Volume Conservation Controversy of the Variable Parameter Muskingum–Cunge Method

Abstract

The study analyzes the volume conservation problem of the variable parameter Muskingum-Cunge VPMC method for which some remedial solutions have been advocated in recent literature. The limitation of the VPMC method to conserve volume is brought out by conducting a total of 6,400 routing experiments. These experiments consist of routing a set of given hypothetical discharge hydro- graphs for a specified reach length in uniform rectangular and trapezoidal channels using the VPMC method, and comparing the routed solutions with the corresponding benchmark solutions obtained using the full Saint-Venant equations. The study consisted of 3,200 routing experiments carried out each in uniform rectangular and trapezoidal channel reaches. Each experiment was characterized by a unique set of channel bed slope, Manning's roughness coefficient, peak discharge, inflow hydrograph shape factor, and time to peak. A parallel study was carried out using an alternate physically based variable parameter Muskingum discharge hydrograph VPMD routing method proposed by Perumal in 1994 under the same routing conditions, and the ability of both the VPMC and VPMD methods to reproduce the benchmark solutions was studied. It is brought out that within its applicability limits, the VPMD method is able to conserve mass more accurately than the VPMC method. The reason for the better performance of the former over the latter method is attributed to the physical basis of its development. It is argued that adoption of artificial remedial measures to overcome the volume conservation problem makes the VPMC method semiempirical in nature, thereby losing the fully physically based characteristics of the method. The paper also dwells on the problems of negative initial outflow or dip in the beginning of the Muskingum solution, and the negative value of the Muskingum weighting parameter. Besides, the effect of incorporating the inertial terms in the estimation of Muskingum parameters and their impact on the overall Muskingum routing solutions is addressed by conducting another set of 6,400 numerical experiments using both the VPMC and VPMD methods.