Parameter Estimation for the Nonlinear Forms of the Muskingum Model

The Muskingum model is one of the most widely used methods adopted for river flood routing. Apart from the conventional linear form, there are three possible nonlinear forms associated with the weighted flow and the storage volume, which are required to be incorporated in the Muskingum model. Comparative evaluation of these nonlinear forms has been carried out in this study. This study is based on the application of Microsoft Excel Solver, which has been used to estimate the optimal values of the model parameters in the nonlinear Muskingum models. The calibrated models have been verified by using two very common benchmark data sets of nonlinear Muskingum channel flood routing from the literature. The comparison between the models calibrated for all the three general nonlinear forms by using two distinct objective functions, namely, sum of squares of deviation (SSQ) and mean absolute relative error (MARE), in nonlinear optimization has been presented. Sensitivity analysis for different initial values for the model parameters has also been carried out for the optimization. From this study, it is found that the first form of nonlinear Muskingum model provided better results. Existing literature shows more focus on the use of this form of nonlinear Muskingum model and less consideration for the other two nonlinear forms. This may have been due to higher degree of nonlinearity involved in the other two nonlinear forms, which increases the complexity of obtaining optimal solutions and also requires more computational time. This paper presents a broad comparison of all three nonlinear forms of Muskingum models with respect to the efficiencies of the models to generate desired optimal solutions.