Directional Ocean Wave Research Articles

Parametric Estimation of Directional Wave Spectra from Moored FPSO Motion Data Using Optimized Artificial Neural Networks

This paper introduces a comprehensive, data-driven framework for parametrically estimating directional ocean wave spectra from numerically simulated FPSO (Floating Production Storage and Offloading) vessel motions. Leveraging a mid-fidelity digital twin of a spread-moored FPSO vessel in the Guyana Sea, this approach integrates a wide range of statistical values calculated from the time histories of vessel responses—displacements, angular velocities, and translational accelerations. Artificial neural networks (ANNs), trained and optimized through hyperparameter tuning and feature selection, are employed to estimate wave parameters including the significant wave height, peak period, main wave direction, enhancement parameter, and directional-spreading factor. A systematic correlation analysis ensures that informative input features are retained, while extensive sensitivity tests confirm that richer input sets notably improve predictive accuracy. In addition, comparisons against other machine learning (ML) methods—such as Support Vector Machines, Random Forest, Gradient Boosting, and Ridge Regression—demonstrate the present ANN model’s superior ability to capture intricate nonlinear interdependencies between vessel motions and environmental conditions.

A Kelp Inspired High‐Power Density Triboelectric Nanogenerator with Stacking Structure for Multiple Directional Ocean Wave Energy Harvesting

AbstractOcean wave energy is one of the most promising green energies in the wild. However, it is still challenging to effectively collect wave energy due to its randomness and irregularity. In this work, a kelp inspired high‐power density triboelectric nanogenerator (K‐TENG) is presented for harvesting wave energy with characteristics in multiple directions. The proposed K‐TENG consists of a series of stacked leaf‐like units. The influence of configuration parameters, including pellet diameters, pellet numbers, unit sizes, oscillation frequency, swing amplitude, and wave directions on output performances of leaf‐like units, are extensively investigated. Experimental data indicates that a single leaf‐like unit can achieve a maximum output voltage of 623.14 V as well as a maximum current of 1.48 µA and realize energy harvesting from different wave directions. A K‐TENG composed of 15 leaf‐like units demonstrates a high‐power density of 18.77 W m−3 at a wave frequency of 2.5 Hz, which successfully powers a digital watch and 414 light‐emitting diodes (LEDs). This work is hoped to provide a simple and reliable route to effectively harvest ocean wave energy.

Ocean Wave Directional Distribution from GPS Buoy Observations off the West Coast of Ireland: Assessment of a Wavelet-Based Method

Abstract Knowledge of the directional distribution of a wave field is crucial for a better understanding of complex air–sea interactions. However, the dynamic and unpredictable nature of ocean waves, combined with the limitations of existing measurement technologies and analysis techniques, makes it difficult to obtain precise directional information, leading to a poor understanding of this important quantity. This study investigates the potential use of a wavelet-based method applied to GPS buoy observations as an alternative approach to the conventional methods for estimating the directional distribution of ocean waves. The results indicate that the wavelet-based estimations are consistently good when compared to the framework of widely used parameterizations for the directional distribution. The wavelet-based method presents advantages in comparison with the conventional methods, including being purely data-driven and not requiring any assumptions about the shape of the distribution. In addition, it was found that the wave directional distribution is narrower at the spectral peak and broadens asymmetrically at higher and lower scales, particularly sharply for frequencies below the peak. The directional spreading appears to be independent of the wave age across the entire range of frequencies, implying that the angular width of the directional spectrum is primarily controlled by nonlinear wave–wave interactions rather than by wind forcing. These results support the use of the wavelet-based method as a practical alternative for the estimation of the wave directional distribution. In addition, this study highlights the need for continued innovation in the field of ocean wave measuring technologies and analysis techniques to improve our understanding of air–sea interactions. Significance Statement This study presents a wavelet-based technique for obtaining the directional distribution of ocean waves applied to GPS buoy. This method serves as an alternative to conventional methods and is relatively easy to implement, making it a practical option for researchers and engineers. The study was conducted in a highly energetic environment characterized by high wind speeds and large waves, providing a valuable dataset for understanding the dynamics of marine environment in extreme conditions. This research has implications for improving our understanding of directional characteristics of ocean waves, which is crucial for navigation, offshore engineering, weather forecasting, and coastal hazard mitigation. This study also highlights the challenges associated with understanding wave directionality and emphasizes a need for further observations.

Spatiotemporal wave forecast with transformer-based network: A case study for the northwestern Pacific Ocean

Spatiotemporal wave forecast with transformer-based network: A case study for the northwestern Pacific Ocean

Motor Sizing of a Ship-Mounted Two-DoF Manipulator System Considering Variations of Ocean Wave Direction

Motor Sizing of a Ship-Mounted Two-DoF Manipulator System Considering Variations of Ocean Wave Direction

Wave-by-wave forecasts in directional seas using nonlinear dispersion corrections

We develop a new methodology for the deterministic forecasting of directional ocean surface waves based on nonlinear frequency corrections. These frequency corrections can be pre-computed based on measured energy density spectra and, therefore, come at no additional computational cost compared to linear theory. The nonlinear forecasting methodology is tested on highly nonlinear synthetically generated seas with a variety of values of average steepness and directional spreading and is shown to consistently outperform a linear forecast.

A multivariate pseudo-likelihood approach to estimating directional ocean wave models

Abstract Buoy data in the form of multivariate time series are routinely recorded at many locations in the world’s oceans. Such data can help characterise the ocean wavefield by modelling the frequency-direction spectrum. State-of-the-art methods for estimating the parameters of such models do not make use of the full spatiotemporal content of the buoy observations due to unnecessary assumptions and smoothing. We explain how the multivariate debiased Whittle likelihood can be used to jointly estimate all parameters of such frequency-direction spectra directly from recorded time series. We apply the method to North Sea buoy data and discuss challenging practical issues.

Global ocean wave fields show consistent regional trends between 1980 and 2014 in a multi-product ensemble

Historical trends in the direction and magnitude of ocean surface wave height, period, or direction are debated due to diverse data, time-periods, or methodologies. Using a consistent community-driven ensemble of global wave products, we quantify and establish regions with robust trends in global multivariate wave fields between 1980 and 2014. We find that about 30–40% of the global ocean experienced robust seasonal trends in mean and extreme wave height, period, and direction. Most of the Southern Hemisphere exhibited strong upward-trending wave heights (1–2 cm per year) and periods during winter and summer. Ocean basins with robust positive trends are far larger than those with negative trends. Historical trends calculated over shorter periods generally agree with satellite records but vary from product to product, with some showing a consistently negative bias. Variability in trends across products and time-periods highlights the importance of considering multiple sources when seeking robust change analyses.

Online wave direction and wave number estimation from surface vessel motions using distributed inertial measurement arrays and phase-time-path-differences

A common approach for finding the direction of ocean waves is to use the phase-time-path-differences (PTPDs) between a static array of various types of sensors mounted on either the sea surface or seabed. However, some practical drawbacks of such arrays are that they tend to be expensive, difficult to install, and fixed in location. We show that the PTPD approach can be generalized to a portable shipboard array of spatially distributed sensors rendering it more practical. In this respect, we derive a nonlinear PTPD model for shipboard sensor arrays and prove that the wave direction and wave number can be resolved from a minimum of three noncollinear sensors using observability analysis. Moreover, based on our PTPD model, we propose an unscented Kalman filter algorithm for online estimation of the wave direction and wave number, which offers a convenient framework for adding multiple measurements and incorporating uncertainties. Our experimental results from model basin testing with a model ship equipped with several inertial measurement units (IMUs) confirm that the wave direction and wave number can be estimated from the wave-induced motions of a surface vessel with a minimum of three noncollinear IMUs. In this study, we consider parameter estimation for regular waves and assume a dynamically positioned surface vessel with small roll and pitch angles. • Consider phase-time-path-differences between shipboard inertial measurement units. • Propose an unscented Kalman filter to find wave direction and wave number. • Observability analysis shows a minimum of three noncollinear sensors are needed. • Considered a dynamically positioned surface vessel and regular harmonic waves. • Online wave estimation and quantitative error analysis.

Estimating Significant Wave Height from SAR with Long Integration Times

Synthetic aperture radar (SAR) is an important means of estimating significant wave height with obvious advantages of all-day, all-weather, high resolution and wide swath coverage. At present, the estimation methods of significant wave height are based on visible ocean waves in SAR images. However, due to the characteristic of long integration time for low-frequency SAR (such as P-band, L-band), the ocean waves are usually invisible in SAR images. In addition, in the case that there are multiple wave systems, significant wave height of only one wave system can be estimated for the reason that only a blurred wave system can be observed in SAR images. In order to solve the above two problems, a method of estimating significant wave height from SAR with long integration times is proposed in this paper. Firstly, each ocean wave system is refocused from single-look complex (SLC) data, respectively. Then, without any additional processing, the 180° ambiguity of wave propagation direction is removed based on the optimum focus setting. Finally, significant wave height is estimated in combination with azimuth cutoff, wavelength and propagation direction of ocean waves. This method is applied to two airborne SAR field data with long integration times. One case is that ocean waves are invisible in SAR images, the other is that there are two wave systems on the real ocean surface, but only one is visible in the SAR images. The results show that the proposed method can estimate significant wave height in the cases of invisible ocean waves and multiple ocean waves. The estimation results of significant wave height are compared with the European Centre for Medium-Range Weather Forecast (ECMWF) data, and the error is basically stable within 0.2 m, which verifies the effectiveness of the proposed method.

Effects of Ocean Wave Directional Spectra on Doppler Retrievals of Ocean Surface Current

The Doppler shift of microwave radar signal is determined by the relative motion between radar and ocean surface, including contributions from the movement of the radar platform and the wind-wave-induced motion (phase velocity of the resonant Bragg waves and orbital motions of ocean waves that are longer than the Bragg waves) in addition to the ocean surface current. One of the main challenges in ocean surface current retrieval is the accurate estimation of the wind-wave-induced Doppler shift, which needs to be accurately removed from the total Doppler shift to determine the surface current. In this study, we investigate the effects of different wave directional spectra on estimates of the wind-wave-induced Doppler shift using a modulation transfer function (MTF)-based and time-independent Doppler model. Our results show that the wind-wave-induced Doppler shift estimates are highly dependent on the selection of wave spectra and the directional spreading function. This study also confirms the importance of ocean wave spectra parameterization on Doppler estimation of the ocean current. We find that Apel’s spectra model is a more consistent fit to the observations, but the optimal spreading function is wind-speed-dependent.

Statistical Comparison of Ocean Wave Directional Spectra Derived From SWIM/CFOSAT Satellite Observations and From Buoy Observations

The comparison and verification of ocean wave spectrum by remote sensing and by in-situ measurements at the spectral level is quite rare, because the use of the traditional comparison method lead to very limited spatio-temporal matching pairs. In this paper, a new comparison method is proposed. With this method, under different sea conditions (wind wave mainly/swell mainly) and sea surface conditions (wind speed smaller than 20m/s, significant wave height from 1m to 7m), mean directional wave height spectra from SWIM (Surface Waves Investigation and Monitoring) are compared at the spectral level to the buoy counterparts, in different classes of sea-state. This includes the comparison of the omni-directional wave height spectrum and the directional function at the peak wave number. The comparison results show that under medium and high sea conditions, wave directional spectra provided by the SWIM beams at 8 ° and 10 ° incidence have a high consistency with those from buoy data. Under low sea conditions, the measurement bias of SWIM wave directional spectra mainly comes from three phenomena which are, by order of importance, an abnormal lifting of spectral energy caused by non- wave components at low wave numbers (parasitic peak), from the non-linear surfboard effect in the radar imaging mechanism and from a slight underestimation of speckle noise spectral density.

Directional and Frequency Spread of Surface Ocean Waves From SWIM Measurements

AbstractThe “China France Oceanography Satellite” (CFOSAT) launched in 2018 now routinely provides directional ocean wave spectra at the global scale. It consists of analyzing the normalized radar cross‐section measured by the near‐nadir pointing Ku‐Band real‐aperture scanning radar SWIM (Surface Waves Investigation and Monitoring). The significant wave height, dominant wavelength and direction are provided as the main parameters, but here, we analyze additional parameters, namely the frequency width of the omni‐directional spectra, the directional spread of the dominant waves, and the related Benjamin‐Feir index. This latter was proposed in the literature to estimate the probability of extreme waves. We discuss the geographical distributions of these parameters, their relation with sea‐state conditions, and their similarities and differences with respect to the same parameters obtained from the MFWAM numerical wave model and buoy data. We find that the SWIM omni‐directional spectra are narrower and more peaked than the model spectra and that these differences are more obvious in the high sea‐state conditions encountered in the Southern Ocean. We find that under the intense conditions of the Southern Ocean, the SWIM directional spread at the peak is the smallest for swell, the largest for young wind seas, and takes intermediate values for mature wind seas. The directional Benjamin‐Feir index is similar for SWIM and MFWAM, but this is mainly due to compensating effects in the parameters contributing to this index. The results indicate that these shape parameters may be used in the future to better describe the wave space‐time evolution.

In the eye of the storm

AbstractThe airborne NOAA Wide Swath Radar Altimeter (WSRA) is a 16 GHz digital beamforming radar altimeter that produces a topographic map of the waves as the aircraft advances. The wave topography is transformed by a two-dimensional FFT into directional wave spectra. The WSRA operates unattended on the aircraft and provides continuous real-time reporting of several data products: (1) significant wave height, (2) directional ocean wave spectra, (3) the wave height, wavelength, and direction of propagation of the primary and secondary wave fields, (4) rainfall rate and (5) sea surface mean square slope (mss). During hurricane flights the data products are transmitted in real-time from the NOAA WP-3D aircraft through a satellite data link to a ground station and on to the National Hurricane Center (NHC) for use by the forecasters for intensity projections and incorporation in hurricane wave models. The WSRA is the only instrument that can quickly provide high-density measurements of the complex wave topography over a large area surrounding the eye of the storm.

The Effect of the Difference in Intensity and Track of Tropical Cyclone on Significant Wave Height and Wave Direction in the Southeast Indian Ocean.

This study aims to analyze the effect of the differences in intensity and track of tropical cyclones upon significant wave heights and direction of ocean waves in the southeast Indian Ocean. We used the tropical cyclone data from Japan Aerospace Exploration Agency (JAXA) starting from December 1997 to November 2017. The significant wave height and wave direction data are reanalysis data from Copernicus Marine Environment Monitoring Service (CMEMS), and the mean sea level pressure, surface wind speed, and wind direction data are reanalysis data from European Center for Medium-Range Weather Forecasts (ECMWF) from December 1997 to November 2017. The results show that the significant wave height increases with the increasing intensity of tropical cyclones. Meanwhile, the direction of the waves is influenced by the presence of tropical cyclones when tropical cyclones enter the categories of 3, 4, and 5. Tropical cyclones that move far from land tend to have higher significant wave height and wider affected areas compared to tropical cyclones that move near the mainland following the coastline

Mapping of Directional Ocean Wave Spectra in Hurricanes and Other Environments

The NOAA Wide Swath Radar Altimeter (WSRA) and its processing are described. The WSRA provides real-time measurements of sea surface significant wave height and directional wave spectra during flights in hurricanes and other environments. The characteristics of near nadir scattering from the sea surface and the resulting distortion of the wave topography measured by the WSRA are discussed, as well as the simulation which generated a matrix to correct the directional wave spectra produced from the WSRA wave topography.

Indigenous Knowledge in Disaster Risk Reduction

The importance of indigenous knowledge in reducing risk from disasters and natural calamities has been widely discussed in the social sciences by scholars arguing for integrative frameworks and participatory processes. This type of knowledge is vital for archipelagic developing countries, such as the Philippines, situated in a geographical area exposed to natural hazards. However, despite its potential contribution to disaster prevention, mitigation, response, rehabilitation and recovery, along with possible combination strategies with western scientific knowledge towards reducing vulnerability and disaster risk management, the literature on the integration of specific communities' indigenous knowledgebased disaster preparedness and adaptation is still limited. The novel contribution of this article is in the discussion of the unique indigenous knowledgeidentified in the cases of San Miguel Island, Camotes Island and Alabat Island, which is utilized even up to the present. Particularly, this study identifies substantial aspects of indigenous knowledge that contribute to disaster risk reduction in the three selected cases. Findings reveal myriad indigenous knowledge pertaining to intensity, height, direction and movement of ocean waves; intensity of winds; sudden surfacing of deep-sea creatures and unease of animals; different patterns of clouds, darkening of skies and foggy horizons, among others. In closely examining indigenous knowledge, this study sheds new light by providing meaningful insights for its contribution to disaster preparedness.

Two New Methods for the Extraction of Significant Wave Heights From Received HF-Radar Time Series

For close to half a century, the usual procedure to determine ocean surface information from HF-radar data has been to first form the Doppler spectrum from the received time series, and then process the result to extract important wave parameters, such as significant wave height, primary wave period, principal wave direction, or even the full directional ocean wave spectrum. In the current work, we bypass the calculation of the Doppler spectrum and still calculate the significant wave height ( $H_{s}$ ) from the received radar data using two related proposed methods. The first calculates $H_{s}$ from the variances of the short-time Fourier transform coefficients of the first-order received field. The second uses the estimated variance of the received electrical field signal to determine $H_{s}$ . Both methods require an initial external calibration stage, which can be either performed analytically from the data or by deploying a wave buoy. The validity of the proposed methods is tested with field data from which a significant correlation with the values of $H_{s}$ measured independently by a wave buoy is obtained.

Directional Surface Wave Spectra from Point Measurements of Height and Slope

AbstractWe describe here a method for recovering directional ocean surface wave spectra obtained from height and slope measurements made over a small area, the iterative deconvolution method (IDM). We show that IDM is a more reliable method for estimating directional wave spectra than more common spectral estimation techniques by comparing it with the widely used maximum entropy method (MEM). IDM is based on the observation that pitch–roll buoys produce directional spectra that are the true spectra convolved with an angular windowing function and are therefore much broader than the true spectra. We test IDM against simulated data and find that it does a better job of retrieving the known input spectra than does MEM, which often produces false double peaks or incorrect angular widths. We compare IDM recoveries to spectra obtained using a nonstandard processing technique, the wavelet directional method (WDM) on data from a compact array of wave staffs on Lake Ontario. We find that IDM produces directional wave spectra very nearly identical to those obtained using WDM, verifying both techniques. Finally, we processed standard NDBC buoy directional spectra and showed that IDM recovers ocean wave spectra that narrow in the Strait of Juan de Fuca and that follow a changing wind in the expected manner. Neither of these phenomena are reliably obtained using MEM due to its tendency to produce false bimodal peaks and peaks that are too narrow.

Classification of the global Sentinel-1 SAR vignettes for ocean surface process studies

Abstract Spaceborne synthetic aperture radar (SAR) can provide finely-resolved (meters-scale) images of ocean surface roughness day-or-night in nearly all weather conditions. This makes it a unique asset for many geophysical applications. Initially designed for the measurement of directional ocean wave spectra, Sentinel-1 SAR wave mode (WV) vignettes are small 20 km scenes that have been collected globally since 2014. Recent WV data exploration reveals that many important oceanic and atmospheric phenomena are also well captured, but not yet employed by the scientific community. However, expanding applications of this whole massive dataset beyond ocean waves requires a strategy to automatically identify these geophysical phenomena. In this study, we propose to apply the emerging deep learning approach in ocean SAR scenes classification. The training is performed using a hand-curated dataset that describes ten commonly-occurring atmospheric or oceanic processes. Our model evaluation relies on an independent assessment dataset and shows satisfactory and robust classification results. To further illustrate the model performance, regional patterns of rain and sea ice are qualitatively analyzed and found to be very consistent with independent remote sensing datasets. In addition, these high-resolution WV SAR data can resolve fine, sub-km scale, spatial structure of rain events and sea ice that complement other satellite measurements. Overall, such automated SAR vignettes classification may open paths for broader geophysical application of maritime Sentinel-1 acquisitions.