Modeling Looped Ratings in Muskingum-Cunge Routing

The Muskingum-Cunge flood routing model is extended to the realm of looped ratings. This is accomplished by reformulating the conventional four-point model to use the local water surface slope and the Vedernikov number in the expression for hydraulic diffusivity. The developed model was successful in generating looped ratings under a wide range of kinematic/diffusive unsteady flow conditions. Numerical experiments were used to test the looped-rating Muskingum-Cunge model. Resolution level, flood wave period, baseflow, and peak-inflow baseflow ratio were varied to determine loop thickness and percentage mass conservation. Comparison of the looped-rating Muskingum-Cunge model with a dynamic wave model (a complete solution of the St. Venant equations) showed that both models are capable of generating looped ratings and outflow hydrographs of comparable accuracy.