Stochastic bivariate time series models of waves in the North Sea and their application in simulation-based design

In this paper, we present and evaluate three long-term wave models for application in simulation-based design of ships and marine structures. Designers and researchers often rely on historical weather data as a source for ocean area characteristics based on hindcast datasets or in-situ measurements. The limited access and size of historical datasets reduces repeatability of simulations and analyses, making it difficult to assess the sampling variability of performance and loads on marine vessels and structures. Markov, VAR and VARMA wave models, producing independent long-term time series of significant wave height (H_s) and spectral peak period (T_p), is presented as possible solutions to this problem. The models are tested and compared by addressing how the models affect interpretation of design concepts and the ability to replicate statistical and physical characteristics of the wave process. Our results show that the VAR and VARMA models perform sufficiently in describing design performance, but does not capture the physical process fully. The Markov model is found to perform worst of the tested models in the applied tests, especially for measures covering several consecutive sea states.     

中国浙江和福建海域台风浪变化特征和趋势

基于非结构网格的海浪-海流耦合模式SWAN+ADCIRC(Simulating Waves Nearshore+Advanced Circulation model),模拟了1997—2016年共20年间所有影响浙江和福建海域台风过程期间的海浪过程。利用4个台风过程期间的海浪观测数据对模拟结果进行了验证,模拟结果和实测结果吻合较好。基于该长时间序列台风浪模拟结果,分别分析了浙江和福建海岸带台风浪有效波高极值以及台风浪有效波高大于1m和1.5m的持续时间。结果显示,在福建北部海岸带台风浪有效波高极值和台风浪有效波高大于1m的持续时间(tHs1)有显著增长的趋势。其中,台风浪高极值的增长趋势最大可达0.05m/a,tHs1的增长趋势位于0.54至1.72h/a之间。分析tHs1与ENSO指数的关系发现,福建省南部海域台风浪与ENSO指数有较显著的负相关,浙江省北部海域台风浪与ENSO指数有较显著的正相关,ENSO信号对这两个海域的台风浪有着较显著的影响。     

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.     

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。     

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 w     

Dynamic pressures on inclined cylinders due to freak waves

The dynamic pressure distribution around a cylinder tilted along and against the principal wave direction is measured. The cylinder was exposed to the action of random waves in the presence and absence of extreme waves. Six inclinations from the vertical plane, three along and three against the wave direction, were considered. The cylinder in upright position was also studied. The variation of dimensionless peak pressure (pressure maximum/average highest one-third wave height, H_1/3) with the relative wave height (maximum wave height/H_1/3) for locations facing the wave and at the rear of the cylinder for different angles of inclinations of the cylinder are reported for the two kinds of waves mentioned earlier. The statistical properties of the different asymmetries in the pressure traces are also discussed.     

Characteristics of a breaking wind-wave field in the light of the individual wind-wave concept

The relation between the intensity of breaking of individual wind-wave crests and parameters of wave size and wave form (e. g., height, period, steepness and skewness) is examined, and the process of change of these parameters is studied in a wind-wave tank (reference wind speed 15 m sec⁻¹, fetch 16 m). Distributions of the wave form parameters are different for breaking and nonbreaking waves. Fully breaking waves seem to hold the relationH ∞T ², whereH is the individual wave height andT is the period. The condition of breaking is not simply determined by the simple criterion of Stokes' limit. Wave height and steepness of a breaking wave are not always larger than those of a nonbreaking wave. This suggests the existence of an overshooting phenomenon in the breaking wave. The wave form parameters are found to change cyclically in a statistical sense during the wave propagation. The period of the cycle in the present case is estimated to be longer than four wave periods. An intermittency of wave breaking is associated with this cyclic process. Roughly speaking, two or three succeeding breaking-waves sporadically exist among a series of nonbreaking waves along the fetch.     

随机波浪中畸形波在三维岛礁地形上的试验研究

在试验水池中,开展了波浪在岛礁地形上演化问题的研究。首先在实验水池中建立了西太平洋某岛礁地形的模型,然后采用改进的JONSWAP谱,由造波机产生不同周期、波高的随机波浪。试验中观察到了不同类型畸形波生成的过程及不同波面形态的畸形波。对偏度、峰度及水深与畸形波要素H_m/H_s（H_m表示波列中的最大波高, H_s为有效波高）的关系进行了详细的分析,同时,对畸形波波高H_fr与偏度的关也进行了分析。通过对试验结果分析,发现峰度与畸形波要素i>H_m/H_s呈正相关, H_fr增大时相应的偏度也会呈现增大的趋势。此外,水深的变化剧烈时（如斜坡、海山位置）有助于畸形波的发生。     

南海北部海区波高与厄尔尼诺关系探究

以欧洲中期天气预报中心的23年再分析风场数据为基础,采用HIRHAM风场模式和SWAN海浪模型对南海北部海域的波浪场进行推算,并将南海北部海域的有效波高与厄尔尼诺指数作对比,探究两者的关系,分析结论如下：（1）南海海域波高具有较强的季节性变化特征,冬季波高大于夏季波高;（2）南海北部海域月平均波高与Niño3.4指数呈负相关,大部分海域呈中度相关,台湾和菲律宾之间的部分海域呈高度相关;（3）在强厄尔尼诺年,南海北部海域的有效波高明显偏小,且厄尔尼诺指数变化越大,波高越小;反之,在强拉尼娜年,南海北部海域的有效波高较大。     

Experimental study of unidirectional irregular wave slamming on the three-dimensional structure in the splash zone

The experimental investigation of unidirectional random wave slamming on the three-dimensional structure in the splash zone is presented. The experiment is conducted in the marine environment channel in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. The test wave is unidirectional irregular wave. The experiments are carried out with perpendicular random waves (β=0°) and oblique random waves (β=15°, 30°, 45°), the significant wave heights H_1/3 ranging from 7.5 to 20 cm with 2.5 cm increment, the peak wave periods T_p ranging from 0.75 to 2.0 s with 0.25 s increment, and the clearance of the model with respect to the significant wave height s/H_1/3 ranging from 0.0 to 0.5 with 0.1 increment. The statistical analysis results of different test cases are presented. The statistical distribution characteristics of the perpendicular irregular wave impact pressures are compared with that of the oblique irregular wave on the underside of the structure. The effect of the wave direction β on the wave impact forces on the underside of the structure is determined. The relation between the impact forces and the parameters such as the significant wave height, the relative structure width and the relative clearance of the structure is also discussed.     

A review of the analyses of ocean wave groups

The most common parameters and functions used to characterize wave groups in linear seas are reviewed and interrelated in a unified manner. A three-axes representation of run lengths is used to characterize wave groups using exponential and Markov chain approximations. A relationship between four parameters (Q_p, Q_e, κ², and ρ²) and the correlation coefficient between consecutive wave heights [r_HH(1)] is demonstrated. The wave-height function method is reviewed in some detail in order to relate the run length theory with envelope theories. The theoretical estimates used to demonstrate the relationships between the various parameters must be considered as only first-order trends to parameter estimates computed from real wave data due to the statistical variability in these estimates when computed from real wave data.     

黄渤海海域波浪时空变化特征分析

本文利用欧洲中期预报中心(ECMWF)第五代再分析数据集(ECMWF Reanalysis v5 ERA5,ERA5),对中国黄渤海海域2000-2019年的波浪进行了统计分析。得到如下的结论：1.黄渤海海区波浪具有明显的季节性,渤海区域有效波高呈现出周边小,中间大的特点;黄海海域有效波高Hs呈现由南向北降低的趋势;研究区域冬季有效波高均值大于其他季节。2.平均周期T的季节分布类似于有效波高的季节均值分布。渤海仅秋冬季T的均值存在大于4s的区域;黄海海域T的季节分布也呈现由南向北递减的趋势,其中长江口外海区域秋冬季T的季节均值可达6s。3.有效波高距平场EOF分解结果显示,第一模态表明了波浪变化具有明显的季节性特征;第二模态反映了季风的季节转换对有效波高的影响;第三模态代表的可能是地形的变化对有效波高变化的影响。4．代表点统计结果显示：整个渤海地区的常浪向为 NNE~NE,强浪向以 NE和 NNE 为主;黄海海域的常浪向为SSE-SE向,强浪向以 N和 SSE 为主。     

Inter-comparison of model-predicted wave heights with satellite altimeter measurements in the north Indian Ocean

A numerical model based on a wind-wave energy transport formulation of Toba is developed to generate hindcast wave height data for the equatorial and the north Indian Ocean, which is otherwise a data-sparse region. The intercomparison between model-predicted wave heights for three years (1987–1989) obtained utilising analysed surface wind fields' data, and model grid averaged GEOSAT Altimeter significant wave height data showed moderate match, particularly for H_S greater than 1 m.     

Long-term evolution of Baltic Sea wave climate near a coastal segment in Poland; its drivers and impacts

The paper analyses long-term variability of wave climate near Poland for the 1958–2002 period. With spectral and cross-spectral analysis, linear regression and singular spectrum analysis the modes of long-term variability were quantified for the most energetic months (November–February). For monthly indices of North Atlantic Oscillation from 1950 until 2006, it was established that the long-term trends of NAO and significant wave height demonstrate a gentle coupling. For Januaries this relationship is strongest and dates back to 1960, for Februaries a certain consistency appears since 1975. For Novembers and Decembers no statistically discernible coupling was found. Thus, the Baltic Sea appears to be the easternmost NAO-affected region, despite its separation from the Atlantic. The hydrodynamic variability also includes a non-trivial oscillation in the January wave energy records with T=8 years. The same periodicity was identified with the multi-channel SSA technique in the long-term shoreline data of a neighboring beach. The study shows that even almost entirely isolated water bodies are becoming exposed to global climatic phenomena and accelerated erosion of sandy beaches, typical for the South Baltic region. On the other hand, the 8-year hydrodynamic cycle can be viewed as the driver of long-term shoreline evolution.     

Extreme value statistics for wave run-up on a natural beach

Statistics of wave run-up maxima have been calculated for 149 35-minutes data runs from a natural beach. During the experiment incident wave height varied from 0.4 to 4.0 m, incident wave period from 6 to 16 s, and beach face slope from 0.07 to 0.20. Four extreme statistics were calculated; the maximum run-up height during each run, the 2% exceedence level of shoreline elevation, the 2% exceedence height for individual run-up peaks, and the 2% exceedence level for swash height as determined by the zero-upcrossing method. These statistics were best parameterized when normalized by the incident significant wave height and plotted against the Iribarren number, ξ = β/(H/L₀)^1/2. The swash data (with set-up removed) showed less scatter than total run-up (with set-up included). For Iribarren number greater than 1.5 the run-up was dominated by the incident frequencies, for lower Iribarren number longer period motions dominated the swash. A reasonable value of wave steepness for a fully developed storm sea is 0.025 so that a storm Iribarren number can be estimated as 6.3 times the beach slope. Using this and an offshore design wave height, the included graphs may provide guidance in determining a design run-up height.     

Wave groupiness and spectral bandwidth as relevant parameters for the performance assessment of wave energy converters

To date the estimation of long-term wave energy production at a given deployment site has commonly been limited to a consideration of the significant wave height H_s and mean energy period T_e. This paper addresses the sensitivity of power production from wave energy converters to the wave groupiness and spectral bandwidth of sea states. Linear and non-linear systems are implemented to simulate the response of converters equipped with realistic power take-off devices in real sea states. It is shown in particular that, when the converters are not much sensitive to wave directionality, the bandwidth characteristic is appropriate to complete the set of overall wave parameters describing the sea state for the purpose of estimating wave energy production.     

以海浪波要素表示的外频谱形式

孙孕等（１９９４）提出了外频谱的概念,并推导出外频谱的理论形式,但其控制参量是由内频谱导出的,不便于实际应用,通过对实测海浪数据的分析,得到了控制外频谱的３个和内频谱有关的参量与波浪要素之间的关系,进而将外频谱表示以有效波高和有效波周期作为控制参量的形式,应用实测资料将本文得到的外频谱形式与理论外频谱进行了比较,发现二者符合良好。     

Wave climate off northern Norway

The wave climate off northern Norway is considered and the investigation is based on wave measurements made at Tromsøflaket by means of a waverider buoy during the years 1977–1981. Data quality of waverider measurements is briefly commented upon; however, more emphasis is given to an evaluation of the long-term representativity of the actual measuring period and to a procedure accounting approximately for a lack of representativity. The wave climate is presented in terms of a smoothed joint probability density function of the significant wave height, H_s, and the spectral peak period, T_p. Based on this distribution a consistent design curve in the H_s, T_p space is established.