Issues in optimal parameter estimation for the nonlinear Muskingum flood routing model

This study answers two questions raised in the parameter estimation optimization for the nonlinear Muskingum flood routing model. The first question is whether a new global optimum was still found after the existing global optimum had already been found. In order to fairly verify this question, a standard routing procedure for the nonlinear Muskingum model, which has not been clearly described previously, is proposed. Because the routing procedure was coded in a spreadsheet, any researcher can easily test it after downloading it. The second question is the reason why various approaches, such as Lagrange multiplier, Broyden–Fletcher–Goldfarb–Shanno (BFGS), genetic algorithm, harmony search and particle swarm optimization, have tackled only Wilson's data set as the parameter estimation optimization for the nonlinear Muskingum model, because Wilson's data have a unique structure which is differentiated from other data sets. This study also provides various data sets to compare.