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.     

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.     

Environmental contours using copulas

A procedure is proposed for constructing environmental contours using copula theory. Copulas are functions that define the multivariate probability distribution of a random vector or a set of random variables, and, thus, also determine their dependence structure. Constructing environmental contours requires knowledge of the joint probability distribution of the environmental variables. In many practical applications, the available statistical data is used to estimate the marginal distributions and the linear correlation matrix, and then the Nataf distribution model is employed to obtain the multivariate probability distribution. It turns out that such an approach implies a particular model of dependence structure defined by a Gaussian copula, which might not always be the appropriate one. In this work, some classes of bivariate copulas are considered for modeling the dependence structure of the environmental variables. We examine measures of association, rank-based methods for estimation of copulas, goodness of fit tests for copulas, and copula selection criteria, and apply them to metocean data from hindcasts of tropical storms and extra-tropical events in the Gulf of Mexico. A formulation is proposed for expressing the variates that define the environmental contours as functions of copulas. It is then applied for computing environmental contours of significant wave height, peak spectral period and wind velocity using the estimated copula models.     

基于非对称Archimedean Copula的三变量风浪重现水平分析

采用非对称Archimedean Copula函数与Kendall分布函数分析极端波况下的波高、周期和风速三变量联合概率分布与风险率及其设计分位数,为海岸海洋工程设计和风险评估提供参考依据。以粤东汕尾海域的实测风浪数据为例,使用非对称Gumbel-Hougaard Copula函数计算三变量风浪联合分布的"或"重现期、"且"重现期和二次重现期及其最可能的风浪设计值。主要结论如下:对比不同设计风浪重现期显示,"或"重现期的风险率偏高,"且"重现期的风险率偏低,二次重现期更准确地反映了特定设计频率情况下三变量风浪的风险率;按目前有关规范设计要求的单变量风浪要素设计值已经达到安全标准,按三变量"或"重现期和三变量同频率设计值推算的风浪设计值偏高,以最大可能概率推算的三变量风浪要素的二次重现期设计值可为相关工程安全与风险管理提供新的选择。     

Climate Variations of Certain Wave Parameters at the Inlet of Novorossiysk Bay

The main purpose of the study is an analysis of the wave climate of Novorossiysk Bay (Black Sea) for 1979–2019. The analysis is based on mathematical modeling results obtained with the modern DHI MIKE 21 SW spectral wave model. The wave model was verified using numerous instrumental data of the wind-wave parameters in the Black Sea and Sea of Azov. As follows from the research, the average power of storm waves in Novorossiysk Bay area is about 8 kW/m. The maximum power ranges from 50 to 100 kW/m but can reach 200 kW/m or more. The total duration of storm waves for one year is 40–60 days. The maximum duration of one storm can be up to three days but does not exceed two days on average. The mean storm duration is usually 10–11 h. The largest number of storms (above 130) was recorded in 2004; on average, there are about 100 storms annually. In recent decades, in the area of Novorossiysk Bay, the maximum wind-wave heights and the total number of storms has increased with statistical control. It is also highly probable that the average annual power of combined waves and maximum storm duration have increased; i.e., the time of continuous wave impact has increased.

     

Assessment of uncertainty in environmental contours due to parametric uncertainty in models of the dependence structure between metocean variables

A key factor for computing environmental contours is the appropriate modeling of the dependence structure among the environmental variables. It is known that all the information on the dependence structure of a set of random variables is contained in the copulas that define their multivariate probability distribution. Provided that copula parameters are estimated by means of statistical inference using observations, recordings, numerical or historical data, uncertainty is unavoidably introduced in their estimates. Parametric uncertainty in the copulas parameters then introduces uncertainty in the environmental contours. This study deals with the assessment of uncertainty in environmental contours due to parametric uncertainty in the copula models that define the dependence structure of the environmental variables. A point estimation approach is adopted to estimate the statistics of the uncertain coordinates of the environmental contours considering they are given in terms of inverse functions of conditional copulas. A case study is reported using copulas models estimated from storm hindcast data for the Gulf of Mexico. Uncertainty in environmental contours of significant wave height, peak period and wind speed is assessed. The accuracy of the point estimation of the mean and variance of the contour coordinates is validated based on Monte Carlo simulations. A parametric study shows the manner in which greater parametric uncertainty induces larger variability in the environmental contours. The influence of parametric uncertainty for different degrees of association is also analyzed. The results indicate that variability between contours considering parametric uncertainty can be meaningful.     

大亚湾风暴潮波浪传播数学模型

本文建立了大亚湾风暴潮涌浪传播数学模型,以任意多边形离散计算海区,每一多边形构成单元,以波浪运动学和动力学守恒方程模拟单元内能量传递,以风暴潮过程模拟边界入射波高过程,用风暴潮涌浪传播基本方程和波能缓坡方程结合模拟湾口巨浪向湾内的传播过程。通过分析大亚湾不同种类岸线反射系数的概率分布,并结合实测波高对模型进行率定,最终确定模型参数。将大亚湾特征点计算波高与统计推荐波高比较进行模型验证,结果显示SE向波高与H_(13%)推荐波高对应较好,可以用于大亚湾海区的波浪预报。计算当大亚湾口分别出现10年一遇、50年一遇及100年一遇的波高时,在E、ESE以及ES向入射波浪条件下大亚湾海域极值波高的分布。分别对风暴潮涌浪在不同类型岸线的爬高以及风暴潮涌浪传播对岸线的作用力进行计算。     

曹妃甸粉沙质海岸围垦后港内泥沙研究

粉沙质海岸离岸围垦后港内淤积引人关注。基于平面二维潮流数学模型,采用网格嵌套技术,模拟了渤海、曹妃甸海域潮流场;该海域泥沙为粘性沙,且围垦后港内流速很小,采用悬沙运动数学模型模拟了潮流和波浪作用下正常天气和大风天的含沙量场,分析了大风后含沙量衰减过程,计算了正常天气年淤积强度和大风天泥沙淤积厚度。计算表明,外海泥沙主要通过甸头东侧老龙沟进入港池水域。正常天气下,港内流速小,基本处于淤积环境,但由于外海含沙量小,港池水域年淤积厚度小于10 cm。大风浪作用下,曹妃甸海域含沙量明显增大,由老龙沟进入三港池的泥沙沿程落淤,港内普遍淤积,泥沙淤积厚度在5 cm以内。     

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.     

Experimental and numerical investigations of monopile ringing in irregular finite-depth water waves

In storm conditions, nonlinear wave loads on monopile offshore wind turbines can induce resonant ringing-type responses. Efficient, validated methods which capture such events in irregular waves in intermediate or shallow water depth conditions are needed for design. Dedicated experiments and numerical studies were performed toward this goal. The extensive experimental campaign at 1:48 scale was carried out for Statoil related to the development of the Dudgeon wind farm, and included both a rigid model and a flexible, pitching-type, single degree-of-freedom model. Twenty 3-hour duration realizations for 4 sea states and 2 water depths were tested for each model. A high level of repeatability in ringing events was observed. Uncertainties in the experimental results were critically examined. The stochastic variation in the 3-hour maximum bending moment at the sea bed was significantly larger than the random variation in repetition tests, and highlighted the need for a good statistical basis in design. Numerical simulations using a beam element model with a modified Morison wave load model and second order wave kinematics gave reasonable prediction of the ringing response of the flexible model, and of the measured excitation forces on the rigid model in the absence of slamming. The numerical model was also used to investigate the sensitivity of the responses with respect to damping and natural period. A simple single degree-of-freedom model was shown to behave similarly to a fully flexible model when considering changes in natural frequency and damping.     

Applications of EMD to analyses of high-frequency beachface responses to Storm Bebinca in the Qing'an Bay,Guangdong Province,China

On average, five to six storms occur in the Qiongzhou Strait every year, causing significant damage to coastal geomorphology and several property losses. Tropical Storm Bebinca is the most unusual and complex storm event that has occurred in this region over the last 10 years. To detect the high-frequency beachface responses to the storm, a pressure sensor was deployed in the surf zone to record the free sea surface height, and the heights of grid pile points on the beachface were measured manua...     

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5.30 m,平均周期为3.3 s,最大周期为8.3 s,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。     

Storm evolution characterization for analysing stone armour damage progression

Storm evolution is fundamental for analysing the damage progression of the different failure modes and establishing suitable protocols for maintaining and optimally sizing structures. However, this aspect has hardly been studied and practically the whole of the studies dealing with the subject adopt the Equivalent triangle storm. As against this approach, two new ones are proposed. The first is the Equivalent Triangle Magnitude Storm model (ETMS), whose base, the triangular storm duration, D, is established such that its magnitude (area describing the storm history above the reference threshold level which sets the storm condition), H_T, equals the real storm magnitude. The other is the Equivalent Triangle Number of Waves Storm (ETNWS), where the base is referred in terms of the real storm's number of waves, N_z. Three approaches are used for estimating the mean period, T_m, associated to each of the sea states defining the storm evolution, which is necessary to determine the full energy flux withstood by the structure in the course of the extreme event. Two are based on the Jonswap spectrum representativity and the other uses the bivariate Gumbel copula (H_s, T_m), resulting from adjusting the storm peaks. The representativity of the approaches proposed and those defined in specialised literature are analysed by comparing the main armour layer's progressive loss of hydraulic stability caused by real storms and that relating to theoretical ones. An empirical maximum energy flux model is used for this purpose. The agreement between the empirical and theoretical results demonstrates that the representativity of the different approaches depends on the storm characteristics and point towards a need to investigate other geometrical shapes to characterise the storm evolution associated with sea states heavily influenced by swell wave components.     

A numerical study on the impact of tidal waves on the storm surge in the north of Liaodong Bay

A storm surge is an abnormal sharp rise or fall in the seawater level produced by the strong wind and low pressure field of an approaching storm system.A storm tide is a water level rise or fall caused by the combined effect of the storm surge and an astronomical tide.The storm surge depends on many factors,such as the tracks of typhoon movement,the intensity of typhoon,the topography of sea area,the amplitude of tidal wave,the period during which the storm surge couples with the tidal wave.When coupling with different parts of a tidal wave,the storm surges caused by a typhoon vary widely.The variation of the storm surges is studied.An once-in-a-century storm surge was caused by Typhoon 7203 at Huludao Port in the north of the Liaodong Bay from July 26th to 27th,1972.The maximum storm surge is about 1.90 m.The wind field and pressure field used in numerical simulations in the research were derived from the historical data of the Typhoon 7203 from July 23rd to 28th,1972.DHI Mike21 is used as the software tools.The whole Bohai Sea is defined as the computational domain.The numerical simulation models are forced with sea levels at water boundaries,that is the tide along the Bohai Straits from July 18th to 29th（2012）.The tide wave and the storm tides caused by the wind field and pressure field mentioned above are calculated in the numerical simulations.The coupling processes of storm surges and tidal waves are simulated in the following way.The first simulation start date and time are 00：00 July 18th,2012; the second simulation start date and time are 03：00 July 18th,2012.There is a three-hour lag between the start date and time of the simulation and that of the former one,the last simulation start date and time are 00：00 July 25th,2012.All the simulations have a same duration of 5 days,which is same as the time length of typhoon data.With the first day and the second day simulation output,which is affected by the initial field,being ignored,only the 3rd to 5th day simulation results are used to study the rules of the storm surges in the north of the Liaodong Bay.In total,57 cases are calculated and analyzed,including the coupling effects between the storm surge and a tidal wave during different tidal durations and on different tidal levels.Based on the results of the 57 numerical examples,the following conclusions are obtained：For the same location,the maximum storm surges are determined by the primary vibration（the storm tide keeps rising quickly） duration and tidal duration.If the primary vibration duration is a part of the flood tidal duration,the maximum storm surge is lower（1.01,1.05 and 1.37 m at the Huludao Port,the Daling Estuary and the Liaohe Estuary respectively）.If the primary vibration duration is a part of the ebb tidal duration,the maximum storm surge is higher（1.92,2.05 and 2.80 m at the Huludao Port,the Daling Estuary and the Liaohe Estuary respectively）.In the mean time,the sea level restrains the growth of storm surges.The hour of the highest storm tide has a margin of error of plus or minus 80 min,comparing the high water hour of the astronomical tide,in the north of the Liaodong Bay.     

Estimation of wind speed and wave height during cyclones

Wave and wind characteristics based on the cyclones, in the vicinity of the Nagapattinam coastline (east coast of India) were estimated. In all, 11 cyclones have crossed near the study region during 1960–1996. For the four severe cyclones, the isobaric charts were collected at three hourly intervals from the India Meteorological Department. The storm variables such as central pressure, radius of maximum wind, speed of forward motion and direction of storm movement were extracted and the method based on standard Hydromet pressure profile, were used for the hindcast of storm wind fields. For all the cyclones the maximum significant wave height within the storm and its associated spectral peak period was estimated using the Young’s model considering the moving wind field and the results are compared with the hurricane wave prediction techniques provided in the shore protection manual published by the US Army Corps of Engineers in 1984. The study shows that the estimated wind speed and the data reported by ships were comparable. Empirical expressions relating wind speed, wave height and wave period to storm parameters were derived. The design wave height for different return periods was obtained by fitting a two-parameter Weibull distribution to the estimated significant wave heights. The design wave height was 9.39 m for 1 in 100 year return period for a direct hit of cyclone.     

Evaluation of two spectral wave models for wave hindcasting in the Mackenzie Delta

Climate change, reduced sea ice and increased ice-free waters over extended areas for longer summer periods potentially lead to increased wave energy in the Beaufort Sea (Wang et al., 2015; Khon et al., 2014) [1], [2], which is a major concern for coastal and offshore engineering activities. We compare two spectral wave models SWAN (Simulating WAves Nearshore) and MIKE 21 SW (hereafter MIKE21) in simulations of storm-generated waves in the Mackenzie Delta region of the southern Beaufort Sea. SWAN model simulations are performed using two nested grids system, whereas MIKE21 uses an unstructured grid system. Forcing fields are defined by hourly hindcast winds. Moving ice edge boundaries are incorporated during storm simulations. Modelled wave spectra from four storms are shown to compare well with field observations. Two established whitecapping formulations in SWAN are investigated: one dependent on mean spectral wave steepness, and the other on local spectral steepness. For the Beaufort Sea study area, we suggest that SWAN wave simulations using the latter local spectral steepness formulation are better than those using the former mean spectral steepness formulation. MIKE21 simulations also tend to agree with SWAN results using the latter whitecapping formulation.     

海南岛近岸养殖区台风浪预报技术研究

随着海南深水网箱养殖规模的不断扩大,海浪精细化预报的需求越来越紧迫。以海南岛周边海域为目标区域,基于近岸海洋模式ADCIRC(Advancedcirculationmodel)和海浪模式SWAN(Simulating WavesNearshore),建立了海南岛近岸养殖区台风浪数值预报系统。该系统采用非结构高分辨率网格,近岸分辨率达到了100m。选取2014年第9号超强台风"威马逊"(RAMMASUN)进行针对海南岛近岸养殖区的台风浪数值模拟后报。模拟结果与实测数据较为吻合。采用全球预报系统GFS(Global Forecast System)风场和气压场数据作为驱动场对2018年7月的一次热带风暴过程进行预报,48小时、24小时预报的有效波高和实测结果比较平均相对误差分别为20.75%和17.0%。总体来说,该模型的预报精度可以满足近岸养殖区台风浪预报业务的需求。     

Hydrodynamic and sedimentary responses to two contrasting winter storms on the inner shelf of the northern Gulf of Mexico

Results are presented from the deployment of three bottom-mounted instrumentation systems in water depths of 6–9 m on the sandy inner shelf of Louisiana, USA. The 61-day deployment included nine cold front passages that were associated with large increases in wind speed. Two of the most energetic cold front passages were characterized by distinct meteorological, hydrodynamic, bottom boundary layer, and sedimentary responses and may potentially be treated as end-member types on a continuum of regional cold front passages. Arctic surges (AC storms) have a very weak pre-frontal phase followed by a fairly powerful post-frontal phase, when northeasterly winds dominate. Migrating cyclones (MC storms) are dominated by a strong low-pressure cell and have fairly strong southerly winds prior to the frontal passage, followed by strong northwesterly winds.

On the basis of measurements taken during this study, AC storms are expected to have a lower average significant wave height than MC storms and are dominated by short-period southerly waves subsequent to the frontal passage. Currents are weak and northerly during the pre-frontal phase, but become very strong and southwesterly following the passage. Sediment transport rate during AS storms was not as high as during MC storms, and the mean and overall direction tended to be southwesterly to westerly, with low-frequency flows producing easterly transport, and wind-wave flows producing southeasterly transport.

MC storms had the most energetic waves of any storm type, with peaks in significant wave height occurring during both the pre- and post-frontal phases. The wave field during MC storms tended to be more complex than during AS storms, with an energetic, northerly swell band gradually giving way to a southerly sea band as the post-frontal phase progressed. Currents during MC storms were moderate and northerly during the pre-frontal phase, but became much stronger and southeasterly during the post-frontal phase. Shear velocity was high during both the pre- and post-frontal phases of the storm, although sediment transport was highest following the frontal passage. Mean and overall sediment transport was directed southeasterly during MC storms, with low-frequency and wind-wave flows producing northerly transport. In summary, the data sets presented here are unique and offer insight into the morphosedimentary dynamics of mid-latitude, micro-tidal coasts during extratropical storms.