A Re-Parameterized and Improved Nonlinear Muskingum Model for Flood Routing

Abstract

The nonlinear form of the Muskingum model has been widely applied to river flood routing. There are four variants of the nonlinear Muskingum model based on alternative formulations of the nonlinear storage equation. This paper proposes a new Muskingum model with an improved, seven-parameter, nonlinear storage equation. The proposed model provides more degrees of freedom in fitting observed hydraulic data than other nonlinear Muskingum models. The proper estimation of the proposed Muskingum nonlinear model’s parameters is essential to achieve accurate flood-routing predictions. This paper introduces a hybrid method for the estimation of Muskingum parameters. The parameter-estimation method combines the shuffled frog leaping algorithm (SFLA) and the Nelder-Mead simplex (NMS). The proposed Muskingum model and parameter estimation method were applied to the routing of several hydrographs. Our results indicate improved performance of the methodology described in this work when compared with those of other Muskingum models.