Case Study Bivariate Seasonal Design Flood Estimation Based on Copulas Jiabo Yin 1 ; Shenglian Guo 2 ; Zhangjun Liu 3 ; Kebing Chen 4 ; Fi-John Chang 5 ; and Feng Xiong 6 Abstract: Seasonal design floods reflecting seasonal variation information are very important for reservoir operation and management. The seasonal design flood estimation method currently used in China is based on univariate frequency analysis and assumes that the seasonal and annual design frequencies are equal, which neither satisfies flood prevention standards nor considers the interdependence between different seasonal floods. The Danjiangkou reservoir located in the Han River basin, the first pilot basin of most regulated water resources management policy in China, was selected as a case study. After dividing the entire flood season into subseasons, a dependent structure of summer and autumn floods was established by copula functions. Three bivariate flood quantile selection methods, namely the equivalent frequency combination (EFC) method, conditional expectation combination (CEC) method, and conditional most likely combination (CMLC) method, were performed to estimate unique seasonal design floods to meet the needs in engineering and compared with the univariate design values. The evaluation criteria and a boundary identification method were used to assess the rationality of these combination methods. Compared with the CEC and EFC methods, the CMLC method has smaller root-mean square error (RMSE) and bias values by 12.9–34.8% and 22.6–36.4%, respectively. The CMLC and EFC methods are within the feasible regions, whereas the CEC estimators are beyond the feasible range. The results of economic analysis show that the CMLC method can enhance the floodwater use rate from 79.7 to 82.8% for the wet year and from 91.8 to 93.7% for the dry year in comparison with the EFC method. The CMLC method is more rational in physical realism and recommended for estimating seasonal design floods in the Danjiangkou reservoir, which would provide rich information as references for flood risk assessment, reservoir scheduling, and management. DOI: 10.1061/(ASCE)HE.1943-5584.0001594. © 2017 American Society of Civil Engineers. Author keywords: Seasonal design flood; Reservoir operation; Bivariate analysis; Feasible region; Copula functions. Introduction Floods are among the most frequent and costliest natural disasters in terms of human hardship and economic loss. More than 90% of the damage related to all natural disasters is caused by floods and associated debris flows (Chen et al. 2015). Reservoirs are one of the most efficient key infrastructure components in flood control, water allocation, and other relevant water resources management activ- ities (Yoon et al. 2016). According to the World Commission on Dams (WCD 2000), most large reservoir projects worldwide are failing to produce the level of benefits that provided the economic justification for their development. Currently, with the rapid devel- opment of the social economy and water demands, the water resources shortage problem has deteriorated, and the function of reservoirs in terms of flood water use has become increasingly important in China (Ouyang et al. 2015). According to the Chinese Flood Control Act, the water level of a reservoir should not be kept higher than the flood limiting water level (FLWL) during the flood season to provide adequate storage for flood prevention. The conventional FLWL is determined by the reservoir routing of the annual design flood hydrographs. However, the design flood, based on the annual maximum flood series, ne- glects flood seasonality, and the conventional FLWL is often fixed during the whole flood season. This results in overdimensioning for flood prevention and waste of floodwater in most years (Chen et al. 2010). For floodwater use, it is very valuable to use seasonal flood information in flood frequency analysis so as to operate the reser- voir more effectively during flood season without increasing the flood risk (Zhang et al. 2016). Because of flood seasonality, the entire flood season could be divided into several subseasons, such as two subseasons, namely summer flood season and autumn flood season (Chen et al. 2015; Jiang et al. 2015). In each subseason, a different reservoir operation policy, i.e., different FLWLs, can be used to obtain more economic benefits without decreasing flood prevention standards. This approach has been implemented for the improvement of flood use in many counties, such as China (MWR 2006; Tan et al. 2017), the United States (USACE 1998), Vietnam (Ngo et al. 2007), and so on. There are several approaches being used to divide entire the flood season into multiple flood subseasons. One method is based on different meteorological and climate phenomena that generate 1 Ph.D. Candidate, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China. E-mail: jboyn@whu.edu.cn 2 Professor, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China (corresponding author). E-mail: slguo@whu.edu.cn 3 Ph.D. Candidate, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China. E-mail: liuzhangjun@whu.edu.cn 4 Ph.D. Candidate, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China. E-mail: chenkb@whu.edu.cn 5 Professor, Dept. of Bioenvironmental Systems Engineering, National Taiwan Univ., Taipei 10617, Taiwan, ROC. E-mail: changfj@ntu.edu.tw 6 Ph.D. Candidate, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China. E-mail: fxiong07@whu.edu.cn Note. This manuscript was submitted on April 10, 2017; approved on June 13, 2017; published online on October 14, 2017. Discussion period open until March 14, 2018; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydrologic Engineering, © ASCE, ISSN 1084-0699. © ASCE 05017028-1 J. Hydrol. Eng. J. Hydrol. Eng., 2017, 22(12): 05017028 Downloaded from ascelibrary.org by NTU on 01/09/18. Copyright ASCE. For personal use only; all rights reserved.