基于非对称Archimedean Copula的三变量风浪重现水平分析
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摘要
采用非对称Archimedean Copula函数与Kendall分布函数分析极端波况下的波高、周期和风速三变量联合概率分布与风险率及其设计分位数,为海岸海洋工程设计和风险评估提供参考依据。以粤东汕尾海域的实测风浪数据为例,使用非对称Gumbel-Hougaard Copula函数计算三变量风浪联合分布的"或"重现期、"且"重现期和二次重现期及其最可能的风浪设计值。主要结论如下:对比不同设计风浪重现期显示,"或"重现期的风险率偏高,"且"重现期的风险率偏低,二次重现期更准确地反映了特定设计频率情况下三变量风浪的风险率;按目前有关规范设计要求的单变量风浪要素设计值已经达到安全标准,按三变量"或"重现期和三变量同频率设计值推算的风浪设计值偏高,以最大可能概率推算的三变量风浪要素的二次重现期设计值可为相关工程安全与风险管理提供新的选择。
The joint probability distribution for triple variables(i.e.,wave height,wave period and wind speed under extreme wave condition) was analyzed by using 3-dimensional asymmetric Archimedean copula functions.And the trivariate stormy wave risk probabilities were further explored based on the Kendall distribution function in order to provide the basis for the coastal marine engineering design and risk assessment.A case is studied by using annual maximum wave heights and the relevant wave periods and wind speeds measured in Shanwei sea waters of eastern Guangdong,the primary return periods and secondary return periods of trivariate stormy wave joint distribution and the most likely design values were computed by using the asymmetric Gumbel-Hougaard copula.The main conclusions of this study can be summarized as follows:Comparing the risk probabilities of trivariate stormy waves among the different design return periods,the 'OR' joint return period showed higher risk probabilities,and the risk probabilities of 'AND' joint return period were lower,while the secondary return periods were more accurately depicted the risk probabilities under these specific design frequencies.According to the relevant specifications of the current design requirements,the univariate wave design values have reached safety standards.The estimated storm wave design values with the trivariate 'OR' return period and triple variables with the same frequencies were obviously higher than expected.The most-likely design realization of the secondary return period can serve as the new selection for coastal marine engineering and risk management.
The joint probability distribution for triple variables(i.e.,wave height,wave period and wind speed under extreme wave condition) was analyzed by using 3-dimensional asymmetric Archimedean copula functions.And the trivariate stormy wave risk probabilities were further explored based on the Kendall distribution function in order to provide the basis for the coastal marine engineering design and risk assessment.A case is studied by using annual maximum wave heights and the relevant wave periods and wind speeds measured in Shanwei sea waters of eastern Guangdong,the primary return periods and secondary return periods of trivariate stormy wave joint distribution and the most likely design values were computed by using the asymmetric Gumbel-Hougaard copula.The main conclusions of this study can be summarized as follows:Comparing the risk probabilities of trivariate stormy waves among the different design return periods,the 'OR' joint return period showed higher risk probabilities,and the risk probabilities of 'AND' joint return period were lower,while the secondary return periods were more accurately depicted the risk probabilities under these specific design frequencies.According to the relevant specifications of the current design requirements,the univariate wave design values have reached safety standards.The estimated storm wave design values with the trivariate 'OR' return period and triple variables with the same frequencies were obviously higher than expected.The most-likely design realization of the secondary return period can serve as the new selection for coastal marine engineering and risk management.
引文
Corbella S,Stretc h D D,2012.Multivariate return periods of sea storms for coastal erosion risk assessment.Natural Hazards and Earth System Sciences,12:2699-2708.
Ganguli P,Reddy M,2013.Probabilistic assessment of flood risks using trivariate copulas.Theor Appl Climatol 111:341-360.
Grimaldi S,Serincesco F,2006.Asymmetric copula in multivariate flood frequency analysis.Advances in Water Resources,29(8):150-164.
Nelson R B,2006.An introduction to copulas(Second edition).New York:Springer.
Requena A I,Mediero L,Garrote L,2013.Bivariate return period based on copulas for hydrologic dam design:comparison of theoretical and empirical approach.Hydrol.Earth Syst.Sci.Discuss.,10,557-596.
Salvadori G,De Michele C,2004.Frequency analysis via copulas:Theoretical aspects and applications to hydrological events.Water Resources Research,40,W12511,doi:10.1029/2004WR003133.
Salvadori G,De Michele C,2010.Multivariate multiparameter extreme value models and return periods:A copula approach.Water Resource Research,46,W10501,doi:10.1029/2009WR009040.
Salvadori G,Michele D C,Durante F,2011.On the return period and design in a multivariate framework.Hydrology and Earth System Sciences,15:3293-3305.
Salvadori G,Tomasicchio G R,Alessandro F D,2013.Multivariate approach to design coastal and off-shore structures.Journal of Coastal Research,65:386-391.
陈子燊,曹深西,2012.基于Copula函数的波高与周期长期联合分布.海洋通报,31(6):8-13.
陈子燊,2011.波高与风速联合概率分布研究.海洋通报,30(2):158-163.
董胜,周冲,陶山山,等,2011.基于Clayton copula函数的二维Gumbel模型及其在海洋平台设计中的应用.中国海洋大学学报,41(10):117-120.
方钟圣,戴顺孙,金承仪,1989.海洋特征波高和周期的长期联合分布及其应用.海洋学报,11(5):535-543.
黄强,陈子燊,2015.基于二次重现期的多变量洪水风险评估.湖泊科学,27(2):352-360.
李天元,郭生练,闫宝伟,等,2013.基于多变量联合分布推求设计洪水过程线的新方法.水力发电学报,32(3):10-15.
秦振江,孙广华,闫同新,等,2007.基于Copula函数的联合概率法在海洋工程中的应用.海洋预报,24(2):83-90.
徐龙军,陈祉宏,周道成,等,2013.基于Archimedean Copula模型的风浪联合分布第二重现期.天津大学学报(自然科学与工程技术版),46(2):114-120.
张雨,宋松柏,2011.基于Archimedean Copula的三维干旱特征变量联合分布研究.中国农村水利水电,1:65-68.
周道成,段忠东,2003.耿贝尔逻辑模型在极值风速和有效波高联合概率分布中的应用.海洋工程,21(2):45-51.
Ganguli P,Reddy M,2013.Probabilistic assessment of flood risks using trivariate copulas.Theor Appl Climatol 111:341-360.
Grimaldi S,Serincesco F,2006.Asymmetric copula in multivariate flood frequency analysis.Advances in Water Resources,29(8):150-164.
Nelson R B,2006.An introduction to copulas(Second edition).New York:Springer.
Requena A I,Mediero L,Garrote L,2013.Bivariate return period based on copulas for hydrologic dam design:comparison of theoretical and empirical approach.Hydrol.Earth Syst.Sci.Discuss.,10,557-596.
Salvadori G,De Michele C,2004.Frequency analysis via copulas:Theoretical aspects and applications to hydrological events.Water Resources Research,40,W12511,doi:10.1029/2004WR003133.
Salvadori G,De Michele C,2010.Multivariate multiparameter extreme value models and return periods:A copula approach.Water Resource Research,46,W10501,doi:10.1029/2009WR009040.
Salvadori G,Michele D C,Durante F,2011.On the return period and design in a multivariate framework.Hydrology and Earth System Sciences,15:3293-3305.
Salvadori G,Tomasicchio G R,Alessandro F D,2013.Multivariate approach to design coastal and off-shore structures.Journal of Coastal Research,65:386-391.
陈子燊,曹深西,2012.基于Copula函数的波高与周期长期联合分布.海洋通报,31(6):8-13.
陈子燊,2011.波高与风速联合概率分布研究.海洋通报,30(2):158-163.
董胜,周冲,陶山山,等,2011.基于Clayton copula函数的二维Gumbel模型及其在海洋平台设计中的应用.中国海洋大学学报,41(10):117-120.
方钟圣,戴顺孙,金承仪,1989.海洋特征波高和周期的长期联合分布及其应用.海洋学报,11(5):535-543.
黄强,陈子燊,2015.基于二次重现期的多变量洪水风险评估.湖泊科学,27(2):352-360.
李天元,郭生练,闫宝伟,等,2013.基于多变量联合分布推求设计洪水过程线的新方法.水力发电学报,32(3):10-15.
秦振江,孙广华,闫同新,等,2007.基于Copula函数的联合概率法在海洋工程中的应用.海洋预报,24(2):83-90.
徐龙军,陈祉宏,周道成,等,2013.基于Archimedean Copula模型的风浪联合分布第二重现期.天津大学学报(自然科学与工程技术版),46(2):114-120.
张雨,宋松柏,2011.基于Archimedean Copula的三维干旱特征变量联合分布研究.中国农村水利水电,1:65-68.
周道成,段忠东,2003.耿贝尔逻辑模型在极值风速和有效波高联合概率分布中的应用.海洋工程,21(2):45-51.