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The main objective of the present study is the combination of short- with long-term wave statistics in deep waters in order to achieve a more accurate description of the long-term wave climate in shallower waters. Such a description would provide vital information for many engineering applications in deep and intermediate waters, including design of coastal structures. This task can be accomplished by accumulating the statistics for all short-term sea conditions, considering the frequency of occurrence of each sea state during a certain period of years. A modification of an existing relationship has been developed aiming at achieving this purpose. More specifically, by using the relative frequencies of occurrence of the significant wave height (Hs) and mean zero-crossing wave period (Tm), measured at a specific location, as well as the short-term joint distributions of wave height (H) and period (T) associated with each sea state, the long-term joint distribution of H and T can be produced at that location in deep waters. Then, the long-term joint probability density function of Hs and Tm and the long-term joint probability function of H and T can be estimated at any intermediate water depth by considering wave directionality in deep waters and wave transformation of each individual wave, as waves propagate from the open sea towards shallower waters. Wave measurements obtained at three different locations in the Aegean (Greece) have been examined and compared. The results showed that, as waves propagate from deep to shallower waters, wave statistics differ from those in deeper waters, especially when waves become significantly depth limited. It is noted that this individual wave analysis refers to short-crested waves, thus wave directionality and refraction have been considered. However, in this approach, the nonlinear wave – wave interactions have not been taken into account.

This study aims to simulate and predict the influence of reclamation on saltwater intrusion and storm surge in the Pearl River Estuary, China by using the FVCOM Surface Wave Module (FVCOM-SWAVE). The study shows that the reclamation has a great influence on tidal velocity and direction, especially in some areas where narrow waterways are formed. Reclamation resulted in an increase in salinity due to impeded runoff, and reduced significant wave height in the nearby sea area. It has a positive effect on reducing storm surge disasters. However, the geographic scope of impact has been small and there is almost no change away from the reclamation area.

This study presents the first spatial calibration of SWAN model physical parameters based on satellite observations for the Black and Azov Seas. Currently, the wind-wave model performance is unknown in several coastal and offshore areas due to the gap in wave buoy measurements. The development and increase of altimetry satellites allow collecting a large number of observations in a reasonable time, and thus to calibrate spatially wave models. Therefore, the present study aims to determine the best physical parameterization of the unstructured SWAN model based on satellite data for coarse domain over Black and Azov Seas and for local domain implementations. For this purpose, the significant wave height (SWH) was simulated using 44 physical settings for both ERA5 and CFSR winds. The spatial calibration is based on observations from seven altimetry satellites (Jason-3, Sentinel-3A, Sentinel-3B, Cryosat-2, SARAL/AltiKa, CFOSAT, and Hai Yang-2B). The spatial calibration and evaluation of the wind-wave model performance show an informative variation in the wave model performance, which can depend on several factors such as coastal morphology and the wind source accuracy and the physical setting of the wind-wave model. It raises several findings concerning the spatial sensitivity of the SWAN model to the used wind field, the wind and whitecapping source terms, whitecapping coefficient (Cds), and the windscaling tunable parameter, and the wind growth formulates using the ST6 package. Thus, this study allows observing the spatial response of the SWAN model as a function of physical parameterizations. The SWAN model calibration improved the simulation accuracy considerably overall Black and Azov Sea areas, using both CFSR and ERA5. The SWAN model using the ERA5 winds has provided a higher correlation and better accuracy in large part of the seas. It is highly recommended for the whole Black and Azov Seas to define the wind input term and whitecapping term based on ( Komen et al., 1984 ), with a Cds coefficient of 0.8E-5. Considering the spatial error statistics, the same finding was obtained when the model results were compared with Utrish wave buoy measurements in the northeastern part of the Black Sea. Therefore, for local nested model implementation, it is also recommended to define the optimal configuration based on the error statistics mapped in the present paper.

The performance of the third generation wave model WAVEWATCH III (version 6.07) using the ST6 source term package, developed by Zieger et al. (2015) and then updated by Liu et al. (2019), is investigated in the context of wave growth and dissipation in the west coast of Ireland. A sensitivity analysis is carried out to establish preliminary values of the parameters involved in the configuration of the wind input term S i n by tuning the CDFAC parameter to potentially eliminate a bias in the wind field and the a 0 parameter that controls the strength of swell decay due to wind effects. A system of nested structured grids is used to model long-distance swells generated in the Atlantic Ocean that propagate all the way to the west coast of Ireland. The bias, the root-mean-square, the correlation coefficient and the scatter index statistical parameters, and the probability density function are used to validate the model by comparing the significant wave height from four local buoys measurements with numerical results. Comparisons between measurements and numerical data show a good overall agreement. The most appropriate value obtained for the drag coefficient CDFAC is 0.9, which represents a 10% decrease from the value proposed in the last versions of the package. Depending on the buoy selected for the analysis, the values tested for the second investigated parameter a 0 lead to a reduction of the bias in the comparisons, together with a reduction of the other statistical parameters. These results confirm the values proposed in previous work for future developments.

A thorough understanding of the long-term trends and extreme characteristics in the significant wave height (SWH) contributes greatly to coastal and offshore engineering activities and mitigation of marine disasters. In this study, the annual spatiotemporal variability of the SWH in the South China Sea (SCS) and the return periods for six locations are evaluated based on ERA5 wave reanalysis in a long time period (1950–2020). Long-term trends are estimated by using a popular non-parametric method, the Theil-Sen estimator, and then mapped to show the spatial variability of mean and extreme SWH. Basin-averaged analysis is also performed to investigate the general tendency of the mean SWH in the SCS, with an increasing rate of 0.11 cm/year. The well-known Mann-Kendall test is used to assess the significance of the trends. Significant positive trends in extreme SWH are mainly distributed in the eastern part of the central SCS around the Luzon Strait and the southwestern part of the SCS. In the extreme value analysis, by comparing 2 classical extreme value distribution models combined with 5 sampling methods, the Generalized Pareto Distribution incorporating the Peak Over Threshold (GPD-POT) method has turned out to be suitable for evaluating the return periods in the SCS based on 71-year SWH dataset. Extreme value analysis for different time lengths shows a correlation between the return level and the time span. Small and medium samples may lead to unstable parameter estimation and increased errors. The 100-year return values obtained by GPD-POT using the 71-year wave reanalysis are more credible at P1-P6 with 8.86, 11.79, 11.35, 10.52, 6.50 and 7.71 m, respectively. Both the estimated return periods and the number of extreme events quantified by the Method of Independent Storms (MIS) indicate that extreme events are closely related to the number of tropical cyclones. Seasonally, most extreme events in the SCS occur from June to December, with the summertime maximum SWH situated above the 15th degree of northern latitude and rapidly shifting to south in the fall.

This paper investigates the performance of a small axisymmetric buoy under wave-by-wave near optimal control in surge, heave, and pitch modes in long-crested irregular waves. Wave prediction is obtained using a deterministic propagation model. The paper describes the overall formulation leading up to the derivation of the feedforward control forces in surge and heave, and the control moment in pitch. The radiation coupling between surge and pitch modes is accounted for in the model. Actuation is relative to deeply submerged reaction masses. Heave oscillations are constrained by the swept-volume limit. Oscillation constraints are also applied on the surge and pitch oscillations. The paper discusses time-domain simulations for an irregular wave input with and without the present control. Also discussed are results obtained over a range of irregular wave conditions derived for energy periods from 7 s to 17 s, and a significant wave height of 1 m. It is found that, while the gains in power capture enabled by the present control are significant, the actuation forces are also very large, given the small size of the buoy. Further, due to the small size, heave is found to be the dominant contributor to power capture, with relatively modest contributions from surge and pitch.

This paper investigates the intact and damage survivability of a floating–moored Oscillating Water Column (OWC) device using physical model experiments and Computational Fluid Dynamics (CFD) simulations. Different extreme wave conditions have been tested using irregular and regular wave conditions. The device was moored to the tank floor via four vertical taut lines and the effect of the mooring line pre–tension on the device response was studied. It was found that the instantaneous position of the floating device was a key factor in the survivability analysis such that a certain irregular wave train that might not include the largest wave could induce the maximum response. Reducing the pre–tension minimized the maximum surge, but significantly increased the maximum tension due to mooring slack events causing snatch loads. A design regular wave with a period equal to the peak period and a height of 1.9–2.0 times the significant wave height could reasonably predict the same maximum line tension as the irregular sea state, but a smaller wave height was required to achieve the maximum surge. A single failure in the mooring system increased the maximum tension by 1.55 times the intact tension. For a damaged mooring system, using the same design regular wave condition derived from the survivability analysis with an intact mooring system could result in overestimating the maximum tension by more than 20% in comparison to the tension from the irregular sea state, but a smaller regular wave height or a different regular wave condition representing another sea state could lead to the same maximum tension. This highlighted the importance of investigating survival conditions with a damaged mooring system instead of simply using the same conditions derived for the intact mooring system.

Based on the 45-year (09/1957-08/2008) European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-40) wave reanalysis dataset, this study analyzes interannual and interdecadal variabilities and intraseasonal oscillations of sea surface wind speed (WS), wind sea wave height (Hw), swell wave height (Hs) and significant wave height (Hs) in the Roaring Forties and tropical waters of the Indian Ocean, to determine swell propagation characteristics. The results show: (1) monthly variabilities of Hs in the Roaring Forties are in good agreement with those in tropical waters of the Indian Ocean; swell plays a dominant role in mixed waves throughout most of the Indian Ocean; and WS, Hw, Hs, and Hs exhibit a significant increasing trend over the 45-year study period. (2) Hs in the Roaring Forties and tropical waters of the Indian Ocean share a common period of 9.8–10.4 years on an interdecadal scale; and WS and Hs in the Roaring Forties and Hs in the tropical waters of the Indian Ocean share a common period of approximately 8 days (weekly oscillation) on an intraseasonal scale. (3) Swell of the Roaring Forties needs approximately 30 h to fully respond to the wind in this region. Approximately 84 h are required for Hs to propagate from the Roaring Forties to the tropical waters of the south Indian Ocean, while it takes approximately 132–138 h for Hs to propagate from the Roaring Forties to the tropical waters of the north Indian Ocean.

s Design of coastal structures without considering dependence of environmental variables can lead to over- or under estimation of their cross-sectional dimensions, imposing significant economic costs on marine projects. In this paper, the design of a conventional rubble mound breakwater at the Makran coasts on the southern coast of Iran has been carried out using a commonly applied, as well as a joint probability approach. The results of these two design methods have been compared. In this regard, joint probability analysis of water level and significant wave height has been performed. For this purpose, first an appropriate threshold was determined using a systematic and methodological approach, and then using the Copula functions, a joint probability distribution was fitted. In the next step, the critical point of the rubble mound breakwater design was determined, acting as the basis of further investigations. The results indicate that the volume of armor and filter layers of the breakwater are reduced by about 5% and 10%, respectively, which is very economically attractive for engineering projects. Also, suggestions were made for an appropriate selection of 1- and 50-year tidal levels for the common design method to be used in the design codes. Finally, the effects of climate change on the overtopping failure mechanism of the breakwater were discussed, indicating that a higher freeboard and a lower overtopping discharge in the new design approach can reduce vulnerability of the structure against climate change effects in the future.

Ocean waves are crucial for the engineering community, both in the open ocean and in the coastal zone. By studying a 40-year (1979-2018) global hindcast, a systematic and long-term analysis on the temporal variation and spatial pattern of wave parameters is performed, with a focus on wave period. The mean and maximal conditions of peak period reflect the dominance of the swell and the region where it generates. The variabilities of the significant wave height and peak period show that high latitudes in the Southern Hemisphere (SH) have a generally large wave with a small dispersion. Trend patterns of peak period present similarities and differences, which can be associated with the climate mode. Spatial scopes of influence by this mode show the signal in the peak period, exceeding the local correlation zone and presenting a remote correlation. The joint characteristic of the significant wave height and peak period presents the differences of representative and extreme sea states in tropical regions and high latitudes, such as a large variation in high latitudes of the Northern Hemisphere (NH) and an extreme peak period occurring simultaneously with small significant wave height in tropical regions.

The impact of biofouling is investigated on the accuracy of the records of a wave buoy moored in shallow water. The effects of biofouling on the vertical and horizontal motions of the buoy are analyzed through check factors. Regarding the heave motion, the most critical frequencies of the power spectrum are identified, and selected to run CFD simulations to further evaluate the hydrodynamic impact of heavy biofouling. The time evolution of check factors allowed identifying the increase of accumulated mass, which became more critical in the last two months of the period of observation, associated with the modification of heave, surge or sway, and pitch or roll signals. The top high frequencies with periods below 3s are the most affected, with attenuation of the vertical motion. The spectrum at mid frequencies up to 15s is not modified and a small effect at low frequencies is reported. The impact of biofouling on the bulk wave parameters derived from the heave motion is minimal. Small differences of 0.4% up to 1.7% are found for significant wave height, associated with underestimation of short-length waves, and no difference was noticed on the estimation of peak period.

The fatigue assessment plays an increasing role for the offshore structural safety. Many fatigue assessment methods have been developed for this purpose. Among those methods, the time domain method is regarded as the most accurate method but less adopted in practice due to time consuming. In order to improve the efficiency of the time domain method, an innovative block partition and equivalence method of the wave scatter diagram is developed for offshore structural fatigue assessment. After the wave scatter diagram is partitioned into several blocks, the newly developed method, involves determination of the equivalent wave height, wave period and occurrence probability of the representative sea states based on modified energy equivalent principle. The equivalent wave period of the representative sea state is calculated via the spectral moment formula in which the equivalent spectral moments of zero and second order are obtained based on the weighted averaging principle. Combining with the determined wave period, the equivalent significant wave height can be determined by reversing the wave spectrum integral formula, where the equivalent wave energy of a divided block of the wave scatter diagram is modified by introducing a factor to compensate the effect of low- and high-amplitude cycles fatigue damage. The equivalent occurrence probability is equal to the summation of the original sea states’ occurrence probability within the divided block. The developed method has the advantage of preserving the stochastic characteristics of the short term sea states within the divided block during determining the representative sea state. At the same time the newly developed method has no limitation on block partition and can be applied on different offshore structure. Two structural models, a fixed mono-pile platform and a floating semi-submersible platform, are demonstrated in the numerical examples. Results indicate that the newly developed method is robust, computationally affordable, and accurate within engineering expectations.

As more than a quarter of India’s population resides along the coastlines, it is of utmost importance to predict the significant wave height as accurately as possible to cater the needs of safe and secure life. Presently Indian National Centre for Ocean Information Services (INCOIS) provides wave height forecasts on regional as well as local level ranging from 3 hours to 7 days ahead using numerical models. It is evident from numerical model forecasts at specific locations that the significant wave heights are not predicted very accurately. The obvious reason behind this is the ‘wind’ used in these models as a forcing function is itself forecasted wind (ECMWF wind (European Centre for Medium-range Weather Forecasting)) and hence many times the forecasts, differ very largely from the actual observations. These models work on larger grid size making it as major impediment in employing them particularly for location specific forecasts even though they work reasonably well for regional level. Present work aims in reducing the error in numerical wave forecast made by INCOIS at four stations along Indian coastline. For this ‘error’ between forecasted and observed wave height at current and previous time steps was used as input to predict the error 24 hr ahead in advance using ANN since it has been effectively used for wave forecasting (univariate time series forecasting in general) since last two decades or so. This predicted error was then added or subtracted from numerical wave forecast to improve the prediction accuracy. It is observed that numerical model forecast improved considerably when the predicted error was added or subtracted from it. This hybrid approach will add to the usefulness of the wave forecasts given by INCOIS to its stake holders. The performance of improved wave heights is judged by correlation coefficient and other error measures like RMSE, MAE and CE.

The influence of the statistical dependence between significant wave height and peak period on the reliability assessment of mooring lines is examined. Provided that copulas are functions that fully define the joint probability distribution of a set of random variables, they are used to describe the dependence structure of the environmental variables. Results of a case study and parametric analysis of mooring lines of an FPSO are presented and discussed. Copula models, such as Frank, Gumbel and Gaussian, fitted to hindcast data of extreme sea states at a site in the Gulf of Mexico are used. They are estimated in terms of Kendall’s τ measure of association between the environmental variables. Use of the Gaussian copula is equivalent to the widely known and practical approach of assembling joint distributions using Nataf distribution where the dependence structure isparameterized with the linear correlation matrix. Marginal distributions of extreme value data of significant wave height and peak period for the site were employed. The results showed that the dependence structure has considerable effect on the computation of the reliability index. The differences in the estimates of reliability using the Gaussian copula compared to the other copulas can be significantly large. The influence of the uncertainty in significant wave height, and of the mean and uncertainty of the breaking strength is also analyzed.

The quantitative assessment of the influence of rough weather avoidance on the wave climate ships experience in their oceanic routes is presented. The only meteorological source that naturally includes this effect is the database derived from the Voluntary Observing Ships’ programme, which is here compared with the state-of-the-art ERA-interim numerical re-analysis. The results of this work allow quantifying the reduction of the mean significant wave height encountered by ships in their operations for a more aware planning of the missions and better assessment of the environmental conditions.

Since ocean waves are mainly wind induced, carrying out coastal engineering projects and investigating environmental issues call for determination of wind-generated wave characteristics, especially in nearshore areas. In this study, a nested grid SWAN model and a hybrid approach combining artificial neural network (ANN) and coarse grid SWAN modeling results are used to hindcast the significant wave height in two nearshore locations in the Persian Gulf. However, the results are only valid in the regions where they are trained and tested. The models were calibrated in order to minimize the scatter index and the performances were compared, and the results show that the scatter index for significant wave height for both nearshore locations is less using the hybrid model rather than the nested one and there is no significant difference for the other error indices using both approaches. Regarding that the nesting approach is costly and consumes much more time in comparison to the hybrid one, and also taking into account that the nested model is unable to correctly calibrate wave height and other wave parameters, simultaneously and additional calibration may be required, the alternative hybrid approach is suggested to be used in wave simulation in nearshore areas. It is because the proposed hybrid model takes advantage of both SWAN and ANN merits while trying to avoid their limitations.

The aim of this research is to use spectral techniques in evaluating the irregular wave performance of a novel wave energy converter concept that combines an oscillating surge wave energy converter with control surfaces. The control surfaces allow the wave energy converter to have a time-varying geometry that enables the hydrodynamic exciting and radiation coefficients to be altered. In the current state of development the device geometry is controlled on a sea state-to-sea state time scale and combined with control of the power take-off (PTO) on a wave-to-wave time scale to maximize power capture, increase capacity factor, and reduce design loads. Analysis begins with the application of linear hydrodynamic theory to evaluate the device performance in terms of absorbed power, foundation loads, and accumulation of fatigue damage on the PTO. To determine the linear PTO damping coefficient that maximizes the time-averaged absorbed power for a given sea state, an optimization problem was constructed while incorporating a motion constraint on the maximum pitch amplitude of motion. The inclusion of the motion constraint prevents linear scaling of the performance results with the significant wave height. Previous studies on the modeling of oscillating surge wave energy converter designs have included nonlinear hydrodynamics. Therefore, a quadratic viscous drag moment was added to the system dynamics through use of a quasi-linear viscous damping coefficient. The same performance quantities were calculated for both the linear and nonlinear models while assuming an irregular wave surface elevation described by a Bretscheider spectrum. One major effect of including the viscous drag moment was flattening of the capture width and structural load curves with respect to the wave spectrum peak frequency while reducing the sensitivity with respect to the significant wave height compared to the linear analysis.

Wind-wave generation and propagation processes in the Persian Gulf during October and November 2010 were simulated with a third-generation numerical wave model. Several different numerical configurations were used, with output at an instrument pier near the Doha, Qatar coast used to examine the efficacy of these approaches. Three wind sources were used: two sets of wind hindcasts which span the extent of the Gulf; and 15-min averaged winds measured at the pier and distributed as a spatially constant wind field for the model. Domain size, and its nearshore effect, was examined by using three domains of varying sizes and resolutions. Boundary conditions from nesting between larger and smaller domains were also varied to determine how incoming wave conditions from larger domains located further offshore can affect nearshore wave conditions. The effect of wind field, boundary conditions and domain size were quantified by examining the histograms, correlation coefficient, and root-means-square differences, of various parameters (significant wave height, wave height due to swells, peak period, and mean approach direction) for each wave condition at the site. It is determined that significant wave heights at the pier are strongly dependent on the wind fields used and also have some dependence on the use of boundary conditions, while nearshore peak periods are very dependent on the use of boundary conditions. Furthermore, the distribution of wave mean angles tends to be narrower for cases in which hindcast winds and boundary conditions were used. These results are consistent with the sporadic appearance of a strong, unidirectional wind field over the Persian Gulf basin.

The waves caused by typhoons pose a serious threat to offshore production activities, especially the sheltering ability of fishing ports. Numerical models are of great importance to forecast the waves generated by typhoons. In this study, the MIKE21 spectral wave model was combined with the Holland wind field model to simulate the wave characteristics of Kanmen Fishing Port (KFP) under the influence of the typhoon Lekima, and the berthing capacity of KFP was evaluated. The results showed that calculated significant wave height and wind speed were in good agreement with the observations, and the d trend evaluation considered the model performance to be excellent. The model results showed that the significant wave height near KFP was remarkably affected by the typhoon Lekima and the maximum significant wave height in the fishing port exceeded 2 m. When the typhoon Lekima was passing, the KFP with a total area of 3.92 km2 lost 45.2% of its berthing area, and 54.8% of the fishing port's permitted berthing area can only berth 1,348 vessels. When the typhoon was at level 16 (wind speed 52 m/s), 102 small-sized fishing vessels or 72 medium-sized fishing vessels or 44 large-sized fishing vessels would have no place to stay with each additional level (wind speed increased by 5 m/s).

This paper presents a bivariate regional frequency analysis applied to vectors of extreme significant wave heights and concurrent zero up-crossing wave period over an area in the North Atlantic ocean. The analysis is based on a bivariate index-wave/period approach and the assumption of a common regional growth curve within homogeneous regions. The main benefits of performing a regional frequency analysis as opposed to at-site analysis based on data from one location only are twofold: It may give more accurate predictions of extreme conditions due to the increased amount of data made available for the statistical analysis, and results for ungauged locations can be obtained easily by interpolation of the index wave/period. Previous regional frequency analyses for ocean waves have been restricted to the univariate case. However, design conditions for marine and coastal structures will typically be characterised by the joint distribution of several metocean variables. Hence, it is useful to perform multivariate analyses of the extreme ocean environment. As a minimum, information about the joint distribution of significant wave height and period is often needed. This paper outlines the various steps involved in a bivariate regional frequency analysis and presents the results of such an analysis applied to data covering the North Atlantic ocean over a period of 30 years.

Wave measuring equipment are subject to malfunction that can be caused by various reasons such as maintenance, navigation accidents, errors in communications and biofouling of sensors. This can eventually result in loss of valuable data before the equipment is fixed. A continuous data set is often critical for modelling and/or analysis of wave conditions. Data gaps in wave records can be filled using numerical modelling. This study presents an alternative method for filling missing data based on publicly available wind and wave information and artificial neural networks (ANN). The ANN developed in this study uses offshore hindcast wave and wind information (significant wave height, peak wave period and direction, wind speed and direction) from a data set publicly available for any region of the globe. The results of the application of this method to two one-week gaps in wave measurements are compared against a spectral wave model developed and implemented to estimate wave conditions at the measurement location. The ANN results for the validation period show slightly better statistical performance when compared to the wave model results in terms of the correlation coefficient, root mean square error, bias and scatter index. ANN are viable alternative methods to wave modelling for filling gaps in data and have several advantages since specific knowledge of wave models is not required, input data to feed the neural network is available for any region of the globe and the processing time is highly reduced when compared to numerical modelling.

In this study, a series of physical model tests were carried out in a wave flume to study the pore pressures around a mono-pile under irregular waves. The mono-pile was installed to the position of 0.6 m below the seabed surface. The main purpose of this study is to analyze the distribution of pore-water pressure around and beneath the mono-pile under irregular waves. Five different wave spectra were used in the tests. The experimental results conclude that: (1) the pore-water pressure around the pile increases as the increase of significant wave height and period; (2) the maximum pore-water pressure decreases as the increase of seabed depth (z), this trend is significant near the seabed surface (z ≥ −0.3 m), and the influence is not obvious for the region below 0.3 m; (3) at the depth of 0.15 m below the seabed surface ( z = −0.15 m), the maximum pore pressure occurs in front of the pile, and at the depth of 0.1 m below the bottom of the pile ( z = −0.7 m), the maximum pore-water pressure occurs behind it; (4) the irregular wave-induced seabed response is larger than that of the representative regular wave; and (5) the irregular waves with Pierson–Moscowitz ( P − M ) spectrum introduce the most significant seabed response among various wave spectra.

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. NATO Science for Stability Program

The environmental contour concept, in conjunction with the Inverse First Order Reliability Method, is often used to determine the extreme response of marine structural systems. This technique is a powerful option to determine the extreme response associated to a probability of exceedance without the need to perform a long-term analysis, where a large number of short-term simulations are needed. However, there are significant uncertainties involved in its determination, such as the uncertainties related with the probabilistic model used for the environmental variables, as well as the ones related with the threshold selection when the peaks over threshold (POT) method is applied. This paper shows the results of a comparative analysis of the extreme tension of the most loaded mooring line of an FPSO subjected to environmental conditions in deep water, derived from environmental contour lines which were defined with different probabilistic models to represent the significant wave height and different criteria to establish the threshold for the POT methodology. The results showed that the probabilistic model has an important effect on the extreme response of the FPSO and this epistemic uncertainty should be accounted for in the calibration of the design safety factors.

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.

Compared with solar and wind energy, wave energy is a kind of renewable resource which is enormous and still under development. In order to utilize the wave energy, various types of wave energy converters (WECs) have been proposed and studied. And oscillating-body WEC is widely used for offshore deployment. For this type of WEC, the oscillating motion of the floater is converted into electricity by the power take off (PTO) system, which is usually mathematically simplified as a linear spring and a damper. The linear PTO system is characteristic of frequency-dependent response and the energy absorption is less powerful for off resonance conditions. Thus a nonlinear snap through PTO system consisting of two symmetrically oblique springs and a linear damper is applied. A nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two oblique springs to the original length of both springs. JONSWAP spectrum is utilized to generate the time series of irregular waves. Time domain method is used to establish the motion equation of the oscillating-body WEC in irregular waves. And state space model is applied to replace the convolution term in the time domain motion equation. Based on the established motion equation, the motion response of both the linear and nonlinear WEC is numerically calculated using 4th Runge–Kutta method, after which the captured power can be obtained. Then the influences of wave parameters such as peak frequency, significant wave height, damping coefficient of the PTO system and the nonlinear parameter γ on the power capture performance of the nonlinear WEC is discussed in detail. Results show that compared with linear PTO system, the nonlinear snap through PTO system can increase the power captured by the oscillating body WEC in irregular waves.

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.

Climate change is a topic discussed worldwide. There is concern about how climate change will influence human activities, including offshore engineering. Climate change will alter the metocean data used for design purposes. These changes will possibly cause some impact on the structural responses of ships and offshore structures, more specifically fatigue damage accumulation and extreme responses. These possible impacts will depend on the structure life span, structure geographic location and climate change scenario assessed, among other aspects. This paper discusses the results of dynamic stochastic analyses and long-term extreme response estimates of a Steel Catenary Riser (SCR) connected to a semi-submersible platform considering future climate change scenarios for two locations: South East Brazilian Coast and North Atlantic Ocean. The long-term response is estimated by the Environmental Contour Method (ECM). Climate change is assessed by using different climate change scenarios available. The climate change scenarios considered in this work are the Representative Concentration Pathways (RCPs) RCP 4.5 and RCP 8.5 proposed and described by the Intergovernmental Panel on Climate Change (IPCC). Specifically, this work focuses at the influence of climate change on the wave parameters, significant wave height (Hs) and zero up-crossing period (Tz), and their impact on the structural responses of a SCR, for both locations aforementioned. The results obtained suggest that climate change can affect the structure response in different ways, depending on the geographic location. They show an increasing trend for the long-term structural response in the Brazilian location and a slight decreasing trend for the North Atlantic Ocean location. However, these results show high variability due to considerable uncertainties in the ocean climate forecasts, related mainly to shortcomings in global climate models.

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.

During their operation life-cycle, tension leg platforms (TLPs) may experience, under wave and wind loading, response amplitudes that affect their operational and structural reliability. Uncertainties related to the excitation characteristics (for example significant wave height or zero up-crossing period) or to the TLP-model properties (for example modulus of elasticity for tendons or location of center of mass) significantly impact the predicted dynamic response of the platform and ultimately the calculated reliability, or more generally the TLP-risk. A simulation-based, probabilistic framework is discussed here for detailed estimation of this risk and for identification of the importance of the different uncertain model parameters (i.e. risk factors). The TLP-risk is quantified as the expected value, over the established probability distributions for these uncertain parameters, of some chosen risk consequence measure. It is calculated using stochastic (Monte Carlo) simulation, which imposes no constraints on the complexity of the models considered and can facilitate an accurate estimation exploiting recent development in computer and computational science. The identification of the importance of the risk factors is established using an efficient, sampling-based global sensitivity analysis. An illustrative example is discussed in which risk is quantified in terms of the reliability for the structural integrity and operational serviceability for a rectangular TLP. The impact of uncertainties related to the excitation and TLP models is separately addressed, whereas the influence on the estimated risk of model prediction errors is also examined.

Wave energy is an emerging and promising renewable energy technology. As the first pre-commercial and commercial prototypes are being tested at sea, there is a need for developers, governments and investors to be able to reliably estimate the energy production of devices as a function of the sea states they are to be deployed in. This estimation has traditionally relied on only two sea state parameters, the significant wave height and the energy period, but these do not account for frequency or directional spreading. The present paper investigates the suitability of further parameters to refine performance predictions. This is achieved through extensive wave tank testing of three types of wave energy converters (WECs) with different directionality properties. Statistical analyses of the measurements show the significant impact of frequency and directional spreading on the performance of WECs. Parametric models of the devices’ performance were devised for numerous sea state parameters. These results suggest that the traditional estimation method should be extended in order to include at least a parameter related to the spectral bandwith.

This paper presents a stochastic model in space and time for significant wave height, a Bayesian hierarchical space-time model. The model consists of different components in a hierarchical manner including a component to model the contribution from long-term trends in the wave climate. As far as the authors are aware, no such model of significant wave height to date exploits the flexible framework of Bayesian hierarchical space-time models, which allow modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet at the same time remains intuitive and easily interpreted. Furthermore, including a trend component in the model is a novel feature. The model presented in this paper has been fitted to significant wave height data for monthly maxima over an area in the North Atlantic ocean, and aims at describing the temporal and spatial variability of the data over a period of more than 44 years for the chosen area. In particular, the model identifies long-term trends present in the data. Subsequently, it will be explored how the results from the model can be linked to structural loads and response calculations. The proposed approach is illustrated by an example showing the potential impact of the estimated long-term trends of significant wave height on the wave-induced structural loads of an oil tanker.

Design of an offshore wind turbine requires estimation of loads on its rotor, tower and supporting structure. These loads are obtained by time-domain simulations of the coupled aero-servo-hydro-elastic model of the wind turbine. Accuracy of predicted loads depends on assumptions made in the simulation models employed, both for the turbine and for the input wind and wave conditions. Currently, waves are simulated using a linear irregular wave theory that is not appropriate for nonlinear waves, which are even more pronounced in shallow water depths where wind farms are typically sited. The present study investigates the use of irregular nonlinear (second-order) waves for estimating loads on the support structure (monopile) of an offshore wind turbine. We present the theory for the irregular nonlinear model and incorporate it in the commonly used wind turbine simulation software, FAST, which had been developed by National Renewable Energy Laboratory (NREL), but which had the modeling capability only for irregular linear waves. We use an efficient algorithm for computation of nonlinear wave elevation and kinematics, so that a large number of time-domain simulations, which are required for prediction of long-term loads using statistical extrapolation, can easily be performed. To illustrate the influence of the alternative wave models, we compute loads at the base of the monopile of the NREL 5MW baseline wind turbine model using linear and nonlinear irregular wave models. We show that for a given environmental condition (i.e., the mean wind speed and the significant wave height), extreme loads are larger when computed using the nonlinear wave model. We finally compute long-term loads, which are required for a design load case according to the International Electrotechnical Commission guidelines, using the inverse first-order reliability method. We discuss a convergence criteria that may be used to predict accurate 20-year loads and discuss wind versus wave dominance in the load prediction. We show that 20-year long-term loads can be significantly higher when the nonlinear wave model is used.

The performance of two well accepted formulations for white capping and wind input of third generation wave models, viz., WAM-3 and WAM-4, were investigated using parallel unstructured SWAN (PunSWAN). Several alternative formulations were also considered to evaluate the effects of higher order steepness and wave number terms in white capping formulations. Distinct model configurations were calibrated and validated against available in situ measurements from the Gulf of Mexico. The results showed that some of the in situ calibrated models outperform the saturation level calibrated models in reproducing the idealized wave growth curves. The simulation results also revealed that increasing the power of the steepness term can enhance the accuracy of significant wave height ( H s ) , at the expense of a higher bias for large waves. It also has negative effects on mean wave period ( T a ) and peak wave period ( T p ) . It is also demonstrated that the use of the quadratic wave number term in the WAM-3 formulation, instead of the existing linear term, ameliorates the T a underestimation; however, it results in the model being unable to reach any saturation level. In addition, unlike H s and T p , it has been shown that T a is sensitive to the use of the higher order WAM-4 formulation, and the bias is decreased over a wide range of wave periods. However, it also increases the scatter index (SI) of simulated T a . It is concluded that the use of the WAM-4 wind input formulation in conjunction with the WAM-3 dissipation form, is the most successful case in reproducing idealized wave growth curves while avoiding T a underestimation of WAM-3 and a potential spurious bimodal spectrum of WAM-4; consequently, this designates another perspective to improve the overall performance of third generation wave models.

This study aims to assess the quality of two sources of surface winds, i.e. the ECMWF (European Center for Medium Range Weather Forecasts) modeled and the measured data, for wave modeling in the Persian Gulf. A third generation model, i.e. SWAN was employed for wave simulation and the results were compared with the recorded wave data. It was found that ECMWF underestimates the wind magnitude and the results of the wave modeling need to be modified. In addition, it was revealed that the adaptation of the model parameters cannot lead to a comprehensive improvement of the model’s results. The calibration of the wave model for high waves led to the overestimation of low waves. On the other hand, the employed measured wind data was found to be a relatively good source for wave hindcasting at the studied location. Extreme value analysis was also conducted based on the measured and modeled wave data to investigate the influence of wave simulation on the estimation of design wave height. It was found that the Weibull distribution is better fitted to the measured and modeled wave data. Modeled wave heights forced by the ECMWF wind showed a different behavior compared with the measured and modeled wave heights forced by the measured wind from the viewpoint of the exceedance probability. A marginal difference was found between extreme wave heights obtained from measured and modeled data.

The paper provides a bivariate distribution of wave power and wave height, as well as a bivariate distribution of wave power and wave period; both bivariate distributions are for individual waves within a sea state. This is relevant for e.g. making assessments of wave power devices and their potential for converting energy from waves. The results can be applied to compare systematically the wave power potential for individual waves in a given sea state at different locations.

Hindcasting of wave parameters is necessary for many applications in coastal and offshore engineering and is generally made with the help of sophisticated numerical models. This paper presents alternative hindcast models based on Artificial Neural Networks (ANNs), Fuzzy Inference System (FIS) and Adaptive-Network-based Fuzzy Inference System (ANFIS). The data set used in this study comprises wave and wind data gathered from deep water location in Lake Ontario. Wind speed, wind direction, fetch length and wind duration were used as input variables, while significant wave height, peak spectral period and mean wave direction were the output parameters. Different topologies of ANNs were considered to predict the wave parameters and the relative importance of input parameters were determined. Finally, the results of ANNs-based models, FIS- and ANFIS-based models were compared. Results indicated that error statistics of soft computing models were similar, while ANFIS models were marginally more accurate than FIS and ANNs models.

Directional spreading of wave energy is popularly modeled with the help of the Cosine Power model and it mainly depends on the spreading parameter. This paper describes the variation of the spreading parameter estimated based on the wave data collected at four locations along the East as well as the West side of the Indian coast. The directional spreading parameter was correlated with other characteristic wave parameters, like non-linearity parameter, and directional width. Working empirical relationships between them have been established. The mean spreading angle was found to be slightly lower than the directional width with a correlation coefficient of 0.8. The maximum spreading parameter, s , underwent a sudden reduction in its value with the increase in the value of directional width. The average value of the maximum spreading parameter for the locations studied was found to be 23. The study shows that the spreading parameter can be related to significant wave height, mean period and water depth through the non-linearity parameter and can be estimated with an average correlation coefficient of 0.7 for the Indian coast and with higher correlation coefficient of 0.9 for the high waves ( H S > 1.5 m ) .

A new wavelet analysis methodology is used to estimate the statistics of steep waves using a wave gauge array. The method is applied to open ocean wave height data from the Flux, Etat de la mer et Teledetection en Condition de fetch variable (FETCH) experiment (1998) and the Adverse Weather experiment (2000). Results from the analysis of surface wave measurements show high wave slope crests appearing over a wide range of wavenumbers and frequencies for both low wind and high wind forcing conditions. For all cases considered, the steep wave statistic obtained from the analysis of the array of wave gauges reveals a larger amount of steep waves at high wavenumbers than at low wavenumbers at high wave slope thresholds. This trend is modulated in the case of high wind and at medium wave slope thresholds due to Doppler shifting which causes wave frequencies higher than the dominant wave to be associated with wavenumbers much lower than those given by the linear dispersion relationship. The steep wave statistic also decreases with wave slope threshold at a faster rate for the low wind forcing condition than the high wind forcing condition. Directionality analysis shows that most of the steep waves move in the downwind direction.

Ocean surface waves are both random in time and nonlinear. For a linear random model of the sea surface, the average shape of a large crest is found to be the scaled auto-correlation function, as is shown mathematically by Lindgren [Lindgren G. Some properties of a normal process near a local maximum. Ann Math Stat 1970;41:1870-83] and Boccotti [Boccotti P. Some new results on statistical properties of wind waves. Appl Ocean Res 1983;5:134-40]. Using field data from the North Sea, the applicability of this simple result is discussed. Stokes-type corrections up to fifth order are incorporated in an approximate but robust manner, valid at least locally in space and time. Exact second-order wave theory is used to check the accuracy of the approximate Stokes treatment and to clarify the magnitude and character of the second-order contributions. A giant wave, called the New Year wave, recorded at the Draupner platform in the North Sea at 15:20 on 1st January 1995, is examined. In a sea-state with a significant wave height of approximately 12 m, this freak wave, which has a peak elevation of 18.5 m above still water level, was unambiguously recorded. The local asymmetries of this wave are removed using the Stokes model, allowing the probability of occurrence of this remarkable event to be estimated, based on the standard Rayleigh distribution for linear crest amplitude. It is concluded that new physics, not incorporated in standard approaches to offshore engineering design, may have played an important role in the generation of this freak wave. © 2005 Elsevier Ltd. All rights reserved.

We present a statistical analysis of some of the largest waves occurring during 793 h of surface elevation measurements collected during 14 severe storms in the North Sea. This data contains 104 freak waves. It is found that the probability of occurrence of freak waves is only weekly dependent on the significant wave height, significant wave steepness and spectral bandwidth. The probability does show a slightly stronger dependency on the skew and kurtosis of the surface elevation data, but on removing the contribution to these measures from the presence of the freakwaves themselves, this dependency largely disappears. Distributions of extreme waves are modelled by fitting Generalised Pareto distributions, and extreme value distributions and return periods are given for freak waves in terms of the empirical fitted parameters. It is shown by comparison with these fits that both the Rayleigh distribution and the fit of Nerzic and Prevosto severely under-predict the probability of occurrence of extreme waves. For the most extreme freak wave in our data, the Rayleigh distribution over-predicts the return period by about 300 times when compared to the fitted model.

A new methodology for the analysis, missing-value completion and simulation of an incomplete nonstationary time series of wave data is presented and validated. The method is based on the nonstationary modelling of long-term time series developed by the authors [J. Geophys. Res. 100 (1995) 16,149]. The missing-value completion is performed at the level of the series of the uncorrelated residuals, obtained after having removed both any systematic trend (e.g. monotone and periodic components) and the correlation structure of the remaining stationary part. The incomplete time series of uncorrelated residuals is then completed by means of simulated data from a population with the same probability law. Combining then all estimated components, a new nonstationary time series without missing values is constructed. Any number of time series with the same statistical structure can be obtained by using different populations of uncorrelated residuals. The missing-value completion procedure is applied to an incomplete time series of significant wave height, and validated using two synthetic time series having the typical structure of many-year long time series of significant wave height. The missing-value patterns used for validation have been obtained from existing (measured) wave datasets with 16.5 and 33% missing values, respectively.

A method for artificially generating operational sea state histories has been developed. This is a distribution free method to simulate bivariate non stationary and non Gaussian random processes. This method is applied to the simulation of the bivariate process (Hs, Tp) of sea state parameters. The time series respects the physical constraints existing between the significant wave height and the peak period. Furthermore, we show that the persistence properties of the simulations match to those of the observations.