Parameter Estimation of Nonlinear Muskingum Models Using Nelder-Mead Simplex Algorithm

Abstract

The linear form of the Muskingum model has been widely applied to river flood routing. However, a nonlinear relationship between weighted-flow and storage volume exists in most rivers, making the use of the linear Muskingum model inappropriate. On the other hand, the application of the nonlinear Muskingum model suffers from hydrologic parameters estimation. The current study aims at presenting the objective approach of the Nelder-Mead simplex (NMS) algorithm for the purpose of estimating the parameters of the nonlinear Muskingum model. The performance of this algorithm is compared with other reported parameter estimation techniques together with a historical example. Results of the implementation of this procedure indicate that the NMS algorithm is efficient for the estimating parameters of the nonlinear Muskingum models. This algorithm is easy to be programmed, and it is quite efficient for finding an optimal solution very quickly. Although this technique requires an initial guess for the parameter estimation, results of the sensitivity analysis of the initial parameter values showed that in 84.8% of the cases, the optimum or near-optimum results are achieved.