滨海城市雨潮遭遇联合分布模拟与设计
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摘要
滨海城市河流常常遭受暴雨和潮汐顶托双重影响导致洪涝灾害,需要重视雨潮遭遇联合分布模拟与设计。以深圳市西乡河为例,采用年最大值法(AM)和超定量序列法(POT)两种选样方法,基于Copula方法模拟24 h暴雨遭遇日高潮位的联合分布特征,对比雨潮遭遇传统重现期和二次重现期差异,根据同频法和权函数法反推计算雨潮设计组合值。结果表明:雨潮边缘分布最优模型均为广义正态分布(GNO),不同选样方法雨量分布模型参数差异明显。雨潮之间呈现较弱的正相依性,Archimedean Copulas均能较好地模拟雨潮遭遇联合分布特征,最优模型为Gumbel-Hougaard Copula。同频法反推雨潮设计组合值,二次重现期雨量和潮位均大于传统联合重现期,POT选样的潮位大于AM。权函数法选出的雨潮设计组合值,偏重于较高的潮位,雨量设计值较小。当明确了选样方法、联合分布模型和重现期类型,给定联合重现期的雨潮设计组合值是个此消彼长的过程,若选择较大的雨量设计值,则潮位值变小,反之亦然。从防洪潮设计安全角度考虑,POT选样方法及二次重现期设计更为安全。
Instream flood in a coastal city usually occurs under the influence of heavy rain and high tidal level. Thus,modeling and design of joint distribution of precipitation and tide require increased attention. With Xixianghe River basin of Shenzhen city,Southern China,used as a case,24-hour data of heavy rain and comparative daily high tidal level are used for two sampling methods,namely,annual maximum( AM) and peaks over threshold( POT). The joint distribution model of precipitation and tide is established by using Copula functions. In this model,the difference between the traditional and second return periods of joint distribution of precipitation and tide is analyzed. The pair values of precipitation and tide are investigated according to two optimally designed methods,namely,equalized frequency method and most-likely weight function. Results show that the generalized normal distribution( GNO) is optimally selected to model the marginal distribution of precipitation and tide,but the differences of model parameters in precipitation are remarkable. Although precipitation and tide exhibit a weak positive dependence,Archimedean Copulas can well model their joint distribution,and the Gumbel-Hougaard Copula is selected as the optimal bivariate model. According to the equalized frequency method,the pair values of precipitation and tide designed by the second return period are greater than those designed by the traditional return period,and those designed by the POT series are greater than those designed by the AM series. However,the designed values of tide level are greater when associated with lower precipitation on the basis of the most-likely weight function. Provided that the sampling method,the joint distribution model,and the type of joint return period are confirmed,a reciprocal situation for a pair of designed values of precipitation and tide is manifested for given joint return periods,that is,a greater designed value of precipitation corresponds to a smaller designed value of tide,and vice versa. In ensuring a secure engineering design against flood disasters due to heavy rain and high tidal level in the coastal city,the sampling of POT and the bivariable design of the second return period are safer than those of AM and the traditional return period,respectively.
Instream flood in a coastal city usually occurs under the influence of heavy rain and high tidal level. Thus,modeling and design of joint distribution of precipitation and tide require increased attention. With Xixianghe River basin of Shenzhen city,Southern China,used as a case,24-hour data of heavy rain and comparative daily high tidal level are used for two sampling methods,namely,annual maximum( AM) and peaks over threshold( POT). The joint distribution model of precipitation and tide is established by using Copula functions. In this model,the difference between the traditional and second return periods of joint distribution of precipitation and tide is analyzed. The pair values of precipitation and tide are investigated according to two optimally designed methods,namely,equalized frequency method and most-likely weight function. Results show that the generalized normal distribution( GNO) is optimally selected to model the marginal distribution of precipitation and tide,but the differences of model parameters in precipitation are remarkable. Although precipitation and tide exhibit a weak positive dependence,Archimedean Copulas can well model their joint distribution,and the Gumbel-Hougaard Copula is selected as the optimal bivariate model. According to the equalized frequency method,the pair values of precipitation and tide designed by the second return period are greater than those designed by the traditional return period,and those designed by the POT series are greater than those designed by the AM series. However,the designed values of tide level are greater when associated with lower precipitation on the basis of the most-likely weight function. Provided that the sampling method,the joint distribution model,and the type of joint return period are confirmed,a reciprocal situation for a pair of designed values of precipitation and tide is manifested for given joint return periods,that is,a greater designed value of precipitation corresponds to a smaller designed value of tide,and vice versa. In ensuring a secure engineering design against flood disasters due to heavy rain and high tidal level in the coastal city,the sampling of POT and the bivariable design of the second return period are safer than those of AM and the traditional return period,respectively.
引文
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[9]武传号,黄国如,吴思远.基于Copula函数的广州市短历时暴雨与潮位组合风险分析[J].水力发电学报,2014,33(2):33-40.(WU C H,HUANG G R,WU S Y.Risk analysis of combinations of short duration rainstorm and tidal level in Guangzhou based on Copula function[J].Journal of Hydroelectric Engineering,2014,33(2):33-40.(in Chinese))
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[12]SALVADORI G,MICHELE C D,DURANTE F.On the return period and design in a multivariate framework[J].Hydrology and Earth System Sciences,2011,15(11):3293-3305.
[13]许世远,王军,石纯,等.沿海城市自然灾害风险研究[J].地理学报,2006,61(2):127-138.(XU S Y,WANG J,SHI C,et al.Research of the natural disaster risk on coastal cities[J].Acta Geographica Sinica,2006,61(2):127-138.(in Chinese))
[14]SALVADORI G,MICHELE C D.Frequency analysis via copulas:theoretical aspects and applications to hydrological events[J].Water Resources Research,2004,40(12):229-244.
[15]MASSEY F J.The Kolmogorov-Smirnov test for goodness of fit[J].Journal of the American Statistical Association,2012,46(253):68-78.
[16]DOBRIC J,SCHMID F.A goodness of fit test for copulas based on Rosenblatt's transformation[J].Computation Statistics and Data Analysis,2007,51(9):4633-4642.
[17]GENEST C,REMILLARD B,BEAUDOIN D.Goodness-of-fit tests for copulas:a review and a power study[J].Insurance Mathematic Economy,2009,44(2):199-213.
[18]TU X J,SINGH V P,CHEN X H,et al.Uncertainty and variability in bivariate modeling of hydrological droughts[J].Stochastic Environmental Research and Risk Assessment,2016,30(5):1317-1334.
[19]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 Q,CHEN Z S.Multivariate flood risk assessment based on the secondary return period[J].Journal of Lake Sciences,2015,27(2):352-360.(in Chinese))
[20]李天元,郭生练,闫宝伟,等.基于多变量联合分布推求设计洪水过程线的新方法[J].水力发电学报,2013,32(3):10-14,38.(LI T Y,GUO S L,YAN B W,et al.Derivative design flood hydrograph based on trivariate joint distribution[J].Journal of Hydroelectric Engineering,2013,32(3):10-14,38.(in Chinese))
[2]陈永勤,孙鹏,张强,等.基于Copula的鄱阳湖流域水文干旱频率分析[J].自然灾害学报,2013,22(1):75-84.(CHEN Y Q,SUN P,ZHANG Q,et al.Copula-based analysis of hydrological drought frequency in Poyang Lake basin[J].Journal of Natural Disasters,2013,22(1):75-84.(in Chinese))
[3]刘曾美,陈子燊.区间暴雨和外江洪水位遭遇组合的风险[J].水科学进展,2009,20(5):619-625.(LIU Z M,CHEN Z S.Risk study of the bivariate encounter of interzone rainstorm and flood level of the outer river[J].Advances in Water Science,2009,20(5):619-625.(in Chinese))
[4]谢华,罗强,黄介生.基于三维Copula函数的多水文区丰枯遭遇分析[J].水科学进展,2012,23(2):186-193.(XIE H,LUO Q,HUANG J S.Synchronous asynchronous encounter analysis of multiple hydrologic regions based on 3D copula function[J].Advances in Water Science,2012,23(2):186-193.(in Chinese))
[5]谢华,冯晓波.感潮河段洪潮遭遇概率研究[J].灌溉排水学报,2012,31(1):54-57.(XIE H,FENG X B.Flood and storm tide encounter analysis in tideway-comparison of multivariate hydrological probability models[J].Journal of Irrigation and Drainage,2012,31(1):54-57.(in Chinese))
[6]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(11):1278-1285.(LIU Z M,QIN G H,CHEN Z S,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(11):1278-1285.(in Chinese))
[7]ZHENG F,WESTRA S,SISSON S A.Quantifying the dependence between extreme rainfall and storm surge in the coastal zone[J].Journal of Hydrology,2013,505(21):172-187.
[8]LIAN J J,XU K,MA C.Joint impact of rainfall and tidal level on flood risk in a coastal city with a complex river network:a case study of Fuzhou City,China[J].Hydrology and Earth System Sciences,2013,9(6):7475-7505.
[9]武传号,黄国如,吴思远.基于Copula函数的广州市短历时暴雨与潮位组合风险分析[J].水力发电学报,2014,33(2):33-40.(WU C H,HUANG G R,WU S Y.Risk analysis of combinations of short duration rainstorm and tidal level in Guangzhou based on Copula function[J].Journal of Hydroelectric Engineering,2014,33(2):33-40.(in Chinese))
[10]XU K,MA C,LIAN J J,et al.Joint probability analysis of extreme precipitation and storm tide in a coastal city under changing environment[J].Plos One,2014,9(10):1-11.
[11]CLAPS P,LAIO F.Can continuous streamflow data support flood frequency analysis?an alternative to the partial duration series approach[J].Water Resources Research,2003,39(8):375-384.
[12]SALVADORI G,MICHELE C D,DURANTE F.On the return period and design in a multivariate framework[J].Hydrology and Earth System Sciences,2011,15(11):3293-3305.
[13]许世远,王军,石纯,等.沿海城市自然灾害风险研究[J].地理学报,2006,61(2):127-138.(XU S Y,WANG J,SHI C,et al.Research of the natural disaster risk on coastal cities[J].Acta Geographica Sinica,2006,61(2):127-138.(in Chinese))
[14]SALVADORI G,MICHELE C D.Frequency analysis via copulas:theoretical aspects and applications to hydrological events[J].Water Resources Research,2004,40(12):229-244.
[15]MASSEY F J.The Kolmogorov-Smirnov test for goodness of fit[J].Journal of the American Statistical Association,2012,46(253):68-78.
[16]DOBRIC J,SCHMID F.A goodness of fit test for copulas based on Rosenblatt's transformation[J].Computation Statistics and Data Analysis,2007,51(9):4633-4642.
[17]GENEST C,REMILLARD B,BEAUDOIN D.Goodness-of-fit tests for copulas:a review and a power study[J].Insurance Mathematic Economy,2009,44(2):199-213.
[18]TU X J,SINGH V P,CHEN X H,et al.Uncertainty and variability in bivariate modeling of hydrological droughts[J].Stochastic Environmental Research and Risk Assessment,2016,30(5):1317-1334.
[19]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 Q,CHEN Z S.Multivariate flood risk assessment based on the secondary return period[J].Journal of Lake Sciences,2015,27(2):352-360.(in Chinese))
[20]李天元,郭生练,闫宝伟,等.基于多变量联合分布推求设计洪水过程线的新方法[J].水力发电学报,2013,32(3):10-14,38.(LI T Y,GUO S L,YAN B W,et al.Derivative design flood hydrograph based on trivariate joint distribution[J].Journal of Hydroelectric Engineering,2013,32(3):10-14,38.(in Chinese))