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The nonlinear Muskingum model is a hydrologic flood-routing method useful when the storage flow relation departs from the classic linear assumption. This paper extends versions of the nonlinear Muskingum model by introducing a parameterized initial storage condition. The extended nonlinear Muskingum values have an increased number of degrees of freedom that allows an enhanced capacity to accurately predict outflow hydrographs provided that parameter estimation is optimized as proposed in this work. The parameters of the nonlinear Muskingum models are estimated with the weed optimization algorithm (WOA), and the excellent performance of the extended nonlinear Muskingum models is demonstrated with several types of hydrographs using several criteria of statistical efficiency. The implementation results show that the nonlinear Muskingum model’s predictions outperform those of the best results …