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。     

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。     

极值波高与历时联合分布的重现水平分析

使用美国北卡罗来纳州的 FRF 1985—2016 年的极值波高及其持续时间数据，采用最优的 Gumbel-Hougaard copula函数和 Kendall 分布函数构建极值波高和相应历时不同组合的联合概率分布模式，分析各个组合的遭遇概率、“或”重现期、“且”重现期和 Kendall 重现期，以出现最大可能概率的方法推算各组合联合设计值。结果表明：Kendall 重现期所对应的累积频率更准确地代表了特定设计频率下的风险率；重现期分别为 5 年、10 年、20 年、50 年、100 年、200 年推算的 Kendall重现期设计值介于“或”重现期和“且”重现期设计值之间，小于相应的边缘分布设计值；基于 Kendall 重现期的极值波高及其持续时间不同重现期组合推算的结果可为海洋工程构筑物设计与风险管理提供新的选择与参考。     

基于Archimedean Copula函数的风浪联合统计分析

选取渤海海域某导管架平台24年的年最大波高和相应风速,基于Gumbel分布对2个边缘分布的拟合优度检验,采用Archimedean Copula函数族中的4种函数构建两变量联合概率分布模型,并进行了拟合优度评价。利用优选出的Clayton Copula函数,计算风浪联合分布的联合重现值。以海洋平台响应作为约束条件,进行了二维Clayton Copula函数的风浪联合统计分析。研究结果表明:基于Copula函数构造的二维分布,考虑了风浪之间的相关性,在相同重现值设计参数下,可以降低导管架平台的结构响应,从而可以降低海洋平台的环境条件设计标准。     

重现期设计波高相对应的波浪周期推算方法的讨论

一、前言关于重现期设计波高相对应的波浪周期的推算方法在《港口工程技术规范》第二篇第一册第22条中规定:“与某一重现期的设计波高相对应的波浪周期的推算方法有两种:1.按第四章的风浪要素计算图直接查出与该设计波高相对应的周期(平均周期T);2.用波高最大值相对应周期(T)所组成的系列进行频率分析,以确定与设计波高为同一重现期的周期值。当地大的波浪主要为风浪时,可用方法1;当地大的波浪主要为涌浪或混合浪时,可用方法2。”     

基于Copula函数的波高与周期长期联合分布

基于二元copula函数构建波高与相应波周期的长期联合分布。以粤东汕尾海域最大波高与相应平均周期为研究实例,经分析获得以下结果:(1)经拟合优度检验优选的年最大波高与相应周期的边缘分布分别为皮尔逊三型分布和广义极值分布,二者之间的较优连接函数为Archimedean类的Gumbel-Hougaard copula函数;(2)同频率条件下年最大波高和相应周期联合概率分布的设计要素值高于单变量的设计值,其中波高设计值的差异略大于周期设计值;(3)同现重现期和联合重现期的设计值可作为海岸海洋工程建设中的设计波高和相应周期的上限和下限;(4)条件概率1表明,同频率下的年最大波高和相应周期的遭遇概率很高,其组合概率可作为工程建筑物损毁风险率。     

基于Copula函数的海岸增水高度与相应风速的遭遇概率分析

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-Hougaard Copula;(3) 重现期介于2~200 a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。     

登陆中国东南沿海热带气旋气压变化的重现期分析

为正确考虑和衡量核电厂选址风暴潮灾害分析中热带气旋登陆过程时出现的气压填塞量的取值,利用1949-2014年在我国东南沿海登陆的台风气压资料,建立了登陆前TC中心气压与登陆后气压填塞量二维Copula联合分布函数,通过同现重现期表征出两种样本筛选条件下两种边缘分布的相关关系。结果表明:Frank Copula函数可以适应样本联合分布;考虑在台湾登陆的TC样本与不考虑时相比,相同同现重现期水平在登陆前气压边缘分布方向上要增加10 h Pa左右;气压填塞量在25 h Pa以内时,填塞量越小,同现重现期越大。     

青岛港日最大降水量及其出现日期的联合统计分析

以青岛地区近30年历年日最大降水量(R_Y)与其在该年中的出现日期(L_Y),以及各月的日最大降水量(R_M)与其在该月中的出现日期(L_M)的13个样本序列为例,基于4种二维Copula函数(Clayton Copula、Frank Copula、Gumbel-Hougaard Copula和Gaussian Copula)建立二维联合分布模型;通过假设检验和拟合优度评价,选取拟合较优的二维Frank Copula函数所构建的日最大降水量及其出现日期的联合分布模型,对(R_Y,L_Y)和各月(R_M,L_M)进行了详细分析。通过历年各月日最大降水量及其出现日期的联合统计分析,在一定联合重现期时,当日最大降水量给定某一重现值时,可以估计该值在一年中(或某个月份中)最可能的出现日期,为合理港口装卸作业给建设意见。     

北部湾乌雷站台风浪、风暴增水数值结果的联合概率分析

对1949?2002年北部湾乌雷站台风浪和风暴增水的数值模拟结果进行分析,得出54a的台风浪和风暴增水的极值序列,作出二者联合概率分布图,其分布近似于指数分布,进而运用GUMBELⅡ联合概率分布函数对其拟合,在找出联合概率分布函数过程中分析得出了台风浪和风暴增水不同重现期的单要素极值和联合分布要素极值及相应概率(具体给出),其结果对海洋工程设计有一定的参考价值。     

基于危险率分析的风浪联合重现期研究

采用二维逻辑冈贝尔分布,基于工程使用期和危险率,提出海洋工程结构设计过程中海洋环境要素(风速和波高)联合重现期的确定方法,并且以某海区资料为例,介绍基于危险率分析的风浪联合重现期分析过程.通过此例,在考虑工程使用期和危险率的基础上进行联合重现期的计算使海洋工程结构物设计过程中重现期的选取更加合理,安全性以及投资建造成本更加明确.     

Wave energy assessment based on trivariate distribution of significant wave height,mean period and direction

Based on the Vine copula theory, a trivariate statistical model of significant wave height, characterized wave period and mean wave direction was constructed. To maintain the properties of the different types of variables, a special copula function was derived from the model developed by Johnson and Wehrly based on the maximum entropy principle. It was then combined with the Archimedean copulas to construct the proposed model. An effective algorithm for generating corresponding joint pseudo-random numbers was also developed. Statistical analysis of hindcast data for the significant wave height, mean wave period, and direction, which were collected from an observation point in the North Atlantic every three hours from 1997 to 2001, was performed. The marginal distributions of the significant wave height and mean wave period were fitted by a modified maximum entropy distribution, and the mean wave direction was fitted by a mixture of von Mises distributions. It was shown that the proposed model is a good fit for the data. The seasonal wave energy resources in the target area were assessed using the model estimates. Histograms of the directional wave energy, wave energy roses, and scatter and energy diagrams were presented.     

Extreme waves for Kuwaiti territorial waters

The extreme significant wave heights and the corresponding wave periods were predicted for return periods of 12, 25, 50, 100 and 200 yr for 19 different locations in Kuwaiti territorial waters. Though the total coast length of Kuwait is only about 500 km including all islands and the total area of the Kuwaiti territorial water is about 7611 km², the extreme significant wave height vary from 1.86 to 4.02 m for 100 yr return period, among these 19 locations. In general Weibull distribution is found to fit the data well compared to the Gumbel distribution. The input wave data for the present work is obtained by hind casting waves using a WAM model. Wave data is hindcasted for a total period of 12 yr, starting from 1 January 1993 to 31 December 2004. From the joint probability of wave height and wave period, a simple polynomial relationship is obtained between the significant wave height and mean period for all the 19 locations. It is found that the wave period for wave heights of 100 yr return period cannot exceed 6.5 s. A large number of coastal projects are in progress and many new projects are planned for the near future in the Kuwaiti territorial waters. The results of the present study will be highly useful for optimal design of these projects.     

Non-stationary extreme value models to account for trends and shifts in the extreme wave climate due to climate change

The extreme values of wave climate data are of great interest in a number of different ocean engineering applications, including the design and operation of ships and offshore structures, marine energy generation, aquaculture and coastal installations. Typically, the return values of certain met-ocean parameters such as significant wave height are of particular importance. There exist many methods for estimating such return values, including the initial distribution approach, the block maxima approach and the peaks-over threshold approach. In a climate change perspective, projections of such return values to a future climate are of great importance for risk management and adaptation purposes. However, many approaches to extreme value modelling assume stationary conditions and it is not straightforward how to include non-stationarity of the extremes due to for example climate change. In this paper, various non-stationary GEV-models for significant wave height are developed that account for trends and shifts in the extreme wave climate due to climate change. These models are fitted to block maxima in a particular set of wave data obtained for a historical control period and two future projections for a future period corresponding to different emission scenarios. These models are used to investigate whether there are trends in the data within each period that influence the extreme value analysis and need to be taken into account. Moreover, it will be investigated whether there are significant inter-period shifts or trends in the extreme wave climate from the historical period to the future periods. The results from this study suggest that the intra-period trends are not statistically significant and that it might be reasonable to ignore these in extreme value analyses within each period. However, when it comes to comparing the different data sets, i.e. the historical period and the future projections, statistical significant inter-period changes are detected. Hence, the accumulated effect of a climatic trend may not be negligible over longer time periods. Interestingly enough, such statistically significant shifts are not detected if stationary extreme value models are fitted to each period separately. Therefore, the non-stationary extreme value models with inter-period shifts in the parameters are proposed as an alternative for extreme value modelling in a climate change perspective, in situations where historical data and future projections are available.     

渤海和黄海北部波高与周期联合分析

分析波高与周期的联合分布特征对于海洋平台设计、海洋工程建筑等有着重要的意义。基于SWAN模型模拟的波浪后报数据对渤海和黄海北部1999~2018年的波浪特征进行了统计分析。分别对20年的波高和周期数据进行了统计分析,得到了研究区域20年有效波高和波周期的季平均值和最大值的区域分布特征。然后以散布图的形式刻画了整个区域20年波高和周期的联合分布特征。为了更深入地研究波高和周期的联合分布规律,选择了两个研究点A1和A2,A1在渤海内部相对近岸,A2在黄海北部深海区。统计结果表明,在A1和A2,波高与周期的联合分布特征较为相似,均呈现斜三角形的分布特征,然而大波高大周期的波浪却呈现不同的分布特征。最后,利用20年的波浪后报数据,在A1和A2点构建了有效波高和谱峰周期的联合概率模型,并采用IFORM法得到了50年、100年和200年重现周期的环境等值线,为研究海域海上结构物的可靠性设计提供了参考。