Variable parameter Muskingum-Cunge method for flood routing in a compound channel

Abstract

This paper investigates the properties of the Variable Parameter Muskingum-Cunge method (VPMC) for flood routing, using several hypothetical flood hydrographs in a prismatic compound channel with significant floodplains. Two variants of the VPMC method (MVPMC3, VPMC4-1) are tested and these tests show that VPMC4-1 is relatively better. However, both schemes still suffer, to different degree, a loss of outflow volume which depends on bed slope and roughness of the floodplains. Furthermore, a well-known initial leading edge 'dip' occurs under certain conditions, and a less well-known phenomenon, referred to as trailing edge 'oscillations', is found to occur on the recession stage of the outflow hydrograph in steep channels. These oscillations become more serious as the roughness of the floodplains increases, but gradually disappear with decreasing bed slope. These oscillations are a consequence of the variation in the convective wave speed in a compound channel and have, to the Authors' knowledge, not been reported before in the literature on flood routing. A condition for selecting appropriate space and time steps in order to eliminate both 'dip' and 'oscillations' is obtained. A scheme with the routing parameters (c and D) modified to take account for the effect of the longitudinal hydrostatic pressure term is compared with an earlier VPMC method and shown to exhibit an improvement in terms of volume loss. Two empirical relationships to estimate the percentage of volume loss for a given bed slope are presented. Finally, different approaches for predicting the c∼Q relationship in the VPMC method are shown to have some effect on the outflow hydrographs, particularly for compound channels with mild bed slopes.