波高周期联合分布四种重现水平对比分析*

基于Gumbel-Hougaard copula、Kendall和生存Kendall函数对比分析波高和周期联合分布的4种重现水平。以位于北卡罗来纳州Duck的美国陆军工程师团FRF (Field Research Facility)实验场观测的波高与周期样本为例, 计算二者联合分布的“或”重现期、“且”重现期、Kendall重现期和生存Kendall重现期及其联合设计值。主要结论如下: 对比设定重现期, 相对于“或”联合重现期, Kendall重现期可更准确地反映波高周期联合分布的风险率; 相对于“且”联合重现期, 生存Kendall重现期可更准确地反映波高周期同时超值情况下的风险率。按目前有关规范设计要求的单变量波高设计值基本达到设计标准, 按两变量“或”重现期和波高周期两变量同频率设计值推算的设计值偏高, 以最大可能概率推算的两变量的Kendall重现期和生存Kendall重现期设计值可为海岸海洋工程安全与风险管理提供新的选择。

Comparative analysis on four recurrence levels of joint distribution of wave height and period*

In this study, we comparatively analyzed four designed wave recurrence levels of bivariate joint distribution of wave height and wave period by using Archimedean copula function, Kendall distribution function and survival Kendall distribution function. The annual maximum wave height and corresponding wave period of US Army Corps of Civil Engineers Field Research Facility (FRF) at Duck of North Carolina, US as an example, the “OR” primary return periods, “AND” primary return periods, Kendall return periods and survival Kendall return periods of bivariate joint distribution and the most likely designed wave quantiles were computed by using the optimally fitted Gumbel-Hougaard copula. The main conclusions of this study are summarized as follows: Comparing different specific wave return periods, the Kendall return periods can more accurately reflect wave risks relative to “OR” primary return periods, while the survival Kendall return periods can more accurately reflect wave risks when two wave variables are supercritical at the same time with respect to “AND” primary return periods. The univariate wave height or wave period designed value has reached a higher design standard according to the relevant specifications of the current design requirements. The estimated wave design quantiles of the “OR” primary return periods and two variables with the same frequency are obviously higher than those of univariate wave elements. The most-likely design realizations of the Kendall return periods and the survival Kendall return periods can serve as the new selections for safety and risk management of coastal engineering projects.