极值波高建模中不确定性的模糊量化方法

A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height and the extrapolation for extremes are obtained based on high quantile estimations. The quality of these results is compared and discussed. Then, the proposed fuzzy model, which combines Poisson process and generalized Pareto distribution(GPD) model, is applied to characterizing the wave extremes in the time series data. The estimations for a long-term return value are considered as time-varying as a threshold is regarded as non-stationary. The estimated intervals coupled with the fuzzy theory are then introduced to construct the probability bounds for the return values. This nontraditional model is analyzed in comparison with the traditional model in the degree of conservatism for the long-term estimate. The impact on the fuzzy bounds of extreme estimations from the non stationary effect in the proposed model is also investigated.     

A New Model of Peaks over Threshold for Multivariate Extremes

The peaks over threshold（POT） methods are used for the univariate and multivariate extreme value analyses of the wave and wind records collected from a hydrometric station in the South China Sea. A new multivariate POT method： Multivariate GPD（MGPD） model is proposed, which can be built easily according to developed parametric models and is a natural distribution of multivariate POT methods. A joint threshold selection approach is used in the MGPD model well. Finally, sensitivity analyses are carried out to calculate the return values of the base shear, and two declustering schemes are compared in this study.     

A new method for determining threshold in using PGCEVD to calculate return values of typhoon wave height

In using the PGCEVD (Poisson-Gumbel Compound Extreme Value Distribution) model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution (P-Ⅲ) model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-Ⅲ model and can be used for the return wave height in every direction.     

Accessing extremes of mid-latitudinal wave activity: methodology and application

A statistical methodology is proposed and tested for the analysis of extreme values of atmospheric wave activity at mid-latitudes. The adopted methods are the classical block-maximum and peak over threshold, respectively based on the generalized extreme value (GEV) distribution and the generalized Pareto distribution (GPD). Time-series of the 'Wave Activity Index' (WAI) and the 'Baroclinic Activity Index' (BAI) are computed from simulations of the General Circulation Model ECHAM4.6, which is run under perpetual January conditions. Both the GEV and the GPD analyses indicate that the extremes of WAI and BAI are Weibull distributed, this corresponds to distributions with an upper bound. However, a remarkably large variability is found in the tails of such distributions; distinct simulations carried out under the same experimental setup provide sensibly different estimates of the 200-yr WAI return level. The consequences of this phenomenon in applications of the methodology to climate change studies are discussed. The atmospheric configurations characteristic of the maxima and minima of WAI and BAI are also examined.     

Automated threshold selection methods for extreme wave analysis

The study of the extreme values of a variable such as wave height is very important in flood risk assessment and coastal design. Often values above a sufficiently large threshold can be modelled using the Generalized Pareto Distribution, the parameters of which are estimated using maximum likelihood. There are several popular empirical techniques for choosing a suitable threshold, but these require the subjective interpretation of plots by the user.In this paper we present a pragmatic automated, simple and computationally inexpensive threshold selection method based on the distribution of the difference of parameter estimates when the threshold is changed, and apply it to a published rainfall and a new wave height data set. We assess the effect of the uncertainty associated with our threshold selection technique on return level estimation by using the bootstrap procedure. We illustrate the effectiveness of our methodology by a simulation study and compare it with the approach used in the JOINSEA software. In addition, we present an extension that allows the threshold selected to depend on the value of a covariate such as the cosine of wave direction.     

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WAVEWATCH Ⅲ (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...     

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.     

A Bayesian method for the estimation of return values of wave heights

Bayesian statistics offer a novel means of estimating return values of wave heights and hence of establishing design criteria for offshore structures. The Bayesian method has significant advantages over the classical method since it enables all types of uncertainty (physical, parameter, distribution) associated with the design wave prediction to be handled in a consistent manner in the same analysis.The basic principles of the Bayesian method for drawing inferences are outlined step-by-step. It is shown how Bayesian estimators of return values for wave heights are established by taking an expectation over all parameters and contending distributions. When the Bayesian procedure is applied to large data sets, such as wave data sets, computational difficulties could be encountered, making a “remedial” procedure necessary. However, the Bayesian procedure has been used successfully with wave data sets from the northern North Sea. Furthermore, the associated remedial procedure is such that the program can be made suitable for many existing computers, e.g. desk computers.     

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。     

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.     

Modelling uncertainty in long-term predictions of significant wave height

This paper deals with the application of different methods to estimate the occurrences of high sea states. A case study of the Norwegian continental shelf is considered. The Annual Maxima Method and the Peak Over Threshold Method are used to obtain return values for 25, 50 and 100 years. Several parametric models are used to fit the long-term distribution of significant wave height and to obtain predictions of extremes values. It is shown that the prediction of these sea states depends very much on the tail behaviour of the fitted distribution.     

A simulation study on the uncertainty of environmental contours due to sampling variability for different estimation methods

Environmental contours are often used in design of marine structures to identify extreme environmental conditions that may give rise to extreme loads and responses. Recently, attention has been given to the fact that different methods exist for establishing such contours, and that in some cases significant differences may be obtained from the various methods.In this study, another aspect of the uncertainty related to the calculation of environmental contours is addressed, namely the uncertainty due to sampling variability when environmental contours are constructed based on metocean data of finite sample size. The uncertainty of environmental contours for the joint distribution of significant wave height and wave period for different sample sizes (10, 25 and 100 years of data) are investigated considering different underlying datasets and for different estimation methods for the joint distribution. Both cases where samples are drawn from a known joint distribution of wave height and periods and cases where samples are drawn from a real hindcast dataset and fitted to the joint distribution are considered. The uncertainty of the estimated contours is quantified and discussed in light of differences that can be anticipated from the different methods used to calculate the contours. Moreover, the potential bias from assuming different estimation methods is illustrated.     

江苏及邻近海域深水波浪与增水联合概率分析

采用Gumbel Logistic模型对江苏及邻近海域深水极值波浪与增水进行了联合概率分析。首先对联合概率模型参数进行拟合,得到联合超越概率与经验联合超越概率比较图。在此基础上开展有效波高和增水年极值序列联合概率分析,比较了三种经验有效波高与增水重现期组合事件的联合概率,结果表明在选定的13个代表点位处,有效波高在二者的联合概率分布中处于主导地位,采用100年一遇有效波高与10年一遇增水组合事件作为100年一遇联合事件偏保守;而50年一遇有效波高与50年一遇增水以及10年一遇有效波高与100年一遇增水组合事件的联合概率则随着点位的移动而高于或低于100年一遇的水平。     

太平洋波高熵的分布变化规律研究

使用1992年IO月到1998年12月连续共75个月、230个重复周期的Topex／Poseidon卫星高度计有效波高资料，对南、北太平洋波高熵的空间分布特征和时间变化规律进行了研究。统计分析了太平洋波高熵的多年的空间分布特征和多年各月的时间变化规律。结果表明，太平洋波高熵呈现出中间低、南北高的马鞍形空间分布特征和明显季节变化的规律，与太平洋的平均有效波高和气候分布特征和变化规律相一致。给出了南北太平洋模拟波高熵的计算公式及计算稳定性检验。     

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。     

A generalized approach for long-term modelling of extreme crest-to-trough wave heights

This paper deals with the long-term modelling of high sea waves. The solution is given for the return period of sea storms during which an arbitrary chosen number of waves, with crest-to-trough heights exceeding a fixed threshold, occur. This return period is derived starting from the Equivalent Triangular Storm (ETS) model, which associates a triangle to each actual storm and thus represents a significant wave height time series at a fixed location by means of a sequence of triangular storms. The short-term statistics is then applied to investigate the occurrence of large crest-to-trough wave heights during a given storm. Finally, by combining the statistical distribution of significant wave heights, the ETS model and the short-term wave statistics, the solution is given for the return periods R_N and R_N of a sea storm in which N or at least N waves higher than a fixed threshold occur. The values of R_N are then calculated, starting from data of two buoys moored in the Pacific Ocean and in the Mediterranean Sea.     

Return period and risk calculations for ocean wave energy applications

The statistical behavior of wave energy at a site strongly depends on the wave characteristics. Wave energy converters fail to produce energy when there are no sufficiently available wave heights. Hence, evaluation of return periods and risk values of the minimum wave height becomes important for wave energy studies. A time index representing the minimum wave height is proposed here for ocean wave applications. Persistence plays a significant role in the calculation of return period and risk. Although ignoring the serial independence makes calculations easy, it leads to overestimations of the real status. In this paper, return periods and risk values are compared with each other by taking into consideration independent and dependent situations. Application of the study is achieved for the stations located in the Pacific Ocean and Gulf of Mexico.     

1988-2002年黄海和渤海风浪后报

本文对黄海和渤海风浪开展长期后报实验,时间范围覆盖1988至2002年,并分析相应的区域波候特征。首先,模式输出的月平均有效波高和卫星数据比对一致。其次,我们讨论了气候态月平均有效波高和平均波周期的时空分布特征。有效波高和平均波周期的气候态空间分布都呈现出西北-东南、或由近岸向深水区增加的趋势,这种空间的分布特征和局地的风强迫和水深密切相关。同时,海浪参数的季节变化也较显著。进一步,我们统计分析了风场和有效波高的极值,给出并揭示了黄海和渤海多年一遇有效波高的空间结构,并讨论了有效波高极值和风强迫极值之间的联系。     

基于随机集合的非传统型有效波极值模型

The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the available methods for the modeling of the extreme significant wave height on a statistical basis, the peak over threshold method has attracted most attention. This method employs Poisson process to character- ize time-varying properties in the parameters of an extreme value distribution. In this paper, the peak over threshold method is reviewed and extended to account for subjectivity in the modeling. The freedom in selecting the threshold and the time span to separate extremes from the original time series data is incorpo- rated as imprecision in the model. This leads to an extension from random variables to random sets in the probabilistic model for the extreme significant wave height. The extended model is also applied to different periods of the sampled data to evaluate the significance of the climatic conditions on the uncertainties of the parameters.