洪峰流量与水位不同遭遇条件下的防洪设计
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摘要
采用Archimedean Gumbel-Hougaard copula函数和Kendall分布函数分析洪峰流量和洪峰水位联合分布的重现水平。以西江高要水文站1951-2010年的年最大洪峰流量和相应洪峰水位为例,计算了二者联合分布下的"或"重现期、"且"重现期和Kendall重现期及其最可能的设计值。主要结论如下:(1)洪峰流量和洪峰水位的遭遇条件概率显示存在着多种防洪设计标准;(2)对比"或"联合重现期和"且"重现期,Kendall重现期更准确地反映了Q-H组合的风险率;(3)以出现最大概率原理推算的不同洪峰流量和水位遭遇概率组合的Kendall重现期设计值为多种防洪标准选择与风险管理提供了更多的参考依据。
The return levels of the joint distribution of flood peak discharges and flood peak water levels were analyzed by Archimedean Gumbel-Hougaard copula and Kendall distribution function in this article.Using the annual maximum flood peak discharges and corresponding flood peak water levels between years1951 to 2010 at Gaoyao hydrologic station in Xijiang River,the ‘OR' return period,‘AND' return period and Kendall return period with the most likely design quantiles were calculated. The main conclusions of this study can be summarized as follows:(1) The conditional probability of flood peak flow and flood water level shows various flood control design standards.(2) Compared with the "OR"return periods and"AND"return periods,Kendall return periods more accurately reflect the risk rate of the combination of flood elements.(3) Based on the principle of maximum probability,the calculated design quantiles of Kendall return periods under the different combination condition of flood peak flow and water level can provide more options for flood control standard selection and risk management.
The return levels of the joint distribution of flood peak discharges and flood peak water levels were analyzed by Archimedean Gumbel-Hougaard copula and Kendall distribution function in this article.Using the annual maximum flood peak discharges and corresponding flood peak water levels between years1951 to 2010 at Gaoyao hydrologic station in Xijiang River,the ‘OR' return period,‘AND' return period and Kendall return period with the most likely design quantiles were calculated. The main conclusions of this study can be summarized as follows:(1) The conditional probability of flood peak flow and flood water level shows various flood control design standards.(2) Compared with the "OR"return periods and"AND"return periods,Kendall return periods more accurately reflect the risk rate of the combination of flood elements.(3) Based on the principle of maximum probability,the calculated design quantiles of Kendall return periods under the different combination condition of flood peak flow and water level can provide more options for flood control standard selection and risk management.
引文
[1]谢华,黄介生.两变量水文频率分布模型研究述评[J].水科学进展,2008,19(3):443-452.XIE Hua,HUANG Jiesheng.A review of bivariate hydrological frequency distribution[J].Advances in Water Science,2008,19(3):443-452.
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[6]陈子燊,黄强,刘曾美.基于非对称Archimedean copula与kendall分布函数的三变量洪水风险评估[J].水科学进展,2016,27(5):763-771.CHEN Zishen,HUANG Qiang,LIU Zengmei.Risk assessment of trivariate flood based on asymmetric Archimedean Copulas[J].Advances in Water Science,2016,27(5):763-771.
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[8]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.
[9]郭生练,刘章君,熊立华.设计洪水计算方法研究进展与评价[J].水利学报,2016,47(3):302-314.GUO Shenglian,LIU Zhangjun,XIONG Lihua.Advances and assessment on design flood estimation methods[J].Journal of Hydraulic Engineering,2016,47(3):302-314.
[10]SALVADORI G,de MICHELE C.Frequency analysis via copulas:theoretical aspects and applications to hydrological events[J].Water Resources Research,2004,40(12):W12511-17.
[11]黄强,陈子燊.基于二次重现期的多变量洪水风险评估[J].湖泊科学,2015,27(2):352-360.HUANG Qiang,CHEN Zishen.Multivariate flood risk assessment based on the secondary return period[J].J Lake Sci,2015,27(2):352-360.
[12]SALVADORI G,MICHELED C,DURANTE F.On the return period and design in a multivariate framework[J].Hydrology and Earth System Sciences,2011,15:3293-3305.
[13]SALVADORI G,DURANTE F,de MICHELE C.Multivariate return period calculation via survival functions[J].Water Resources Research,2013,49:2308-2311.
[14]NELSEN R B.An introduction to copulas(springer series in statistics)[M].New York:Springer,1999:216.
[15]GRALER B,van den BERG M J,VANDENBERGHE S,et al.Multivariate return periods in hydrology:a critical and practical review focusing on synthetic design hydrograph estimation[J].Hydrology and Earth System Sciences,2013,17:1281-1296.
[2]ZHANG L,SINGH V P.Bivariate flood frequency analysis using the copula method[J].Journal of Hydrologic Engineering,2006,11(2):150-164.
[3]肖义,郭生练,刘攀,等.分期设计洪水频率与防洪标准关系研究[J].水科学进展,2008,19(1):54-60.XIAO Yi,GUO Shenglian,LIU Pan,et al.Seasonal flood frequency analysis and flood prevention standard[J].Advances in Water Science,2008,19(3):54-60.
[4]方彬,郭生练,肖义,等.年最大洪水两变量联合分布研究[J].水科学进展,2008,19(4):505-511.FANG Bin,GUO Shenglian,XIAO Yi,et al.Annual maximum flood occurrence dates and magnitudes frequency analysis based on bivariate joint distribution[J].Advances in Water Science,2008,19(4):505-511.
[5]熊立华,郭生练.两变量极值分布在洪水频率分析中的应用研究[J].长江科学院院报,2004,21(2):35-37.XIONG Lihua,GUO Shenglian.Application study of a bivariate extremal distribution in flood frequency analysis[J].Journal of Yangtze River Scientific Research Insititute,2004,21(2):35-37.
[6]陈子燊,黄强,刘曾美.基于非对称Archimedean copula与kendall分布函数的三变量洪水风险评估[J].水科学进展,2016,27(5):763-771.CHEN Zishen,HUANG Qiang,LIU Zengmei.Risk assessment of trivariate flood based on asymmetric Archimedean Copulas[J].Advances in Water Science,2016,27(5):763-771.
[7]VOLPI E,FIORI A.Design event selection in bivariate hydrological frequency analysis[J].Hydrological Sciences Journal,2012,57(8):1506-1515.
[8]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.
[9]郭生练,刘章君,熊立华.设计洪水计算方法研究进展与评价[J].水利学报,2016,47(3):302-314.GUO Shenglian,LIU Zhangjun,XIONG Lihua.Advances and assessment on design flood estimation methods[J].Journal of Hydraulic Engineering,2016,47(3):302-314.
[10]SALVADORI G,de MICHELE C.Frequency analysis via copulas:theoretical aspects and applications to hydrological events[J].Water Resources Research,2004,40(12):W12511-17.
[11]黄强,陈子燊.基于二次重现期的多变量洪水风险评估[J].湖泊科学,2015,27(2):352-360.HUANG Qiang,CHEN Zishen.Multivariate flood risk assessment based on the secondary return period[J].J Lake Sci,2015,27(2):352-360.
[12]SALVADORI G,MICHELED C,DURANTE F.On the return period and design in a multivariate framework[J].Hydrology and Earth System Sciences,2011,15:3293-3305.
[13]SALVADORI G,DURANTE F,de MICHELE C.Multivariate return period calculation via survival functions[J].Water Resources Research,2013,49:2308-2311.
[14]NELSEN R B.An introduction to copulas(springer series in statistics)[M].New York:Springer,1999:216.
[15]GRALER B,van den BERG M J,VANDENBERGHE S,et al.Multivariate return periods in hydrology:a critical and practical review focusing on synthetic design hydrograph estimation[J].Hydrology and Earth System Sciences,2013,17:1281-1296.