Statistical properties of successive wave heights and successive wave periods

Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss model [Næss A. On the distribution of crest to trough wave heights. Ocean Engineering (1985);12(3):221–34] and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights.Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregressive model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. Thus, the joint distribution of three successive wave heights can be obtained by combining conditional bivariate distributions. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation.Successive wave periods with corresponding wave heights exceeding a certain threshold have also been studied. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights, can be approximated by a multivariate Gaussian distribution.The theoretical distributions are compared with observed wave data obtained from field measurements in the central North Sea and in the Japan Sea, with laboratory data and numerical simulations.     

Wave climate in a groin field

Wave records at seven different locations within a groin field have been analysed by both statistical and spectral approaches to study the general wave climate. The wave heights and periods from the wave records were obtained by both upcross and downcross methods for the statistical approach. The variation of different wave height and wave period parameters with respect to the time of measurement at a particular location and its variation at different locations within the groin field at a particular instant of time are presented and discussed in detail in this paper. It is generally found that the wave heights follow the Weibull distribution.     

海洋重现期波高统一化计算方法

重现期波高是港口海岸及海洋工程设计中不可回避的一个重要设计参数,尤其对深水海港、海上平台、海底油气管道、沿海核电站等重大涉海工程设计具有巨大的经济价值和深远的社会效益。但是,现有重现期波高推算缺乏统一的计算方法,导致计算结果相差悬殊。研究重现期波高的统一化计算方法,分析重现期波高计算中存在的各种不确定因素,提出减少这些不确定因素的新方法,建立误差小、应用方便、方法统一的重现期波高计算方法。基于澳大利亚悉尼站的长期连续观测波浪数据,研究发现:广义帕累托函数(generalized Pareto distribution III,GPD-III)和威布尔(Weibull)是重现期波高计算的最佳候选极值分布函数,新推导的函数形状参数计算公式较好提高重现期波高的计算精度,极值波高数据的分析方法和样本大小是影响重现期波高计算精确度的两个重要因素,短期波浪资料和年极值法可能高估重现期波高值。逐个风暴的极值波高数据分析法及最佳候选极值分布函数GPD-III和Weibull建议应用于涉海工程设计的重现期波高推算。     

广西沿海年极值波高分析

经分析发现广西沿海极值波高不符合用的P－Ⅲ型分布，并分析了其符合的分布函数，结果表明对Weibull分布符合最好，为解决Weibull分布参数难于确定的问题，引入了共轭梯度法计算其参数，最终计算了多年一遇极值波高。     

Wave height distribution in shallow water

Probability distribution of shallow water wave heights, obtained from a pressure type recorder, are examined. It is tested with the theoretical distributions of (a) Rayleigh, (b) Weibull, (c) Gluhovski, (d) Ibrageemov and (e) Goda. The best fit is shown by the Gluhovski probability density function with a correlation coefficient greater than 0.8. The functions of Weibull, Ibrageemov and Goda fit only half of the tested cases. The role of wave steepness in the wave height distribution is found to be negligible.     

Probability distribution of wave heights attenuated by salt marsh vegetation during tropical cyclone

Zero-crossing wave heights, obtained from the field measurement of random waves propagating through salt marsh vegetation (Spartina alterniflora) during a tropical storm, were analyzed to examine their probability distribution. Wave data (significant wave heights up to 0.4 m in 0.8 m depth) were collected over a two-day period along a 28 m transect using three pressure transducers sampling at 10 Hz. Wave height distribution was observed to deviate from the Rayleigh distribution. The observed probability densities of the larger wave heights were reduced significantly by vegetation, producing wave heights lower than those predicted by the Rayleigh distribution. Assuming Rayleigh distributed wave heights for the incident waves to the vegetation patch, existing vegetation-induced wave attenuation formulations are used to derive a special form of two-parameter Weibull distribution for wave heights in the inundated wetland. The scale parameter of the distribution is theoretically shown to be a function of the shape parameter, which agrees with the measurements, effectively reducing the proposed distribution to a one-parameter type. The derived distribution depends on the local parameters only and fits well to the observed distribution of wave heights attenuated by vegetation. Empirical relationships are developed to estimate the shape parameter from the local wave parameters.     

Maximum entropy principle and statistical distribution of ocean wave heights

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印尼ADIPALA海域较长周期波浪统计特征分析

对印尼ADIPALA海岸观测的较长周期波浪数据进行了统计分析,给出了不同统计波高特征值之间的关系以及统计特征周期和相对水深的关系;并就波浪统计中的波高分布,采用威布尔分布形式进行拟合,得到波高累积分布;给出了最大波高计算公式,可为工程设计提供参考。     

波高的长期极值统计分布

通过对国内外常用的４种极值波高分布模式的拟合与比较,得到了以下结论：（１）由于地区差异,港口工程技术规范给出的一单一模式并非具有普遍性,对同一工程应该采用多种理论分布进行计算比较,从中选择最佳模式。（２）应用麦奎尔特法拟合Ｗｅｉｂｕｌｌ分布实现了对未知参数的一举寻优,解的收敛速度快,结果稳定且精度高。同时对其它几种分布实现了资料的微机化处理;（３）本文算例用４种极值分布对不同重视值波高进行了比较,     

Laboratory study of the nonlinear transformation of irregular waves over a mild slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.     

Laboratory Study of the Nonlinear Transformation of Irregular Waves over A Mild Slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope (1?40). Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.     

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.     

A Comparative Study of the Statistical Distributions of Wave Heights

Distribution of wave heights and surface elevations of wind-driven waves are studied.Recordsof surface elevations obtained from both field observations and laboratory measurements are analyzed.Wave heights can be approximated by normal,two-parameter Weibull,and/or Rayleigh distribution.However,while the first two models may have almost equal probabilities to fit measured data quite satis-factorily,the Rayleigh distribution does not appear to be a good model for the majority of the cases stu-died.Surface elevations from field data are well described by the Gaussian model,but as with increasingwind speeds,water surface in a wind-wave flume deviates from normality,and the Edgeworth's form ofthe type A Gram-Charlier series is then applied.     

响水近岸海域波浪特性研究

基于响水波浪站累计一整年的现场观测资料,分析了波高和波周期的年内变化特性,研究了波浪的统计特性和波谱特性,并总结归纳了该海域各特征波要素之间以及各波谱参数之间的转换关系。结果显示:响水海域全年有效波高的变化幅度在0.10~2.80 m之间,年平均值为0.56 m;最大波高的变化幅度在0.15~5.58 m之间,年平均值为0.93 m;平均波周期的变化范围为1.91~9.02 s,年平均值为3.90 s。夏季大波高发生频率明显要小于冬、春季节,波浪季节性变化较为显著。就波高和波周期分布而言,通过拟合得出的Weibull分布较为适合本海域实测波高分布和波周期分布。波谱特性方面,本海域双峰谱占到总数的62.5%,且低频谱峰值普遍高于高频谱峰值,其中低频谱峰出现在0.04 Hz左右,高频谱峰则出现在0.15~0.20 Hz之间,分别为本海域涌浪和风浪所集中的频率区间。采用回归分析方法进一步分析了各特征波要素之间以及各波谱参数之间的关系,发现多数波参数之间存在显著的相关性,但受波浪浅水变形影响,各参数之间的比值与理论深水关系有所区别。本文的研究成果可为沿海建筑物的设计以及防灾减灾提供参考和依据。     

Forecasting of tsunami wave heights at the Russian coast of the Black Sea

Forecasting of tsunami wave heights at the Russian coast of the Black Sea is discussed. Prognostic numerical calculations of tsunamis were carried out for the tsunami sources uniformly distributed in the Black Sea basin (a total of 55 events). Their results are compared with the results of numerical modeling of the historical events (in 1939 and 1966) and the data of not numerous measurements. A preliminary forecast is made on this basis for the tsunami wave heights along the Russian coast of the Black Sea.     

墨西哥湾波候统计特性分析

简要介绍了波候的概念,简述Ｗｅｉｂｕｌｌ分布及对数一正态分布的拟合方法,提出最大熵分布拟合有效波高、峰周期分布的新方法;选取半封闭海湾墨西哥湾内水深不同、地理位置不同的六个观测站一年的连续资料,以上述三种拟合方法对其有效波高,峰周期概率分布进行拟合,并与观测直方图进行比较检验,结果表明,在墨西哥海湾内,最大熵分布优于对数－正态分布,对数－正态分布优于Ｗｅｉｂｕｌｌ分布。     

Short-term statistics of waves measured off Ratnagiri,eastern Arabian Sea

The short-term wave characteristics are required for design and operation of industrial facilities within the coastal areas. Water surface displacement measured using waverider buoy moored at 13 m water depth in the eastern Arabian Sea off the west coast of India have been analyzed to study the short-term statistics of waves covering full one year period. The study indicates that the values of the observed maximum wave height as a function of duration are not consistent with the theoretical expected value. There is significant variation (1.29–2.19) in the ratio between highest 1% wave and significant wave height compared to the theoretical value of 1.67. The data recorded at 13 m water depth indicates that the significant wave height is ∼8% lower than that predicted by the conventional Rayleigh distribution. The theoretical bivariate log-normal distribution represents the joint distributions of wave heights and periods for the study area.     

Modified Weibull distribution for maximum and significant wave height simulation and prediction

Calibration coefficients incorporated in the modified Weibull distribution are more effective for maximum wave height simulation. The parametric relations are derived there from to estimate various wave height statistics including extreme wave heights. The characteristic function of the Weibull distribution is derived. The Weibull distribution is suggested for the newly defined significant wave height simulation by the method of characteristic function. The statistical tools suggested and developed here for predicting the required wave height statistics are validated against the wave data (both deep and shallow) of eastern Arabian Sea comprising rough monsoon conditions also, giving reasonable accuracy.     

Weibull分布参数的粒子群算法估计

基于广西涠洲岛海洋监测站3个方向的年极值波高观测资料,在假设其服从Weibull分布的基础上,运用最小二乘法,矩估计法和最速下降法对Weibull分布的参数进行估计,同时引入粒子群算法确定Weibull分布的3个参数,对文中4种方法得出的拟合结果及运算效率进行比较分析,说明了粒子群算法在估计极值分布参数中的优势.