钦州市台风影响下风雨联合概率分布模型研究
|
摘要
受台风影响,钦州市洪涝灾害频发,基于copula联合概率分布模型研究台风条件下风雨相关关系。选择1971～2016年中引起钦州市降雨的125场台风的最大风速、时段降雨及累积雨量系列作为统计样本,分别采用Gumbel(2P)、Frechet(3P)、Weibull(2P)、Weibull(3P)、GEV、Gamma(2P)和Burr七种边缘分布进行最大风速、各时段雨量的分布拟合,并应用危险率函数法、累计误差法和Kolmogorov-Smirnov检验进行拟合优度评价,选出合适的风、雨边缘分布;采用Archimedean copula族四种函数构建风雨联合概率模型,并根据AIC、OLS准则做风雨联合分布拟合优度评价,选出符合钦州市各风雨联合概率分布的函数模型;通过对2017年"天鸽"和"帕卡"两场台风降雨数据检验可知,该风雨联合模型,结果可靠。表明了基于Archimedean copula函数构造的风雨联合分布模型可应用于台风影响下钦州市降雨情势的预测与分析。
Under the influence of typhoon, frequent flood and waterlogging disasters occur in Qinzhou City. Based on the copula joint probability distribution model, the relationship between wind and rain under typhoon condition has been discussed. The maximum wind speed, periodic rainfall, and cumulative rainfall of 125 rain inducing typhoons in the Qinzhou city from 1971 through 2016 were selected as statistical samples. The seven marginal distribution functions of Gumbel(2 P), Fréchet(3 P), Weibull(2 P), Weibull(3 P), GEV, Gamma(2 P) and Burr were used respectively to analyze the distribution fitting of maximum wind speed and rainfall in different periods, furthermore,the hazard function method, the cumulative error method, and the Kolmogorov Smirnovtest were used to measure the goodness of the fit and select the applicable marginal distributions of the wind and the rainfall. Four kinds of functions of Archimedean copula family have been used to construct the joint probability model of wind and rain. According to the Akaike information criterion(AIC) and Ordinary least squares(OLS) criteria to evaluate the goodness of fit of the joint distribution, the function model is selected, which conforms to the joint probability distribution of the combined wind and rain in Qinzhou City. The selected combined models of wind and rain were tested with the two "Hato" and "Pakhar" rainfall data in 2017, the result shows a great reliability, indicating that the model of joint wind and rain which based on Archimedean copula function can be applied to forecast and analyze the rainfall situation in Qinzhou City under the influence of typhoon.
Under the influence of typhoon, frequent flood and waterlogging disasters occur in Qinzhou City. Based on the copula joint probability distribution model, the relationship between wind and rain under typhoon condition has been discussed. The maximum wind speed, periodic rainfall, and cumulative rainfall of 125 rain inducing typhoons in the Qinzhou city from 1971 through 2016 were selected as statistical samples. The seven marginal distribution functions of Gumbel(2 P), Fréchet(3 P), Weibull(2 P), Weibull(3 P), GEV, Gamma(2 P) and Burr were used respectively to analyze the distribution fitting of maximum wind speed and rainfall in different periods, furthermore,the hazard function method, the cumulative error method, and the Kolmogorov Smirnovtest were used to measure the goodness of the fit and select the applicable marginal distributions of the wind and the rainfall. Four kinds of functions of Archimedean copula family have been used to construct the joint probability model of wind and rain. According to the Akaike information criterion(AIC) and Ordinary least squares(OLS) criteria to evaluate the goodness of fit of the joint distribution, the function model is selected, which conforms to the joint probability distribution of the combined wind and rain in Qinzhou City. The selected combined models of wind and rain were tested with the two "Hato" and "Pakhar" rainfall data in 2017, the result shows a great reliability, indicating that the model of joint wind and rain which based on Archimedean copula function can be applied to forecast and analyze the rainfall situation in Qinzhou City under the influence of typhoon.
引文
[1] 程正泉,陈联寿,徐祥德,等.近10年中国台风暴雨研究进展[J].气象,2005,31(12):3-9.
[2] 董美莹,陈联寿,郑沛群,等.登陆热带气旋暴雨突然增幅和特大暴雨之研究进展[J].热带气象学报,2009,25(4):113-120.
[3] 武占科,赵林,葛耀君.上海地区台风条件风速和雨强联合概率分布统计[J].空气动力学学报,2010,28(4):393-399.
[4] 程正泉,陈联寿,李英.登陆台风降水的大尺度环流诊断分析[J].气象学报,2009,67(5):840-850.
[5] 闫宝伟,郭生练,郭靖,等.多变量水文分析计算方法的比较[J].武汉大学学报(工学版),2009,42(1):10-15.
[6] DONG S,JIAO C S,TAO S S,et al.Joint return probability analysis of wind speed and rainfall intensity in typhoon-affected sea area[J].Natural hazards,2017,86(3):1193-1205.
[7] 王修勇,韩湘逸,孙洪鑫,等.琼州海峡跨海大桥桥址处风雨联合概率分布研究[J].公路交通科技,2016,33(2):60-66.
[8] UM M J,JOO K,NAM W,et al.A comparative study to determine the optimal copula model for the wind speed and precipitation of typhoons[J].International journal of climatology,2017,37(4):2051-2062.
[9] NELSEN R B.An Introduction to copulas[M].Germany:Springer,2006.
[10] 陈立华,王焰,易凯,等.钦州市降雨及入海河流径流演变规律与趋势分析[J].水文,2016,36(6):89-96.
[11] 曹之桦.水文统计学[M].北京:水利电力出版社,1985.
[12] MASSEYF.The Kolmogorov-Smirnov test for goodness of fit[J].Journal of the american statistical association,1951,46(253):68-78.
[13] 马海波,赵东亮,祝薄丽.几种水文频率曲线参数估计方法的比较[J].人民黄河,2016,38(3):9-11.
[14] 数学辞海委员会.数学辞海[M].北京:中国科学技术出版社,2002.
[15] ZHANG L,SINGH V P.Bivariate rainfall frequency distributions using archimedean copulas[J].Journal of hydrology,2007,332(1-2):93-109.
[16] YANG Q.A methodological study on AMH copula-based joint exceedance probabilities and applications for assessing tropical cyclone impacts and disaster risks (part I)[J].Tropical cyclone research and review,2014,3(1):53-62.
[17] 高超,梅亚东,涂新军.基于copula函数的区域降水联合分布与特征分析[J].水电能源科学,2013,36(6):1-5.
[2] 董美莹,陈联寿,郑沛群,等.登陆热带气旋暴雨突然增幅和特大暴雨之研究进展[J].热带气象学报,2009,25(4):113-120.
[3] 武占科,赵林,葛耀君.上海地区台风条件风速和雨强联合概率分布统计[J].空气动力学学报,2010,28(4):393-399.
[4] 程正泉,陈联寿,李英.登陆台风降水的大尺度环流诊断分析[J].气象学报,2009,67(5):840-850.
[5] 闫宝伟,郭生练,郭靖,等.多变量水文分析计算方法的比较[J].武汉大学学报(工学版),2009,42(1):10-15.
[6] DONG S,JIAO C S,TAO S S,et al.Joint return probability analysis of wind speed and rainfall intensity in typhoon-affected sea area[J].Natural hazards,2017,86(3):1193-1205.
[7] 王修勇,韩湘逸,孙洪鑫,等.琼州海峡跨海大桥桥址处风雨联合概率分布研究[J].公路交通科技,2016,33(2):60-66.
[8] UM M J,JOO K,NAM W,et al.A comparative study to determine the optimal copula model for the wind speed and precipitation of typhoons[J].International journal of climatology,2017,37(4):2051-2062.
[9] NELSEN R B.An Introduction to copulas[M].Germany:Springer,2006.
[10] 陈立华,王焰,易凯,等.钦州市降雨及入海河流径流演变规律与趋势分析[J].水文,2016,36(6):89-96.
[11] 曹之桦.水文统计学[M].北京:水利电力出版社,1985.
[12] MASSEYF.The Kolmogorov-Smirnov test for goodness of fit[J].Journal of the american statistical association,1951,46(253):68-78.
[13] 马海波,赵东亮,祝薄丽.几种水文频率曲线参数估计方法的比较[J].人民黄河,2016,38(3):9-11.
[14] 数学辞海委员会.数学辞海[M].北京:中国科学技术出版社,2002.
[15] ZHANG L,SINGH V P.Bivariate rainfall frequency distributions using archimedean copulas[J].Journal of hydrology,2007,332(1-2):93-109.
[16] YANG Q.A methodological study on AMH copula-based joint exceedance probabilities and applications for assessing tropical cyclone impacts and disaster risks (part I)[J].Tropical cyclone research and review,2014,3(1):53-62.
[17] 高超,梅亚东,涂新军.基于copula函数的区域降水联合分布与特征分析[J].水电能源科学,2013,36(6):1-5.
© 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 |