Wave Height Distribution Research Articles

Offshore Structural Reliability Assessment by Probabilistic Procedures—A Review

Offshore installations must be built to resist fatigue as well as extreme forces caused by severe environmental conditions. The structural reliability analysis is the popular practise to assess a variety of natural waves determined by the long-term probability distribution of wave heights and corresponding periods on the site. In truth, however, these structures are subjected to arbitrary wave-induced forces in the open ocean. Hence, it is much more reasonable to account for the changed loading characteristics by determining the probabilistic characteristics of the random loads and outcomes responses. The key challenges are uncertainties and the non-linearity of Morison’s drag element, which results in non-Gaussian loading and response distributions. This study would analyze advances achieved to date in a comprehensive probabilistic review of offshore fixed jacket-type platforms.

Revisiting statistical properties of surf parameter with characteristic wave parameters for single random waves including spectral bandwidth effects

Results from a comparative study of the joint distribution of surf parameter and wave period are provided. First, two transformed joint distributions of wave height and wave period are compared. One of the distributions is a parametric model originating from a best fit to relatively broad-band field data covering a wide range of wave conditions, whilst the other distribution is theoretically based. It appears that the theoretically based distribution does not represent the features of the parametric model especially well, suggesting that parametric models should be used to describe relatively broad-banded data. Then, the theoretically based joint distribution of wave height and wave period is transformed to the joint distributions of surf parameter with wave height and wave period and it is demonstrated how these distributions are affected by the spectral bandwidth. Finally, the theoretically based distribution of wave height and wave period is also transformed to the joint distribution of wave runup time and wave period due to its relation to the stability of rubble-mound breakwaters. Comparisons are made with a limited set of data representing results from small-scale laboratory experiments related to stability of rubble-mound breakwaters. The agreement between measurements and predictions of the distribution of the surf parameter is fair, whilst the agreement is poorer for the probability of resonance.

On the Effects of Non-Gaussian Wave-Slope Distribution on the Failure Probability of an Armour block of Rubble Mound Breakwater

This study examined the effect of non-Gaussian wave slope distribution on the failure probability of an armoring rock of rubble mound breakwater using numerical simulation. Numerical simulation was carried out using the Van der Meer equation and Level III reliability design method based on the Monte Carlo simulation. In doing so, modified Glukhovskiy wave height distribution and situ wave height data collected at Ulleungdo from January 1, 1979-December 31, 2019 were used. Tri-modal Gaissuian wave slope distribution was also used, which showed good agreements with situ wave data collected at Mangbang from April 26, 2017, to April 20, 2018. The probability coefficients of tri-modal Gaussian distribution were estimated using Matlab-based statistics and machine learning toolbox, MLE [Maximum Likelihood Estimates]. In the numerical simulation, the intrinsic limitations of Gaussian distribution were revealed, such as imposing a non-negligible probability mass even in the negative wave slope, under-shooting in longer and shorter waves, and over-shooting in mid-scale waves. In the case of failure probability of an armoring rock, Gaussian distribution was shown to give underestimated failure probability. The extent of underestimation was more considerable at Mangbang, where a tidal terrace of lower depth and gently varying slope was developed than at Ulleungdo. These differences were triggered by the presence of probability plateau formed in wave slope distribution whenever infra-gravity waves appear in random wave packet due to the resonant wave-wave interaction. Therefore, it can be easily conceivable that probability plateau has a significant effect on the armoring rock failure probability. Therefore, PIANC's recommendation that wave slope follows Gaussian distribution needs to be amended. Moreover, the reliability-based design of breakwater should be implemented based on tri-modal Gaussian wave slope distribution, which can accurately reproduce probability plateau.

Machine learning for satellite-based sea-state prediction in an offshore windfarm

Accurate wave forecasts are essential for the safe and efficient maritime operations and, in particular, the maintenance of offshore wind farms. Here, machine learning and remote monitoring from satellites are integrated to provide uniquely detailed predictions of significant wave height (SWH). C-Band Synthetic Aperture Radar images from European Space Agency Sentinel-1 satellites were combined with wave-buoy data from around the UK, using the CEFAS Wavenet. A total of 240 images in wide swarth mode were collected, that represent significant wave height ranging from 0 to 4.7 m. Image properties related to sea surface roughness in dual-polarization mode, together with the wave buoy data, trained an ensemble of artificial neural networks. The trained networks were shown to provide an effective method for the estimation of the SWH, having an RMSE = 0.23 m for SWH<3 m, which is the region of interest for offshore wind energy applications. The methodology enables information on the spatial distribution of wave height in very high resolution to be obtained. Sea-state resolved from the satellite data, using the artificial neural network shows that windfarm infrastructure directly influences wave propagation. The overall variance of significant wave height throughout a wind farm was calculated, providing information on regions of interest with considerably different wave heights as compared to the nearest wave buoy. The new model will help towards improved downscaling of general sea state forecasts, locating hotspots of different wave height properties and correct prioritization of maintenance jobs to perform in wind turbines.

The Rayleigh-Haring-Tayfun distribution of wave heights in deep water

Nearly every known exceedance probability distribution applied to rogue waves has shown disagreement with its peers, suggesting that the underlying phenomenon may be too complex to grasp within a single distribution. In recent studies, this view has been supported by the realisation that there is no distribution suitable for wide ranges of sea states, even though distributions can perform well in a limited and small number of conditions. Towards the better quantitative assessment of rogue wave occurrence, the present work focuses on the apparent discrepancy among the majority of previous works. Furthermore, on the grounds of the uneven distribution of rogue waves found in North Sea observations, a new exceedance probability distribution for rogue waves is introduced. The proposed distribution is a geometrical composition of some of the most popular simple models for waves while introducing additional algebraic structures. The model also obeys empirical physical bounds obtained from the analysis of nearly 350,000 waves from storms recorded in North sea and supports the qualitative analysis of rogue wave occurrence based on the interaction among three sea state parameters.

Wave Height Distributions and Rogue Waves in the Eastern Mediterranean

There is a lack of scientific knowledge about the physical sea characteristics of the eastern part of the Mediterranean Sea. The current work offers a comprehensive view of wave fields in southern Israel waters covering a period between January 2017 and June 2018. The analyzed data were collected by a meteorological buoy providing wind and wave parameters. As expected for this area, the strongest storm events occurred throughout October–April. In this paper, we analyze the buoy data following two main objectives—identifying the most appropriate statistical distribution model and examining wave data in search of rogue wave presence. The objectives were accomplished by comparing a number of models suitable for deep seawater waves. The Tayfun–Fedele third-order model showed the best agreement with the tail of the empirical wave height distribution. The examination of different statistical thresholds for the identification of rogue waves resulted in the detection of 109 unique waves, all of relatively low height. The characteristics of the detected rogue waves were examined, revealing that the majority of them presented crest-to-trough symmetry. This finding calls for a reevaluation of the crest amplitude being equal to or above 1.25, the significant wave height threshold which assumes rogue waves carry most of their energy in the crest.

Evolution of waves in a horizontal pipe propagating on a surface of a liquid film sheared by gas

Different wavy regimes in stratified air–water pipe flow are determined for a wide range of gas and liquid flow rates in a 10 m long horizontal pipe with a diameter of 24 mm. Three sub-regions of wavy stratified flow are identified: ripples, roll waves, and pre-annular wavy flow. Statistical parameters, such as local mean film thickness and its higher moments (root-mean-square, skewness, excess kurtosis) as well as wave characteristics (mean heights and wave height distributions, lengths, propagation velocities, etc.), are measured and analyzed. It is demonstrated that ripples are essentially linear waves and their propagation velocities are described reasonably well by linear wave theory. High amplitude roll and pre-annular waves are substantially nonlinear, and their propagation velocities differ significantly from that of ripples. Transition to roll waves causes a sharp increase in higher statistical moments. Evolution of wave and statistical parameters characterizing each sub-region of stratified gas–liquid pipe flow is studied. Simplified models describing roll waves are presented; the model predictions are verified by experiments.

Freak wave in high-order weakly nonlinear wave evolution with bottom topography change

In deep-water, quasi-resonant four-wave interaction gives rise to the occurrence probability of extreme wave height, which leads to freak wave as a natural disaster. As water wave enters shallow water, four-wave interaction becomes weak and wave shoaling makes this effect become complicated. This study conducts a Monte Carlo simulation in modified Nonlinear Schrödinger equation considering bottom topography change, and gives spatial evolution of high-order nonlinearity in wave train from statistical moment. The result indicates, slope angle plays an important role in a shallow water depth, and steep slope brings about a significant enhancement of extreme event in distribution of maximum wave height and surface elevation.

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.

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.

Distribution characteristics of waves in Sanmen Bay based on field observation

The wave characteristics in the nearshore waters of Sanmen Bay are presented based on the AWAC-measured data from October 2016 to September 2017 at the wave observation station with 7.5m water depth. The wave parameters and the wave spectral variations are statistically analyzed, and the wave height distribution, the wave period distribution, and the joint distribution of wave height and period are discussed. The results indicate that the measured distribution of wave height agrees well with the Weibull distribution. When the spectral width is small, the various theoretical distribution models of wave period have their own reference values for the study of the distribution of measured wave period. The measured distribution of wave period has the best agreement with the Weibull distribution when the spectral width is large. The Longuet-Higgins model (1983) and the Sunfu model can be fitted to the joint distribution of wave height and period in this sea area, but the fitting effect is poor. The dominant wave direction and the strong wave direction are both E, with a frequency value of 40.27%. The maximum wave height (Hmax) of 2.71m was observed during the observation period due to the influence of typhoon Talim.

Marine Climate Projections Toward the End of the Twenty-First Century in the North Atlantic

Abstract An improved understanding of the present and future marine climatology is necessary for numerous activities, such as the operation of offshore structures, optimization of ship routes, and evaluation of wave energy resources. To produce global wave information, the WAVEWATCH III wave model was forced with wind and ice-cover data from an RCP8.5 EC-Earth system integration for two 30-year time slices. The first covering the periods from 1980 to 2009 represents the present climate, and the second, covering the periods from 2070 to 2099, represents the climate at the end of the twenty-first century. Descriptive empirical statistics of wind and wave parameters are obtained for different 30-year time slices, for the North Atlantic Ocean. Regarding wind, magnitude and direction will be used. For wave, significant wave height of the total sea, mean wave period, peak period, mean wave direction, and energy will be investigated. Changes from present to future climate are evaluated, regarding both mean and extreme events. Maps of these empirical statistics are presented. The long-term monthly joint distribution of significant wave heights and peak periods is generated. Changes from present to future climate are assessed, comparing the empirical statistics between time slices.

Note on estimating bed shear stress caused by breaking random waves

This note presents a method of how the bed shear stress caused by breaking random waves on slopes can be estimated. This is obtained by adopting the Sumer et al. (2013) bed shear stress formula due to spilling and plunging breaking waves on hydraulically smooth slopes combined with the Myrhaug and Fouques (2012) joint distribution of surf similarity parameter and wave height for individual random waves in deep water. The conditional mean value of the maxima of mean bed shear stress during wave runup given wave height in deep water is provided including an example for spilling and plunging breaking random waves corresponding to typical field conditions. Another example compares the present results with one case from Thornton and Guza (1983) estimating the wave energy dissipation caused by bed shear stress beneath breaking random waves.

Assessment of typhoon prevention level at fishing port

Due to the need of typhoon grade evaluation in the construction plan of fishing port, the wave height distribution in the fishing port of typhoon 10 and typhoon 12 under adverse path was calculated, and the berthing area of the fishing port was counted. According to the theoretical formula, the wind force and anchor-holding force of the fishing boat are calculated, and the anti-typhoon grade of the anchorage is analyzed, which provides technical support for the construction of the port area.

Asymmetric Wave Distributions of Tropical Cyclones Based on CFOSAT Observations

AbstractObservations of the China‐France oceanography satellite are used to investigate the wave distribution's asymmetry during tropical cyclone (TC) from August 2019 to August 2020. The spatial distribution of TC waves is analyzed based on an individual case, six ocean basins, and TCs categories. A study of super typhoon Hagibis shows that the highest significant wave height (SWH) appears on the typhoon track's right side. Further analysis reveals that the highest SWH is located on the right (left) side of TC tracks in the Northern Hemisphere (Southern Hemisphere). In the Western North Pacific, North Atlantic, Eastern North Pacific, and North Indian Ocean, the highest SWH is on the right side of TCs of 251, 260, 130, and 118 km, respectively. In the South Pacific and South Indian Ocean, the highest SWH is on the left side of 70 and 128 km. According to the TC categories, the largest (smallest) departure happens during the weakest (strongest) TC. The intensifying of TC favors the wavefield's growth and reduces the asymmetry of the wave height's distribution. Both the asymmetric wind fields and the land's orographic effects impact the TC wave's distribution. In the Eastern North Pacific, the TC wind is the weakest, but the departure is not the smallest, probably due to the left continent bounding the wave energy's propagation.

Wave height distribution in unsaturated surf zones

This paper addresses the performance of different wave height distributions in the surf zone on natural beaches on the central west coast of India. The surfzone water level data for different surf zones were analyzed using Fast Fourier Transformation techniques to obtain the wave characteristics viz., wave height, and wave period. Different probability density functions (pdfs) were fit for the surf zone wave heights to identify the best-fit pdf. The quality of the surf zone wave modeling depends on the skill of the identified best-fit pdf in explaining the measured wave height distribution. This study further reiterates that the Rayleigh and Exponential pdfs are a poor fit for the surf zone wave heights. However, Kernel, GEV, and Logistic pdfs were observed to very well fit the surf zone waves. A constant value of power p=2 in the Rayleigh distribution is not suitable for the central west coast of India. The power p varies for different surf zones, and it also varies spatially and temporally. In this study, a simplified approximation for p is estimated using the maximum and the minimum values of significant wave height, root mean square wave height and the total number of waves. This improved Rayleigh pdf was applied for the surf zone waves measured at different locations along the central west coast of India and found to be fit.

Tide–surge and wave interaction around the Taiwan coast: insight from Typhoon Nepartak in 2016

This study mainly aims to hindcast historical Typhoon Nepartak (2016) and to analyze tide–surge and wave interactions. To achieve this goal, a coupled tide–surge–wave model was built around the coast of Taiwan, and it was applied to simulate storm surges and waves during historical typhoon event. To demonstrate its capability, the coupled model was validated with observed water levels, wind speeds, atmospheric pressures, wave heights, and wave periods at different stations. Quantitatively, the model results reasonably reproduced the observed data. Furthermore, the model was utilized to explore the tide, surge, and wave interaction using historical Typhoon Nepartak (2016). The model results revealed that onshore wind enhanced the surge height, while offshore wind decreased the surge height. The atmospheric pressure consistently displayed a positive contribution to surge height. The wind-induced surge height contributing to the total surge height was 136.83% at Taichung Harbor, because the offshore wind mainly dominated the surge height compared to the effect of atmospheric pressure. The atmospheric pressure-induced surge heights contributing to the total surge height were 100.59%, 96.26%, and 99.74% at Kaohsiung Harbor, Hualien Harbor, and Taitung Fugang, respectively, as a result of the atmospheric pressure dominating the surge height. However, the contribution of the wave setup to the total surge height was minor. The path of typhoons at different time frames significantly affected the spatial distributions of surge height and wave height around the coast of Taiwan. The contributions of water level and current to wave height reached a maximum value of approximately 0.3 m at Suao, while the contributions at Penghu, Qigu, and Eluanbi were all less than 0.2 m. This signified that the influence of the water level and current on wave height was not negligible.

Simulation of extreme waves using coupled atmosphere-wave modeling system over the South China Sea

A real-time two-way coupled atmosphere-wave model in the South China Sea (SCS) has been established based on the atmosphere model WRF and the wave model SWAN in this study. We implement a nested computational grid along the SCS in the SWAN model and utilize the WRF model to provide high-resolution mesoscale wind field and pressure field over the SCS under the influence of typhoons. The numerical simulation of the typhoon waves generated by typhoon Kai-tak (1213), Rammasun (1409) and Hato (1713) had been carried out. The results of the numerical simulation are compared with the results of the field observation and the satellite altimeter. The verification results show that the coupled WRF-SWAN model has a high accuracy in the simulation of typhoon waves under the influence of typhoons in the SCS. The results of the simulation reveal the asymmetrical distribution of wind speed and typhoon wave height generated by typhoons in the space. The intensity of the typhoon on the right is greater than that on the left of the typhoon track. The real-time two-way coupled atmosphere-wave model based on the WRF model and the SWAN model can accurately simulate the dynamic process of typhoon and the temporal and spatial distribution of the typhoon waves generated by typhoons. According to the results of the coupled WRF and SWAN model, a corresponding relationship between typhoon wind speed and wave height was obtained, which was combined with the statistical data of typhoon occurring in the SCS during 1949–2019, the distribution characteristics of typhoon wave in the SCS had been simulated. The statistical data grid with a spatial accuracy of 0.5 degree of typhoon waves in the SCS had been established, and then the statistical wave height of typhoon in the SCS based on the Pearson-III distribution had been simulated. Eight characteristic locations have been identified in the SCS, the highest frequency and the hugest height of typhoon wave is near the Luzon Strait, the average of typhoon wave height is reached 9.2 m. The second is southern Taiwan in the eight different selected positions, and the statistical average value of typhoon wave height is close to 8.0 m. Comparison of the Paracel Islands, Spratly Islands and Dongsha Islands, the smallest statistical value of the typhoon wave height is the waves in Spratly Islands, with a mean value of 3.0 m, and the statistical mean value of typhoon wave height near the Paracel Islands and Dongsha Islands are about 6.0 m. Based on the statistical results, combined with the frequency of typhoon in the region, the distribution of typhoon wave height can be calculated at any location in the SCS, and it can be provide to some references for the design of the coastal and ocean engineering.

Research on numerical simulation of typhoon waves with different return periods in nearshore areas: case study of Guishan island Waters in Guangdong province, China

China is one of the countries that are most severely affected by typhoon waves. Typhoon waves often cause catastrophic economic losses and human casualties in the nearshore and offshore areas of China. Risk assessments of nearshore typhoon wave disasters are of great practical significance for the prevention and mitigation of typhoon wave disasters in coastal areas. This study proposes a method of assessing the risks of typhoon wave disasters. The coupled ADCIRC and SWAN model is employed to establish a high-precision numerical model for the study area, which is then used to simulate the process of historical typhoon wave disasters, followed by a statistical analysis of the risk of disasters at the grid scale using the frequency analysis method. The modelling method is empirically analysed, taking the coastal waters from Guishan Island to Zhuhai City, Guangdong Province, as the study area. The processes of 249 typhoon wave disasters in this area were simulated, and the wave height distribution in the 100 m grid of the study area with different return periods calculated. The obtained results can serve as a basis for the development of a methodology for the assessment of typhoon wave disaster risk in coastal areas and could provide a basis for research on disaster-causing mechanisms associated with nearshore waves on the hazard-bearing body. The method proposed in this study can also be applied to other nearshore coastal waters.

The Rayleigh-Haring-Tayfun distribution of wave heights in deep water

The Rayleigh-Haring-Tayfun distribution of wave heights in deep water