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Wave crests of unexpected height and steepness pose a danger to activities at sea, and long-term field measurements provide important clues for understanding the environmental conditions that are conducive to their generation and behavior. We present a novel dataset of high-frequency laser altimeter measurements of the sea surface elevation gathered over a period of 18 years from 2003 to 2020 on an offshore platform in the central North Sea. Our analysis of crest height distributions in the dataset shows that mature, high sea states with high spectral steepness and narrow directional spreading exhibit crest height statistics that significantly deviate from standard second-order models. Conversely, crest heights in developing sea states with similarly high steepness but wide directional spread correspond well to second-order theory adjusted for broad frequency bandwidth. The long-term point time series measurements are complemented with space–time stereo video observations from the same location, collected during five separate storm events during the 2019/20 winter season. An examination of the crest dynamics of the space–time extreme wave crests in the stereo video dataset reveals that the crest speeds exhibit a slowdown localized around the moment of maximum crest elevation, in line with prevailing theory on nonlinear wave group dynamics. Extending on previously published observations focused on breaking crests, our results are consistent for both breaking and nonbreaking extreme crests. We show that wave crest steepness estimated from time series using the linear dispersion relation may overestimate the geometrically measured crest steepness by up to 25% if the crest speed slowdown is not taken into account. Significance Statement Better understanding of the statistics and dynamical behavior of extreme ocean surface wave crests is crucial for improving the safety of various operations at sea. Our study provides new, long-term field evidence of the combined effects of wave field steepness and directionality on the statistical distributions of crest heights in storm conditions. Moreover, we show that the dynamical characteristics of extreme wave crests are well described by recently identified nonlinear wave group dynamics. This finding has implications, for example, for wave force calculations and the treatment of wave breaking in numerical wave models.

From 6 to 8 November 2011, a baroclinic wave moved from North Atlantic to Balearic Sea, produced a cut-off, at all altitudes, and developed into a Tropical-Like Cyclone (TLC) characterized by a deep-warm core. This TLC led to a mean sea level pressure minimum of about 987 hPa, 10 m wind speeds higher than 30 m/s around the eye, and very intense rainfall, especially in the Gulf of Lion and the surrounding areas, close to the mountain chains (floods in Genoa and Elba Island).To explore in details the effect of the sea surface temperature on the TLC development, we employed the coupled modeling system COAWST, which consists of the following models: ROMS for the hydrodynamic part, WRF for the meteorological part and SWAN for the surface wave modeling, using a 5 km horizontal grid over all Mediterranean Sea.COAWST was used with different configurations: Stand Alone (SA) approach using only the atmospheric part, atmosphere-ocean coupled mode (AO), and fully coupled version including also surface waves (AOW). Comparing the three runs, the effects of different simulations on the TLC trajectory are significant only in the later stage of the cyclone lifetime. On the other hand, wind intensity is higher in the SA case w.r.t. both coupled runs. When compared to case AO, winds are about 1 m/s larger, even though the spatial distribution is very similar (possibly because of the lower SST produced by case AO). Case AOW produces less intense winds than SA and AO case in the areas where the wave is most developed (differences are about 2-4 m/s), while winds are more intense nearby the cyclone’s eye. Moreover, the inclusion of the wave model (AOW) has implications in the water column, by increasing the mixing in the ocean, changing the depth of the ocean mixed layer along the track of the TLC, increasing the surface drag and the net heat fluxes from ocean to atmosphere, so that eventually SST in AOW run is colder than in AO.It is observed that SST of the SA case is overestimated compared to the coupled cases, and in particular the best performances are observed using the fully coupled case, with the wave motion implementation. The best description of the SST impacts the cyclone intensity and the amount of precipitation at catchment scale. The vertical profiles show that wave induced mixing modifies the mixed layer structure and cools the water column, removing much of the SST (and Ocean Heat Content) anomaly present in the mixed layer.The date chosen for the run initialization appears important: an earlier initial condition allows to properly simulate the evolution of the cyclone from the cyclogenesis between the inclusion and setting-up of air sea interaction effect, through the coupled models.Warming SST in the Mediterranean Sea induced by climate change might increase TLC frequency and/or intensity, potentially becoming more harmful for coastal populations and infrastractures. Fully coupled AOW models might be better suited for studying such aspects. Funding from the STO Office of Chief Scientist (907EUR30) is gratefully acknowledged.

Climate change and its consequences on coastal erosion, flooding and water quality are becoming a major concern for a significant percentage of littorals in the world. This issue is particularly challenging for gentle-sloping sandy coasts which are vulnerable to slow and continuous changes related to rising sea-levels and to extreme storm surge and wave events.Here we present a multidisciplinary research combining satellite image with machine learning and GIS spatial analysis tools to analyze coastal erosion risk in the Venice shoreline over the period 2015-2019. Firstly, an advanced image preprocessing was performed on satellite images (e.g. co-registration, colors normalization) to prepare the input dataset. Secondly, different supervised and unsupervised machine learning classification methods were tested to accurately define shoreline position by recognizing land-sea areas in each image and the Digital Shoreline Analysis System (DSAS) tool in ArcGis was applied to evaluate the net shoreline movement overtime. Finally, a GIS-based Bayesian Network (BN) approach was developed, to evaluate the probability and uncertainty of coastal erosion risks, and the cascading effects on water quality variation, against multiple ‘what-if’ scenarios related to extreme sea levels and wave conditions under climate change for the period 2040-2050.According to the spatial resolution of the available data for the case study of Venice (Veneto Region-Italy), the proposed BN-model was trained and validated by considering atmospheric, oceanographic and water quality parameters over the 2015-2019 timeframe, allowing to capture local-scale coastal progression and related driving forces.Results showed general shoreline stability in the considered reference timeframe. However, the high presence of anthropogenic structures (e.g. jetties, breakwaters) induces the formation of well-delimited hotspots of erosion/accretion. Future trends from the BN-based scenario analysis, according to RCP8.5 scenario within the 2040-2050 period, showed that, even if in minor extent, water quality parameters (i.e. suspended matter, diffuse attenuation) will increase. On the other hand, shoreline evolution trend will face a decreasing probability of the stable class, which in turn will increase instability.Despite constraints posed by the spatial resolution of the available data for the investigated case, the outcomes of the performed assessment represent valuable information to support adaptive policy pathways in the context of Integrated Coastal Zone Management and Disaster Risk Reduction in the Venice coastal area.

In recent years, the study of extreme ocean waves has gained considerable interest and several theoretical approaches have been developed for their statistical prediction. However, a full understanding of the main mechanisms responsible for the occurrence of extreme waves has not yet been reached in the relatively common case of a crossing sea, where a local wind sea system coexists with a system of swell. In this context, we investigate how the space-time extreme-value statistics of realistic crossing sea states differs from the statistics of the corresponding short-crested wind sea and long-crested swell partitions during tropical cyclone Kong Rey (2018) in the Northwestern Pacific Ocean (Yellow Sea and East China Sea). The investigation is carried out using an ensemble of numerical simulations obtained from a phase-resolving wave model based on the high-order spectral method (HOSM) and focuses on the maximum sea surface elevation (crest height). The reliability of the numerical model outputs has been assessed with space-time measurements of the 3D sea surface elevation field collected from a fixed offshore platform in the area of interest. Our results highlight the different roles that linear and nonlinear effects have in the formation of extreme waves for different combinations of wind sea and swell systems.

Sea surface wave breaking is the dominant process that results in dissipation of ocean surface wave energy. During the breaking process, wave energy is converted into turbulent kinetic energy, and if significantly energetic, entrains air which facilitates air-sea gas transfer and scatters light to create the signature whitecap. Exploiting the broadband scattering of light by the surface whitecaps, this study uses a fixed stereo video system to detect and track individual air-entraining surface breaking waves at wind speeds of up to 16 m/s. The sea surface foam (whitecap) from a breaking event is detected in grayscale images using a brightness thresholding technique based on the image pixel intensity histogram. The movement of individual whitecaps is estimated with optical flow and is used to track whitecaps between consecutive frames. Once breaking events have been tracked through their lifetime, fundamental properties of the whitecap such as the time-evolving foam area [m2], breaking speed [m/s], average crest length [m] and foam area growth and decay timescales [s] are extracted and subsequently aggregated into whitecap statistics. The geometric, kinematic and dynamic quantities obtained for individual whitecaps via this tracking method are used in conjunction with the volume-time-integral method developed in Callaghan et al 2016 to estimate the energy dissipated by each individual whitecap and to then develop an empirical frequency-dependent whitecap energy dissipation source term.

One of the most promising techniques for the analysis of Spatio-Temporal ocean wave fields is stereo vision. Indeed, the reconstruction accuracy and resolution typically outperform other approaches like radars, satellites, etc. However, it is computationally expensive so its application is typically restricted to the analysis of short pre-recorded sequences. What prevents such methodology from being truly real-time is the final 3D surface estimation from a scattered, non-equispaced point cloud. Recently, we studied a novel approach exploiting the temporal dependence of subsequent frames to iteratively update the wave spectrum over time. Albeit substantially faster, the unpredictable convergence time of the optimization involved still prevents its usage as a continuously running remote sensing infrastructure. In this work, we build upon the same idea, but investigating the feasibility of a fully data-driven Machine Learning (ML) approach. We designed a novel Convolutional Neural Network that learns how to produce an accurate surface from the scattered elevation data of three subsequent frames. The key idea is to embed the linear dispersion relation into the model itself to physically relate the sparse points observed at different times. Assuming that the scattered data are uniformly distributed in the spatial domain, this has the same effect of increasing the sample density of each single frame. Experiments demonstrate how the proposed technique, even if trained with purely synthetic data, can produce accurate and physically consistent surfaces at five frames per second on a modern PC.

Issue sup1: Copernicus Marine Service Ocean State Report, Issue 5 Supplement.-- Karina von Schuckmann (Editor), Pierre-Yves Le Traon (Editor), Neville Smith (Chair) (Review Editor), Ananda Pascual (Review Editor), Samuel Djavidnia (Review Editor), Jean-Pierre Gattuso (Review Editor), Marilaure Grégoire (Review Editor), The work was supported by the Copernicus Marine Environment Monitoring Service (CMEMS) LATEMAR project. CMEMS is implemented by Mercator Ocean in the framework of a delegation agreement with the European Union. This work has also been conducted as part of the bilateral project EOLO-1 (“Extreme Oceanic waves during tropical, tropical-like, and bomb cyclones”) between CNR-ISMAR and the University of Tokyo (Japan; Prof. Takuji Waseda). Antonio Ricchi funding have been provided via the PON “AIM” - Attraction and international mobility program AIM1858058. Joanna Staneva acknowledges H2020 IMMERSE Project, Arno Behrens was supported by CMEMS Waveflow project and G. Gayer by ESA Black Sea and Danube Regional Initiative (EO4BS).

The ocean is the most important subsystem of the Earth’s climate system and functions as its heart, regulating the energy distribution of the planet. It has absorbed more than 90% of the energy accumulated since 1971 and about 30% of the emitted anthropogenic carbon dioxide. As a result, water temperature rises and oceans acidify and deoxygenate, which lead to changes in oceanic circulation and biogeochemistry, to rising sea levels, to more extreme weather events, to shifts in the distribution of species and migratory routes, and to loss of species and habitat diversity. Awareness of the importance of oceans for the sustainability of the global human population is increasing, including the conservation of biodiversity and its legacy to future generations [1]. For instance, oceanic organisms are more vulnerable to warming than terrestrial ones, as the former are generally at temperatures near their upper thermal limits and lack of thermal refuges [2]. Half of the atmospheric carbon fixed annually in natural systems is cycled into the ocean mainly by the biological carbon pump in the open ocean, but some of the main areas capturing and storing this carbon (as mangroves, seagrasses, salt marshes, and coastal upwelling ecosystems) cover less than 3% of the world’s ocean surface [3]. Particularly, eastern boundary upwelling systems are highly productive ecosystems, with up to 40% of the reported global fish catch [4].

In February 2017, a wave buoy was deployed in the Southern Ocean, south of New Zealand at 52°45.71′S, 169°02.54′E. For 170 days, the moored buoy transmitted spectral and time domain observations, including measurements during a storm with a particularly large individual wave of 19.4-m crest-to-trough height. We present a detailed analysis of this storm and the measured and modelled spectra, also considering the probability of the occurrence of single large waves. After 170 days, the buoy broke free of its mooring and started drifting eastwards, still transmitting the essential data, thereby providing a unique opportunity to examine large wave events and their corresponding spectral conditions in the Southern Ocean on both moored and free-drifting platforms. The results are discussed quantitatively.

Reliable wave forecasts and hindcasts, together with long-term statistical analysis of extreme conditions, are of utmost importance for monitoring marine areas. Indeed, there is general consensus that high-quality predictions of extreme events during marine storms can substantially contribute to avoiding or minimizing human and material damage, especially in busy waterways such as the Mediterranean and Black Seas. So far, however, the wave climate characterization (average and anomaly relative to the average) has focused on the bulk characterization of the significant wave height Hs, and it has lacked a description of the individual waves, such as the maximum ones that may occur at a given location in the sea. To fill this gap, we provide the intensity and geographical distribution of the maximum waves in the Mediterranean and Black Seas over 27 years (1993-2019), by representing the average annual (1993-2018) and anomaly for 2019 relative to the average of the 99th percentile of the expected maximum wave height Hm and crest height Cm. The analysis combines wave model hindcasts available through CMEMS model setup and the wave model WAVEWATCH III®, both forced with ECMWF ERA5 reanalysis winds. Results show that in 2019 maximum waves were smaller than usual in the Black Sea (anomalies of Hm up to -1.5 m), while in the Mediterranean Sea a markedly positive anomaly (+2.5 m for Hm) was found in the southern part of the basin. The peculiar 2019 configuration seems to be caused by a widespread atmospheric stability over the Black Sea and by depressions that rapidly passed over the Mediterranean Sea.

Over the past decade, model reanalysis data products have found widespread application in many areas of research and have often been used for the assessment of the past and present atmospheric climate. They produce reliable fields at high temporal resolution (1 hour), albeit generally at low-to-mid spatial resolution (0.25°-1.00°). On the other hand, climatological analyses, quite often down-scaled (up to few km) to represent conditions also in enclosed basins, lack the actual historical sequence of events and are often provided at poor temporal resolution (6 hours or daily).In this context, we investigated the possibility of using climate model data to scale ERA5 reanalysis wind (25-km and 1-hour resolution data) to assess the Mediterranean Sea wind and wave climate. We propose a statistical strategy to fuse ERA5 wind speeds over the sea with the past and future wind speeds produced by the COSMO-CLM (8-km and daily-mean data) climatological model. In the method, the probability density function of the ERA5 wind speed at each grid point is adjusted to match that of COSMO-CLM using a histogram equalization strategy. In this way, past ERA5 data are corrected to account for the COSMO-CLM wind distribution, while ERA5 scaled wind sequence can be also projected in the future with COSMO-CLM scenarios. Comparison with past observations of wind and waves confirms the validity of the adopted method.We have tested this strategy for the assessment of the changing wind and, after WAVEWATCH III model runs, also the wave climate in the northern Adriatic Sea, especially in front of Venice and the MOSE barriers. In general, this data fusion strategy may be applied to produce a scaled wind dataset in enclosed basins and improve past and scenario wave modeling applications based on any reanalysis wind data.

Reliable predictions of oceanic waves during storms have always been foremost for offshore design and operation, coastal hazards, and navigation safety. Indeed, many accidents that occurred during storms were ascribed to the impact with unforeseen large waves. In this context, the purpose of this study is to improve the present state extreme wave estimate from spectral wave models. We describe an implementation for the WAM model, and we investigate the use of WAM and WAVEWATCH III fed with common routines designed to evaluate the short-term/range maximum wave statistics. An extensive assessment of models' results in the Adriatic and North Sea is performed using time and space-time wave measurements, and through an intercomparison between WAM and WAVEWATCH III applied with three different input/dissipation source term parametrizations (ST3/4/6). Further, models’ capabilities are investigated, and extreme waves characterized, in the Mediterranean Sea, aiming also at disentangling the wave spectrum bulk parameters that may point to favorable conditions for the generation of high waves. Based on the comparisons between model results and measurements, we conclude that for the model characterization of extremes, the accuracy of the significant wave height is pivotal; differences between models of other spectral parameters seem to have a minor effect.

On December 15, 2009, a very high wave crest was recorded by a local camera at the CNR-ISMAR oceanographic tower, 15 km offshore Venice in the Northern Adriatic Sea (Italy). The height of the estimated crest elevation appears well beyond the value (1,25·Hs) commonly used to identify a wave as freak. We document the wave event with a full description of the corresponding met-ocean conditions and related measurements, of which we provide a critical analysis., Measurement(s) atmospheric wind direction • atmospheric wind speed • wave Technology Type(s) weather station • acoustic AWAC system • waverider buoy • Camera Device Sample Characteristic - Environment coastal sea water Sample Characteristic - Location Adriatic Sea Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.13415780

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.

Stereo imaging of the sea surface elevation provides unique field data to investigate the geometry and dynamics of oceanic waves. Typically, this technique allows retrieving the 4-D ocean topography (3-D space + time) at high frequency (up to 15–20 Hz) over a sea surface region of area ~104 m2. Stereo data fill the existing wide gap between sea surface elevation time-measurements, like the local observation provided by wave-buoys, and large-scale ocean observations by satellites. The analysis of stereo images provides a direct measurement of the wavefield without the need of any linear-wave theory assumption, so it is particularly interesting to investigate the nonlinearities of the surface, wave-current interaction, rogue waves, wave breaking, air-sea interaction, and potentially other processes not explored yet. In this context, this open dataset aims to provide, for the first time, valuable stereo measurements collected in different seas and wave conditions to invite the ocean-wave scientific community to continue exploring these data and to contribute to a better understanding of the nature of the sea surface dynamics., Measurement(s)stereo image • wave height • peak wave period • wave directionTechnology Type(s)Camera Device • computational modeling techniqueFactor Type(s)geographic locationSample Characteristic - Environmentsea surface layerSample Characteristic - LocationBlack Sea • Adriatic Sea • Yellow Sea • Iroise Sea Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.12181158

We perform a critical analysis of the present approach in wave modeling and of the related results. While acknowledging the good quality of the best present forecasts, we point out the limitations that appear when we focus on the corresponding spectra. Apart from the meteorological input, these are traced back to the spectral approach at the base of the present operational models, and the consequent approximations involved in properly modeling the various physical processes at work. Future alternatives are discussed. We then focus our attention on how, given the situation, to deal today with the estimate of the maximum wave heights, both in the long term and for a specific situation. For this, and within the above limits, a more precise evaluation of the wave spectrum is shown to be a mandatory condition.

Reliable prediction of oceanic waves during severe marine storms has always been foremost for offshore platform design, coastal activities, and navigation safety. Indeed, many damaging accidents and casualties during storms were ascribed to the impact with abnormal and unexpected waves. However, predicting extreme wave occurrence is a challenging task, at first, because of their inherent randomness, and because the observation of large ocean waves, of primary importance to assess theoretical and numerical models, is limited by the costs and risks of deployment during severe open-ocean sea-state conditions.In the context of the EU-based Copernicus Marine Environment Monitoring Service (CMEMS) evolution, the LATEMAR project (https://www.mercator-ocean.fr/en/portfolio/latemar/) aimed at improving the modelling of large wave events during marine storms. Indeed, at present, operational systems only provide average and peak wave parameters, with no information on individual waves whatsoever. However, developments of the state-of-the-art third-generation wave models demonstrated that using the directional wave spectrum moments into theoretical statistical models for wave extremes, forecasters are able to accurately infer the expected shape and likelihood of the maximum waves during storms.The main purpose of the activity is therefore to provide the wave models WAM and WAVEWATCH III with common procedures to explicitly estimate the maximum wave heights for each sea state. LATEMAR achieved this goal by: performing an extensive assessment of the model maximum waves using field observations collected from an oceanographic tower; comparing WAM and WAVEWATCH III maximum wave estimates in the Mediterranean Sea; investigating the sensitivity of the maximum waves on the main sea state parameters. All model developments and evaluations resulting from this research project will be directly applicable to the wave model forecasting systems to expand their catalogue.

Over the past decade, reanalysis data products have found widespread application in many areas of research and have often been used for the assessment of the past and present climate. They produce reliable atmospheric fields at high temporal resolution, albeit at low-to-mid spatial resolution. On the other hand, climatological analyses, quite often down-scaled to represent conditions also in enclosed basins, lack the historical sequence of stormy events and are often provided at poor temporal resolution.In this context, we investigated the possibility of using the ERA5 reanalysis 10-m wind (25-km and 1-hour resolution data) to assess the Mediterranean Sea wind climate (past and scenario). We propose a statistical strategy to relate ERA5 wind speeds over the sea to the past and future wind speeds produced by the COSMO-CLM (8-km and 6-hour resolution data) climatological model. In particular, the probability density function of the ERA5 wind speed at each grid point is adjusted to match that of COSMO-CLM. In this way, past ERA5 winds are corrected to account for the COSMO-CLM energy, while ERA5 scaled wind sequence can be projected in the future with COSMO-CLM scenario energy. Comparison with past observations confirms the validity of the adopted method.In the Venezia2021 project, we have applied this strategy for the assessment of the changing wind and, after WAVEWATCH III model runs, also the wave climate in the Northern Adriatic Sea, especially in front of Venice and the MOSE barriers, under two IPCC (RCP 4.5 and 8.5) scenarios.In general, this strategy may be applied to produce a scaled wind dataset in enclosed basins and improve past wave modeling applications based on any reanalysis wind data.

On 12 November 2019, an exceptional flood event occurred in Venice, second only to the one that occurred on 4 November 1966. The maximum recorded sea level value of 189 cm above local datum resulted in the flooding of more than 85% of the pedestrian surface of the historical city. Moreover, with four extremely high tides since 11 November 2019, this has been the worst week for flooding in Venice ever since 1872, when official statistics were first produced. The event that struck Venice and the northern Adriatic Sea on 12 November 2019, although having certain conditions seemingly typical of the events that cause exceptional high waters, also had some peculiar characteristics not observed before and therefore it requires an in-depth analysis. Several factors made this event exceptional: an in-phase timing of the peak of the storm surge and the astronomical tide; an anomalously high monthly mean sea level in the Adriatic Sea induced by a steady low-pressure and wind systems over the Mediterranean Sea associated with large-scale low-frequency atmospheric dynamics; a deep low-pressure system over the central-southern Tyrrhenian Sea that generated strong sirocco (south-easterly) winds along the main axis of the Adriatic Sea pushing the waters towards north; a fast-moving local depression - and the associated wind perturbation - travelling in the north-westward direction along the Italian coast that may have forced long ocean waves (e.g., edge wave); and very strong winds (100 km h-1 on average, with gusts reaching 110 km h-1) over the Lagoon of Venice which led to a further rise in water levels and damage to the historic city. In this study, a large set of available observations and the high-resolution numerical simulations are used to quantify the influence of these drivers on the peak flood event and to investigate the peculiar weather and sea conditions over the Mediterranean Sea during the Venice floods of November 2019.

This study aims at characterizing the distinctive features of a spatio-temporal nonlinear wave surface. We analyze wind-generated 3-D wave fields observed during the passage of an atmospheric front, which led to a wide directional spreading of wave energy. Data were acquired from the ocean research station Socheongcho-ORS (Yellow Sea) with a stereo wave imaging system. They include 3-D (i.e. 2-D + time) measurements of the sea surface elevation with high spatial and temporal resolution over a swath larger than any previous similar deployment. We examine the shape and the nonlinear properties of the wavenumber/frequency 3-D wave spectrum, and the characteristic spatial, temporal and spatio-temporal length scales of the wave field. We then focus on analyzing the probability of occurrence and the spatio-temporal size of the rogue waves we identified in the data. In particular, we provide for the first time an empirical estimate of the extent of the horizontal sea surface spanned by rogue waves. We also propose and assess a novel strategy to determine from the 3-D wave spectrum the vertical current profile, to be then used to map the spectrum on intrinsic frequencies.

The directional distribution of the energy of young waves is bimodal for frequencies above twice the peak frequency; i.e., their directional distribution exhibits two peaks in different directions and a minimum between. Here we analyze in detail a typical case measured with a peak frequency fp = 0.18 Hz and a wind speed of 10.7 m s−1 using a stereo-video system. This technique allows for the separation of free waves from the spectrum of the sea-surface elevation. The latter indeed tend to reduce the contrast between the two peaks and the background. The directional distribution for a given wavenumber is nearly symmetric, with the angle distance between the two peaks growing with frequency, reaching 150° at 35 times the peak wavenumber kp and increasing up to 45 kp. When considering only free waves, the lobe ratio, the ratio of oblique peak energy density over energy in the wind direction, increases linearly with the non-dimensional wavenumber k∕kp, up to a value of 6 at k∕kp ≃ 22, and possibly more for shorter components. These observations extend to shorter components' previous measurements, and have important consequences for wave properties sensitive to the directional distribution, such as surface slopes, Stokes drift or microseism sources.

On 12 November 2019, an exceptional flood event took place in Venice, second only to the one that occurred on 4 November 1966. Moreover, with four extremely high tides since 11 November 2019, this was the worst week for flooding in Venice since the beginning of sea level records (1872). The event that struck Venice and the northern Adriatic Sea on 12 November 2019, although having certain conditions seemingly typical of the events causing exceptional high waters, had some peculiar characteristics not observed before, which deserved an in-depth analysis. Several factors made this event exceptional: the in-phase timing between the peak of the storm surge and the astronomical tide; a deep low-pressure cyclone over the central-southern Tyrrhenian Sea that generated strong Sirocco (south-easterly) winds along the main axis of the Adriatic Sea, pushing waters to the north; a fast-moving local depression – and the associated wind perturbation – travelling in the north-westward direction over the Adriatic Sea along the Italian coast, generating a meteotsunami; very strong winds (28 m s − 1 on average with 31 m s − 1 gusts) over the Lagoon of Venice, which led to a rise in water levels and damages to the historic city; and an anomalously high monthly mean sea level in the Adriatic Sea, induced by a standing low-pressure and wind systems over the Mediterranean Sea, that was associated with large-scale low-frequency atmospheric dynamics. In this study, the large set of available observations and high-resolution numerical simulations have been used to quantify the contribution of the mentioned drivers to the peak of the flood event and to investigate the peculiar weather and sea conditions over the Mediterranean Sea during the Venice floods of November 2019.

Stereo 3D reconstruction of ocean waves is gaining more and more popularity in the oceanographic community and industry. Indeed, recent advances of both computer vision algorithms and computer processing power now allow the study of the spatio-temporal wave field with unprecedented accuracy, especially at small scales. Even if simple in theory, multiple details are difficult to be mastered for a practitioner, so that the implementation of a sea-waves 3D reconstruction pipeline is in general considered a complex task. For instance, camera calibration, reliable stereo feature matching and mean sea-plane estimation are all factors for which a well designed implementation can make the difference to obtain valuable results. For this reason, we believe that the open availability of a well tested software package that automates the reconstruction process from stereo images to a 3D point cloud would be a valuable addition for future researches in this area. We present WASS ( http://www.dais.unive.it/wass ), an Open-Source stereo processing pipeline for sea waves 3D reconstruction. Our tool completely automates all the steps required to estimate dense point clouds from stereo images. Namely, it computes the extrinsic parameters of the stereo rig so that no delicate calibration has to be performed on the field. It implements a fast 3D dense stereo reconstruction procedure based on the consolidated OpenCV library and, lastly, it includes set of filtering techniques both on the disparity map and the produced point cloud to remove the vast majority of erroneous points that can naturally arise while analyzing the optically complex nature of the water surface. In this paper, we describe the architecture of WASS and the internal algorithms involved. The pipeline workflow is shown step-by-step and demonstrated on real datasets acquired at sea.

We consider the observation and analysis of oceanic rogue waves collected within spatio-temporal (ST) records of 3D wave fields. This class of records, allowing a sea surface region to be retrieved, is appropriate for the observation of rogue waves, which come up as a random phenomenon that can occur at any time and location of the sea surface. To verify this aspect, we used three stereo wave imaging systems to gather ST records of the sea surface elevation, which were collected in different sea conditions. The wave with the ST maximum elevation (happening to be larger than the rogue threshold 1.25Hs) was then isolated within each record, along with its temporal profile. The rogue waves show similar profiles, in agreement with the theory of extreme wave groups. We analyze the rogue wave probability of occurrence, also in the context of ST extreme value distributions, and we conclude that rogue waves are more likely than previously reported; the key point is coming across them, in space as well as in time. The dependence of the rogue wave profile and likelihood on the sea state conditions is also investigated. Results may prove useful in predicting extreme wave occurrence probability and strength during oceanic storms.

This paper presents results from an experiment designed to improve the understanding of the relationship between extreme breaking waves and their mechanical loading on heritage offshore lighthouses. The experiment, conducted at La Jument, an iconic French offshore lighthouse, featured several records of wave, current and structure accelerations acquired during severe storm conditions, with individual waves as high as 24 m. Data analysis focuses on a storm event marked by a strong peak in the horizontal accelerations measured inside La Jument. Thanks to stereo-video wave measurements synchronized to the acceleration record we were able to identify and describe the breaking wave responsible for this intense loading. Our observations suggest that this giant wave (19 m high) had a crest elevation high enough to directly hit the lighthouse tower, above the substructure. This paper reveals the potential for conducting ambitious field experiments from offshore lighthouses in order to collect valuable storm waves and wave loading observations. This offers a possible second service life for these heritage structures as in situ laboratories dedicated to the study of the coastal hydrodynamics and its interaction with marine structures. This article is part of the theme issue ‘Environmental loading of heritage structures’.

Given the growing availability of directional spectra of ocean waves, we explore two different statistical approaches to mine large spectra databases: Spectral Partitions Statistics (SPS) and Self-Organizing Maps (SOM). The first method is not new in the literature, while the second one is for the first time here applied to directional wave spectra. The main goal is to improve the characterization of the directional wave climate at a site, providing a more complete and consistent description than that obtained from traditional statistical methods based on integral spectral parameters (e.g., Hs, Tm, θm). Indeed, while the use of integral parameters allows a direct application of standard techniques for statistical analysis, important information related to the physics of the processes may be overlooked (e.g., the presence of multiple wave systems, for instance locally and remotely generated). The two proposed methods do not exclude integral parameters analysis, but they further allow accounting for different events (e.g., with different genesis) independently. Although SPS and SOM are equally valid for both numerical model and observational data, we illustrate their potential using a 37-year long (1979–2015) model dataset of directional wave spectra at a study site in the western Mediterranean Sea. We show that standard integral parameters fail to show the complex and even multimodal conditions at this site, that are otherwise revealed by the directional spectra statistical analysis. Although the processing pathways and the resulting indicators of both SPS and SOM are substantially different, we observe that their results are mutually consistent, and provide a better insight into the physical processes at work.