Swell Components Research Articles

Asymmetric copula–based distribution models for met-ocean data in offshore wind engineering applications

Joint statistical models for long-term wave climate are a key aspect of offshore wind engineering design. However, to find a joint model for sea-state characteristics is often difficult due to the complex nature of the wave climate and the physical constraints of sea-states phenomena. The available records of wave heights and periods are often very asymmetric in their nature. This article presents a copula-based approach to obtain the joint cumulative distribution function of the significant wave heights and the up-crossing mean period. This study is based on 124-month hindcast data concerning Horns Rev 3 offshore wind farm. The extra-parametrization technique of symmetric copulas is implemented to account for the asymmetry present in the data. The analysis of the total sea, the wind-sea and primary swell components is performed separately. The results show that the extra-parametrization technique with pairwise copulas consistently provided a better goodness-of-fit when compared to symmetric copulas. Moreover, it is demonstrated that the separation of the total sea into its components does not always improve the extra-parametrized copula’s performance. Furthermore, this article also discusses copulas application to offshore wind engineering.

Influence of Sea State on Sea Surface Height Oscillation from Doppler Altimeter Measurements in the North Sea

This paper reports on an investigation on the influence of waves on the sea surface height error, σh, as measured by Delay Doppler satellite altimetry (DDA). CryoSat-2 altimeter sea surface height (SSH) data in the North Sea, processed in both DDA and pseudo low resolution mode (PLRM), are correlated with European Centre for Medium-Range Weather Forecasts (ECMWF) co-located sea state data. We find a small, but consistent correlation between the 1 Hz standard deviation, σh, of the 20 Hz altimeter SSH and the ECMWF total significant wave height, SWHt. The same analysis carried out between σh and the swell component of the wave spectrum shows a smaller correlation. In contrast, the correlation between the PLRM σh and any component of the SWH spectrum has not been found to be significant. To provide an explanation of these results, the aliasing effect caused by the interaction between the sea wavelength and the altimeter resolution has been considered; a simple model has, therefore, been produced to simulate the dependence of the aliasing-derived, σA, on the sea wavelength. The alias/wavelength curve obtained helps to explain why—at least for the relatively low wavelength sea data considered—the wave direction and its wavelength have little or no influence on σh.

Spectral wave characteristics along the central coast of eastern Red Sea

The Jeddah coast lies in the central eastern Red Sea, which is characterized by the predominant northwest winds and the associated wind waves throughout the year. A detailed investigation on the spectral wave characteristics in the nearshore regions of the Jeddah coast has not been carried out yet, primarily due to the lack of data. In the present study, we have analyzed the available wave spectra measured at two nearshore locations along the Jeddah coast using wave gauges. The wave spectra were separated into wind sea and swell components using a frequency-based algorithm, and the integral wave parameters corresponding to each component were derived. Although the measurements were limited to the summer season, notable features such as the diurnal variability and the superimposition of wind seas and swells have been identified from the spectra. The superimposition is mainly due to the interaction of the young swells propagated from the northern Red Sea and the local breezes prevailing along the coast at certain periods in a diurnal cycle. Based on the wave speed calculations and the estimated time shifts between the wind and waves, the potential swell regions have been backtracked.

Wind wave climate of west Spitsbergen: seasonal variability and extreme events

Summary Waves are the key phenomenon directly influencing coastal morphodynamics. Facing insufficient observations, wind wave climate of the west coast of Spitsbergen can be characterized on the basis of the modelled data. Here we have used the results of spectral wave models: Wave Watch III (WW3) hindcast and WAM in ERA-interim (ERAi) reanalysis. We have observed the presence of seasonal cycle with difference of up to 1 m between significant wave heights in summer and winter. In wave-direction analysis we have noticed the southwestern swell component of remarkably narrow width, thus we expect unidirectional swell impact on the coastline. Extreme events analysis revealed that storms occur mainly in winter, but the most energetic ones (significant wave height of up to 9.5 m) occur in spring and autumn. We have identified positive trends in storms’ frequency (2 storms per decade) and storms’ total duration (4 days per decade) on the south of the study area. More storms can result in the increase of erosion rate on the south-western coasts of Spitsbergen, but this change may be highly dependent on the sea ice characteristics. Wave heights of wind sea and swell are correlated with the relevant atmospheric circulation indices, especially the North Atlantic Oscillation. In the recent decade, the correlation is stronger with WW3 than with ERAi data, at some locations explaining over 50% (over 30%) of the total variance of wind sea (swell) wave heights. In ERAi data, the relationship with circulation indices seems sensitive to the length of the analysis period.

One Consideration to Characteristics on Natural Period and Damping Effect of a Moored Large Bulk Carrier

In our previous study, investigations on property of ship motions was conducted through a numerical simulation and a field observation of ship motions and mooring loads. From the investigations, it was concluded that low-frequency motions such as sway, surge and yaw were induced significantly by resonant effects with the long-period wave, and resonant roll motion also occurred at the berth due to the swell component of the wave. It is important for the investigations on property of the ship motions to estimate the natural periods of each ship motion and damping effects precisely as possible. In this study, we have conducted a physical model test on free oscillations of the model ship for a large vessel moored along dolphin to obtain the property of the natural periods and the damping effects.

An operational wave forecasting system for the east coast of India

Demand for operational ocean state forecasting is increasing, owing to the ever-increasing marine activities in the context of blue economy. In the present study, an operational wave forecasting system for the east coast of India is proposed using unstructured Simulating WAves Nearshore model (UNSWAN). This modelling system uses very high resolution mesh near the Indian east coast and coarse resolution offshore, and thus avoids the necessity of nesting with a global wave model. The model is forced with European Centre for Medium-Range Weather Forecasts (ECMWF) winds and simulates wave parameters and wave spectra for the next 3 days. The spatial pictures of satellite data overlaid on simulated wave height show that the model is capable of simulating the significant wave heights and their gradients realistically. Spectral validation has been done using the available data to prove the reliability of the model. To further evaluate the model performance, the wave forecast for the entire year 2014 is evaluated against buoy measurements over the region at 4 waverider buoy locations. Seasonal analysis of significant wave height (Hs) at the four locations showed that the correlation between the modelled and observed was the highest (in the range 0.78–0.96) during the post-monsoon season. The variability of Hs was also the highest during this season at all locations. The error statistics showed clear seasonal and geographical location dependence. The root mean square error at Visakhapatnam was the same (0.25) for all seasons, but it was the smallest for pre-monsoon season (0.12 m and 0.17 m) for Puducherry and Gopalpur. The wind sea component showed higher variability compared to the corresponding swell component in all locations and for all seasons. The variability was picked by the model to a reasonable level in most of the cases. The results of statistical analysis show that the modelling system is suitable for use in the operational scenario.

The approximation of a sea surface using a shore mounted X-band radar with low grazing angle

The ability to measure real time surface elevation over a large spatial domain offers large benefits to multiple industries, including offshore operations and marine renewable applications. In combination with a real time short-term wave prediction model safety related marine operations windows can be increased. This focuses on Quiescent Period Prediction during large sea states, and the ability of pre-emptive wave-by-wave tuning of marine energy converters leads to improved efficiencies. This study presents a new method of converting X-band radar sequence into approximate surface elevation in near real time using synthetic wave trough profile estimations, forgoing the use of a linear stochastic model. The artificial wave trough method applies a second order Stokes wave to trough regions where radar shadows occur, these shadows are caused as a result of high surround wave crest height where no surface information is gathered. The calculated surface elevation is validated against in situ sensor data at two locations, a correlation (r) of 0.69 is shown for the Signature 1000 sensor location, while a lower correlation of 0.56 is observed at the wave buoy location. When the phase-averaged wave parameters (Hm0 and Tp) derived from 20min wave spectra for the entire duration of the measurement campaign are compared, a reasonable agreement of 0.62 and 0.41 for the AD2CP and wave buoy location is achieved. The presented method shows a good approximation of wave profile shape, where the swell component is predominantly measured, indicating the potential of X-band radar surface elevation measurements in near real time for nearshore inhomogeneous seas.

Wind-Wave Characterization in a Wind-Jet Region: The Ebro Delta Case

This manuscript describes the wind-wave generation, development and fading in a complex area: a wind-jet region. The study region is the offshore Ebro Delta (NW Mediterranean Sea) where strong cross-shelf winds occur due to a topographic channelization. This leads to relatively short-fetch conditions, which interact with the swell component. The third-generation wave model Simulating WAves Nearshore (SWAN) is implemented and fed by high-resolution wind fields. A combination of buoy and High Frequency (HF) radar data is used for model validation, resulting in a reasonable level of agreement. The numerical results characterize the wind-wave evolution during a wind jet. A bimodal spectrum is observed due to the interaction of swell and sea systems. The wave directional spreading exhibits lower values at the wind-jet axis. Finally, a reliability analysis of the wave data from an HF radar deployed at the region is carried out.

Alongshore momentum transfer to the nearshore zone from energetic ocean waves generated by passing hurricanes

AbstractWave and current measurements from a cross‐shore array of nearshore sensors in Duck, NC, are used to elucidate the balance of alongshore momentum under energetic wave conditions with wide surf zones, generated by passing hurricanes that are close to and far from to the coast. The observations indicate that a distant storm (Hurricane Bill, 2009) with large waves has low variability in directional wave characteristics resulting in alongshore currents that are driven mainly by the changes in wave energy. A storm close to the coast (Hurricane Earl, 2010), with strong local wind stress and combined sea and swell components in wave energy spectra, has high variability in wave direction and wave period that influence wave breaking and nearshore circulation as the storm passes. During both large wave events, the horizontal current shear is strong and radiation stress gradients, bottom stress, wind stress, horizontal mixing, and cross‐shore advection contribute to alongshore momentum at different spatial locations across the nearshore region. Horizontal mixing during Hurricane Earl, estimated from rotational velocities, was particularly strong suggesting that intense eddies were generated by the high horizontal shear from opposing wind‐driven and wave‐driven currents. The results provide insight into the cross‐shore distribution of the alongshore current and the connection between flows inside and outside the surf zone during major storms, indicating that the current shear and mixing at the interface between the surf zone and shallow inner shelf is strongly dependent on the distance from the storm center to the coast.

On the ability of statistical wind-wave models to capture the variability and long-term trends of the North Atlantic winter wave climate

A dynamical wind-wave climate simulation covering the North Atlantic Ocean and spanning the whole 21st century under the A1B scenario has been compared with a set of statistical projections using atmospheric variables or large scale climate indices as predictors. As a first step, the performance of all statistical models has been evaluated for the present-day climate; namely they have been compared with a dynamical wind-wave hindcast in terms of winter Significant Wave Height (SWH) trends and variance as well as with altimetry data. For the projections, it has been found that statistical models that use wind speed as independent variable predictor are able to capture a larger fraction of the winter SWH inter-annual variability (68% on average) and of the long term changes projected by the dynamical simulation. Conversely, regression models using climate indices, sea level pressure and/or pressure gradient as predictors, account for a smaller SWH variance (from 2.8% to 33%) and do not reproduce the dynamically projected long term trends over the North Atlantic. Investigating the wind-sea and swell components separately, we have found that the combination of two regression models, one for wind-sea waves and another one for the swell component, can improve significantly the wave field projections obtained from single regression models over the North Atlantic.

Comparison between wave generation methods for numerical simulation of bimodal seas

This paper describes an investigation of the generation of desired sea states in a numerical wave model. Bimodal sea states containing energetic swell components can be coastal hazards along coastlines exposed to large oceanic fetches. Investigating the effects of long-period bimodal seas requires large computational domains and increased running time to ensure the development of the desired sea state. Long computational runs can cause mass stability issues due to the Stokes drift and wave reflection, which in turn affect results through the variation of the water level. A numerical wave flume, NEWRANS, was used to investigate two wave generation methods: the wave paddle method, allowing for a smaller domain; and the internal mass source function method, providing an open boundary allowing reflected waves to leave the domain. The two wave generation methods were validated against experimental data by comparing the wave generation accuracy and the variance of mass in the model during simulations. Results show that the wave paddle method not only accurately generates the desired sea state but also provides a more stable simulation, in which mass fluctuation has less of an effect on the water depth during the long-duration simulations. As a result, it is suggested that the wave paddle method with active wave absorption is preferable to the internal wave maker option when investigating intermediate-depth long-period bimodal seas for long-duration simulations.

An Adaptive Method of Wave Spectrum Estimation Using X-Band Nautical Radar

In this paper, the dependency of wave spectrum estimation on the analysis window orientation for X-band marine radar data is investigated. The investigation is made for the case where both wind wave and swell components are present. Our results show that more accurate and reliable wave spectrum estimates are obtained when one analysis window for each component (wind waves or swell) is used and is oriented in the up-wave direction of that component. The final wave spectrum estimation is found by averaging the output of those analysis windows. Since the direction of wind waves and swell is not known a priori, a new method is proposed to recursively determine the number and orientation of analysis windows. This method is referred to as the Adaptive Recursive Positioning Method (ARPM). For validation, ocean wave spectra are estimated from X-band marine radar field data using the ARPM and the standard method, using uniformly distributed analysis windows. The results from both methods are compared to ground truth wave spectra acquired using waverider buoy data. Results have shown that the ARPM produces a 10% improvement in the agreement (represented by the correlation coefficient) between the ground truth wave spectrum and the marine radar estimated wave spectrum. This improvement is reflected in a 15% to 30% accuracy enhancement in the wave period estimation and 6 ∘ in peak wave direction. The ARPM not only increases the accuracy of wave period and direction estimation, but it also increases the method’s reliability by producing a lower error standard deviation. Although these improvements are at the price of extra computational time, it has been found that this overhead is acceptable since it is far from the upper bound that requires offline analysis.

Estimation of wind sea and swell using shipboard measurements – A refined parametric modelling approach

Shipboard wave estimation has been of interest in recent years for the purpose of decision support. In this paper, estimation of sea state is studied using ship responses and a parametric description of directional wave spectra. A set of parameters, characterising a given wave spectrum is estimated through an optimisation problem using global search basin with proper constraints. The cost function is established based on the difference between the energies of a set of measured ship responses and the corresponding theoretical spectral moments. A partitioning procedure is applied, which is able to separate swell components from wind seas.

Lymphedema of breast cancer: risk factor and treatment

One of the well-known complication of breast cancer treatment is secondary lymphedema; an accumulation of protein-rich interstitial fluid due to the insufficient capacity of the lymphatic system. Lymphedema are affects about 20-30% of women following breast cancer treatment and the risk factors associated with lymphedema development after breast cancer surgery and or radiotherapy are not well established. Early diagnosis and treatment is considered important for successful management of breast cancer related arm lymphoedema. The objective of this study is to assess the value of risk factor and treatment modality of lymphedema. Electronic searches were conducted in MEDLINE®, EMBASE, CINAHL®, and Social Sciences Citation Index. Articles were included where researchers used qualitative research methods and when a comprehensive description of methods and the study's findings were provided. Among 1210 articles, 30-37% developed lymphedema and 45% associated with incresead body mass index (BMI), 53% related with higher stage of disease. Furthermore; 74% strongly step rise with the number of involved lymph nodes; 41% in comorbid diseases, and the time after surgery showed significant correlation with the development of lymphedema in 32%. Suction-assisted protein lipectomy (SAPL) has been shown to safely and effectively reduce the solid component of swelling in chronic lymphedema and microsurgery procedures, including lymphaticovenous anastomosis (LVA) and vascularized lymph node transfer (VLNT), have been shown to be effective in the management of the fluid component of lymphedema and allow for decreased garment use.

A new method for calibration of unidirectional double-peak spectra

This study aims at presenting a new approach in calibrating standard two-peak design spectra for specific regions in absence of wind data. The main principle in these kinds of fitting for a new area is to minimize the least square error between measured and fitted spectra and there has been less attention to double-peak spectra individual characteristic as co-existence of wind-sea and swell parts in one spectrum. Here, separation frequency, approximately dividing such parts, is implemented to virtually extract wind-sea and swell components of a measured spectrum considering their intrinsic overlap near the separation frequency. Then, they have been easily utilized to calibrate two parts of standard double-peak spectrum in a revisory manner. To verify benefits of this new methodology, it has been applied on Ochi-Hubble as well as Torsethaugen spectra regarding field measurements in a coastal region at Gulf of Oman, Chabahar bay. Results obviously show a better adjustment of formula to field spectrum using this simple approach when compared with output of calibration on integrated field spectrum irrespective of its main characteristic such as availability of two-wave systems.

On the modelling of swell spectra

The ability of the JONSWAP model to describe swell spectra is analysed and the quality of the fit of this model is compared with the fits produced by a Gaussian model. The study is based on directional wave spectra from measurements made at the Maui location situated in the west coast of New Zealand and at the Bonga location situated near the coast of Africa. The analysis is performed for single peak swell sea states and for the swell component of two peaked spectra.The comparison of the spectral parameters and the fit of the models with the measured narrow swell spectra, suggest that the JONSWAP model describes better the swell spectrum than the Gaussian model, in particular in the high frequency range.

Bivariate distributions of significant wave height and mean wave period of combined sea states

This work presents the results of the fit of three bivariate models to twelve years of significant wave height and mean zero-crossing period data of swell, wind sea components, and combined sea states from Australia. The Conditional Modelling Approach defines the joint distribution from a marginal distribution of significant wave height and a set of distributions of mean zero-crossing period conditional on significant wave height. The second model fits the Plackett model to the data, and the last one applies the Box–Cox transformations to the data with the aim of making it approximately normal to fit a bivariate normal distribution to the transformed data. The conditional model with a lognormal distribution for the significant wave height and lognormal distributions for the zero-crossing period gave the best fit for the total sea states and for the wind component. In case of the swell component the conditional model with a Weibull distribution to the significant wave height and a lognormal distribution to the mean zero-crossing period gave a relatively close fit to the data.

Response of the North Atlantic wave climate to atmospheric modes of variability

ABSTRACTThis study investigates the relationship between the wind wave climate and the main climate modes of atmospheric variability in the North Atlantic Ocean. The modes considered are the North Atlantic Oscillation (NAO), the East Atlantic (EA) pattern, the East Atlantic Western Russian (EA/WR) pattern and the Scandinavian (SCAN) pattern. The wave dataset consists of buoys records, remote sensing altimetry observations and a numerical hindcast providing significant wave height (SWH), mean wave period (MWP) and mean wave direction (MWD) for the period 1989–2009. After evaluating the reliability of the hindcast, we focus on the impact of each mode on seasonal wave parameters and on the relative importance of wind‐sea and swell components. Results demonstrate that the NAO and EA patterns are the most relevant, whereas EA/WR and SCAN patterns have a weaker impact on the North Atlantic wave climate variability. During their positive phases, both NAO and EA patterns are related to winter SWH at a rate that reaches 1 m per unit index along the Scottish coast (NAO) and Iberian coast (EA) patterns. In terms of winter MWD, the two modes induce a counterclockwise shift of up to 65° per negative NAO (positive EA) unit over west European coasts. They also increase the winter MWP in the North Sea and in the Bay of Biscay (up to 1 s per unit NAO) and along the western coasts of Europe and North Africa (1 s per unit EA). The impact of winter EA pattern on all wave parameters is mostly caused through the swell wave component.

Development of a bi-modal directional wave spectrum

Addressing sea state in a coastal region of Gulf of Oman by a directional wave spectrum for the very first time is the main focus of this study. The region encounters wind-sea as well as swell. So, proper modeling of the sea state requires in general a double peak spectral model.The research is firstly conducted to calibrate nondirectional Torsethaugen double peak spectrum for the region by entering the separation frequency; a frequency in which wind-sea and swell parts could be divided. This novel calibration procedure is simple while results in much better outcome. Besides, one has to decide about an appropriate Directional Spreading Function (DSF) for the wind-sea and swell components. Then, nine possible combinations of three well-known DSFs have been investigated and calibrated to provide maximum conformity between observed and modeled directional wave spectra.

A validation of an operational wave and surge prediction system for the Dutch coast

Abstract. Knowledge of the actual condition of hydrodynamics in the nearshore and coastal area is essential for coastal monitoring activities. To this end, a coastal operational model system can serve as a tool in providing recent and up-to-date, state-of-the-art hydrodynamics along the coast. In this paper, we apply CoSMoS (Coastal Storm Modeling System), a generic operational wave and tide-surge modelling system applied here to predict waves and water levels along the Dutch coast. The CoSMoS application is not limited to storm impact prediction on the Dutch coast, but can also be applied to other coastal hazards such as rip currents and coastal flooding, in other environments. In this paper, we present the set-up of the CoSMoS system and a validation of the wave and surge model, with deep-water wave buoy data and tidal gauge measurements as ground truth validation material. The evaluation is presented as monthly error measures between computed parameters and observed ones. Hindcast results over the whole year of 2009 show that the simulated wave parameters and surge elevation from the CoSMoS are in good agreement with data, with average root mean square (rms) error over the year of 0.14 m for the surge elevation and 0.24 m for the significant wave height. It is noted that there is a tendency of the wave model to underestimate the height of northerly waves with lower frequencies (swell). Additionally, when a wave separation algorithm is applied on the overall spectrum, results show consistent underestimation of the swell component by the model, which for the Dutch coast will mainly come from the north, where the North Sea is open to the Atlantic Ocean. In the proposed model system, the swell boundary can have a significant effect on the simulated wave results, suggesting room for improvement for the swell boundary conditions to the north and the swell propagation within the Dutch Continental Shelf Model. Finally, we show that in forecast mode, CoSMoS can provide reasonably good wave and surge prediction.