基于G-H copula函数的秦淮河流域洪水风险分析
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摘要
Copula函数构造灵活,适应性强,被广泛应用于多变量水文频率分析计算中。选取G-H copula函数描述洪量、洪峰、洪水位间的相依结构,边际分布模拟考虑广义极值(GEV),对数正态(ln2)和皮尔逊Ⅲ型分布(P-Ⅲ)。以相关性最强的洪峰和洪水位为例进行二维变量洪水风险分析,比较分析其传统重现期和Kendall重现期性质,并计算条件风险率。构建3变量联合风险评价模型,并与二变量情况进行对比。以秦淮河流域为例进行了应用,表明多维联合重现期小于同现重现期,Kendall重现期在两者之间且与单因素重现期误差最小;流域洪峰和洪水位同现风险率最大,洪峰量级越小,洪水位超越风险率越小;基于三维G-H copula函数计算的各变量同频率设计值大于相应单变量设计值,并且相对于二维情况,各重现期与单因素重现期之间的差值明显增大。研究结论可为秦淮河地区水利工程规划设计和洪灾风险评估提供有益参考。
Copula function is commonly used in the flood frequency calculation of multidimensional variables because of its flexible construction and wide adaptability. G-H copula is selected to describe the dependence structure of three flood variables,namely flood volume,peak flow and water level. GEV,Logical-normal and PearsonⅢ distribution are considered for fitting the marginal distribution. A two-dimensional G-H copula flood risk assessment model based on peak flow and water level,which are of the highest dependence,is developed to investigate and analyze the characteristics of joint return period( JRP),co-recurrence return period and Kendall return period( KRP). The conditional risk of different combination of flood events is also computed. A three-dimensional G-H copula model is also developed to compare with the bivariate scenario. Qinhuai river basin is chosen as the study area. The result shows that the multi-dimensional joint return period is quite smaller than the co-recurrence return period. Kendall return period is in between of joint and co-recurrence return period but has the minimum error with the single variable return period. The co-recurrence probability of peak flow and water level turns out to be the highest; the smaller the magnitude of peak flow,the less possible for water level to exceed certain threshold. The design value of flood variables in same frequency computed by trivariate G-H copula is larger than the corresponding single variable design value and the difference of other return period with single variable return period is obviously larger than that of bivariate case. The conclusion can be useful for water resource project planning and design and risk assessment of flood disaster in the studied area.
Copula function is commonly used in the flood frequency calculation of multidimensional variables because of its flexible construction and wide adaptability. G-H copula is selected to describe the dependence structure of three flood variables,namely flood volume,peak flow and water level. GEV,Logical-normal and PearsonⅢ distribution are considered for fitting the marginal distribution. A two-dimensional G-H copula flood risk assessment model based on peak flow and water level,which are of the highest dependence,is developed to investigate and analyze the characteristics of joint return period( JRP),co-recurrence return period and Kendall return period( KRP). The conditional risk of different combination of flood events is also computed. A three-dimensional G-H copula model is also developed to compare with the bivariate scenario. Qinhuai river basin is chosen as the study area. The result shows that the multi-dimensional joint return period is quite smaller than the co-recurrence return period. Kendall return period is in between of joint and co-recurrence return period but has the minimum error with the single variable return period. The co-recurrence probability of peak flow and water level turns out to be the highest; the smaller the magnitude of peak flow,the less possible for water level to exceed certain threshold. The design value of flood variables in same frequency computed by trivariate G-H copula is larger than the corresponding single variable design value and the difference of other return period with single variable return period is obviously larger than that of bivariate case. The conclusion can be useful for water resource project planning and design and risk assessment of flood disaster in the studied area.
引文
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[11]潘璀林,陈子燊.基于GH Copula的韩江水文干旱联合概率分布研究[J].中山大学学报(自然科学版),2015,54(1):110-115.
[12]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.
[13]范嘉炜,黄锦林.基于Kendall重现期的降雨潮位风险分析[J].水电能源科学,2017,35(5):21-24+20.
[14]高玉琴,陈钇西,赵立梅,等.秦淮河流域不同频率降雨联合概率分析[J].水电能源科学,2016,34(3):1-5+23.
[2]黄锦林,范嘉炜,唐造造.基于最大熵-Copula方法的降雨潮位关联性分析——以广州为例[J].灾害学,2017,32(1):65-71.
[3]闫宝伟,郭生练,陈璐,等.长江和清江洪水遭遇风险分析[J].水利学报,2010,41(5):553-559.
[4]CHOWDHARY H,ESCOBAR L A,SINGH V P.Identification of suitable copulas for bivariate frequency analysis of flood peak and flood volume data[J].Hydrology Research,2011,42(2-3):193.
[5]ZHANG L,SINGH V P.Bivariate rainfall frequency distributions using Archimedean copulas[J].Journal of Hydrology,2007,332(1):93-109.
[6]REDDY M J,GANGULI P.Bivariate flood frequency analysis of upper godavari river flows using archimedean copulas[J].Water Resources Management,2012,26(14):3995-4018.
[7]陈子燊,黄强,刘曾美.基于非对称Archimedean Copula的三变量洪水风险评估[J].水科学进展,2016,27(5):763-771.
[8]侯芸芸,宋松柏,赵丽娜,等.基于Copula函数的3变量洪水频率研究[J].西北农林科技大学学报(自然科学版),2010,38(2):219-228.
[9]GANGULI P,REDDY M J.Probabilistic assessment of flood risks using trivariate copulas[J].Theoretical&Applied Climatology,2013,111(1-2):341-360.
[10]袁玉,高玉琴,吴锡.基于HEC_HMS水文模型的秦淮河流域圩垸式防洪模式洪水模拟[J].三峡大学学报(自然科学版),2015,37(5):34-39.
[11]潘璀林,陈子燊.基于GH Copula的韩江水文干旱联合概率分布研究[J].中山大学学报(自然科学版),2015,54(1):110-115.
[12]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.
[13]范嘉炜,黄锦林.基于Kendall重现期的降雨潮位风险分析[J].水电能源科学,2017,35(5):21-24+20.
[14]高玉琴,陈钇西,赵立梅,等.秦淮河流域不同频率降雨联合概率分析[J].水电能源科学,2016,34(3):1-5+23.