KSCE Journal of Civil Engineering (0000) 00(0):1-2 Copyright ⓒ2014 Korean Society of Civil Engineers DOI 10.1007/s12205-014-1566-z  1  pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205 Water Engineering Reply to Discussion of “Application of Excel Solver for Parameter Estimation of the Nonlinear Muskingum Models” by Farzan Hamedi*, Omid Bozorg Haddad**, and Hosein Orouji*** Reza Barati**** Received October 4, 2013/Accepted January 16, 2014/Published Online July 7, 2014 First of all, the author thanks the respected discussers for the useful comments on the original paper. However, the following clarifications and responses are necessary. As mentioned at the end of “Results and Discussion” section of the original paper, the main object of the original study was the evaluation of the Excel solver as efficient, simple and convenient tool for parameter calibration of the nonlinear Muskingum model through the benchmark problem of Wilson (1974). In other words, the original paper focuses on the hydrologic parameters calibration of the of the Muskingum flood routing model. Therefore, the same numerical solution method was used to compare the results with other parameter estimation algorithms. Based on the results of the original paper, the Excel solver was a promising approach to reduce problems of the parameter calibration of the nonlinear Muskingum routing procedure. The discussers claimed that an improved version of Tung’s (1985) method can be considered by changing the initial condition of the traditional numerical solution procedure. They considered initial outflow (i.e., initial condition of the numerical method) as a fraction of initial inflow. However, this modification is not a part of the numerical method. The Muskingum flood routing problems have some input data such as time step, initial condition and inflow hydrograph (i.e., boundary condition). Obviously, all of the input data have significant effects on the numerical solution, and changing each of them alter the output results (i.e., outflow hydrograph). Therefore, it can be said that the initial condition (i.e., initial outflow) is a part of the input data for the numerical solution. Generally, initial conditions are established by specifying a base flow within the channel at the start of the simulation (US Army Corps of Engineers, 1994). It should be noted that the base flow is the magnitude of the flow discharge under normal condition before the flood event occurs in the river basin. Although there are several approaches for the determination of the base flow, it is common for the calibration of the hydrologic parameters to assume the initial outflow as same as either initial observed inflow or initial observed outflow (Cudworth, 1989; Viessman and Lewis, 2003; Samani and Shamsipour, 2004; Raghunath, 2006; Elbashir, 2011; Barati, 2013a, 2013b; Geem, 2013; Barati et al., 2013). About this issue, Chow (1959) mentioned that if the value of the initial outflow at the beginning of the first routing period is assumed, the error involved in assuming the value will not be magnified enough to produce appreciable effect on the result. On the other hand, the assumption of the initial conditions is a common way in other flood routing procedures such as other lumped approaches (e.g., Convex, Modified Att-Kin and Working Values models), the distributed approaches (e.g., dynamic wave, diffusion wave and kinematic wave models), and the semi- distributed approaches (e.g., Muskingum-Cunge family models). It is informative to express that initial conditions are related to natural conditions of river basins. For example, for a flood event induced by dam failure, or a sudden opening of a sluice gate in a flood detention basin, a shock wave usually forms and then pro- pagates forward on an initially dry bed (Xia et al., 2010). Therefore, the natural conditions of each case study must be considered to determine the initial conditions. The traditional Tung’s method had satisfactory results for the field conditions in both calibration and verification steps (Barati, 2010). However, the alternative procedure for estimating initial outflow which proposed by the discussers was only examined in the calibration procedure. Therefore, the different procedures of estimating initial conditions must be challenged in the field con- ditions by considering the calibration and verification steps. In the discussion, the hybrid of Shuffled Frog Leaping Algorithm (SFLA) and gEneralized Reduced Gradient (GRG) was used as an alternative way to optimize the hydrologic parameters of the *Discusser: Hamedi, F., PM.Sc. Student, Department of Irrigation & Reclamation Engineering, Faculty of Agricultural Engineering & Technology, Col- lege of Agriculture & Natural Resources, University of Tehran, Karaj, Tehran, Iran (E-mail Hamedi.f@ut.ac.ir) **Discusser: Haddad, O. B., Associate Professor, Department of Irrigation & Reclamation Engineering, Faculty of Agricultural Engineering & Technol- ogy, College of Agriculture & Natural Resources, University of Tehran, Karaj, Tehran, Iran (E-mail: OBHaddad@ut.ac.ir) ***Discusser: Oruji, H., M.Sc. Graduate of Water Resources Engineering, Department of Irrigation & Reclamation Engineering, Faculty of Agricultural Engineering & Technology, College of Agriculture & Natural Resources, University of Tehran, Karaj, Tehran, Iran (E-mail: Orojih@ut.ac.ir) ****Author: Barati, R. (2013), KSCE J. Civ. Eng., Vol. 17, No. 5, pp. 1139-1148, DOI 10.1007/s12205-013-0037-2/P.G. Researcher, Young Researchers Club and Elites, Mashhad Branch, Islamic Azad University, Mashhad 9187147578, Iran (E-mail: r88barati@gmail.com) Discussion & Replies