基于Vine Copula函数的风浪要素联合概率分布模型

Joint probability distribution model of wind and wave with Vine Copula function

随着全球气候变暖的加剧,极端气候现象发生的频率和强度均可能加大,这对海岸和近海结构的安全不利。基于中国东海的连云港海洋观测站实测风浪数据和Vine Copula理论,建立风浪要素中风速、波高、波浪周期、风向和波向五维随机变量之间的联合概率分布模型。采用极大似然法确定各风浪要素边缘分布模型参数,通过AIC信息准则和均方根误差RMSE进行拟合优度评价,由此建立风浪要素的边缘分布。采用带有基于残差的高斯似然函数的贝叶斯框架估计二维Copula函数的参数,结合AIC信息准则进行拟合优度评价并确定最优Copula函数。绘制最优联合分布概率密度图,与二维频率直方图进行对比以评价模型效果。采用Vine Copula函数建立多维联合概率模型并结合AIC值评价其拟合优度。研究结果表明:建立的Vine Copula模型可以较好地刻画风速、波高、波浪周期、风向和波向五维随机变量之间的联合概率分布。

With the intensification of global climate warming,the probabilities and load intensities of extreme weather phenomenon are gradually increasing,which could threaten the safety of coastal and offshore infrastructures.The present study presents a joint probability distribution model of wind speed,wave height,wave period,wind direction and wave direction with Vine Copula function based on monitoring data from Lianyungang Ocean Station in the East China Sea.Firstly,the marginal probability distributions of wind and wave data are determined,in which the AIC criteria and RMSE index are employed to select the optimal probability distribution model and the maximum likelihood method is used to determine the model parameters Subsequently,the optimal two-dimensional Copula function for wind and wave data is determined via the AIC criteria,and the model parameters are fitted with a Bayesian framework with a residual-based Gaussian likelihood function.To illustrate the goodness of fit,the binary frequency histogram of the original wind and wave data is compared with the proposed two-dimensional Copula function.Finally,the multi-dimensional joint probability distribution model of wind and wave data is established with the Vine Copula function based on the AIC criteria.The results show that the proposed Vine Copula model is able to describe the joint probability distribution between the wind speed,wave height,wave period,wind direction and wave direction.