Comparative evaluation of two physically-based mass conservative variable parameter Muskingum models

The comparative performances of two variable parameter Muskingum flood routing models are evaluated in this study from the perspective of overall reproduction of the routed flood hydrographs characterized by different magnitudes of attenuation of the routed benchmark hydrographs. These two models are the Variable Parameter Muskingum-Cunge-Todini (MCT) model advocated by Todini in 2007, and the Variable Parameter McCarthy-Muskingum (VPMM) model advocated by Perumal and Price in 2013. To investigate this objective, routing studies were undertaken by routing a given hypothetical inflow hydrograph in 25 hypothetical trapezoidal channel reaches of the same geometrical size, but each characterized by different unique combinations of channel bed slopes and Manning’s roughness coefficients. The study results demonstrate that the VPMM model is capable of better reproduction of different levels of attenuation of the routed benchmark hydrographs in small bed slope channels in comparison with that of the MCT model. However, for steep and very steep bed slope channels, where the attenuation is small or insignificant, both the VPMM and MCT models perform equally well due to the reason that the latter model is a specific case of the former model. The study concludes that the application of the VPMM model is more suitable for field routing studies than the MCT model, when the magnitude of the water surface gradient of the inflow hydrograph is characterized by an absolute magnitude of (1/S₀) ∂y/∂x where, S₀ and ∂y/∂x are, respectively, the bed slope of the channel and the relative water surface gradient of the inflow hydrograph. The added advantage of employing the VPMM model is that it has the capability of estimating the stage hydrograph at the end of the routing reach or sub-reaches corresponding to the routed discharge hydrograph in a manner consistent with the numerical solution approach of the full Saint- Venant equations.