基于Copula函数的大坝洪水漫顶风险率计算
|
摘要
洪水漫顶风险率分析计算对于大坝风险管理具有重要意义。本文基于Copula函数计算大坝洪水漫顶风险率,并分析不同Copula函数及峰量相关性对漫顶风险率的影响。清江流域隔河岩水库实例表明:最优的Gumbel Hougaard Copula函数能较好地描述洪峰、洪量的上尾相关性,计算的洪水漫顶风险率为3.79×10~(-5),而Frank和Clayton Copula函数得到的风险率明显偏低。随着洪峰、洪量相关系数的增加,洪水漫顶风险率也增加。假设峰量相互独立的情况下洪水漫顶风险率被低估,而完全相关的情况下则被高估。基于Copula函数的两变量统计方法能够有效捕捉洪峰、洪量的实际相关关系,得到的风险率更加合理,为大坝洪水漫顶风险率分析提供科学依据。
Flood overtopping risk rate is a key factor in reservoir operation and dam safety management.This paper estimates this factor based on Copula functions and analyzes its dependency on the selection of these functions and the correlation between flood peak and volume. We apply the Gumbel-Hougaard Copula function to an analysis of the Geheyan reservoir in the Qing River basin, and demonstrate that its optimal form can better describe the upper tail dependence between flood peak and flood volume, while the Frank and Clayton Copula functions underestimate the risk rate significantly. For this reservoir, the estimated flood overtopping risk rate is 3.79×10~(-5), but it increases as the correlation between flood peak and volume increases. In the cases of full correlation it is overestimated while underestimated in the independence cases. Our bivariate statistical approach based on Copula functions, through effectively capturing the dependence between flood peak and volume, improves the estimation of overtopping risk rate and would be useful for overtopping risk analysis.
Flood overtopping risk rate is a key factor in reservoir operation and dam safety management.This paper estimates this factor based on Copula functions and analyzes its dependency on the selection of these functions and the correlation between flood peak and volume. We apply the Gumbel-Hougaard Copula function to an analysis of the Geheyan reservoir in the Qing River basin, and demonstrate that its optimal form can better describe the upper tail dependence between flood peak and flood volume, while the Frank and Clayton Copula functions underestimate the risk rate significantly. For this reservoir, the estimated flood overtopping risk rate is 3.79×10~(-5), but it increases as the correlation between flood peak and volume increases. In the cases of full correlation it is overestimated while underestimated in the independence cases. Our bivariate statistical approach based on Copula functions, through effectively capturing the dependence between flood peak and volume, improves the estimation of overtopping risk rate and would be useful for overtopping risk analysis.
引文
[1]王栋,朱元甡.防洪系统风险分析的研究评述[J].水文,2003,23(2):15-20.WANG Dong,ZHU Yuansheng.Discussion on state-ofthe-art of risk analysis in flood control system[J].Hydrology,2003,23(2):15-20.(in Chinese)
[2]李爱花,刘恒,耿雷华,等.水利工程风险分析研究现状综述[J].水科学进展,2009,20(3):453-459.LI Aihua,LIU Heng,GENG Leihua,et al.Review of risk analysis of hydraulic engineering system[J].Advances in Water Science,2009,20(3):453-459.(in Chinese)
[3]VOLPI E,FIORI A.Hydraulic structures subject to bivariate hydrological loads:Return period,design,and risk assessment[J].Water Resources Research,2014,50(2):885-897.
[4]CHENG S T,YEN B C,TANG W H.Overtopping risk for an existing dam[R].Champaign:University of Illinois at Urbana-Champaign,1982.
[5]梅亚东,谈广鸣.大坝防洪安全的风险分析[J].武汉大学学报(工学版),2002,35(6):11-15.MEI Yadong,TAN Guangming.Risk analysis for flood prevention and safety of dam[J].Engineering Journal of Wuhan University,2002,35(6):11-15.(in Chinese)
[6]肖义,郭生练,雒征,等.大坝防洪安全风险率的计算方法[J].武汉大学学报(工学版),2005,38(3):10-13.XIAO Yi,GUO Shenglian,LUO Zheng,et al.Estimation of hydrological risk rate for dams[J].Engineering Journal of Wuhan University,2005,38(3):10-13.(in Chinese)
[7]KWON H H,MOON Y I.Improvement of overtopping risk evaluations using probabilistic concepts for existing dams[J].Stochastic Environmental Research and Risk Assessment,2006,20(4):223-237.
[8]李清富,龙少江.大坝洪水漫顶风险评估[J].水力发电,2006,32(7):20-22.LI Qingfu,LONG Shaojiang.Risk assessment of dam overtopping[J].Water Power,2006,32(7):20-22.(in Chinese)
[9]KUO J T,YEN B C,HSU Y C,et al.Risk analysis for dam overtopping:Feitsui Reservoir as a case study[J].Journal of Hydraulic Engineering,2007,133(8):955-963.
[10]莫崇勋,董增川,麻荣永,等.“积分-一次二阶矩法”在广西澄碧河水库漫坝风险分析中的应用研究[J].水力发电学报,2008,27(2):44-49.MO Chongxun,DONG Zengchuan,MA Rongyong,et al.Application study on overtopping risk analysis for Guangxi Chengbihe reservoir by Integrate-FOSM method[J].Journal of Hydroelectric Engineering,2008,27(2):44-49.(in Chinese)
[11]余雷,伍春平,兰盈盈.柘林水库大坝防洪安全风险分析[J].人民长江,2009,40(17):33-35.YU Lei,WU Chunping,LAN Yingying.Risk analysis of dam flood control safety of Zhelin Reservoir[J].Yangtze River,2009,40(17):33-35.(in Chinese)
[12]HSU Y C,TUNG Y K,KUO J T.Evaluation of dam overtopping probability induced by flood and wind[J].Stochastic Environmental Research and Risk Assessment,2011,25(1):35-49.
[13]李传奇,王帅,王薇,等.LHS-MC方法在漫坝风险分析中的应用[J].水力发电学报,2012,31(1):5-9.LI Chuanqi,WANG Shuai,WANG Wei,et al.Overtopping risk analysis using LHS-MC method[J].Journal of Hydroelectric Engineering,2012,31(1):5-9.(in Chinese)
[14]GOODARZI E,SHUI L T,ZIAEI M.Risk and uncertainty analysis for dam overtopping-Case study:The Doroudzan Dam,Iran[J].Journal of Hydro-environment Research,2014,8(1):50-61.
[15]吕弯弯,顾圣平,何蕾,等.基于蒙特卡罗法的土石坝洪水漫顶风险率计算及其敏感性分析[J].长江科学院院报,2015,32(5):48-52.LV Wanwan,GU Shengping,HE Lei,et al.Calculation and sensitivity analysis of risk probability of earth-rock dam overtopping caused by floods based on Monte-Carlo method[J].Journal of Yangtze River Scientific Research Institute,2015,32(5):48-52.(in Chinese)
[16]SALVADORI G,MICHELE C D.On the use of Copulas in hydrology:Theory and practice[J].Journal of Hydrologic Engineering,2007,12(4):369-380.
[17]史黎翔,宋松柏.基于Copula函数的两变量洪水重现期与设计值计算研究[J].水力发电学报,2015,34(10):27-34.SHI Lixiang,SONG Songbai.Calculation of return periods and design values of bivariate floods based on Copula function[J].Journal of Hydroelectric Engineering,2015,34(10):27-34.(in Chinese)
[18]姚瑞虎,覃光华,丁晶,等.洪水二维变量重现期的探讨[J].水力发电学报,2017,36(10):35-44.YAO Ruihu,QIN Guanghua,DING Jing,et al.Preliminary study on flood return periods based on bivariate variables[J].Journal of Hydroelectric Engineering,2017,36(10):35-44.(in Chinese)
[19]冯平,李新.基于Copula函数的非一致性洪水峰量联合分析[J].水利学报,2013,44(10):1137-1147.FENG Ping,LI Xin.Bivariate frequency analysis of nonstationary flood time series based on Copula methods[J].Journal of Hydraulic Engineering,2013,44(10):1137-1147.(in Chinese)
[20]MICHELE C D,SALVADORI G,CANOSSI M,et al.Bivariate statistical approach to check adequacy of dam spillway[J].Journal of Hydrologic Engineering,2005,10(1):50-57.
[21]MEDIERO L,JIMéNEZáLVAREZ A,GARROTE L.Design flood hydrographs from the relationship between flood peak and volume[J].Hydrology and Earth System Sciences,2010,7(4):2495-2505.
[22]REQUENA A I,MEDIERO L,GARROTE L.A bivariate return period based on copulas for hydrologic dam design:accounting for reservoir routing in risk estimation[J].Hydrology and Earth System Sciences,2013,17(8):3023-3038.
[23]PODUJE A C C,BELLI A,HABERLANDT U.Dam risk assessment based on univariate versus bivariate statistical approaches:a case study for Argentina[J].Hydrological Sciences Journal,2014,59(12):2216-2232.
[24]李天元,郭倩,刘国强,等.两变量防洪风险模型研究[J].人民长江,2015,46(23):1-5.LI Tianyuan,GUO Qian,LIU Guoqiang,et al.Study on bivariate flood risk model[J].Yangtze River,2015,46(23):1-5.(in Chinese)
[25]陈子燊,刘占明,赵青.洪水峰量联合分布的4种重现水平对比[J].中山大学学报(自然科学版),2018,57(1):130-135.CHEN Zhishen,LIU Zhanming,ZHAO Qing.Comparative analysis on four recurrence levels of joint distribution of flood peak discharge and volume[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2018,57(1):130-135.(in Chinese)
[26]闫宝伟,郭生练,郭靖,等.基于Copula函数的设计洪水地区组成研究[J].水力发电学报,2010,29(6):60-65.YAN Baowei,GUO Shenglian,GUO Jing,et al.Regional design flood composition based on Copula function[J].Journal of Hydroelectric Engineering,2010,29(6):60-65.(in Chinese)
[27]陈璐,叶磊,卢韦伟,等.基于Copula熵的神经网络径流预报模型预报因子选择[J].水力发电学报,2014,33(6):25-29.CHEN Lu,YE Lei,LU Weiwei,et al.Determination of input variabes for artificial neural networks for flood forecasting using Copula entropy method[J].Journal of Hydroelectric Engineering,2014,33(6):25-29.(in Chinese)
[28]SRAJ M,BEZAK N,BRILLY M.Bivariate flood frequency analysis using the copula function:a case study of the Litija station on the Sava River[J].Hydrological Processes,2015,29(2):225-238.
[29]孙鹏,张强,陈晓宏.基于Copula函数的鄱阳湖流域极值流量遭遇频率及灾害风险[J].湖泊科学,2011,23(2):183-190.SUN Peng,ZHANG Qiang,CHEN Xiaohong.Copulabased evaluation of high-and low-flows frequency of the Lake Poyang Basin and the risk assessment[J].Journal of Lake Science,2011,23(2):183-190.(in Chinese)
[30]刘曾美,覃光华,陈子燊,等.感潮河段水位与上游洪水和河口潮位的关联性研究[J].水利学报,2013,44(11):1278-1285.LIU Zengmei,QIN Guanghua,CHEN Zisheng,et al.Study on the correlation of the water level of the tidal river with upstream flood and estuary tide level[J].Journal of Hydraulic Engineering,2013,44(11):1278-1285.(in Chinese)
[31]肖义,郭生练,刘攀,等.基于Copula函数的设计洪水过程线方法[J].武汉大学学报(工学版),2007,40(4):13-17.XIAO Yi,GUO Shenglian,LIU Pan,et al.Derivation of design flood hydrograph based on Copula function[J].Engineering Journal of Wuhan University,2007,40(4):13-17.(in Chinese)
[32]李天元,郭生练,陈璐,等.基于Copula函数的水库防洪安全设计[J].水力发电学报,2013,32(6):50-56.LI Tianyuan,GUO Shenglian,CHEN Lu,et al.Safety design for reservoir flood control based on Copula function[J].Journal of Hydroelectric Engineering,2013,32(6):50-56.(in Chinese)
[33]POULIN A,HUARD D,FAVRE A C,et al.Importance of tail dependence in bivariate frequency analysis[J].Journal of Hydrologic Engineering,2007,12(4):394-403.
[2]李爱花,刘恒,耿雷华,等.水利工程风险分析研究现状综述[J].水科学进展,2009,20(3):453-459.LI Aihua,LIU Heng,GENG Leihua,et al.Review of risk analysis of hydraulic engineering system[J].Advances in Water Science,2009,20(3):453-459.(in Chinese)
[3]VOLPI E,FIORI A.Hydraulic structures subject to bivariate hydrological loads:Return period,design,and risk assessment[J].Water Resources Research,2014,50(2):885-897.
[4]CHENG S T,YEN B C,TANG W H.Overtopping risk for an existing dam[R].Champaign:University of Illinois at Urbana-Champaign,1982.
[5]梅亚东,谈广鸣.大坝防洪安全的风险分析[J].武汉大学学报(工学版),2002,35(6):11-15.MEI Yadong,TAN Guangming.Risk analysis for flood prevention and safety of dam[J].Engineering Journal of Wuhan University,2002,35(6):11-15.(in Chinese)
[6]肖义,郭生练,雒征,等.大坝防洪安全风险率的计算方法[J].武汉大学学报(工学版),2005,38(3):10-13.XIAO Yi,GUO Shenglian,LUO Zheng,et al.Estimation of hydrological risk rate for dams[J].Engineering Journal of Wuhan University,2005,38(3):10-13.(in Chinese)
[7]KWON H H,MOON Y I.Improvement of overtopping risk evaluations using probabilistic concepts for existing dams[J].Stochastic Environmental Research and Risk Assessment,2006,20(4):223-237.
[8]李清富,龙少江.大坝洪水漫顶风险评估[J].水力发电,2006,32(7):20-22.LI Qingfu,LONG Shaojiang.Risk assessment of dam overtopping[J].Water Power,2006,32(7):20-22.(in Chinese)
[9]KUO J T,YEN B C,HSU Y C,et al.Risk analysis for dam overtopping:Feitsui Reservoir as a case study[J].Journal of Hydraulic Engineering,2007,133(8):955-963.
[10]莫崇勋,董增川,麻荣永,等.“积分-一次二阶矩法”在广西澄碧河水库漫坝风险分析中的应用研究[J].水力发电学报,2008,27(2):44-49.MO Chongxun,DONG Zengchuan,MA Rongyong,et al.Application study on overtopping risk analysis for Guangxi Chengbihe reservoir by Integrate-FOSM method[J].Journal of Hydroelectric Engineering,2008,27(2):44-49.(in Chinese)
[11]余雷,伍春平,兰盈盈.柘林水库大坝防洪安全风险分析[J].人民长江,2009,40(17):33-35.YU Lei,WU Chunping,LAN Yingying.Risk analysis of dam flood control safety of Zhelin Reservoir[J].Yangtze River,2009,40(17):33-35.(in Chinese)
[12]HSU Y C,TUNG Y K,KUO J T.Evaluation of dam overtopping probability induced by flood and wind[J].Stochastic Environmental Research and Risk Assessment,2011,25(1):35-49.
[13]李传奇,王帅,王薇,等.LHS-MC方法在漫坝风险分析中的应用[J].水力发电学报,2012,31(1):5-9.LI Chuanqi,WANG Shuai,WANG Wei,et al.Overtopping risk analysis using LHS-MC method[J].Journal of Hydroelectric Engineering,2012,31(1):5-9.(in Chinese)
[14]GOODARZI E,SHUI L T,ZIAEI M.Risk and uncertainty analysis for dam overtopping-Case study:The Doroudzan Dam,Iran[J].Journal of Hydro-environment Research,2014,8(1):50-61.
[15]吕弯弯,顾圣平,何蕾,等.基于蒙特卡罗法的土石坝洪水漫顶风险率计算及其敏感性分析[J].长江科学院院报,2015,32(5):48-52.LV Wanwan,GU Shengping,HE Lei,et al.Calculation and sensitivity analysis of risk probability of earth-rock dam overtopping caused by floods based on Monte-Carlo method[J].Journal of Yangtze River Scientific Research Institute,2015,32(5):48-52.(in Chinese)
[16]SALVADORI G,MICHELE C D.On the use of Copulas in hydrology:Theory and practice[J].Journal of Hydrologic Engineering,2007,12(4):369-380.
[17]史黎翔,宋松柏.基于Copula函数的两变量洪水重现期与设计值计算研究[J].水力发电学报,2015,34(10):27-34.SHI Lixiang,SONG Songbai.Calculation of return periods and design values of bivariate floods based on Copula function[J].Journal of Hydroelectric Engineering,2015,34(10):27-34.(in Chinese)
[18]姚瑞虎,覃光华,丁晶,等.洪水二维变量重现期的探讨[J].水力发电学报,2017,36(10):35-44.YAO Ruihu,QIN Guanghua,DING Jing,et al.Preliminary study on flood return periods based on bivariate variables[J].Journal of Hydroelectric Engineering,2017,36(10):35-44.(in Chinese)
[19]冯平,李新.基于Copula函数的非一致性洪水峰量联合分析[J].水利学报,2013,44(10):1137-1147.FENG Ping,LI Xin.Bivariate frequency analysis of nonstationary flood time series based on Copula methods[J].Journal of Hydraulic Engineering,2013,44(10):1137-1147.(in Chinese)
[20]MICHELE C D,SALVADORI G,CANOSSI M,et al.Bivariate statistical approach to check adequacy of dam spillway[J].Journal of Hydrologic Engineering,2005,10(1):50-57.
[21]MEDIERO L,JIMéNEZáLVAREZ A,GARROTE L.Design flood hydrographs from the relationship between flood peak and volume[J].Hydrology and Earth System Sciences,2010,7(4):2495-2505.
[22]REQUENA A I,MEDIERO L,GARROTE L.A bivariate return period based on copulas for hydrologic dam design:accounting for reservoir routing in risk estimation[J].Hydrology and Earth System Sciences,2013,17(8):3023-3038.
[23]PODUJE A C C,BELLI A,HABERLANDT U.Dam risk assessment based on univariate versus bivariate statistical approaches:a case study for Argentina[J].Hydrological Sciences Journal,2014,59(12):2216-2232.
[24]李天元,郭倩,刘国强,等.两变量防洪风险模型研究[J].人民长江,2015,46(23):1-5.LI Tianyuan,GUO Qian,LIU Guoqiang,et al.Study on bivariate flood risk model[J].Yangtze River,2015,46(23):1-5.(in Chinese)
[25]陈子燊,刘占明,赵青.洪水峰量联合分布的4种重现水平对比[J].中山大学学报(自然科学版),2018,57(1):130-135.CHEN Zhishen,LIU Zhanming,ZHAO Qing.Comparative analysis on four recurrence levels of joint distribution of flood peak discharge and volume[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2018,57(1):130-135.(in Chinese)
[26]闫宝伟,郭生练,郭靖,等.基于Copula函数的设计洪水地区组成研究[J].水力发电学报,2010,29(6):60-65.YAN Baowei,GUO Shenglian,GUO Jing,et al.Regional design flood composition based on Copula function[J].Journal of Hydroelectric Engineering,2010,29(6):60-65.(in Chinese)
[27]陈璐,叶磊,卢韦伟,等.基于Copula熵的神经网络径流预报模型预报因子选择[J].水力发电学报,2014,33(6):25-29.CHEN Lu,YE Lei,LU Weiwei,et al.Determination of input variabes for artificial neural networks for flood forecasting using Copula entropy method[J].Journal of Hydroelectric Engineering,2014,33(6):25-29.(in Chinese)
[28]SRAJ M,BEZAK N,BRILLY M.Bivariate flood frequency analysis using the copula function:a case study of the Litija station on the Sava River[J].Hydrological Processes,2015,29(2):225-238.
[29]孙鹏,张强,陈晓宏.基于Copula函数的鄱阳湖流域极值流量遭遇频率及灾害风险[J].湖泊科学,2011,23(2):183-190.SUN Peng,ZHANG Qiang,CHEN Xiaohong.Copulabased evaluation of high-and low-flows frequency of the Lake Poyang Basin and the risk assessment[J].Journal of Lake Science,2011,23(2):183-190.(in Chinese)
[30]刘曾美,覃光华,陈子燊,等.感潮河段水位与上游洪水和河口潮位的关联性研究[J].水利学报,2013,44(11):1278-1285.LIU Zengmei,QIN Guanghua,CHEN Zisheng,et al.Study on the correlation of the water level of the tidal river with upstream flood and estuary tide level[J].Journal of Hydraulic Engineering,2013,44(11):1278-1285.(in Chinese)
[31]肖义,郭生练,刘攀,等.基于Copula函数的设计洪水过程线方法[J].武汉大学学报(工学版),2007,40(4):13-17.XIAO Yi,GUO Shenglian,LIU Pan,et al.Derivation of design flood hydrograph based on Copula function[J].Engineering Journal of Wuhan University,2007,40(4):13-17.(in Chinese)
[32]李天元,郭生练,陈璐,等.基于Copula函数的水库防洪安全设计[J].水力发电学报,2013,32(6):50-56.LI Tianyuan,GUO Shenglian,CHEN Lu,et al.Safety design for reservoir flood control based on Copula function[J].Journal of Hydroelectric Engineering,2013,32(6):50-56.(in Chinese)
[33]POULIN A,HUARD D,FAVRE A C,et al.Importance of tail dependence in bivariate frequency analysis[J].Journal of Hydrologic Engineering,2007,12(4):394-403.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |