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.     

Joint modelling of extreme ocean environments incorporating covariate effects

Characterising the joint distribution of extremes of ocean environmental variables such as significant wave height (H_S) and spectral peak period (T_P) is important for understanding extreme ocean environments and in the design and assessment of marine and coastal structures. Many applications of multivariate extreme value analysis adopt models that assume a particular form of extremal dependence between variables without justification. Models are also typically restricted to joint regions in which all variables are extreme, but regions where only a subset of variables is extreme can be equally important for design. The conditional extremes model of Heffernan and Tawn (2004) provides one approach to overcoming these difficulties.Here, we extend the conditional extremes model to incorporate covariate effects in all of threshold selection, marginal and dependence modelling. Quantile regression is used to select appropriate covariate-dependent extreme value thresholds. Marginal and dependence modelling of extremes is performed within a penalised likelihood framework, using a Fourier parameterisation of marginal and dependence model parameters, with cross-validation to estimate suitable model parameter roughness, and bootstrapping to estimate parameter uncertainty with respect to covariate.We illustrate the approach in application to joint modelling of storm peak H_S and T_P at a Northern North Sea location with storm direction as covariate. We evaluate the impact of incorporating directional effects on estimates for return values, including those of a structure variable, similar to the structural response of a floating structure. We believe the approach offers the ocean engineer a straightforward procedure, based on sound statistics, to incorporate covariate effects in estimation of joint extreme environmental conditions.     

A probability distribution for depth-limited extreme wave heights in a sea state

A model for the depth-limited distribution of the highest wave in a sea state is presented. The distribution for the extreme wave height is based on a probability density function (pdf) for depth-limited wave height distribution for individual waves [Méndez, F.J., Losada, I.J., Medina, R. 2004. Transformation model of wave height distribution. Coastal Eng, Vol. 50, 97:115.] and considers the correlation between consecutive waves. The model is validated using field data showing a good representation of the extreme wave heights in the surf zone. Some important statistical wave heights are parameterized obtaining useful expressions that can be used in further calculations.     

A maximum-entropy compound distribution model for extreme wave heights of typhoon-affected sea areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle.The new model is formed by nesting a discrete distribution in a continuous one,having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper.The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea,and the predicted results are compared with those predicted by use of some other compound distribution models.Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.     

Applying POT methods to the Revised Joint Probability Method for determining extreme sea levels

Newly exposed concepts of POT declustering (Bernardara et al., 2014) within the GPD-Poisson model are applied to the joint probability of tide and surge for determining extreme sea levels, as a variation of the Revised Joint Probability Method (RJPM, Tawn and Vassie, 1989). A mixture model is proposed for the meteorological residual (surge) component with a non-parametric (empirical) density for the bulk values and parametric models for both the lower and upper tails. In particular, a distinction is made between values observed at regular time steps, called sequential values, and the clusters of extreme values, or events, on which the statistical extrapolations are performed. The sea level distribution is obtained by convolution of the tide and surge density functions. Confidence intervals are also proposed. This model is applied to the case study of Brest, France using both hourly and high water values. Two methods for handling tide–surge interaction are presented and discussed and a comparison with a direct approach is made.     

Numerical modelling of a point-absorbing wave energy converter in irregular and extreme waves

Based on the Navier-Stokes (RANS) equations, a three-dimensional (3-D) mathematical model for the hydrodynamics and structural dynamics of a floating point-absorbing wave energy converter (WEC) with a stroke control system in irregular and extreme waves is presented. The model is validated by a comparison of the numerical results with the wave tank experiment results of other researchers. The validated model is then utilized to examine the effect of wave height on structure displacements and connection rope tension. In the examined cases, the differences in WEC’s performance exhibited by an inviscid fluid and a viscous fluid can be neglected. Our results also reveal that the differences in behavior predicted by boundary element method (BEM) and the RANS-based method can be significant and vary considerably, depending on wave height.     

Correlation between successive wave heights and periods in mixed sea states

The degree of dependence between successive wave heights and periods is examined for sea states resulting from the combination of a remotely generated wave field and a locally generated wave system, based on simulated wave records. The sea states analysed represent situations that are swell dominated, wind–sea dominated or they have equivalent energy in the wind–sea and swell components. Results of the analysis of the simulated data have been compared with those expected from the theories for the joint distributions of consecutive wave heights and periods and with the results from a Pierson–Moskowitz target spectrum.     

极端海洋环境对海洋平台疲劳寿命的影响

基于渤海和南海的海洋平台设计环境条件,分析了近年来我国近海极端海洋环境条件的发生规律及其对海洋平台疲劳设计条件的冲击。采用Miner’s线性累积疲劳损伤准则和疲劳可靠性理论,研究了极端海况引起的疲劳损伤对海洋平台疲劳寿命的影响,提出了考虑极端海洋环境条件的海洋平台疲劳设计方法。研究表明,由于近年来全球气候变换带来的极端气象条件频发,导致海洋工程结构经历传统意义上的多年一遇海洋环境条件的概率大大增加,使得现行的海洋平台疲劳设计条件偏离了实际的海洋环境条件。数值算例表明,极端海况引起的疲劳损伤在总的疲劳损伤的比例大大增加,甚至成为疲劳损伤的主要部分。因此,这些极端海况引起的疲劳损伤对结构疲劳寿命的影响不容忽略,考虑极端海洋环境条件的海洋平台疲劳设计符合近年来的灾害性海况频发的现状。     

Uncertainty of the sea state parameters resulting from the methods of spectral estimation

The uncertainty of some commonly used spectral wave parameters resulting from the spectral estimation procedure is assessed. It is observed that the methods of spectral estimation produce a significant uncertainty for all parameters examined, but this is of considerable importance only for the peak period, which is one of the most important parameters to model the wave climate.     

Validation of the Boccotti's generalized model for large nonlinear wave heights from laboratory mixed sea states

The presented work aims at validating the generalization of the asymptotic distribution model of Boccotti for large wave heights recently proposed by Tayfun [1] to laboratory generated mixed sea states with two-peak spectra. The input wave spectra are modelled as the sum of two JONSWAP spectra describing unidirectional wave systems with different or identical directions of propagation (crossing or following mixed seas). In order to account for the effect of the energetically dominant wave system on the largest observed waves, the Boccotti's parameters were calculated at the absolute minimum of the autocorrelation function which can differ from the first minimum for some cases of mixed seas, such as those dominated by the swell or seas with comparable contribution of the two spectral components. So far the proposed model has been validated elsewhere against samples of large wave heights exceeding the significant wave height in wind seas and in mechanically generated long-crested seas, both characterized by unimodal spectra and strong third-order nonlinearities. The present study demonstrates that it can predict equally well the tail of the distributions for mixed seas, irrespective of the type of the mixed sea, particularly when the third-order statistics is relatively large. Typically, the mixed seas from the considered offshore basin experiment display such conditions as the propagation distance from the wavemaker increases, though this effect is less pronounced for mixed following than for mixed crossing wave conditions. Moreover, the generalized model remains valid irrespective of the sign of the fourth-order sum Λ which is a key parameter of the distribution. Its good predictive ability is quantified here by the root-mean-square errors between observations and theory.     

连云港海域极值波高统计分析方法研究

利用连云港1960-2011年连续波浪资料,采用年最大波高法、波高阈值法和年N大波法3种采样方法,结合Gumbel和三参数Weibull两种分布函数,进行设计波高相关计算,并对结果进行讨论和分析,以选出较好的采样方法、分布函数及较优的组合。结果表明,在该海域计算设计波高时,采样方法首选年N大波法,N取值7~8个较优;其次是波高阈值法,阈值取为1.7~2.0 m较合适,即阈值的取值使得每年波高数平均在8~12个左右为宜;年最大值法结果可作参考。Gumbel和三参数Weibull分布函数均可使用,后者比前者的适用性更佳。通过计算分析后可得初步结论,最优组合方式是每年取8个大波,利用三参数Weibull分布函数进行计算。同时给出最优组合下连云港海域不同重现期设计波高值,供设计参考。     

An algorithm for the quality checking of wind speeds measured at sea against measured wave spectral energy

The purpose of this study is to provide a quality-checking tool for the evaluation of wind-wave data from buoys deployed by the National Data Buoy Center (NDBC). In particular, an algorithm is sought that will compare measured wind speed with spectral data in a chosen range. In the past, anemometers have been known to fail without failing completely, returning data that are bad, but not obviously bad. The aim here is to provide an automated test that will flag such data, as well as detecting certain malfunctions of the wave-measuring system. Towards this end, large quantities of data are studied and several approaches to the problem are described before an algorithm is finally recommended. The algorithm takes account of physical properties of the ocean (as observed from this data set) as well as the statistical relationships determined between wind speed and wave energy. The implementation and testing of the algorithm are described.     

Numerical models for evolution of extreme wave groups

The paper considers the application of two numerical models to simulate the evolution of steep breaking waves. The first one is a Lagrangian wave model based on equations of motion of an inviscid fluid in Lagrangian coordinates. A method for treating spilling breaking is introduced and includes dissipative suppression of the breaker and correction of crest shape to improve the post breaking behaviour. The model is used to create a Lagrangian numerical wave tank, to reproduce experimental results of wave group evolution. The same set of experiments is modelled using a novel VoF numerical wave tank created using OpenFOAM. Lagrangian numerical results are validated against experiments and VoF computations and good agreement is demonstrated. Differences are observed only for a small region around the breaking crest.     

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.     

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.     

浙江东矶列岛海域实测波要素及典型台风浪特征分析

利用东矶列岛海域一年实测波浪资料,统计分析波要素特征,以台风“利奇马”为例,分析台风浪演变过程。结果表明：研究海域年平均有效波高0.88 m,年平均周期4.3 s,年最大波高8.67 m出现在夏季台风“利奇马”影响时。研究海域以轻浪为主,其次是小浪和中浪;常浪向为ESE,次常浪向为E和SE;强浪向为SSE,次强浪向为SE。波浪平均持续时间和波高之间符合指数衰减关系。台风“利奇马”影响期间,最大谱峰56.20 m²/Hz,台风浪谱型以双峰谱为主,台风浪类型经历了涌浪—混合浪—风浪—混合浪—涌浪这一演变过程。     

运用SWAN数值模拟对渤海波浪极值参数的研究(英文)

本文以高分辨率后报风场资料为输入,采用SWAN波浪模式,模拟了渤海海域1985年至2004年共20年间的波浪场。通过有效波高数据的比较,可看出波浪数值结果与实测资料符合较好,可以用数值结果分析渤海海域的波浪特征。利用计算的年极值波要素,本文给出并分析了渤海海域不同重现期下的极值参数分布情况。     

波浪变形的数学模型

本文给出一个在复杂水深地形条件下计算包括折射和绕射效应的线性波浪变形数学模型。该模型用差分方法进行求解,并应用于兴化湾江阴岛码头及航道的波浪要素计算,所得结果与其他方法的结果进行比较。通过实际应用说明它是计算开阔海域波浪变形的有力工具。     

Numerical modelling of deep sea air-lift

Deep sea air-lifting of solid particles from depth of 1600 m is simulated with a mathematical model of the three-phase flow in an upward pipe. The computations are carried out for an axisymmetric domain in a transient way. Phase distributions, pressure and velocity profiles together with flow rates for all phases are presented and analysed. The influence of the pipe diameter on the air-lift efficiency was studied for air-lift pipes of different lengths and found to be significant. The lifting efficiency increases with the increase of the pipe diameter due to the reduction of the wall friction influence on the flow. In addition, the efficiency also increases with the increase of the solid particles volume fraction at the inlet. The presented numerical model can be utilized during various stages of the design of the air-lift pumps to help answer fundamental questions on the process, and during their operation to select optimal process parameters and to address possible problems.