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

This paper deals the Copula theory and some of common bivariate Archimedean Copula properties 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 corresponding wind speeds by using goodness-of-fit test among three tri-parameter probability distribution model 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 surge heights 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 minishing design frequency of surge heights;whereas the encounter probabilities increase when the specific surge height frequency along with decrease of wind velocity frequency.