Modified Joint Distribution of Wave Heights and Periods

The modified versions of the linear theoretical model of Longuet-Higgins （1983） are derived in this work and also compared with the laboratory experiments carried out in MAR1NTEK. The main feature of modifications is to replace the mean frequency in the formulation with the peak frequency of the wave spectrum. These two alternative forms of joint distributions are checked in three typical random sea states characterized by the initial wave steepness. In order to further explore the properties ＆these models, the associated marginal distributions of wave heights and wave periods are also researched with the observed statistics and some encouraging results are obtained.

Joint Return Value Estimation of Significant Wave Heights and Wind Speeds with Bivariate Copulas

The joint design criteria of significant wave heights and wind speeds are quite important for the structural reliability of fixed offshore platforms.However,the design method that regards different ocean environmental variables as independent is conservative.In the present study,we introduce a bivariate sample consisting of the maximum wave heights and concomitant wind speeds of the threshold by using the peak-over-threshold and declustering methods.After selecting the appropriate bivariate copulas and univariate distributions and blocking the sample into years,the bivariate compound distribution of annual extreme wave heights and concomitant wind speeds is constructed.Two joint design criteria,namely,the joint probability density method and the conditional probability method,are applied to obtain the joint return values of significant wave heights and wind speeds.Results show that(28.5±0.5)m s^(-1)is the frequently obtained wind speed based on the Atlantic dataset,and these joint design values are more appropriate than those calculated by univariate analysis in the fatigue design.

Joint Distribution of Wave Periods and Rate of Change of Wave Surface Elevation

The rate of change of wave surface elevation is of much importance in ocean engineering, especially for the determination of the limitation of wave breaking. This paper gives a kind of joint distribution of wave periods and the rate of change of wave surface elevation by means of calculation of the two-order to four-order moment of the frequency spectrum based on the linear wave theory. For the first time, the distribution density function of wave periods determined by peaks is provided, and the conclusion is drawn that the rate of change of wave surface elevation obeys the Rayleigh distribution.

On the long-term joint distribution of characteristic wave height and period and its application

By analysing the scatter diagrams of characteristic the wave height H and the period T on the basis of instrumental data from various ocean wave stations, we found that the conditional expectation and standard deviation of wave period for a given wave height can be better predicted by using the equations of normal linear regression rather than by those based on the log- normal law. The latter was implied in Ochi' s bivariate log-normal model(Ochi. 1978) for the long-term joint distribution of H and T. With the expectation and standard deviation predicted by the normal linear regression equations and applying proper types of distribution, we have obtained the conditional distribution of T for given H. Then combining this conditional P(T / H) with long-term marginal distribution of the wave height P(H) we establish a new parameterized model for the long-term joint distribution P(H,T). As an example of the application of the new model we give a method for estimating wave period associated with an extreme wave height.

Joint Occurrence Period of Wind Speed and Wave Height Based on Both Service Term and Risk Probability

Return periods calculated for different environmental conditions are key parameters for ocean platform design.Many codes for offshore structure design give no consideration about the correlativity among multi-loads and over-estimate design values.This frequently leads to not only higher investment but also distortion of structural reliability analysis.The definition of design return period in existing codes and industry criteria in China are summarized.Then joint return periods of different ocean environmental parameters are determined from the view of service term and danger risk.Based on a bivariate equivalent maximum entropy distribution,joint design parameters are estimated for the concomitant wave height and wind speed at a site in the Bohai Sea.The calculated results show that even if the return period of each environmental factor,such as wave height or wind speed,is small,their combinations can lead to larger joint return periods.Proper design criteria for joint return period associated with concomitant environmental conditions will reduce structural size and lead to lower investment of ocean platforms for the exploitation of marginal oil field.

A Maximum-Entropy Compound Distribution Model for Extreme Wave Heights of Typhoon-Affected Sea Areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.

Long-Term Joint Distribution of One-Tenth Large (or Significant) Wave Height with Average Period

In this paper, by using the wave data from a few oceanographic observation stations in the coastal zone of the Yellow Sea, the East China Sea and the South China Sea, the long-term joint distribution of the one-tenth large (or significant) wave height with average period is studied. The statistical data demonstrate that the long- term distribution of the one- tenth wave height or average period fits the log-normal distribution, thus the joint distribution also fits the two-dimensional log-normal distribution. Then the conditional probability distribution of the average period is derived, and the range as well as the mode of the average wave period corresponding to a certain return period of wave height can be calculated easily.

Application of MEP Method to the Study of statistical Properties of Random Waves

The maximum entropy principle (MEP) method and the corresponding probability evaluation method are introduced, and the maximum entropy probability distribution expression is deduced in moment of the second order. Fully developed wave height distribution in deep water and wave height and period distribution for different depths in wind wave channel experiment are obtained from the MEP method, and the results are compared with the distribution and the experimental histogram. The wave height and period distribution for the Lianyungang port is also obtained by the MEP method, and the results are compared with the Weibull distribution and the field histogram.

An Expression of Apparent Energy Distribution of Sea Waves by Wave Charateristics

Based on observed wind waves, the relationships between wave spectrum products and wave characteristics are established successfully, and the apparent energy distribution of sea waves is expressed as a function of wave characteristics.

基于WW3的南海北部有效波高时空变化及其极值重现期估算方法分析

本文基于第3代海浪模式WAVEWATCHⅢ(WW3)模拟的1996–2015年海浪后报数据,分析了南海北部有效波高及其极值的时空变化特征,并采用Pearson-Ⅲ和Gumbel两种极值分布方法对该区极值波高重现期进行了估算。结果表明,南海北部有效波高的季节变化和空间分布与季风风场基本一致,呈现秋冬高春夏低,并自吕宋海峡西侧向西南降低的特征,与ERA5再分析数据结果高度相似。有效波高极值(简称极值波高)的时空分布特征受时间分辨率强烈影响,采用极值数据的分辨率越高(如逐小时),所展现的台风型波浪特征越显著。扣除季节变化信号后的有效波高和年极值波高均体现出较强的线性增高趋势,近20年升高的比例分别为7.7%和31.6%,值得警惕和关注。该区多年一遇极值波高存在若干个大值区,且与台风的路径、强度有直接联系,表明台风是引发该区域极端大浪的最主要机制。对比Pearson-Ⅲ和Gumbel极值分布估算结果发现:若极值波高较低,频率随极值波高升高缓慢降低,此时两种极值分布的估算都比较准确,差异极小,可忽略不计;但当研究时间范围内,某年极值波高远超其他年份时,Pearson-Ⅲ极值分布估算结果明显高于Gumbel极值分布估算结果,且更接近实际极值波高,即Pearson-Ⅲ极值分布在此情况下表现更好。本研究表明对于特定海区,在出现超强台风引发极值波高远超出其他年份时,不同计算方法对极值波高的估算差异较大,会显著影响重现期的评估。此外,南海北部年极值波高的强烈增高趋势,也可能给计算未来极值波高重现期和海上工程防护带来不可忽视的影响。

基于Copula函数的黄海波高周期联合统计分析

为研究黄海中部海域波浪的年极值波高与年极值周期联合分布,基于黄海海域3个位置点1999—2018年SWAN后报波浪数据,采用5种单变量分布拟合年极值波高和年极值周期,通过拟合优度评价得到各位置点年极值波高和年极值周期的最优单变量分布,利用Copula函数理论建立了年极值波高和年极值周期联合分布函数,并与单变量分布波高和周期设计值进行了对比分析。结果表明:黄海中部海域波高周期联合分布可能存在区域性特征;波高周期联合分布得到的波高、周期设计值较同设计频率下的单变量分布设计值高;相同波高和周期设计频率下,单变量重现期最大,条件重现期次之,联合重现期最小。

基于FHDI-GNWM数据的全球波浪宏观分布特征初步分析成果

为分析全球波浪的宏观分布特征,基于2011—2015年共5 a的FHDI-GNWM全球波浪数据,对全球的有效波高Hs、谱峰周期T_(p)和主波向D_(main)进行研究,研究结果表明:全球有效波高Hs平均值总体呈现南半球大于北半球的特点,且在南半球对应于南极绕极流区域形成了一条明显的有效波高Hs平均值大于3.6 m的高值区,与西北太平洋、东太平洋、北大西洋、南大西洋和印度洋等全球主要大洋的波高宏观分布特征差异性较大;全球大部分海域T_(p)平均值大于12 s且T_(p)在各大洲的西海岸要明显大于东海岸;全球主波向分布规律不明显,不同海域的主波向存在明显差异。

短期风浪波高周期联合分布研究

为了准确描述短期风浪波高周期的联合分布,采用条件概率方法提出新的联合分布模型,并给出新的波高周期联合概率密度函数表达式.该表达式仅包含有义波高、平均跨零周期2个参数,便于工程应用.以Pierson-Moscowitz (P-M)谱、布氏谱以及实测波浪谱为靶谱,采用余弦波叠加方法模拟短期波浪,统计分析得到波高周期的经验联合分布.以经验联合分布为基准,对提出的联合分布模型以及现有文献中5种联合分布模型进行对比分析.采用均方根误差评价所有模型与经验分布的匹配程度.均方根误差结果表明,在所有模型中所提模型与经验分布最接近.模型之间的差异,主要体现在周期分布上.在所有模型中,所提模型导出的周期分布与经验分布最接近.所提模型采用显式闭合公式表示,可采用Hermite变换、Rychlic变换,将该模型推广到非高斯波浪情况.

中国近海海浪波高与周期联合分布研究

海浪波高与周期的联合分布是沿海港口、航道及防波堤工程设计的重要参数。对中国大陆沿岸9个代表点波高与周期的联合分布开展研究,对多种联合分布计算方法进行适用性分析。研究结果表明:中国大陆沿岸不同站点处波高和周期的联合分布形式存在一定差异;根据对联合概率密度的比较,基于波高的条件概率的经验方法较三类不同形式的Copula模型更能准确反映不同区域波高和周期的联合概率分布。

海南东方近岸海域海浪观测特征研究

利用海南东方近岸海域2014年至2015年间一整年的海浪观测资料,分析了海浪的时间变化特征。观测时间段内,有效波高最大值为4.03m,平均值0.79m;平均周期最大值为6.32s,平均值为3.58s。该海域冬季波高较大,秋季最小,常浪向为SSW方向,强浪向为WSW向。基于该长期观测数据,文章亦研究了平均周期、有效波高之间的关系,同时还确立了该海域波高与平均持续时间之间的关系。最后讨论了观测时间段内波浪能流密度的变化特征,发现一年中能流密度大于2kW·m^(-1)的频率为26%,且从全年的计算结果来看,观测位置处12月的波浪能较适宜开发,但总体波浪能资源不够丰富。文章对于认识海南东方近岸海域波浪特征以及工程设计都具有重要的意义。

广东阳西近岸海域波浪的分布特征

通过对广东阳西近岸测站1a实测波浪资料及岸边同期风资料的整理与分析,探讨了该海域的波浪特性,得出研究海域不分方向H1/10年平均值为1.00 m,常浪向为SE向,出现的频率为38.35%,强浪向为SE向,观测期间的最大波高出现在0814号"黑格比"台风期间,Hmax值为8.31 m.用已有的理论分布函数对实测统计数据进行拟合,筛选出研究海域的波高分布、周期分布及波高与周期联合分布的特征,结果表明双参数威布尔理论波高分布、杨正己威布尔周期分布、朗格-赫金斯83模式或者孙孚模式较为适用于本海区的波高分布、周期分布、波高周期联合分布;结合相应的风速风向资料,运用回归分析方法,建立了该地区的波高与风速之间、波高与波周期之间的关系.

斋堂岛东南海域波浪特征及海浪谱分析

利用斋堂岛东南海域2013年至2014年的实测波浪资料,统计分析了本海域波浪特征,为波浪能资源评估提供基本波浪参数。统计结果表明,本海域年平均有效波高为0.60 m,最大波高为5.30m,平均周期为3.3s,最大周期为8.3s,常浪向为E-SE向。本文亦讨论了本海域波高分布和波高与周期的关系,并基于JONSWAP谱谱型的基本结构,拟合得到适用于本海域的海浪谱谱型,可为海洋能发电装置的布设及相应的工程建设提供一定的参考。

杭州湾中部波浪统计分布

利用杭州湾中部一年实测波浪资料,分析了实测波高分布、波周期分布和波高周期联合分布。基于双参数威布尔分布模式,采用最小二乘法拟合得出波高分布和波周期分布模式,并与其他理论分布模式作了比较。结果表明:(1)双参数威布尔分布对杭州湾中部实测波高分布的拟合效果好于Gluhovski分布,而且该模式在实测波周期分布上的拟合效果也相对优于孙孚分布和侯一筠分布,但威布尔分布在对大周期比区域的预测值偏小,而其他两者分布则偏大。(2)实测联合分布与孙孚理论的联合分布有所不同。(3)威布尔分布的拟合系数与相关波参数的关系较为复杂,其中周期分布的威布尔系数与谱宽度有较好的相关性,由此可改进威布尔分布的拟合效果。(4)偏东向的流速对波高分布和波周期分布存在微弱的影响。

中国海与西北太平洋波浪长期统计的导算方法

为了满足船舶与海洋工程对波侯数据的需要，本文回顾了以往出版的几种图集资料并分析了其不足之处，着重介绍了当前国际上较新的英国波峰综合模式（NMIMET）和美国海军风浪后报模式（SOWM）及两者的结果图集。为获得中国海与西北太平洋海域更可靠的数据，在对日本气象厅的器测浮标站长期资料的统计结果与相应的船舶报资料按各种方法处理的结果比较基础上，进一步改进了NMIMET模式。这主要是在波高与周期联合概率分布导算方法上，采用一种新的更灵活的联合分布模式以代替原来所用的由Ochi建议的二维对数正态模式；同时对于在模式中需要确定的有关周期的参数，根据新的资料和计算结果对原用的回归公式作出了改进。用改进后的模式导算得到的波高、周期分布与器测浮标站结果更为接近。

基于Copula函数的联合概率法在海洋工程中的应用

本文介绍了Copula函数的定义、属性和几种特殊的Copula函数.将Copula函数应用到近海工程中,用其建立了最大有效波高和最大风速的联合分布函数并检验,结果表明:Copula函数能够比较好的模拟实际的联合概率分布。通过Copula方法,可以由边缘分布和一个连接它们的Copula函数来得出联合分布函数,发挥其描述相关性尤其是尾部相关性的优势。该方法在近海工程的工程可靠度、设计标准和失效概率的计算中具有广泛的应用前景。