muskingum method: Theory and verification

摘要

This paper presents the hydraulic derivation of a fully mass conservative, variable parameter McCarthy-Muskingum (VPMM) method derived directly from the Saint-Venant equations for routing flood waves in prismatic channels having any cross-section shape, and using the Manning's friction law. The approach employed in the development of the method theoretically justifies the heuristic assumption made by McCarthy in 1938 in expressing the channel reach storage of the Muskingum method in terms of prism and wedge storages. The approach advocated in this paper also provides a solution to the mass conservation problem associated with the variable parameter Muskingum routing method, which has been a major issue in the hydrological literature for the last three decades. Moreover, the VPMM method enables the simultaneous computation of the stage hydrograph corresponding to a given inflow or routed discharge hydrograph. The verification of the methodology and the evaluation of its performance in routing floods in three different shapes of a hypothetical channels are presented by reproducing the corresponding numerical solutions of the Saint-Venant equations. The results are also compared with the corresponding results of the mass conservative variable parameter Muskingum-Cunge-Todini method proposed by Todini in 2007 with and without the inclusion of the correction introduced by Cappelaere in 1997 for diffusion.