Discussion of “application of excel solver for parameter estimation of the nonlinear Muskingum models” by Reza Barati

Abstract

An accurate solution method is essential to the calibration of the nonlinear Muskingum model. Most of the earlier researchers have used inaccurate Euler’s solution method which is manipulated to get a better fit for observed Wilson’s data (1974). Euler’s method which is adopted by most previous researchers is not very accurate and results in unsuitable simulation based on the nonlinear Muskingum model as shown in this discussion. This study proposes fourth-order Runge-Kutta method as a suitable and accurate solution method for simulation stage. When more accuracy is needed, the structure of the Muskingum model can be modified to produce more degree of freedom in model calibration procedure. For this purpose, a new five-parameter nonlinear Muskingum model is proposed. The proposed model is easy to formulate and use. The results show that the improvement in the fit of the proposed nonlinear Muskingum model is substantial.