Volume conservation in variable parameter Muskingum-Cunge method

The simple Variable Parameter Muskingum-Cunge (VPMC) method is still frequently used for flood routing. However, difficulties arise in the selection of an appropriate "reference" discharge for evaluating the routing parameters and in the small volume loss that can occur. Several commonly used schemes for the VPMC method are compared through a series of numerical experiments that cover different channel bed slopes and different space/time steps. The tests show that 4-point schemes are better than 3-point schemes, that a certain amount of volume loss (up to 8%) still occurs in all schemes, and that an empirical relationship exists between the volume loss and channel bed slope (S). A new scheme for the VPMC method is presented, with the routing parameters (c and D) being modified to take into account the longitudinal hydrostatic pressure gradient term. This scheme improves the routed hydrographs, not only with regard to the sensitivity of the outflow peak for given space and time steps, but also with regard to volume loss, typically less than 0.5% even for a channel with S = 0.0001.