Wave height distributions in bimodal sea states from offshore basins

The paper presents results for the distribution of wave heights from laboratory generated bimodal sea states. Data collected at the DHI offshore basin are analyzed and compared with results based on wave records from the MARINTEK offshore basin. The comparisons are done for three groups of mixed sea states: wind-sea dominated, swell-dominated and energy-equivalent, determined on the basis of the parameter sea-swell energy ratio (SSER), which have been generated according to the model of Guedes Soares (1984). In some sea states abnormal or freak waves have been observed.The quasi-determinism theory of Boccotti is used to expand some linear narrowband models to second order, thus providing validation of the adequacy of the equations to represent the linear components of the wave heights. Also, the data are compared with the predictions of a third order model using as a nonlinear correction the coefficient of kurtosis. Due to the coexistence of wind-sea and swell, the core of the autocovariance function in some cases demonstrates a global minimum which is the second local minimum in the sequence. This can affect the fitting ability of distributions whose parameters depend on the form of the autocorrelation function or its envelope.The results for MARINTEK and DHI data show similar patterns of fit between predicted and observed exceedance probabilities for the considered classes of bimodal spectra.     

On the adequacy of second-order models to predict abnormal waves

The paper is intended to extend the investigations about the nature of abnormal waves that have been reported in the work of Guedes Soares et al. (Characteristics of abnormal waves in North Sea states. Applied Ocean Research 25, [337–344]). The same dataset gathered at the oil platform North Alwyn in the North Sea during the November storm in 1997 is used along with the time series from the Draupner platform, in which an abnormal wave occurred. The data are reanalyzed from the viewpoint of the applicability of second-order models to fit large waves. The observed results confirm that the second-order approximation is not adequate to describe highly asymmetric and abnormal waves.     

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。     

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.     

Modelling the long-term distribution of significant wave height with the Beta and Gamma models

The paper suggests modelling the long-term distribution of significant wave height with the Gamma, Beta of the first and second kind models. The three models are interrelated, flexible and cover the three different tail types of Extreme Value Theory. They can be used simultaneously as a means of assessing the uncertainty effects that result from choosing equally plausible models with different tail types. This procedure is intended for those applications that require the long-term distribution of significant wave height as input rather than the prediction of extreme values. The models are fitted to some significant wave data as an illustration. Details about maximum likelihood estimation are given in A.     

Wave model predictions in the Black Sea: Sensitivity to wind fields

This paper evaluates the impact of using different wind field products on the performance of the third generation wave model SWAN in the Black Sea and its capability for predicting both normal and extreme wave conditions during 1996. Wind data were obtained from NCEP CFSR, NASA MERRA, JRA-25, ECMWF Operational, ECMWF ERA40, and ECMWF ERA-Interim. Wave data were obtained in 1996 at three locations in the Black Sea within the NATO TU-WAVES project. The quality of wind fields was assessed by comparing them with satellite data. These wind data were used as forcing fields for the generation of wind waves. Time series of predicted significant wave height (H_mo), mean wave period (T_m02), and mean wave direction (DIR) were compared with observations at three offshore buoys in the Black Sea and its performance was quantified in terms of statistical parameters. In addition, wave model performance in terms of significant wave height was also assessed by comparing them against satellite data.The main scope of this work is the impact of the different available wind field products on the wave hindcast performance. In addition, the sensitivity of wave model forecasts due to variations in spatial and temporal resolutions of the wind field products was investigated. Finally, the impact of using various wind field products on predicting extreme wave events was analyzed by focussing on storm peaks and on an individual storm event in October 1996. The numerical results revealed that the CFSR winds are more suitable in comparison with the others for modelling both normal and extreme events in the Black Sea. The results also show that wave model output is critically sensitive to the choice of the wind field product, such that the quality of the wind fields is reflected in the quality of the wave predictions. A finer wind spatial resolution leads to an improvement of the wave model predictions, while a finer temporal resolution in the wind fields generally does not significantly improve agreement between observed and simulated wave data.     

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。     

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.     

Prediction of Long-Term Extreme Response of Fish Cage Using Environmental Contour Method

The fish cage design requires accurate predictions of long-term extreme loads and responses. Compared with the time-consuming full long-term analysis method integrating all the probability distribution of the short-term extremes,the environmental contour method gains much attention in predicting the long-term extreme values due to the less computational effort. This paper investigates the long-term extreme response of a fish cage using the environmental contour method. The fish cage is numerically simulated based on the lumped-mass method and the curved beam theory. Based on the one-dimensional(1D) and two-dimensional(2D) environmental contour, the extreme responses,including the surge and heave motions, mooring force, and vertical bending of the floater, are predicted for different return periods and compared with the full long-term analysis results. Results indicate that the 1D method greatly underestimates the extreme values. The 2D environmental contour method with a higher percentile level, namely90%, provides reasonable estimations and seems to be suitable for the long-term value analysis. Sensitivity studies show that the mooring arrangement and the bending stiffness have great effects on the bending moment and the mooring force and the mooring line pre-tension has minor effects on the fish cage response.     

长期极值统计理论及其在海洋环境参数统计分析中的应用

海洋环境极值参数(如风速、流速、波高、周期等)在海洋工程设计中具有重要意义。利用次序统计和极值理论方面的较新研究成果，从理论上证明了多种统计分布中Weibull分布是最优的，使长期极值统计建立在一个更坚实的基础上；同时引入基于序列统计的最大似然估计方法。利用大量数据．对最小二乘估计方法和最大似然估计法进行对比分析，指出最大似然估计法是精确估计．而最小二乘估计方法是保守估计。     

Assessment of extreme wind and waves in the Colombian Caribbean Sea for offshore applications

Interest in Colombia’s offshore industry has increased over the past years. Therefore a detailed characterization of extreme wind and waves, in terms of return periods, numbers of events and its duration during the annual cycle, is needed. Two sets of high-resolution data are used in the statistical extreme value analysis (EVA). The significant wave height data (0.125°, 6 h) are from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis available for the past 35 years (1979–2014). Surface winds (0.25°, 6 h) from the Cross-Calibrated Multi-Platform Ocean Surface Wind Vector Analyses (CCMP) of NASA/GSFC/NOAA (NASA/Goddard Space Flight Center/National Oceanic and Atmospheric Administration) are available for the past 24 years (1987–2011). Three well-known methods are applied to the data: the Block Maxima (BM), the Peak-Over-Threshold (POT) and the Method of Independent Storm (MIS). Several probabilistic models (Gumbel, Generalized Extreme Value, Weibull and Pareto) are evaluated for the BM and different threshold values for the POT and MIS. The results show that waves can reach up to 3.8 m and winds can be as strong as 31 m/s when considering the 50–100-year return periods. However, the wave model could underestimate values by up to one meter; hence, there is a probability of higher values in the region. Seasonally, most extreme events occur during the dry season (December–March) and during the Mid-Summer-Drought (MDS) or Veranillo months (June–July). Local conditions, including the reinforcement of the Caribbean Low Level Jet (CLLJ) and the occurrence of cold atmospheric fronts, are important drivers of extreme metoceanic variability. The total number of extreme wind events varied spatially and temporally from 15 to 65 and the mean duration from 15 to 25 h. A total number of extreme wave events ranging from <10 to 80 were computed during the annual cycle in the areas of interest, with a mean duration of less than 40 h.     

Uncertainty analysis on extreme value analysis of significant wave height at eastern coast of Korea

In this study, we considered the problem of estimating long-term predictions of design wave height based on the observation data collected over 10–15 years along the eastern-coast of the Korean peninsula. We adopted a method that combines Bayesian method and extreme value theory. The conventional frequency analysis methods must be reconsidered in two ways. First, the conventional probability distributions used in the frequency analysis should be evaluated to determine whether they can accurately model the variation in extreme values. Second, the uncertainty in the frequency analysis should also be quantified. Therefore, we performed a comparative study of the Gumbel distribution and GEV distribution to show the higher efficiency of the latter. Further, we compared the Bayesian MCMC (Markov Chain Monte Carlo) scheme and the MLE (Maximum Likelihood Estimation) with asymptotic normal approximation for parameter estimation to confirm the advantage of the Bayesian MCMC with respect to uncertainty analysis.     

Statistical simulation of wave climate and extreme beach erosion

Recent developments in extreme values modelling have been used to develop a framework for determining the coastal erosion hazard on sandy coastlines. This framework quantitatively reproduced the extreme beach erosion volumes obtained from field measurements at Narrabeen Beach, Australia. This encouraging finding was achieved using Kriebel and Dean's [Kriebel, D.L. and Dean, R.G., 1993. Convolution method for time-dependent beach profile response. Journal of Waterway, Port, Coastal and Ocean Engineering, 119(2): 204–226.] simple beach erosion and accretion model. The method includes allowances for joint probability between all basic erosion variates including; wave height, period and direction, event duration, tidal anomalies and event spacing. A new formulation for the dependency between wave height and period has been developed. It includes the physical wave steepness limitation. Event grouping, where significantly more erosion can occur from two closely spaced storms is handled by temporally simulating the synthetic wave climate and the resulting beach erosion and accretion.     

Estimation of mean and extreme waves in the East China Seas

Accurately estimating the mean and extreme wave statistics and better understanding their directional and seasonal variations are of great importance in the planning and designing of ocean and coastal engineering works. Due to the lack of long-term wave measurement data, the analysis of extreme waves is often based on the numerical wave hind-casting results. In this study, the wave climate in the East China Seas (including the Bohai Sea, the Yellow Sea and the East China Sea) for the past 35 years (1979–2013) is hind-casted using a third generation wave model – WAMC4 (Cycle 4 version of WAM model). Two sets of reanalysis wind data from NCEP (National Centers for Environmental Prediction, USA) and ECMWF (European Centre for Medium-range Weather Forecasts) are used to drive the wave model to generate the long-term wave climate. The hind-casted waves are then analysed to study the mean and extreme wave statistics in the study area. The results show that the mean wave heights decrease from south to north and from sea to land in general. The extreme wave heights with return periods of 50 and 100 years in the summer and autumn seasons are significantly higher than those in the other two seasons, mainly due to the effect of typhoon events. The mean wave heights in the winter season have the highest values, mainly due to the effect of winter monsoon winds. The comparison of extreme wave statistics from both wind fields with the field measurements at several nearshore wave observation stations shows that the extreme waves generated by the ECMWF winds are better than those generated by the NCEP winds. The comparison also shows the extreme waves in deep waters are better reproduced than those in shallow waters, which is partly attributed to the limitations of the wave model used. The results presented in this paper provide useful insight into the wave climate in the area of the East China Seas, as well as the effect of wind data resolution on the simulation of long-term waves.     

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.     

Estimation of Design Wave Height for the Waters around the Korean Peninsula

Long term wave climate of both extreme wave and operational wave height is essential for planning and designing coastal structures. Since the field wave data for the waters around Korean peninsula is not enough to provide reliable wave statistics, the wave climate information has been generated by means of long-term wave hindcasting using available meteorological data. Basic data base of hindcasted wave parameters such as significant wave height, peak period and direction has been established continuously for the period of 25 years starting from 1979 and for major 106 typhoons for the past 53 years since 1951 for each grid point of the North East Asia Regional Seas with grid size of 18 km. Wind field reanalyzed by European Center for Midrange Weather Forecasts (ECMWF) was used for the simulation of waves for the extratropical storms, while wind field calculated by typhoon wind model with typhoon parameters carefully analyzed using most of the available data was used for the simulation of typhoon waves. Design wave heights for the return period of 10, 20, 30, 50 and 100 years for 16 directions at each grid point have been estimated by means of extreme wave analysis using the wave simulation data. As in conventional methodsi of design criteria estimation, it is assumed that the climate is stationary and the statistics and extreme analysis using the long-term hindcasting data are used in the statistical prediction for the future. The method of extreme statistical analysis in handling the extreme events like typhoon Maemi in 2003 was evaluated for more stable results of design wave height estimation for the return periods of 30–50 years for the cost effective construction of coastal structures.     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.     

Statistical Simulation of Boxing Day Tsunami of The Indian Ocean and a Predictive Equation for Beach Run up Heights Based on Work-Energy Theorem

The tsunami similar to the one that has occurred in December 26, 2004 (Boxing Day Tsunami) in the Indian Ocean is simulated using the expression derived from Modified Weibull Distribution (for maximum wave height simulation) for extreme wave height predictions. The tuning coefficient plays a significant role in estimating the tsunami heights at various stages. It follows well defined mathematical laws at different stages. It is time dependent in the first three stages and depth dependent in the last two stages. The beach run-up heights estimated by the expression derived from the work-energy relation are comparable with observed values with reasonable accuracy.