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Open AccessArticle

Case Study: On Objective Functions for the Peak Flow Calibration and for the Representative Parameter Estimation of the Basin

Department of Civil Engineering, Inha University, Incheon 22212, Korea
Department of Land, Water and Environment Research, Korea Institute of Civil Engineering and Building Technolody (KICT), Goyang 10223, Korea
Urban Disaster Prevention & Water Resource Research Center, Korea Research Institute for Human Settlement, Sejong 30147, Korea
Author to whom correspondence should be addressed.
Water 2018, 10(5), 614;
Received: 26 March 2018 / Revised: 24 April 2018 / Accepted: 7 May 2018 / Published: 9 May 2018
(This article belongs to the Section Hydrology)
The objective function is usually used for verification of the optimization process between observed and simulated flows for the parameter estimation of rainfall–runoff model. However, it does not focus on peak flow and on representative parameter for various rain storm events of the basin, but it can estimate the optimal parameters by minimizing the overall error of observed and simulated flows. Therefore, the aim of this study is to suggest the objective functions that can fit peak flow in hydrograph and estimate the representative parameter of the basin for the events. The Streamflow Synthesis And Reservoir Regulation (SSARR) model was employed to perform flood runoff simulation for the Mihocheon stream basin in Geum River, Korea. Optimization was conducted using three calibration methods: genetic algorithm, pattern search, and the Shuffled Complex Evolution method developed at the University of Arizona (SCE-UA). Two objective functions of the Sum of Squared of Residual (SSR) and the Weighted Sum of Squared of Residual (WSSR) suggested in this study for peak flow optimization were applied. Since the parameters estimated using a single rain storm event do not represent the parameters for various rain storms in the basin, we used the representative objective function that can minimize the sum of objective functions of the events. Six rain storm events were used for the parameter estimation. Four events were used for the calibration and the other two for validation; then, the results by SSR and WSSR were compared. Flow runoff simulation was carried out based on the proposed objective functions, and the objective function of WSSR was found to be more useful than that of SSR in the simulation of peak flow runoff. Representative parameters that minimize the objective function for each of the four rain storm events were estimated. The calibrated observed and simulated flow runoff hydrographs obtained from applying the estimated representative parameters to two different rain storm events were better than those retrieved from parameters estimated using a single rain storm event. The results of this study demonstrated that WSSR is adequate in peak flow simulation, that is, the estimation of peak flood runoff. In addition, representative parameters can be applied to a flow runoff simulation for rain storm events that were not involved in parameter estimation. View Full-Text
Keywords: objective functions; SSARR model; pattern search; WSSR; representative parameter objective functions; SSARR model; pattern search; WSSR; representative parameter
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Kim, J.; Kim, D.; Joo, H.; Noh, H.; Lee, J.; Kim, H.S. Case Study: On Objective Functions for the Peak Flow Calibration and for the Representative Parameter Estimation of the Basin. Water 2018, 10, 614.

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