Sea Surface Elevation Fields Research Articles

Space-time statistics of extreme ocean waves in crossing sea states

The study of extreme ocean waves has gained considerable interest in recent years, due to their importance for offshore design and navigation safety, and several theoretical approaches have been developed for their statistical description. However, in the case of crossing seas, where two or more wave systems of different characteristics are present, a full understanding of the main physical mechanisms responsible for the occurrence of very high individual waves is still lacking. As a consequence, the prediction of extremes in such conditions currently relies on integrated parameters of the total sea state, such as the spectral wave steepness. In this study, to gain further insight into the role of the crossing wind sea and swell wave systems in producing extreme individual waves, we investigate realistic sea states during typhoon Kong-rey (2018) using an ensemble of numerical simulations obtained from a phase-resolving wave model based on the High-Order Spectral (HOS) method. The reliability of the numerical fields is assessed for the first time with stereo wave measurements of the sea surface elevation field collected from an offshore platform in the area of interest. We show that, in specific conditions, space-time extreme crest heights in crossing seas can be larger than in unimodal seas due to second-order bound wave interactions between the wind sea and the swell. To improve existing prediction capabilities, we propose a novel formulation for the wave steepness in crossing seas, which includes nonlinear effects up to the second order and accounts for the spectral parameters of the interacting wave systems.

On the extreme value statistics of spatio-temporal maximum sea waves under cyclone winds

Principles of the spatio-temporal statistics are used to investigate the characteristics of short-term/range extreme sea waves and related sea-state parameters under cyclone winds (northern hemisphere). We base our analysis upon consistent stereo-imaging observations of the 3D (2D space + time) sea surface elevation field, and spectral wave model results in the Northwestern Pacific during tropical storm Kong-rey (2018). The focus is on the extreme value analysis of individual maximum sea surface elevations (crest heights) and maximum crest-to-trough wave heights. Results highlight the sea areas around the storm centre where the spatio-temporal highest waves are more likely, and, via scale analysis, the principal mechanisms responsible for the occurrence of extreme conditions in bimodal (composed of wind-sea and swell) and short-crested storm seas. We find that individual waves are the highest to the north-east of the translating cyclone, where sea states are more energetic. However, in the south/south-west of the centre, where opposing wind-sea/swell sea states dominate, directional spread and bound nonlinear interactions are enhanced. In this area, more extreme waves may occur, having the maximum crest and wave heights mean values in excess of 1.3 and 2.1 times the significant wave height, respectively. This set of results provides insights into the role of the dispersive and directional focusing enhanced by nonlinearities up to the second order as an effective mechanism for the formation of extreme waves under cyclone winds. To examine what physical mechanism is behind the generation of extreme waves in different regions around the cyclone, we also explore for comparison areas where nonlinear four-wave interactions are more likely to occur.

Analysis of Dangerous Sea States in the Northwestern Mediterranean Area

Extreme sea waves, although rare, can be notably dangerous when associated with energetic sea states and can generate risks for the navigation. In the last few years, they have been the object of extensive research from the scientific community that helped with understanding the main physical aspects; however, the estimate of extreme waves probability in operational forecasts is still debated. In this study, we analyzed a number of sea-states that occurred in a precise area of the Mediterranean sea, near the location of a reported accident, with the objective of relating the probability of extreme events with different sea state conditions. For this purpose, we performed phase-resolving simulations of wave spectra obtained from a WaveWatch III hindcast, using a Higher Order Spectral Method. We produced statistics of the sea-surface elevation field, calculating crest distributions and the probability of extreme events from the analysis of a long time-series of the surface elevation. We found a good matching between the distributions of the numerically simulated field and theory, namely Tayfun second- and third- order ones, in contrast with a significant underestimate given by the Rayleigh distribution. We then related spectral quantities like angular spreading and wave steepness to the probability of occurrence of extreme events finding an enhanced probability for high mean steepness seas and narrow spectra, in accordance with literature results, finding also that the case study of the reported accident was not amongst the most dangerous. Finally, we related the skewness and kurtosis of the surface elevation to the wave steepness to explain the discrepancy between theoretical and numerical distributions.

Toward real-time optical estimation of ocean waves’ space-time fields

Stereo 3D reconstruction is continuously increasing its popularity in the study of mid-to small-scale sea waves. In the recent past, different approaches have been proposed to reconstruct the space-time sea surface elevation field from synchronized stereo frames. Usually, the reconstruction is performed by first recovering a dense and sparse 3D point cloud from stereo pairs and then by interpolating it into a regular grid. Even considering state-of-the-art methods, with typical image resolutions, it's unlikely to perform the first step in less than dozens of seconds (without paralellization), that can easily doubled if we include the subsequent interpolation step. This will limit the applicability of stereo based wave analysis for all the approaches (like monitoring or data assimilation) in which the time between the raw acquisition and the output of processed data is critical.In this paper, we propose a new method to directly estimate the sea surface spectrum over time from a sequence of stereo frames. We exploit the frequency dispersion relation of gravity waves and the (Non-uniform) Fast Fourier Transform to continuously update the 3D surface and 2D wavenumber spectrum estimations given a sparse set of matching features between the two frames. This effectively combines the two aforementioned steps with a performance gain of more than an order of magnitude while keeping a reconstruction accuracy that is extremely close to the current state-of-the-art approaches. Code is available at https://gitlab.com/fibe/wassfast.

Wave group focusing in the ocean: estimations using crest velocities and a Gaussian linear model

Wave group focusing gives rise to the formation of large gravity waves at the surface of the ocean, some of which are called rogue waves and represent a natural hazard for ships and offshore platforms. For safety purposes, it is crucial to predict when and where these large waves will appear and how large they will be. This work focuses on crest velocities, a quantity that is relatively easy to extract from sea surface elevation fields. It is shown that there is a direct link between crest velocity gradient and wave group linear dispersive focusing. Studying analytically the focusing of one-dimensional Gaussian wave packets under linear evolution makes it possible to derive estimates of quantities at focus, based only on crest velocity measurements. In this way, the focusing time, focusing size and focusing amplitude (relative to instantaneous amplitude) of an isolated Gaussian wave packet can be estimated. Our work is also applicable to second-order non-linear waves. Limitations due to higher-order non-linear effects are studied in numerical simulations of the non-linear Schrodinger equation.

Stereo wave imaging from moving vessels: Practical use and applications

Stereo wave imaging of the sea surface elevation has become an effective instrumentation to gather small- and medium-range 3-D wind wave data. Indeed, fruitful applications of stereo techniques have provided new insights into directional wave spectra, space–time distributions of wave maxima, and small-scale wave statistics. So far, however, stereo systems have been deployed mainly on fixed structures (e.g. oceanographic platforms or lighthouses) in order to simplify the installation and maintenance procedures. Nonetheless, advances in stereo calibration and processing suggest that stereo deployments are also feasible onboard moving vessels, thus broadening the impact of these observations on the study of wind waves. In this context, this study aims at discussing how the stereo processing designed to gather reliable wave data from fixed structures should be managed to operate on a moving structure. In particular, estimate of stereo cameras orientation and position with respect to the mean sea plane is of utmost importance. We discuss this aspect by using a synthetic sea state and stereo data collected during an oceanographic campaign onboard a research vessel. Results suggest that, without complementary data sources for ship motion compensation, the sea surface elevation field should include at least about sixteen spatial (2-D) waves to gather a robust estimate of the mean sea plane and consequently realistic wave parameters (e.g. the significant wave height). In this respect, our results provide also insight into the uncertainty of estimates in case of a limited number of 2-D waves is collected by the stereo system. Finally, applications of stereo wave imaging on a moving structure are discussed, with particular emphasis on the collection of space–time wave fields for assessment of numerical models and operational wave observation onboard vessels.

Rogue Waves: Results of the MaxWave Project

Safety of shipping is an ever growing concern. In a summary, Faulkner investigated the causes of shipping casualties (2002, “Shipping Safety: A Matter of Concern,” Ingenia, The Royal Academy of Engineering, Marine Matters, pp. 13–20) and concluded that the numbers of unexplained accidents are far too high in comparison to other means of transport. From various sources, including insurers data over 30% of the casualties are due to bad weather (a fact that ships should be able to cope with) and a further 25% remain completely unexplained. The European project MaxWave aimed at investigating ship and platform accidents due to severe weather conditions using different radars and in situ sensors and at suggesting improved design and new safety measures. Heavy sea states and severe weather conditions have caused the loss of more than 200 large cargo vessels within the 20years between 1981 and 2000 (Table 1 in Faulkner). In many cases, single “rogue waves” of abnormal height as well as groups of extreme waves have been reported by crew members of such ships. The European Project MaxWave deals with both theoretical aspects of extreme waves and new techniques to observe these waves using different remote sensing techniques. The final goal is to improve the understanding of the physical processes responsible for the generation of extreme waves and to identify geophysical conditions in which such waves are most likely to occur. Two-dimensional sea surface elevation fields are derived from marine radar and space borne synthetic aperture radar data. Individual wave parameters such as maximum to significant wave height ratios and wave steepness, are derived from the sea surface topography. Several ship and offshore platform accidents are analyzed and the impact on ship and offshore design is discussed. Tank experiments are performed to test the impact of designed extreme waves on ships and offshore structures. This article gives an overview of the different work packages on observation of rogue waves, explanations, and consequences for design.

A wavelet-based algorithm to estimate ocean wave group parameters from radar images

In recent years, new remote sensing techniques have been developed to measure two-dimensional (2-D) sea surface elevation fields. The availability of these data has led to the necessity to extend the classical analysis methods for one-dimensional (1-D) buoy time series to two dimensions. This paper is concerned with the derivation of group parameters from 2-D sea surface elevation fields using a wavelet-based technique. Wave grouping is known to be an important factor in ship and offshore safety, as it plays a role in dangerous resonance phenomenons and the generation of extreme waves. Synthetic aperture radar (SAR) data are used for the analysis. The wavelet technique is introduced using synthetic ocean surfaces and simulated SAR data. It is shown that the group structure of the ocean wave field can be recovered from the SAR image if the nonlinear imaging effects are moderate. The method is applied to a global dataset of European Remote Sensing satellite (ERS-2) wave mode data. Different group parameters including the area covered by the largest group and the number of groups in a given area are calculated for over 33 000 SAR images. Global maps of the parameters are presented. For comparison, classical 1-D grouping parameters are calculated from colocated wave model data showing good overall agreement with the wavelet-derived parameters. ERS-2 image mode data are used to study wave fields in coastal areas. Waves approaching the island of Sylt in the North Sea are investigated, showing the potential of the wavelet technique to analyze the spatial wave dynamics associated with the bottom topography. Observations concerning changes of wavelength and group parameters are compared to linear wave theory.

Measurement of 2-D Sea Surface Elevation Fields Using Complex Synthetic Aperture Radar Data

Measurement of 2-D Sea Surface Elevation Fields Using Complex Synthetic Aperture Radar Data

Measurement of 2-D sea surface elevation fields using complex synthetic aperture radar data

A method is presented to derive two-dimensional sea surface elevation fields from complex synthetic aperture radar (SAR) data. Applied to spaceborne SAR data as acquired by European Remote Sensing 2 (ERS-2) or the Environmental Satellite (ENVISAT), the method allows to analyze the structure of ocean wave fields, e.g., wave grouping or individual wave heights on a global scale. The technique, thus, provides wave parameters not obtained with common SAR wave retrieval schemes, which are designed to estimate the 2-D wave spectrum, i.e., second-order statistical moments of the wave field. Estimates of sea surface elevation fields are obtained based on the existing theory of SAR ocean wave imaging, i.e., the modulation of the SAR image intensity due real aperture radar and motion-related effects. A power series expansion is derived for SAR intensity images that enables the analysis of nonlinear effects as well as to derive a quasi-linear approximation of the SAR imaging model in the spatial domain. A statistical analysis is performed based on a global dataset of 2D wave spectra provided by the European Centre for Medium-Range Weather Forecast. Distributions are given for the relative error of the quasi-linear approximation in the spatial domain. It is shown that the error can be reduced by smoothing the SAR image in the azimuthal direction at the cost of lower resolution. Smoothed elevation fields are retrieved by the minimization of a cost function defined in the Fourier domain based on the quasi-linear approximation of the imaging process. A multilook technique is applied to infer the information on wave propagation directions, which is required because the SAR transfer function is non-Hermitian, i.e., the SAR image is not determined by the frozen sea surface, but wave motion has a significant impact. The method is applied to simulated SAR images as well as to data acquired by ERS-2. The errors of the retrieved wave field due to image noise, uncertainties in the SAR imaging model, and bandwidth limitations are analyzed. In particular, the fact that the estimated elevation field is smoothed due to the finite system resolution and smearing effects associated with wave motion is discussed. A statistical test is proposed to check the homogeneity of the SAR image. The method makes sure that atmospheric effects are not misinterpreted as being caused by ocean waves.

Mapping the mean sea surface elevation field from satellite altimetry data using optimal interpolation

Abstract Optimal interpolation technique is applied to satellite altimetry data in order to recover a sea surface elevation signal from the data, which includes a large satellite radial orbit error, also to make a map of temporal mean sea surface dynamic topography (SSDT, the mean surface height relative to the geoid). The method is applied to Seasat data for a study area southeast of Japan, for which a fairly precise gravimetric geoid is available. Estimated mean elevation field relative to the best available geoid qualitatively shows existence of the Kuroshio in a limited local area close to Honshu, Japan. But for the whole of the area studied, the elevation field is much more rugged than expected mean SSDT and appears to include a relatively large geoid error; namely, the mapped mean sea surface elevation field cannot describe the mean SSDT field. Instead, correction of the provided geoid is evaluated by this altimetrically estimated elevation field together with the mean SSDT estimated from hydrograph...

A numerical computation of the wind-driven current in the Bohai Sea : Dou, Zhenxing, Cunzhi Zhang and Yanfeng Zhang, 1987. Acta oceanol. sin. (English version), 6(3):344–352. Inst. of Mar. Environ. Protection, State Oceanic Admin., Dalian, People's Republic of China

On the basis of shallow water equations, a 2-dimensional model for the wind-driven current is developed in this paper to simulate the mean wind-driven circulation and sea-surface elevation fields respectively in winter and summer, and to describe the general nature of the wind-driven current in the Bohai Sea.Numerical results show that the patterns of the wind-driven circulation in Bohai are mainly the cyclonic circulation in winter and both cyclonic and anticyclonic circulations in summer. A theoretical argument based on vorticity is put up to explain the generating-mechanism of large eddies near the strait, which are considered to be the direct results of the wind stress interaction with topography gradients.