Distribution Of Significant Wave Height Research Articles

Joint probabilistic modeling of extreme wind-wave conditions under typhoon impact and applications to extreme response analysis of floating offshore wind turbines

The joint probabilistic modeling of extreme wind and wave conditions under typhoon impact is a critical task for extreme response analysis of floating offshore wind turbines (FOWTs) deployed in typhoon-prone areas. However, wind and wave observations under typhoon impact are quite limited, which poses great challenges to the probabilistic modeling task. Although some sophisticated programs can be employed to simulate typhoon-induced wave fields, they suffer from unbearable computational burdens. To improve the accuracy and efficiency of joint probabilistic modeling of extreme wind and wave conditions under typhoon impact, an approach that synthesizes the typhoon hazard analysis method and copula-based conditional modeling method is proposed in the present study. The proposed joint distribution model is expressed as the product of the distribution of extreme wind speed and the conditional distribution of significant wave height. The distribution of extreme wind speed is estimated through the typhoon hazard analysis method, and the conditional distribution of significant wave height is modeled by the copula-based method. The effectiveness of the proposed method is verified by comparing with observation data. Applications of the proposed method to extreme response analysis of FOWTs are illustrated as well.

Joint Probability Distribution of Significant Wave Height and Peak Wave Period Using Gaussian Copula Method

Joint Probability Distribution of Significant Wave Height and Peak Wave Period Using Gaussian Copula Method

Wave environment analysis at Norwegian harbours for land-based aquaculture facilities using a combined phase-averaging and phase-resolving numerical modelling approach

Numerical wave modelling of Norwegian coastal areas is challenging due to the drastically varying bathymetry, irregular coastline, and large domains of interest. The widely used phase-averaging models are limited by such bathymetric and topographic conditions. Phase-resolving models provide higher accuracy regarding strong nonlinear wave transformations with the trade-off of a higher computational cost. This study provides a combined phase-averaging and phase-resolving modelling approach to analyse the wave conditions for on-shore aquaculture facilities at the site candidates Fiskenes and Breivik, Andøya, Norway. The phase-averaging spectral model SWAN is used for the offshore sea state analysis based on the offshore hind-cast data. The analysis is performed on cascade nested grids, with increasing accuracy closer to the proposed harbour locations. A novel interpolation algorithm is proposed to provide comprehensive sea state information with every offshore wave directions without requiring additional simulations. The critical wave conditions are identified from SWAN and used as input to the open-source phase-resolving fully nonlinear potential flow model REEF3D::FNPF. Four scenarios are investigated and densely spaced wave gauges in the entire computational domain provide the distribution of significant wave height. The combined and cascade simulation approach helps to achieve a balance between computational efficiency and accuracy for large-scale marine environment assessment. The results show detailed wave statistics in the entire area of relevance near both harbours and provide a quantitative reference for both the site choice and the harbour design.

Environmental contours of sea states by the I-FORM approach derived with the Burr-Lognormal statistical model

Environmental contours are constructed using the Inverse-First Order Reliability Method based on return periods of one and twenty years. The paper proposes the use of the Burr distribution to model the marginal distribution of long-term significant wave heights and uses the conditional approach, by combining this marginal with conditional log-normal distributions of peak wave periods. The resulting environmental contours constructed based on the implementation of the Burr-Lognormal model are compared with the contours constructed with the commonly applied Weibull-Lognormal model considered as the baseline. Statistical tests of fit are used, and they do not reject any of the two models being compared, indicating that both approaches are acceptable. The environmental contours from the newly implemented scheme are different from the ones of the reference approach, as expected. Return values obtained with both marginal distributions of significant wave heights show differences comparable to the ones reported in other comparisons of methods reported in the literature.

Effects of Terrain near Taiwan Island on Typhoons with Different Tracks and Typhoon Waves

The terrain, such as Taiwan Island, have been shown to have complex effects on typhoons and the associated typhoon waves. Terrain effects change with typhoon tracks. In this study, three types of typhoon tracks (northern, middle and southern) were defined according to the relationship between the typhoon tracks and Taiwan Island. Typhoons on these three tracks and typhoon waves were simulated using the Weather Research and Forecasting–Simulating Waves Nearshore model. In each type of typhoon, a control case without the Taiwan topography was simulated to compare with real cases. The results showed that typhoons on different tracks were affected by the terrain of Taiwan Island in different ways. Taiwan Island had weakening, decelerating and deflective effects on typhoons. The ranking for the weakening effect was middle track (81%) > southern track (69%) > northern track (3%). The decelerating effect was 7% in the northern track and 25% in the southern track. The deflective effect of the terrain makes typhoons on the northern (southern) track deflect toward the south (north). When a typhoon on a middle track passed over Taiwan Island, a new center of low pressure would replace the former center and make the track discontinuous. In addition, the influence of typhoons on regions near Taiwan Island changed with the typhoon’s tracks. The influence ranking of typhoons in Taiwan Island was the middle track > southern track > northern track, which was consistent with that of typhoons in the Taiwan Strait and opposite to that of typhoons in Fujian Province. The influence ranking of typhoons on the Taiwan Strait was the opposite of the typhoon intensity ranking, which suggests that the intensities of wind and waves in the strait were more related to typhoon tracks than typhoon intensity. The variations in the significant wave height were similar to those of the wind speed, but there was a time lag (2 h) between them due to the wave growth process and swells. In addition, the significant wave height distribution sometimes differed from the wind speed distribution under the influence of swells and terrain.

Current Effect on Wave Condition around Island in the South China Sea

Abstract Currents have a significant impact on wave parameters around islands. In this study, high-resolution unsteady current simulations based on island geography and wind fields from Weather Research and Forecasting (WRF) Model are used as input sources. The wave action balance model uses an unstructured grid to assess the wave conditions in the Atoll during Typhoon Noul. The characteristic wave parameters, with and without the effect of currents, are compared with the field observation data, including significant wave height, wave period, and the spatial distribution of significant wave height. The results show that simulated significant wave heights and wave periods are close to observed data, considering the effect of currents. The energy and shape of the spectrum are also verified during Typhoon Noul, and the observed agreement is improved when considering the currents. The effects of current within the Atoll are relatively weaker compared to the surroundings, while stronger current effects are observed in the deeper water outside the Atoll. Refraction caused by current expands the area of moderate sea state behind the island. Significance Statement Several innovations of this article are as follows: 1) the influence of currents on wave conditions at the Atoll; 2) exploring the impact of currents using key parameters, such as significant wave height, wave period, and wave spectrum, especially during the passage of Typhoon Noul; 3) swell emerges as the dominant factor influencing wave conditions as the center of Typhoon Noul gradually moves away; and 4) refraction caused by current expands the area of moderate sea state behind the island.

Relationship between Large-Scale Variability of North Pacific Waves and El Niño-Southern Oscillation

Ocean waves are crucial for driving various oceanic processes. In this study, the spatial and temporal distribution of significant wave height (SWH) in the North Pacific (NP) is analyzed using the 42-year ERA5 reanalysis dataset from European Centre for Medium-Range Weather Forecasts (ECMWF). The presence of an ENSO signal is confirmed in wave fields of the North Pacific. Furthermore, the spatial distributions of swells and wind waves are analyzed using the Empirical Orthogonal Function (EOF) method, revealing that waves can transport large-scale signals from the NP to lower latitudes through swells. In addition, our research reveals a relationship between ENSO and Stokes drift in the NP. Stokes drift contributes positively to the maintenance of stable sea surface temperatures (SSTs) by transporting more (less) water towards the equatorial Pacific during El Niño (La Niña year) years. It is further noted that during strong ENSO events, the strength of the Stokes drift anomaly intensifies accordingly, which implies a strong link between wave-induced transport and ENSO.

Analysis of the North Atlantic offshore energy flux from different reanalysis and hindcasts

To date there is a wide range of wave reanalysis and hindcasts available to the scientific and engineering community which are commonly used for different applications, including downscaling or the estimation of the wave energy resource (Morim et al., 2022). These long datasets have been created using different combinations of forcing fields, physical parameterizations, and numerical choices (like spatial and spectral resolution). All these elements have a direct effect on the accuracy of the wave models’ output (e.g., Alday et al., 2021) and thus, they are one of the main reasons for the differences between these products. In the present study we analyze the significant wave heights and peak periods characteristics from a selection of global datasets. We additionally include results from a hindcast created using the WAVEWATCH III model, with adjustments specially aimed to reduce uncertainties of the wave energy resource along the Atlantic coasts of Europe. Models’ output is compared with buoys and altimeter data from the latest ESA (European Space Agency) CCI Sea State V3 product. Preliminary validation of the hindcast we have generated for the North Atlantic already show an important bias reduction for wave heights in the 2.5 to 11.5 range compared to ERA5 wave product. Using the relevant wave parameters, we estimate the power density and quantify the differences between databases. Then, based on scatter diagrams obtained from the joint distributions of significant wave height and peak period, the differences in the power captured by wave energy converters (WEC) related to different wave data sources will be quantified (e.g., Babarit et al., 2011; Henriques et al., 2016).

Environmental Contours in the Adriatic Sea for Design and Analysis of Marine Structures

The environmental contours represent an approach for defining extreme environmental conditions, resulting in extreme responses of marine structures with a given return period. Over the past decade, an increasing number of studies have been developed dealing with the methods for defining environmental contours and enhancing their practical application in different marine environments. In the present study, environmental contours describing significant wave heights and peak wave periods are created for the Adriatic Sea. This small semi-enclosed sea basin within the Mediterranean Sea encounters increasing maritime and offshore activities. Considering also a great but still unused potential for the installation of renewable energy facilities, the main motives for the presented study are concluded. The environmental contours are established based on 24 years of hindcast wave data extracted from the WorldWaves database. Joint distributions consisting of the marginal distribution of significant wave height and conditional distributions of peak wave periods are used as a basis for the creation of environmental contours using the IFORM and ISORM methods. Return periods of 1 year, 25 years, and 100 years are considered relevant for the marine operation, design of ships, and offshore structures, respectively. A possibility of environmental contour practical application to the calculation of global wave loads upon ship structures is presented. Based on the uncertainty assessment performed, conservative environmental contours for the whole Adriatic are also presented.

Typhoon field construction and wind-induced wave model optimization based on topographic parameters

In recent years, most of the research on typhoon in Fujian Province of China has stayed in the typhoon wave simulation under the influence of wind fields. In order to study the influence of land terrain on typhoon wave fields, the terrain height parameters are introduced into the wind field simulation through the third-generation typhoon wave numerical model. The numerical simulation results of the model are verified and analyzed by referring to the data of significant wave height and wind speed of typhoon Fung-wong (200808) and typhoon Jangmi (200815) when it is across Taiwan Island. The results show that the relative error of the maximum wind speed and the significant wave height is reduced after the wind field optimization, which is more consistent with the observed data. The model accuracy is improved after optimization; Typhoon Fung-Wong, which crossed Taiwan, showed the most significant reduction in wind speed. Significant wave height is positively correlated with wind speed. The wave height distribution shows a gradually decreasing trend from the cyclone center to the coast, and the significant wave heights of the typhoon moving direction show pronounced asymmetry. Affected by the land topography, the distribution of significant wave height generally shows a downward trend, and the area of height water level area decreases.

Finding a New Home: Rerouting of Ferry Ships from Merak–Bakauheni to East Indonesian Trajectories

As an archipelagic country, Indonesia needs ferry transportation to connect and support the economic activities between areas bounded by the sea. The famous crossing route is the Merak–Bakauheni one, which connects the Java and Sumatra economic corridors. Many ships operate on this route, but limited port facilities significantly affect the efficiencies of the services provided, hence, they have to be moved. Therefore, this research analyzed the suitability of ships to operate on the eastern crossing. The analysis method used the financial aspect (revenue) feasibility, the suitability of the port infrastructure, and the oceanographic conditions. The financial analysis used the ships’ operating cost method to determine the crossing passage rates based on their specifications. It simulated the ships with various load factors to identify potential gains or losses. Furthermore, the infrastructure suitability analysis used the under keel clearance and comparative methods to compare the suitability of the ship dimensions and tonnage with the port infrastructure capacity. The oceanographic analysis used the Weibull method to simulate the redefinition of the distribution of significant wave heights, which was compared with the ratio of the ship dimensions and wave slope to determine its heel angle using the IMO Weather Criterion method (IS Code 2008). The results showed that the relocation of ships from the Merak–Bakauheni route directly to Eastern Indonesia through the existing crossing routes is feasible from the aspect of shipping safety, but it is not feasible financially or in terms of infrastructure. The Benoa–Labuan Bajo route is a potential new route recommendation, with regulatory support for the operation of ships in the form of tariffs and operational costs, and it permits the use of subsidized fuel. On the other hand, ship owners must consider modifying the ramp door to suit the port wharf structure.

Description of the Joint Probability of Significant Wave Height and Mean Wave Period

The bivariate probability distribution of significant wave heights and mean wave periods has an indispensable guiding role in the implementation of offshore engineering, which has attracted great attention. This work gives a new bivariate method to describe the bivariate distribution of significant wave height and mean wave period at the NanJi, BeiShuang, and XiaoMaiDao stations from 2018 to 2020. A mixed lognormal distribution is used for univariate probability analysis of wave data, and the method of connecting two mixed lognormal distributions with copula functions is applied to construct bivariate distribution. The results show that compared with Weibull and lognormal distributions, the mixed lognormal distribution shows good performance in fitting marginal distributions. In the bivariate probability analysis, the conditional model overestimates the probability of lower wave heights, and the bivariate function model has a poor fitting effect in the region with larger periods. In contrast, the copula model based on mixed lognormal distribution is more suited to describe the joint distribution of significant wave height and mean wave period.

Modelling trivariate distribution of directional ocean data in the Barents Sea seasonal ice zone

The Arctic Ocean has proved to possess a wealth of natural oil and gas resources. Although the ice cover complicates marine industrial activities and transportation, exploratory drilling and processing facilities operation is possible in the region where the sea ice is only present for a portion of the year. This study focuses on the statistical characteristics of directional wave climate in the seasonal ice zone of the Barents Sea. The joint distributions of significant wave height, mean wave period, and mean wave direction were constructed using a mixture trivariate distribution model. The total ocean data were classified into four groups based on the relative weights of the energy content of wind wave and swell fields. The joint distribution for each wave component was constructed by the vine copula model, where the marginal distributions can be well described by the mixture univariate distribution models, the bivariate distributions of angular-linear variables were fitted by the Johnson-Wehrly model adequately, and the bivariate distribution of the linear-linear variable can be accurately modelled by a product of two Gaussian copulas. The results suggested that the mixture trivariate distribution for the total sea state constructed by a linear combination of the four submodels is capable of providing reasonable description for the directional wave data. To generate trivariate samples for model evaluation, an improved pseudorandom number generation algorithm was applied. Furthermore, the environmental contours associated with return periods of 1-, 5-, 20-, and 100-year in different directions were calculated and used to determine the extreme tensions of a semi-submersible platform model based on the global maxima approach.

Typological representation of the offshore oceanographic environment along the Alaskan North Slope

Erosion and flooding impacts to Arctic coastal environments are intensifying with nearshore oceanographic conditions acting as a key environmental driver. Robust and comprehensive assessment of the nearshore oceanographic conditions require knowledge of the following boundary conditions: incident wave energy, water level, incident wind energy, ocean temperature and salinity, bathymetry, and shoreline orientation. The number of offshore oceanographic boundary conditions can be large, requiring a significant computational investment to reproduce nearshore conditions. This present study develops location-independent typologies to reduce the number of boundary conditions needed to assess nearshore oceanographic environments in both a Historical (2007–2019) and Future (2020–2040) timespan along the Alaskan North Slope. We used WAVEWATCH III® and Delft3D Flexible Mesh model output from six oceanographic sites located along a constant ∼50 m bathymetric line spanning the Chukchi to Beaufort Seas. K-means clustering was applied to the energy-weighted joint-probability distribution of significant wave height (Hs) and peak period (Tp). Distributions of wave and wind direction, wind speed, and water level associated with location-independent centroids were assigned single values to describe a reduced order, typological rendition of offshore oceanographic conditions. Reanalysis data (e.g., ASRv2, ERA5, and GOFS) grounded the historical simulations while projected conditions were obtained from downscaled GFDL-CM3 forced under RCP8.5 conditions. Location-dependence for each site is established through the occurrence joint-probability distribution in the form of unique scaling factors representing the fraction of time that the typology would occupy over a representative year. As anticipated, these typologies show increasingly energetic ocean conditions in the future. They also enable computationally efficient simulation of the nearshore oceanographic environment along the North Slope of Alaska for better characterization of coastal processes (e.g., erosion, flooding, or sediment transport).

Global Validation of SWIM/CFOSAT Wind Waves Against Voluntary Observing Ship Data

AbstractThe article presents a joint analysis of wind and wave characteristics derived from Voluntary Observing Ship (VOS) data and measurements of the innovative Ku‐band radar SWIM (Surface Waves Investigation and Monitoring) carried by Chinese‐French Ocean SATellite (CFOSAT). Global distributions of significant wave height and wind speed in both data sets demonstrate good qualitative and quantitative agreement, especially in regions with a high spatio‐temporal density of visual observations. A particular focus is made on discriminating wave systems by joint analysis of separately observed wind sea and swell characteristics in VOS and the partitions of wave spectra measured by SWIM. It is shown that three wave partitions from SWIM cannot be clearly attributed to wind sea, first, and secondary swell systems. The first partition aggregates both wind sea and swell in the operational wavelength range of the SWIM radar, while the second and third partitions fit neither wind sea, nor swell. A comparison of VOS and SWIM data within a 50 km radius and a 30 min time lag shows a very close match for most parameters in terms of mean values, yet with relatively high dispersion of individual measurements.

A truncated, translated Weibull distribution for shallow water sea states

Reliable probabilistic information of the long-term ocean wave climate is important in many coastal and ocean engineering applications such as the design of marine and coastal structures. There is therefore a need to establish accurate models for the long-term distribution of relevant metocean variables. One of the most important wave parameters in marine design is the significant wave height, which is a measure of the severity of the sea state, and wave loads are typically described in terms of this and other variables. Hence, a lot of effort has been put on the proper probabilistic modelling of significant wave height. However, probability distributions proposed to model significant wave height have mostly focused on deep water conditions and less efforts have been put on shallow water conditions. This paper proposes a truncated, translated Weibull distribution for the long-time distribution of significant wave height in shallow waters and demonstrates that the model fit shallow water data quite well. In particular, the proposed model describes shallow-water wave data better than the commonly used 3-parameter Weibull distribution, which is often the preferred distribution for deep water locations.

Discussion/comments of “Parameterization of nearshore wave breaker index” by Chi Zhang, Yuan Li, Yu Cai, Jian Shi, Jinhai Zheng, Feng Cai and Hong Shuai

The purpose of these comments and discussion has been to point out that wave statistics can be incorporated in future applications of the nearshore wave breaker index formula proposed by Zhang et al. (2021). This is demonstrated by using a joint distribution of significant wave height and spectral peak period provided by Li et al. (2015).

Comprehensive Wind and Wave Statistics and Extreme Values for Design and Analysis of Marine Structures in the Adriatic Sea

Wind and waves present the main causes of environmental loading on seagoing ships and offshore structures. Thus, its detailed understanding can improve the design and maintenance of these structures. Wind and wave statistical models are developed based on the WorldWaves database for the Adriatic Sea: for the entire Adriatic Sea as a whole, divided into three regions and for 39 uniformly spaced locations across the offshore Adriatic. Model parameters are fitted and presented for each case, following the conditional modelling approach, i.e., the marginal distribution of significant wave height and conditional distribution of peak period and wind speed. Extreme significant wave heights were evaluated for 20-, 50- and 100-year return periods. The presented data provide a consistent and comprehensive description of metocean (wind and wave) climate in the Adriatic Sea that can serve as input for almost all kind of analyses of ships and offshore structures.

CMIP5 model performance of significant wave heights over the Indian Ocean using COWCLIP datasets

Wind-generated surface gravity waves forms an integral part in modulating the air-sea exchange processes. Information of wave parameters is also very essential in planning marine- and coastal-related activities. It is now well recognized that wind-wave activity shows changing trends over the global ocean basins. Numerous studies have addressed the projected changes in significant wave height for the Indian Ocean (IO) region, and there is a need to conduct thorough performance evaluation of global climate models (GCMs) over this region for futuristic planning. With this motivation, the present study examined the performance of historical dynamical wave climate simulations generated under the Coordinated Ocean Wave Climate Projections (COWCLIP) experiment. The simulations utilized near-surface wind speed datasets from 8 CMIP5 (Fifth phase of Coupled Model Intercomparison Project) GCMs to force a spectral wave model. The skill level of individual GCM forced wave simulations and multi-model mean (MMM) in reproducing the significant wave height (SWH) over four different sub-domains in the IO was evaluated with reference to the ECMWF Reanalysis 5th Generation (ERA5) datasets. Several performance metrics such as the Taylor Skill, M-Score, Model Climate Performance Index (MCPI), and Model Variability Index (MVI) are employed to establish the skill level of model simulations. The study deciphers that model performance is highly reliant on the region and its characteristics. Representation of the historical wave climate over the Arabian Sea (AS) and the Bay of Bengal (BoB) regions is remarkable in the COWCLIP datasets. However, there are discrepancies noticed in SWH distribution over the South Indian Ocean (SIO) attributed to model limitations in adequately reproducing swell wave fields over that region. The MMM constructed using the best-performing models (MRI-CGCM3, ACCESS1.0, INMCM4, HadGEM2-ES, and BCC-CSM1.1) is found consistent at all the sub-domains. The study signifies that the performance evaluation of GCM forced wave simulations is crucial before employing them for practical applications. Best-performing models listed from this study can be used to establish futuristic scenarios of SWH in a changing climate for the IO region.

Effects of Wave–Current Interactions on Bay–Shelf Exchange

AbstractBay–shelf exchange is critical to coastal systems because it promotes self-purification or pollution dilution of the systems. In this study, the effects of wave–current interactions on bay–shelf exchange are explored in a micromesotidal system—Daya Bay in southern China. Waves can enlarge the shear-induced seaward transport and reduce the residual-current-induced landward transport, which benefits the bay–shelf exchange; however, tides work oppositely and slow the wave-induced bay–shelf exchange through vertical mixing and reduced shear-induced exchange. Five wave–current interactions are compared, and it is found that the depth-dependent wave radiation stress (WRS) contributes most to the bay–shelf exchange, followed by the wave dissipation as a source term in the turbulence kinetic energy equation, and the mean current advection and refraction of wave energy (CARWE). The vertical transfer of wave-generated pressure to the mean momentum equation (also known as the form drag) and the combined wave–current bottom stress (CWCBS) play minor roles in the bay–shelf exchange. The bay–shelf exchange is faster under southerly wind than under northerly wind because the bay is facing southeast; synoptic events such as storms enhance the bay–shelf exchange. The CARWE terms are dominant in both seasonal and synoptic variations of the bay–shelf exchange because they can considerably change the distribution of significant wave height. The WRS changes the bay–shelf exchange mainly through altering the flow velocity, whereas the wave dissipation on turbulence alters the vertical mixing. The form drag and the CWCBS have little impact on the bay–shelf exchange or its seasonal and synoptic variations.