Comparison of VPMM, VPMC and Multilinear Muskingum Method Applied to Compound Channels

Abstract

The VPMM (Variable parameter McCarthy Muskingum) model is derived directly from the Saint Venant equations applied to a gradually varied 1-D unsteady flow in rigid bed channels without considering lateral inflow or outflow. In the VPMM method, the model parameters are determined from the flow and channel characteristics which changes at every time step. The Muskingum-Cunge is a viable alternative to the classical Muskingum method, particularly for the cases where hydrologic data (i.e. streamflow data) are not available, but where hydraulic data (cross-sectional data and channel slopes) can be readily ascertained. The Muskingum-Cunge method matches the numerical diffusion of the discrete model with the physical diffusion of the analytical model. Variable parameter Muskingum-Cunge (VPMC) method and its modified versions conserve more mass than the classical Muskingum-Cunge method. Multilinear Muskingum method is based on time distribution scheme. The methods are being reviewed with varying parameters at each routing time step unlike the then existing multilinear models. The paper reviews VPMM, VPMC and Multilinear Muskingum method, and their applications to some study areas, with their applicability conditions. The study concludes by analyzing their improvements and modifications to the existing models.