Sea State Parameters Research Articles

On the distribution of ocean wave crest heights in varying wave conditions

This paper addresses the statistical distribution of wave crest heights in ocean environments. This is much needed in several engineering applications including risk and reliability assessment of marine and coastal structures and is an important input for design of ocean structures. However, even though crest height distributions have received a lot of attention within both academia and the industry, current state-of-the-art models have notable shortcomings and do not describe the distribution of crest heights well in all sea states. In particular, commonly used models do not accurately describe the upper tail in certain unstable wave conditions. This will be addressed in this paper, which investigates in what sea-state conditions, established crest height distributions describe the data well and under what conditions, these models fail to fit well to the data. A large dataset of crest heights observed in different sea states is analyzed, and various goodness-of-fit tests are applied to determine when the different statistical models are appropriate. Then rejection rates of the various statistical models will be linked to selected sea-state parameters to identify wave conditions where alternative statistical models are needed. Results from this study indicate that the well-known Forristall distribution, which is known to capture second-order effects well, fails to perform well in some sea states. Different variants of the Tayfun–Fedele distribution are also analyzed, and results suggest that this represent a slight improvement. Somewhat surprisingly, sea-state parameters such as significant wave height (HS), significant wave steepness (S1), and the Benjamin–Feir index (BFI) do not seem to be very influential on the probability of rejecting these distributions, even though empirical skewness and kurtosis play a significant role. The implications of this for describing the distribution of crest heights well in certain sea-state conditions are discussed.

Effect of shoaling length on rogue wave occurrence

The impact of shoaling on linear water waves is well known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the ‘rapid’ nature of the shoaling process, i.e. shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the length and angle of a shoal's slope. We investigate the effects of the shoaling process rapidness on the evolution of key statistical and spectral sea-state parameters. We let the wave field evolve over a slope with constant angle in all cases while we vary the slope length. Our results indicate that the non-equilibrium dynamics is not affected by the slope length, because further extending the slope length does not influence the magnitude of the statistical and spectral measures as long as the non-equilibrium dynamics dominates the wave evolution. Thus, the shoaling effect on rogue waves is deduced to be mainly driven by the slope magnitude rather than the slope length.

A Deep Learning Strategy for the Retrieval of Sea Wave Spectra from Marine Radar Data

In the context of sea state monitoring, reconstructing the wave field and estimating the sea state parameters from radar data is a challenging problem. To reach this goal, this paper proposes a fully data-driven, deep learning approach based on a convolutional neural network. The network takes as input the radar image spectrum and outputs the sea wave directional spectrum. After a 2D fast Fourier transform, the wave elevation field is reconstructed, and accordingly, the sea state parameters are estimated. The reconstruction strategy, herein presented, is tested using numerical data generated from a synthetic sea wave simulator, considering the spectral proprieties of the Joint North Sea Wave Observation Project model. A performance analysis of the proposed deep-learning estimation strategy is carried out, along with a comparison to the classical modulation transfer function approach. The results demonstrate that the proposed approach is effective in reconstructing the directional wave spectrum across different sea states.

Nine months of daily LiDAR, orthophotos and MetOcean data from the eroding soft cliff coast at Happisburgh, UK

The dynamic interaction between cliff, beach and shore-platform is key to assessing the sediment balance for coastal erosion risk assessments, but this is poorly understood. We present a dataset containing daily, 3D,colour LiDAR scans of a 450 m coastal section at Happisburgh, Norfolk, UK. This previously para-glaciated region comprises mixed sand-gravel sediments, which are less well-understood and well-studied than sandy beaches. From Apr-Dec 2019, 236 daily surveys were carried out. The dataset presented includes: survey areas, transects LiDAR scans, georeferenced orthophotos, meteorological- and oceanographical conditions during the Apr-Dec observation period. Full LiDAR point-clouds are available for 67 scans (Oct-Dec). Hourly time-series of offshore sea-state parameters (significant wave height, mean propagation direction, selected spectral periods) were obtained by downscaling the ERA5 global reanalysis data (global atmosphere, land surface and ocean waves) using the numerical model Simulating Waves Nearshore (SWAN). We indicate how to obtain hourly precipitation time-series by interpolating ERA5 data. This dataset is important for researchers understanding the interaction between cliff, beach and shore-platform in open-coast mixed-sand-gravel environments.

Airborne GNSS reflectometry for coastal monitoring of sea state

Sea level rise and sea state variability, resulting from climate change and global warming, are critical research areas. However, current techniques for observing and monitoring these phenomena have limitations in terms of spatial and temporal resolution, particularly in dynamic coastal zones. GNSS Reflectometry (GNSS-R) is an emerging bistatic radar-based technique that utilizes the GNSS direct (transmitter-receiver) and reflected (transmitter-reflection point-receiver) signals to extract properties of the reflecting surface. This study explores the potential of airborne GNSS-R as a means to monitor sea state in coastal areas by using the Doppler spread and reflectivity as observables. The paper aims to derive a sea state factor from the reflected signal power and the Doppler shift distribution to analyze its correlation with wind speed and significant wave height data obtained from the ERA5 model. The experiment involved four flights conducted along the coast between Calais and Boulogne-sur-Mer, France, in July 2019. A GNSS software receiver processes the direct and reflected signals, tracking and re-tracking the reflected signals with the aid of a specular reflection model. The resulting in-phase and quadrature components are analyzed in the spectral domain every minute to estimate the power, the surface reflectivity, and the relative Doppler shift. The findings reveal that the sea state factor and Doppler spreading are sensitive to sea state conditions, correlated with the ERA5 parameters, and influenced by the elevation angle of GNSS satellites. At low elevations (E<10°), the sea state factor demonstrates an inverse relationship (anti-correlation) with the wind speed and significant wave height, while the Doppler distribution shows a correlation with these parameters. Both correlations decrease with increasing elevation angle. This research underscores the potential of airborne GNSS-R for monitoring sea state variability in coastal areas enhancing our understanding of the relationships between GNSS-R measurements and sea state parameters.

A new method for analysis of marine sustainable energy systems

This paper proposes to utilise a new adaptive kernel density estimation (KDE) methodology based on linear diffusion processes for predicting the probability distribution tails of sea-state parameters. A key conclusion was reached that the proposed new methodology can lead to more accurate prediction results than traditional methods based on fittings to a measured significant wave height data set at National Data Buoy Center station 46014. This proposed methodology was subsequently utilised for deriving an accurate 50-year environmental contour line that was used in the dynamic analysis of a two-body point absorber wave energy converter. After systematically analysing the calculation results, another key conclusion was drawn that it is advantageous to use a more reliable contour line derived using the proposed new methodology for long-term dynamic analysis of wave energy converters. In summary, the proposed new adaptive KDE methodology is recommended to be utilised and to be refined continuously in future research work in the field of long-term reliability analysis of marine sustainable energy systems.

A new method for long-term safety analysis of marine structures

This paper proposes to utilise a new adaptive kernel density estimation (KDE) method based on a linear diffusion process for fitting the significant wave height data in order to calculate the sea state parameter distribution tails more accurately, particularly the higher, more extreme values. The accuracy of the proposed method has been demonstrated based on fittings to two measured ocean wave datasets. This proposed method has subsequently been utilised for deriving accurate 50-year and 500-year environmental contour lines. The advantages of using a more reliable contour line derived from using the proposed new method for long-term safety analysis of marine structures have been substantiated.

Robust adaptive analysis of extreme dynamic responses of wave energy converters

In the current study, a new adaptive binned kernel density estimation method has been introduced. In the proposed new method, Fourier transforms have been utilized to accomplish the convolution rather than performing the convolution by hand. By utilizing the fast Fourier transform, direct and inverse Fourier transforms have been found in a relatively short amount of time when implementing the new method. Upon analyzing the computed results, it has been observed that the newly proposed adaptive binned kernel density estimation distribution curve exhibits a high level of smoothness in the tail region. Furthermore, it demonstrates a strong alignment with the histogram derived from the recorded ocean wave dataset obtained at the NDBC station 46053. These are the major advantages of the proposed new method comparing with other existing methods such as the parametric method, the ordinary KDE method, and Abramson's adaptive KDE method. The specific research gap identified in the field is that none of the existing methods can predict the sea state parameter probability distribution tails both accurately and efficiently, and the proposed new method has successfully addressed this research gap. Upon careful examination of the calculation results, it becomes evident that the projected 50-year extreme power-take-off heaving force value, derived using the newly proposed method, is 1989300N. This value significantly surpasses (by more than 9.5%) the forecasted value of 1816200N obtained through the application of the Rosenblatt-I-SORM contour method. The findings of this study suggest that the newly proposed adaptive binned kernel density estimation method exhibits robustness and demonstrates accurate forecasting capabilities for the 50-year extreme dynamic responses of wave energy converters.

Evaluation of SAR-Based Sea State Parameters and Roughness Length Derivation Over the Coastal Seas of the USA

Evaluation of SAR-Based Sea State Parameters and Roughness Length Derivation Over the Coastal Seas of the USA

Statistical Modeling and Applications of Joint Distributions for Significant Wave Height, Spectral Peak Period, and Peak Direction of Propagation: A Case Study in the Norwegian Sea

The estimation of long-term extreme response is a crucial task in the design of marine structures. The target extreme responses are typically defined by annual exceedance probabilities of 10−2 and 10−4. Various approaches can be employed for this purpose, with preference given to statistical long-term analysis, which involves aggregating the exceedance probabilities of all potential sea states contributing to the exceedance of the target extremes. A joint model encompassing important metocean parameters such as wind, waves, and current is often necessary. This study specifically focuses on waves and wave-induced responses. In characterizing short-term sea state conditions, significant wave height (Hs), spectral peak period (Tp) and peak direction of propagation (Φp) are identified as the most important sea state characteristics. The objective of this work is to present the results of the joint model for the three sea state parameters, i.e., Hs, Tp and Φp, at an offshore site in the Norwegian Sea. The conditional modeling approach is applied using long-term hindcast data, and different statistical models are discussed for fitting the marginal and conditional distributions. The fitted parameters for all directional sectors are provided, offering a comprehensive representation of the joint model for direct use in long-term response analysis. Two case studies are included to illustrate the application of the fitted joint model in long-term response analyses. The case studies identify the governing wave directions and the most important combinations of short-term sea state characteristics regarding the estimation of long-term extreme responses.

Weather-type statistical downscaling for ocean wave climate in the Chinese marginal seas

A comprehensive understanding of wave characteristics and their variability, based on reliable long-term wave data, is essential in the design, construction, operation and management in offshore and coastal applications. This study aims to downscale multivariate wave data in the Chinese marginal seas at different time scales by employing two weather-type statistical downscaling models. The calibration of both models involves the usage of historical data from ERA5 reanalysis, with sea level pressure and the squared sea level pressure gradient as the predictors and wave parameters as the predictands. The predictor definition considers the swell components in the local wave data. Both models categorize the atmospheric predictors into different weather types using the K-means algorithm (KMA), with and without regression-guided clustering (referred to as WTD-RG and WTD, respectively). Each weather type is associated with sea state parameters. The downscaled wave data from both models are validated against ERA5 data. The results show that both models can generally reproduce the wave statistics for the significant wave height, mean wave direction, mean wave energy flux, and 95th percentile of the significant wave height. However, the WTD-RG model performs better than the WTD model. Additionally, the ERA5 data reveal increasing trends in the mean significant wave height for most areas of the East China Sea and South China Sea and decreasing trends in the Bohai Sea, Yellow Sea, and Beibu Gulf from 1959 to 2021. These patterns are well captured by the WTD-RG model but not by the WTD model.

Investigating High-Resolution Spatial Wave Patterns on the Canadian Beaufort Shelf Using Synthetic Aperture Radar Imagery at Herschel Island, Qikiqtaruk, Yukon, Canada

The Arctic is experiencing the greatest increase in air temperature on Earth. This significant climatic change is leading to a significant positive trend of increasing wave heights and greater coastal erosion. This in turn effects local economies and ecosystems. Increasing wave energy is one of the main drivers of this alarming trend. However, the data on spatial and temporal patterns of wave heights in the Arctic are either coarse, interpolated or limited to point measurements. The aim of this study is to overcome this shortcoming by using remote sensing data. In this study, the Synthetic Aperture Radar (SAR) satellite TerraSAR-X (TS-X) and TanDEM-X (TD-X) imagery are used to obtain sea state information with a high spatial resolution in Arctic nearshore waters in the Canadian Beaufort Sea. From the entire archive of the TS-X/TD-X StripMap mode with coverage around 30 km × 50 km acquired between 2009 and 2020 around Herschel Island, Qikiqtaruk (HIQ), all the ice-free scenes were processed. The resulting dataset of 175 collocated scenes was used to map the significant wave height (Hs) and to link spatial and temporal patterns to local coastal processes. Sea state parameters are estimated in raster format with a 600 m step using the empirical algorithm CWAVE_EX. The statistics of the Hs were aggregated according to spatial variability, seasonality and wind conditions. The results show that the spatial wave climate is clearly related to the dominant wind regime and seasonality. For instance, the aggregation of all the scenes recorded in July between 2009 and 2020 results in an average of 0.82 m Hs, while in October the average Hs is almost 0.40 m higher. The analysis by wind direction shows that fetch length and wind speed are likely the most important variables influencing the spatial variability. A larger fetch under NW conditions results in a mean wave height of 0.92 m, while waves generated under ESE conditions are lower at 0.81 m on average.

COMPARISON OF FIELD AND FORECAST METOCEAN DATA IN THE GERMAN BIGHT

Offshore wind energy can contribute significantly to achieve greenhouse gas neutrality in the near future. But the planning, construction and operation of offshore wind parks is associated with high costs. In particular, the operation and maintenance (OandM) costs account for a major fraction and in turn are also dependent on appropriate weather windows in which working vessels can operate. A precise knowledge of how wind, sea state and currents affect each other, as well as the most accurate possible prediction of the development, is essential to maximize these periods and reduce the resulting costs. For the German Bight, the high-resolution coastal wave model (CWAM) is often used for this purpose. The CWAM is based on WAM (Hasselmann et al. 1988) and was developed by the German Meteorological Service (DWD) and German Maritime and Hydrographic Agency (BSH) in cooperation with the Helmholtz-Zentrum Hereon. Compared to other WAM models it offers the advantages of higher resolution, as well as the consideration of current speeds and tide-dependent water depths. The BSH also operates multiple measuring stations in the German Bight, which enable real-time investigation of sea state parameters. The general objective of this study is to compare historical data sets from in situ measurements in the German Bight with numerical forecast data and to identify which factors influence the accuracy of the CWAM and why deviations occur.

New prediction method for reliability analysis of ocean sustainable energy systems

With the aim of overcoming the shortcomings of traditional approaches, in this paper, an exponential Weibull distribution for fitting the significant wave height data is proposed in order to calculate more accurately the sea-state parameter distribution tails and to extrapolate well. This proposal is applied in predicting the probability distribution tails of a measured ocean wave dataset, and its accuracy is clearly demonstrated. The proposal is subsequently utilised in combination with Monte Carlo sampling to form a new environmental contour method for deriving a 50 year contour line based on the aforementioned measured ocean wave dataset. The derived environmental contour line is compared with that predicted by using a traditional contour line approach. Additionally, the engineering significance of using a more reliable environmental contour line, such as the one derived using the proposed new method for predicting the long-term design force values for an ocean sustainable energy system is highlighted. In conclusion, the newly proposed environmental contour method is recommended to be used when predicting the extreme dynamic response values for the safe and successful design of ocean sustainable energy systems.

An adaptive binned kernel density estimation method for analysis of wave energy converters

ABSTRACT This research proposes a new adaptive binned Kernel Density Estimation (KDE) method to fit significant wave height data in order to more accurately calculate the sea state parameter distribution tails. The brief details of the proposed new methodology are to utilize the fast Fourier transform to perform the convolution of the data with the kernel to find the kernel density estimates on the bin nodes. The Crámer-von Mises test statistic for the proposed adaptive KDE distribution is calculated to be 0.0926 based on a measured wave data set. The Crámer-von Mises test statistic value for the fitted 3-parameter Weibull distribution based on the identical measured data set is 251.2463, indicating a much poorer fit to the empirical distribution function. The advantages of using a more reliable and accurate contour line derived using the proposed new method for long term reliability analysis of wave energy converters have been finally substantiated.

Estimation of sea state parameters from ship motion responses using attention-based neural networks

On-site estimation of sea state parameters is crucial for ship navigation. Extensive research has been conducted on model-based estimation utilizing ship motion responses. Model-free approaches based on machine learning (ML) have recently gained popularity, and estimation from time-series of ship motion responses using deep learning (DL) methods has given promising results. In this study, we apply the novel, attention-based neural network (AT-NN) for estimating wave height, zero-crossing period, and relative wave direction from raw time-series data of ship pitch, heave, and roll. Despite reduced input data, it has been demonstrated that the proposed approaches by modified state-of-the-art techniques (based on convolutional neural networks (CNN) for regression, multivariate long short-term memory CNN, and sliding puzzle neural network) improved estimation MSE, MAE, and NSE by up to 86%, 66%, and 56%, respectively, compared to the best performing original methods for all sea state parameters. Furthermore, the proposed technique based on AT-NN outperformed all tested methods (original and enhanced), improving estimation MSE by 94%, MAE by 74%, and NSE by 80% when considering all sea state parameters. Finally, we proposed a novel approach for interpreting the uncertainty estimation of neural network outputs based on the Monte-Carlo dropout method to enhance the model’s trustworthiness.

Sea state estimation based on the motion data of a moored FPSO using neural networks: An evaluation with multiple draft conditions

Useful information for offshore systems can be obtained by monitoring sea state parameters, but the accurate estimation of the on-site wave condition is challenging. This paper deals with motion-based wave estimation using neural networks. The main novelty of this contribution is the evaluation of the performance of the data-driven inference system with motion data from different draft conditions. The study is based on the simulated motions of a Floating Production Storage and Offloading (FPSO) unit with multiple loadings, subjected to typical sea conditions observed offshore the Brazilian coast. The inference models were trained to estimate two independent sets of wave related parameters, corresponding to modal wave statistics, which were post processed to identify single and double-peaked sea states. Results showed that estimation errors were quite similar along the evaluated drafts, with an overall good agreement between estimations and reference values. However, a limitation of the method regarding less frequent sea conditions was observed, even when significant wave response is induced. Also, an analysis of the robustness of the estimation models with respect to a draft variation of ± 0.5 m was carried out considering the global wave statistics, presenting small average deviations compared to the expected values.

Satellite Remote Sensing of Surface Winds, Waves, and Currents: Where are we Now?

AbstractThis review paper reports on the state-of-the-art concerning observations of surface winds, waves, and currents from space and their use for scientific research and subsequent applications. The development of observations of sea state parameters from space dates back to the 1970s, with a significant increase in the number and diversity of space missions since the 1990s. Sensors used to monitor the sea-state parameters from space are mainly based on microwave techniques. They are either specifically designed to monitor surface parameters or are used for their abilities to provide opportunistic measurements complementary to their primary purpose. The principles on which is based on the estimation of the sea surface parameters are first described, including the performance and limitations of each method. Numerous examples and references on the use of these observations for scientific and operational applications are then given. The richness and diversity of these applications are linked to the importance of knowledge of the sea state in many fields. Firstly, surface wind, waves, and currents are significant factors influencing exchanges at the air/sea interface, impacting oceanic and atmospheric boundary layers, contributing to sea level rise at the coasts, and interacting with the sea-ice formation or destruction in the polar zones. Secondly, ocean surface currents combined with wind- and wave- induced drift contribute to the transport of heat, salt, and pollutants. Waves and surface currents also impact sediment transport and erosion in coastal areas. For operational applications, observations of surface parameters are necessary on the one hand to constrain the numerical solutions of predictive models (numerical wave, oceanic, or atmospheric models), and on the other hand to validate their results. In turn, these predictive models are used to guarantee safe, efficient, and successful offshore operations, including the commercial shipping and energy sector, as well as tourism and coastal activities. Long-time series of global sea-state observations are also becoming increasingly important to analyze the impact of climate change on our environment. All these aspects are recalled in the article, relating to both historical and contemporary activities in these fields.

Assessment of WAVEWATCH-III in Wind Wave Modeling of the Xisha Islands

The Xisha islands is a unique area where offshore structures can be utilized as exploration bases in the remote sea. Forecasting of sea state parameters is critical for the design and operation of offshore structures. The goal of this work is to establish an effective operational model to simulate wind waves in the Xisha Islands based on the third-generation wave model WAVEWATCH-III. During the process, two significant difficulties are highlighted and addressed: grid modeling optimization and physical source terms assessment. Typhoon-induced waves using different grid modeling techniques and physical parameterizations were modeled and evaluated using buoy measurements near islands and reefs. It was found that the unstructured triangular grid had a better performance than the other grid options in complex terrain environments like the Xisha Islands. The ST2 source-term package can provide efficient and accurate results in significant wave heights than the other source-term packages in the South China Sea.

Robust adaptive analysis of dynamic responses of offshore sustainable energy systems

The state of the problem in the field of ocean engineering is that all the existing parametric or non-parametric models can not accurately and efficiently predict the sea state parameter probability distribution tails. Therefore, a research motivation has been developed to propose a new method to forecast in the tail region. In this paper the work objectives and scope are to propose a new adaptive kernel density estimation method formulated on the theory of linear diffusion processes and to utilize this method for predicting the sea state parameter probability distribution tails and for calculating the 50-year extreme Power-Take-Off heaving force value. The key findings are that our proposed new method is robust and can forecast well the 50-year extreme design force values for offshore sustainable energy systems.