Two new mathematical forms of the nonlinear Muskingum model called NL4 and NL5, involving four and five parameters, respectively, can be used in river flood routing. The accuracy of the estimation of the Muskingum model parameters is essential for flood routing. This paper proposes a novel hybrid algorithm, based on the shuffled frog leaping algorithm (SFLA) and Nelder-Mead simplex (NMS), for the estimation of parameters of two new nonlinear Muskingum models. The proposed methodology is applied by considering minimization of the sum of the square deviation (SSD) between observed and routed outflows in (1) experimental, (2) real, and (3) multimodal examples. Results show that the SSD is 0.91, 3.97, and 4.44% smaller (better) than pertinent values obtained by the genetic algorithmgeneralized reduced gradient (GA-GRG) method in experimental, real, and multimodal examples, respectively.

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This paper introduces a hybrid non-linear Muskingum model for flood routing. The proposed hybrid model has more degrees of freedom for fitting observed data than other non-linear Muskingum models. The main goal of this work is to develop a comprehensive model for outflow routing. The proposed hybrid model's predictive skill is evaluated with experimental, real and multimodal hydrograph-routing problems. The results confirm the predictive skill of the hybrid model based on the minimisation of the sum of the square deviation (SSD) between observed and routed outflows, the sum of the absolute value of the deviations (SAD) between the observed outflow and the computed outflow, and the deviations between the peak of the routed and actual outflows (DPO). Results from this study show the hybrid model improved the SSD by 79, 15 and 5%, SAD by 50, 2 and 5%, and the DPO by 77, 4 and 34% compared with the best alternative Muskingum model in solving the experimental, real and multimodal example problems, respectively.