Discussion of “Estimation of Nonlinear Muskingum Model Parameter Using Differential Evolution” by Dong-Mei Xu, Lin Qiu, and Shou-Yu Chen

Abstract

The discussers appreciate the authors and their valuable study, but consider it necessary to clarify the several issues to prevent misunderstandings and wrong evaluations regarding the application of the differential evolution (DE) method to the nonlinear Muskingum model. The authors state that they applied the procedure given in Geem (2006) as a routing algorithm. However, although the χ, m, and SSQ values that the authors obtained conform to the results of the study given in literature, the K parameter is considerably different. The routing procedure proposed in Tung (1985) and Geem (2006), also used by the authors, were coded in a Matlab environment by the discussers. When the parameters that the authors give as an optimum solution (K 1⁄4 0.5175, χ 1⁄4 0.2869, m 1⁄4 1.8680) were placed in this code, the values given in Table 1 were obtained. It is necessary to state that unit time was used in the routing procedure proposed in Tung (1985) and Geem (2006), and this situation was explained in the related references (Geem 2011; Karahan et al. 2013). The authors stated that they used the routing procedure proposed in Geem (2006) in their studies. In this case, as shown in the fourth column of Table 1, outflow values calculated forΔt 1⁄4 1 h are so different than the measured values that the measured SSQ value becomes 19956.4461. Outflow values given by the authors are only obtained for Δt 1⁄4 6 h; this value was calculated by the discussers and presented in the last column of Table 1. If the authors, as they state, have exactly followed routing procedure proposed in Geem (2006), like other parameters for the same objective function, the K parameter should conform to the values given in literature. This situation has to be clarified. Generally, the selection of the solution space of the parameters in optimization problems plays an important role with respect to solution quality. If the approximate solutions of these parameters are known a priori, then an optimal parameter value can easily be determined by using any heuristic or gradient-based method (Karahan 2013). Input and output hydrograph values are used to determine nonlinear Muskingum model parameters. Wilson data (Wilson 1974), which was used for test purposes in this study, was also used by many researchers in the literature and is a problem whose solution space was known formerly. The parameter space used for Wilson data in literature is generally K 1⁄4 0–0.20, χ 1⁄4 0.2–0.3 and m 1⁄4 1.5–2.5 (Kim et al. 2001). The authors did not explain which range they selected as parameter space in the paper. This is a significant absence in terms of testing analysis. Since there is no information about this subject in the paper, random solution vectors of the same number as the population number (NP 1⁄4 30) that the authors used were produced by using the solution space given above and presented in Table 2. Let r1, r2, and r3 values be randomly chosen as 5, 9, and 21, respectively. In this case, the obtained trial vector is (0.0993039, 0.314946, 1.374150) in the mutation step. The output hydrograph corresponding to this vector is given in Table 3. As seen in Table 3, output hydrograph values in between 84–126 hours are complex numbers and meaningless in a physical sense. SSQ value for the stated output hydrograph is −3.73Eþ 05-ð2.58Eþ 05Þi. The calculated SSQ value is also a complex number, which results in preventing the application of the selection operator of the DE algorithm and the collapse of the optimization algorithm. Routing procedure that will be applied for the application of the DE in determination of nonlinear Muskingum parameters must be different than the one given in the paper—or, to apply the given procedure, it is necessary to know the solution previously and to search it in a narrow range around the optimum solution. Undoubtedly, if the solution is known formerly, an optimization process is not required. Therefore, the authors must clearly state the routing procedure they followed and the parameter space they used. The discussers downloaded differential evolution (DE) code (Price and Storn 2012) and determined nonlinear Muskingum model parameters for three different solution spaces given in Table 4 by using the routing procedure given in Geem (2006). All calculations were repeated 1,000 times in order to reduce to a minimum level the dependence of the used algorithm on the initial values, and analyses results were summarized in Table 5 and Table 6. The global solution, near-global solution, and unfeasible solution expressed in Table 5 and Table 6 show the values of SSQ 1⁄4 36.7679, SSQ 1⁄4 36.7680, and SSQ > 36.7680, respectively. Table 1. Computed Outflow Values