基于Copula函数的海岸增水高度与相应风速的遭遇概率分析  

Analysis on encounter probabilities for coastal surge heights and corresponding wind velocities based on Copula functions

作　　者：陈子燊[1] 刘曾美[2] 李志强[3] 

机构地区：[1]中山大学水资源与环境系,广东广州510275 [2]华南理工大学水利水电工程系,广东广州510640 [3]广东海洋大学海洋工程系,广东湛江524088

出　　处：《海洋学报》2012年第6期11-18,共8页

基　　金：国家自然科学基金资助项目(40576041);2009年广东省水利创新研究项目(2009-42)

摘　　要：简要论述了Copula理论与几种常用的二维Archimedean Copula函数的性质和适用性。以粤东汕头海域妈屿历年最高增水高度与相应风速的遭遇为研究实例,在分别采用3个三参数的概率分布模式:广义极值分布(GEV)、Weibull分布(WBL)和皮尔逊Ⅲ型(P-Ⅲ)分布对两个边缘分布(年最高增水高度与相应风速)拟合优度检验基础上构建了两变量联合概率分布模型。主要结果如下:(1)年最大增水高度与相应风速的边缘分布分别服从Weibull分布和P-Ⅲ型分布;(2)拟合优度检验指标表明二者的最优连接函数为Archimedean Copula类的Gumbel-HougaardCopula;(3)重现期介于2～200a之间的边缘分布与同频率的联合分布的重现水平相对差值大约介于6.7%～22.2%之间;(4)特定风速设计频率条件下,随年最大增水设计频率的减小,二者的遭遇概率也随之迅速减小;反之,特定增水设计频率随风速条件频率的减小,二者的遭遇概率随之明显增大。This paper deals the Copula theory and some of common bivariate Archimedean Copula proper- ties and suitability. A case study is given by using yearly maximum surge heights and corresponding wind speeds collected at Mayu gauge in Shantou sea waters of eastern Guangdong. Bivariate joint distribution model is built up through optimized two marginal distribution of yearly maximum surge heights and corre- sponding wind speeds by using goodness-of-fit test among three tri-parameter probability distribution mod- el including Generalized extreme value distribution,Pearson pattern three and Weibull distribution. Some conclusions were reached in the following; （1） Optimized marginal distributions of yearly maximum surgeheights and corresponding wind speeds can be represented by the Weibull distribution and Pearson pattern three distribution, respectively; （2） Gumbel-Hougaard Copula that belongs to Archimedean copula family is the optimal copula selected by the goodness-of-fit test; （3） Compare to the joint distribution, the relative differences of the special frequency design values of the marginal distribution of yearly maximum surge heights fall in between 6.7% and 22.2% for the return periods between 2 and 200 year; （4） The encounter probabilities of yearly maximum surge heights given wind velocity rapidly decrease along with the minis- hing design frequency of surge heights;whereas the encounter probabilities increase when the specific surge height frequency along with decrease of wind velocity frequency.

关 键 词：增水高度和相应风速 边缘分布 联合分布 COPULA函数 条件分布与遭遇概率 

分 类 号：P731.22[天文地球—海洋科学]