Reply to discussion of “application of excel solver for parameter estimation of the nonlinear Muskingum models” by Ali R. Vatankhah

Flood routing is a mathematical procedure in order to predict the variation of the magnitude of a flood wave when it propagates along natural rivers or artificial channels. The accuracy of flood routing is an important subject for research in the hydrology and hydraulics. This study focuses on the effects of the numerical solution method and the nonlinear storage equation of the Muskingum flood routing procedure. The simulation results indicate that the Tung’s method has better results (up to 41.26–79.47% for the different nonlinear storage equations) than the Fourth-Order Runge-Kutta method. Therefore, the Tung’s method is more accurate than the other method. Furthermore, based on the previous studies, the Tung’s method has satisfactory results in the field conditions in both calibration and verification steps. On the other hand, the proposed five-parameter nonlinear storage equation improves fitting to the outflow data by 85.21% than the three-parameter equation.