<figure><img src="image_105.png" /><figcaption>**Fig. 3** Left: 3-D surface points can be estimated by triangulating exiting rays passing through corresponding image points. Right: wave field estimation process. A subset of the stereo frames are used to compute the *extrinsic parameters* (R, T) necessary to create a dense 3-D point cloud for each stereo-pair. Each point cloud is interpolated in a regular surface grid and a spatio-temporal wave field is obtained by stacking all the reconstructed surfaces.</figcaption></figure>

wrt. the epipolar constraint). In all our sequences we obtained hundreds of matches with an average epipolar error ranging from 0.3 to 0.5 pixels. Considered that the epipolar constraint is subject to just 5 degrees of freedom, we believe that such high number of correct matches is a good indication of an actual good calibration of the *extrinsic parameters*.

After the extrinsic calibration, the *wass_stereo* program is executed for each stereo pair to produce a dense point cloud. The number of reconstructed points vary with the scene but is ~3 × 10⁶ points (for 5 Megapixel cameras). A plane is fitted in a least-squares sense to each 3-D point cloud to produce an estimate of the mean sea plane position in the right camera reference frame. The accuracy of the reconstructed plane depends to the number of wave and crest lengths that are visible in the camera field of view¹⁹. To reduce the uncertainty, we take advantage of the quasi-Gaussian nature of the sea surface elevation to average the plane parameters among each record. The obtained average sea plane is then used to compute the transformation mapping the 3-D data from the camera to a geographic reference frame with the z-axis pointing upward with respect to the gravity vector. The details of this transformations are explained in¹⁹.

Each geographically-aligned point cloud is linearly interpolated on a regular horizontal 2-D grid to produce a discretized surface elevation map, which is generally used for wave analysis. In the results presented in this study, the x-axis is set along the cameras supporting bar (positive direction towards the right camera), and the y-axis points away from the cameras. If a sequence of image pairs was collected, the above-mentioned operations are repeated at each instant and the final result will be a (2-D + time) burst of sea surface elevations. An examples of a typical stereo-image pair and the measured 3-D surface geometry can be seen in Fig. 4.

**Experimental setup.** Each wave data set presented in this study was acquired using an experiment setup ad-hoc designed to best represent its initial research purpose. At the time of this publication, this data set contains twelve records: seven recorded at the Marine Hydrophysical Institute platform in the Black Sea; three recorded from the Acqua Alta oceanographic research tower in the Adriatic Sea; one recorded at the Sogheongho Ocean Research Station in the Yellow Sea; one recorded at La Jument lighthouse in the Iroise Sea. For each experimental setup, principal parameters are reported in the Table 1 and details of each station (see Fig. 5) are given in the following paragraphs.

*Black Sea (BS).* The Black Sea data set was acquired by a stereo imaging system mounted on the research platform of the Marine Hydrophysical Institute, 500 meters of the coast next to Katsiveli coast in the Black Sea (44.39°N, 33.98°E). The water depth at the observation area is about 30 m. The stereo video system was mounted 11 m above the sea surface and used a pair of synchronized 5 Megapixel (2048 × 2456 pixels) BM-500GE JAI cameras. The data set acquired in 2011 used cameras equipped with a 5-mm focal lens¹⁰,¹⁷. In 2013, to observe a larger
<figure><img src="image_106.png" /><figcaption>**Fig. 4** Example of stereo-image pair (from the Acqua Alta tower in the northern Adriatic Sea, Italy) and 3-D wave field on top of the right image (the colorscale is proportional to the sea surface elevation $ζ$).</figcaption></figure>

<figure><img src="image_107.png" /><figcaption>**Fig. 5** Location of the four stations with deployed stereo systems for oceanic wave observation. From west to east: La Jument lighthouse (LJ), the Acqua Alta tower (AA), the Marine Hydrophysical Institute (BS), and the Sogheongho Ocean Research Station (YS).</figcaption></figure>

<table><caption>**Table 1.** Stereo-image data sets: Record starting time; acquisition frame rate (fps); number of synchronized pair of images (# imag.); approximate record duration (Durr.); Left-to-right camera distance, baseline (B); Reference to explore the stereo set up and wave data (Ref.).</caption><thead><tr><td>ID</td><td>Record (UTC)</td><td>fps (Hz)</td><td># imag.</td><td>Dur. (min)</td><td>B (mm)</td><td>Ref.</td></tr></thead><tbody><tr><td>BS 01</td><td>2011/10/01 16:18:00</td><td>15</td><td>10828</td><td>7</td><td>2030</td><td>10</td></tr><tr><td>BS 02</td><td>2011/10/04 11:38:00</td><td>12</td><td>14375</td><td>20</td><td>2030</td><td>10</td></tr><tr><td>BS 03</td><td>2011/10/04 13:07:00</td><td>12</td><td>21574</td><td>30</td><td>2030</td><td>10</td></tr><tr><td>BS 04</td><td>2011/10/04 15:30:00</td><td>12</td><td>21575</td><td>30</td><td>2030</td><td>10</td></tr><tr><td>BS 05</td><td>2013/09/22 13:00:01</td><td>10</td><td>17981</td><td>30</td><td>1872</td><td>12</td></tr><tr><td>BS 06</td><td>2013/09/25 12:15:01</td><td>12</td><td>21578</td><td>30</td><td>1872</td><td>12</td></tr><tr><td>BS 07</td><td>2013/09/30 10:20:01</td><td>12</td><td>21578</td><td>30</td><td>1872</td><td>12</td></tr><tr><td>AA 01</td><td>2014/03/27 09:10:00</td><td>12</td><td>43161</td><td>60</td><td>2545</td><td>31</td></tr><tr><td>AA 02</td><td>2015/03/05 10:35:00</td><td>12</td><td>21573</td><td>30</td><td>2545</td><td>—</td></tr><tr><td>AA 03</td><td>2015/05/15 09:00:00</td><td>12</td><td>21552</td><td>30</td><td>2545</td><td>—</td></tr><tr><td>YS 01</td><td>2017/05/13 05:00:00</td><td>10</td><td>6000</td><td>10</td><td>5040</td><td>27</td></tr><tr><td>LJ 01</td><td>2018/01/03 09:39:38</td><td>10</td><td>18000</td><td>30</td><td>5445</td><td>28</td></tr></tbody></table>

area of the sea surface, it was used the same cameras but with wide-angle lenses¹². The cameras were installed on the eastern corner of the deck of the platform, point to a direction 82° clockwise of North. Additionally, in the other side of the platform the sea surface elevation was also measured at a 10 Hz by six restive strings arranged in a centered pentagon of radius 25 cm recorded sea surface elevations with an accuracy of 2 mm providing the data for frequency-directional spectrum estimations in the range of 0.1–1 Hz. A more detailed description of the platform instrumentation is given by²⁵. The wind speed and direction, air temperature, humidity, pressure and water temperature are measured at the center of the platform, 23 m above the sea level by a “Davis Vantage Pro 2” meteorological station.

**Acqua Alta (AA).** The Acqua Alta stereo data set was collected using an imaging system installed on the north-east side of the Acqua Alta oceanographic research tower, located in the northern Adriatic Sea (Italy,
<table><caption>**Table 2.** Experimental conditions: significant wave height ($H_s$); peak wave period ($T_p$); peak wave direction ($D_p$); estimated wind speed at 10-m height ($U_{10}$); wind direction (WD); expected wave age ($C_p/U_{10}$) from deep water linear theory without current $C_p = gT_p/2\pi$; near-surface current speed (C) and direction (CD) from AWAC at AA platform and from X-band radar at LJ.</caption><thead><tr><th>ID</th><th>H<sub>s</sub> (m)</th><th>T<sub>p</sub> (s)</th><th>D<sub>p</sub></th><th>U<sub>10</sub> (m/s)</th><th>WD</th><th>C<sub>p</sub>/U<sub>10</sub></th><th>C (m/s)</th><th>CD (°N)</th></tr></thead><tbody><tr><td>BS 01</td><td>0.30</td><td>3.03</td><td>WSW</td><td>10.7</td><td>WSW</td><td>0.44</td><td>—</td><td>—</td></tr><tr><td>BS 02</td><td>0.36</td><td>2.63</td><td>WSW</td><td>10.1</td><td>WSW</td><td>0.41</td><td>—</td><td>—</td></tr><tr><td>BS 03</td><td>0.45</td><td>3.03</td><td>SW</td><td>12.2</td><td>WSW</td><td>0.37</td><td>—</td><td>—</td></tr><tr><td>BS 04</td><td>0.55</td><td>3.70</td><td>SW</td><td>12.9</td><td>WSW</td><td>0.45</td><td>—</td><td>—</td></tr><tr><td>BS 05</td><td>0.66</td><td>4.30</td><td>E</td><td>8.7</td><td>E</td><td>0.77</td><td>—</td><td>—</td></tr><tr><td>BS 06</td><td>0.41</td><td>4.10</td><td>SW</td><td>6.1</td><td>N</td><td>1.05</td><td>—</td><td>—</td></tr><tr><td>BS 07</td><td>0.65</td><td>5.70</td><td>SW</td><td>15.2</td><td>N</td><td>0.58</td><td>—</td><td>—</td></tr><tr><td>AA 01</td><td>1.36</td><td>4.49</td><td>ENE</td><td>9.9</td><td>ENE</td><td>0.71</td><td>0.24</td><td>45</td></tr><tr><td>AA 02</td><td>1.99</td><td>6.56</td><td>ENE</td><td>12.9</td><td>ENE</td><td>0.80</td><td>0.13</td><td>47</td></tr><tr><td>AA 03</td><td>1.33</td><td>5.69</td><td>ESE</td><td>10.2</td><td>E</td><td>0.87</td><td>0.15</td><td>84</td></tr><tr><td>YS 01</td><td>1.94</td><td>6.70</td><td>SW</td><td>16.0</td><td>NW</td><td>0.65</td><td>—</td><td>—</td></tr><tr><td>LJ 01</td><td>10.03</td><td>13.33</td><td>W</td><td>14.7</td><td>W</td><td>1.41</td><td>0.92</td><td>323</td></tr></tbody></table>

45.32°N, 12.51°E), 15 km offshore the Venice littoral (Italy). The Acqua Alta tower is managed by the Institute of Marine Sciences (ISMAR) of the Italian National Research Council (CNR) and it is the only manned platform in the Mediterranean Sea dedicated to the oceanographic research. On the tower stereo cameras were mounted at 12.5 m above the mean sea surface, looking to northeast (45°N clockwise) and the local water depth in front of the cameras view is about 17 m. The stereo imaging system also uses two BM-500GE JAI digital cameras mounting 5-mm focal length lenses (see$^{26}$). The wind speed and direction are measured at the south-east corner of the tower, about 15 m above the sea level. Supplementary instrumentation (e.g. a Nortek AWAC) was continuously used to assess the stereo observations. More details about this setup can be found at$^{14}$.

**Yellow Sea (YS).** The Yellow Sea data were collected from the Socheongcho Oceanic Research Station (37°25′23.28″N 124°44′16.94″E), managed by the Korea Institute of Ocean Science and Technology. A couple of visible-range, synchronized digital cameras (8-bit grayscale, with 2456 × 2048 pixel resolution and 3.45 µm square active elements) mounting 8 mm distortion lenses, were placed 5.04 m apart and 33 m above the mean sea level on the east side of the station. The cameras set looking to east (90°N clockwise) and were rotated down-looking with an inclination angle of about 25°. At the station, the local depth is on average 50 m, the sea current spectrum is dominated by semi-diurnal tides, with a tidal ellipse having principal axis oriented northwest-southeast, and maximum speed along that direction in excess of 1 m/s. More details about this setup can be found at$^{27}$.

**La Jument (LJ).** La Jument, lighthouse is located offshore of Ushant island, Western Brittany, Iroise Sea, France (48°25′20.00″N 5°8′2.28″W). This lighthouse is extreme exposition to North East Atlantic storms waves and strong tidal currents. The waves that shoal over the very steep up-wave bathymetry can violently break over the lighthouse and generate sea spray that can go up well over the lighthouse lantern. The stereo video data was collected there is part of the DiMe project dealing with the characterization of extreme breaking waves. This lighthouse lies over a rocky platform that drops abruptly on its western boundary. The upper deck of the lighthouse is located at about 45 m above the mean sea level, but it is very sensitive to a macro-tidal conditions that can range up to 8 m. This makes possible the observation of very high sea states in intermediate to shallow waters with a large field of view and a minimal shadowing effect. The bathymetry around it decreases very sharply going toward the ocean. The depth at 50 m from the cameras view is about 30 m and goes to 60 m at 300 m away from the lighthouse. The video cameras were set near to the top of the lighthouse (about 45 m high) and looking at 246°N. The distance between the cameras were 5.445 m. The video system also the same 5 Megapixel BM-500GE JAI cameras with 5-mm wide angle lens (same as$^{12}$, BS_2013 records). The system was set to 10 Hz sampling frequency. More details about this experiment and this lighthouse can be found at$^{28}$.

## Data Records

This data set combines a sample of stereo records acquired at different locations, considering several sea state conditions and related to different research projects. However, the goal is to feed the data set with new records as soon as they will become available from new research campaigns at$^{30}$. A summary of the main sea state characteristics of each experiment is presented in Table 2.

The data acquired at BS in 2011 (BS 01 to 04) is mostly composed by young wave propagating in the same wind direction. This data was used by$^{10}$ to investigate the properties of short breaking waves and compared with the dissipation source function in the energy balance equation$^{17}$ used BS 02 to 04 to investigate the energy level and its directional distribution to investigate non-linear wave interaction at frequencies up to 1.4 Hz and for wave length from 0.6 to 12 m. Based on the 3-D wavenumber/frequency spectrum $E(k_x, k_y, f)$ they separate the linear waves from the bound second-order harmonics and found that the harmonics were negligible for frequencies $f$ up to 3 times $f_p$, but account for most of the energy at higher frequencies. In the range $2f_p$ to $4f_p$, they observed that
<figure><img src="image_108.png" /><figcaption>**Fig. 6** The 3-D surface grid computed by the reconstruction pipeline rendered on top of the original image captured by the right stereo camera. The rendering is produced by the provided *wassncplot* tool together with the mapping between image pixels and 3-D coordinates in the geographical reference frame of the grid.</figcaption></figure>

the full frequency spectrum decays like $f^{-5}$, which means a steeper decay of the linear spectrum. At BS 03¹⁷, observed a pronounced bi-modal direction distribution, with two peaks on either side of the wind direction, separated by 150° at $4f_p$.

The BS 05 to 07, were acquired in 2013 and used by¹² to investigate the longer waves modulation impact on short wave breaking. Those acquisitions consists in bi-modal sea state conditions with short wave breaking. BS 05 consists in a case of longer and shorter wave propagating in the same direction (East). The longer wave was $H_s = 0.4$ m with a peak at 4.25 s, while the local short wave system is dominated by 3 s waves from East and modal amplitude around 10 cm. BS 06 is characterized by longer and shorter waves propagating almost in orthogonal direction, with 0.4 m and 4 s swell and very short short wave driven by the local wind, with 1.8 s peak period and 10 cm amplitude. BS 07 occurs under strong northerly wind conditions, with an 0.65 m opposing swell of 5.6 s peak period from the south-west, 135° from the wind direction. The short wave spectrum has a 0.32 m wave height and 1.8 s peak period from North.

AA stereo images portray space-time wave fields generated by prevailing east northeasterly winds producing, generally, fetch-limited waves in the northern Adriatic Sea. The AA 01 record was acquired during a cross-sea condition, being the dominant wave components aligned with the local wind (ENE) while a swell was produced by southeasterly winds blowing in the central Adriatic Sea. Breaking events at different scales and directions are visible in the stereo images. Space-time wave fields show the presence of second-order harmonics and a bimodal distribution of the short-wave energy. These data were used to investigate the benefit of using stereo observations to calibrate the X-band marine radar MTF³¹. Wave elevations stored in the NetCDF4 file were low-pass filtered at 1.5 Hz to remove the influence of high-frequency quantization noise. AA 02 data were acquired during a ENE wind-forced condition. Wave breaking occur for dominant waves (along the peak direction) and for short waves (angled with respect the peak direction). Occasionally foam stripes aligned with the wind are detectable. AA 03 consists of easterly wave fields. Very few breakers are visible within the images.

YS data include wind-generated 3-D wave fields observed during the passage of an atmospheric front, which led to a wide directional spreading of wave energy. Two independent wave systems were detected in the data, clearly identified in the 3-D wavenumber/frequency spectrum $E(k_x, k_y, f)$. Using this record²⁷, examined 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. Data were also used to analyze the probability of occurrence and the spatio-temporal size of rogue waves, in particular the extent of the horizontal sea surface region they span.

LJ 01 consist in our biggest sea state condition recorded by the moment, with individual wave heights up to 23.6 m. This case was recently used by²⁸ to characterize extreme breaking waves and their mechanical loading on heritage lighthouses at sea. They focus their study in a particular wave breaking event with a crest elevation high enough to pass over the substructure and hit directly the lighthouse tower. This event was marked by a strong peak in the horizontal accelerations measured inside the lighthouse and an extreme wave "runup" that reaches more than 42 m blinding the cameras lenses.

## Technical Validation

The key variables to be validated is the sea surface elevation derived with the stereo processing. Whenever possible, stereo data have been assessed with reference instrumentation expected to have at least the same performance as the imaging system. As many factors may influence the quality of the wave observations, we provide below the description of the principal ones providing the target values for an optimal data set. Five sources of uncertainty can impact the observations: the uncertainty in the internal parameter calibration (internal calibration error, *err*<sub>ic</sub>), the uncertainty in the external parameter calibration (external calibration error, *err*<sub>ec</sub>), the uncertainty in the determination of the corresponding pixels (matching error, *err*<sub>ma</sub>), the uncertainty in the recovery of 3-D coordinates (quantization error, *err*<sub>qu</sub>), the uncertainty in the determination of the transformation between the camera reference system and the water reference system with the elevation-axis vertical and pointing upward (camera orientation error, *err*<sub>co</sub>).

As far as the errors *err*<sub>ic</sub> and *err*<sub>ec</sub> are concerned, the calibration procedures adopted for the analysis of the stereo images here presented followed standard strategies. The internal calibration has been always performed in controlled conditions (laboratory) before the deployment in the field and produced a maximum error of fractional of pixels (<0.5 pixel) that can be considered negligible for all applications. The external calibration was
<figure><img src="image_109.png" /><figcaption>**Fig. 7** Example of left and right stereo image gray values histograms. The histogram of the left image transformed to match the right image is shown with a dashed black line.</figcaption></figure>

<figure><img src="image_110.png" /><figcaption>**Fig. 8** Example of matched pixels between left and right images.</figcaption></figure>

performed using the auto-calibration procedure described in¹⁹, which has been proven to be as accurate as standard procedures, and for the data here presented provided errors of 0.5 pixel on average. To determine the orientation and displacement between the camera reference system and the still sea water surface, and hence camera orientation error, *err*<sub>co</sub>, the strategy proposed by⁸ has been adopted in all cases. This method that has been proved to be accurate on field²⁶,³² and synthetic¹⁹ data.

The reliability of the matched pixels is determined by *err*<sub>ma</sub>, which is governed, on the one hand, by the quality of the calibration procedure and, on the other hand, by the similarity between the left and right images. In general, sharper images are matched with a higher accuracy, as well as accurate matching requires that left- and right-image gray values belong to the same range. These conditions were obtained using small exposure time, around 2 ms at maximum, and gain factor below 30%. Within these limits, those two values were adjusted to fulfill the condition the image histograms have the same median values (around 110–120 for 8-bit images) and span. For difference in median gray values larger than around 10, an histogram matching procedure can be adopted (Fig. 7). A good indicator of the impact of *err*<sub>ma</sub> is the number of pixel matched (otherwise discarded by the dense-stereo processing). For the stereo cases here provided most of the image pixels were matched (around 3 millions for 5 Mpixel cameras), with missing correspondences only on the few bright and dark uniform regions (Fig. 8). In addition, occasional mismatches may occur close to the edges of the matched area. To account for those potential errors (resulting in unwanted spikes), for the wave analysis (e.g. space-time spectral or statistical) it is recommended to consider only those points lying in the central part of the matched area.

With the left- and right-image pixel matched, what remains to quantify is the value of the 3-D err<sub>qu</sub> for each surface point. It depends on the camera cell size and pixel numbers, the focal length, the baseline, the camera reciprocal orientation, and the distance from the stereo-camera system to the scene of interest. An example of the spatial distribution of the quantization error²² is shown in Fig. 9, for a stereo camera installation 33-m high.
<figure><img src="image_111.png" /><figcaption>**Fig. 9** Example of the 2-D horizontal map of the vertical component (*err*<sub>*z*</sub>) of the quantization error within the field of view of the stereo cameras. Stereo system specifications: height of 33 m, baseline of 5 m, focal lens length 5 mm, 5 Megapixel cameras.</figcaption></figure>

<figure><img src="image_112.png" /><figcaption>**Fig. 10** BS records collected in 2011 and 2013: frequency spectrum *E*(*f*) estimated from the stereo system, compared with data from a wire wave gauge mounted on the platform. (Left) Example of BS 01 wave spectrum recorded by stereo video system compared with a wave gauge. The spectrum from stereo data is averaged over a 10.8-m side square analysis window, and thus the random sampling error is smaller for the shorter waves with many uncorrelated waves in the field of view. (Right) Comparison between wave gauge and stereo video wave spectrum for all BS records provided at this dataset. The color scale represents the wave frequency of that sampled data. In the gray box are shown the squared Pearson correlation coefficient (*R*<sup>2</sup>), the Root Mean Square Error (RMSE) and the Normalized Root Mean Square Error (NRMSE).</figcaption></figure>

<table><caption>**Table 3.** Expected root mean square error RMS and estimated high frequency limit *f*<sub>lim</sub> for each experimental setup.</caption><thead><tr><th></th><th>RMS<sub>z</sub></th><th>RMS<sub>x</sub></th><th>RMS<sub>y</sub></th><th>f<sub>lim</sub>(Hz)</th></tr></thead><tbody><tr><td>BS 01–04</td><td>0.01 m</td><td>0.01 m</td><td>0.08 m</td><td>1.2</td></tr><tr><td>BS 05–07</td><td>0.01 m</td><td>0.01 m</td><td>0.08 m</td><td>1.4</td></tr><tr><td>AA 01–03</td><td>0.01 m</td><td>0.02 m</td><td>0.05 m</td><td>1.5</td></tr><tr><td>YS 01</td><td>0.03 m</td><td>0.05 m</td><td>0.17 m</td><td>0.9</td></tr><tr><td>LJ 01</td><td>0.09 m</td><td>0.14 m</td><td>0.35 m</td><td>0.5</td></tr></tbody></table>
When other sources of data were available, the stereo video system was compared with other sensors (see the Reference studies provided in Table 1). Figure 10 exemplifies a frequency spectrum $E(f)$ estimated from the stereo video system and a wave gauge at BS in 2011 and 2013. More detailed validation for each stereo video dataset can be found at the acquisition documentation (see$^{10,12,27,31}$).

However, this kind of comparison was not always available for all the data provided in this study. As a consequence, the quantization error is the most direct value to estimate the expected accuracy of the observations. Table 3 reports the root-mean-square (RMS) values of the three components of $err_{gu}$, namely vertical ($RMS_z$) and 2-D horizontal ($RMS_x, RMS_y$), and the estimated low-high frequency limits ($f_{lim}$) for each experiment.

The assessment presented in Table 3 was optimized according to different research objectives. So these results could be adjusted for other study purposes, for example, in most of the cases, the quantization error could be reduced by looking at a smaller region closer to the cameras, and the high and low-frequency limits may be improved by applying different filtering techniques. So the results here presented follows our specific interests, but by providing in this study the raw stereo images and all the processing codes we invite the scientific community to improve this processing according to its own interest.

## Usage Notes

The stereo-image data set is archived at$^{30}$ https://sextant.ifremer.fr/eng, https://doi.org/10.12770/af599f42-2770-4d6d-8209-13f40e2c292f. Data provided in this repository are organized according to the station and year of the experiment (e.g. BS_2011, BS_2013, AA_2014 ...). Each record is characterized by the time that the acquisition starts and the frame rate in Hz, e.g. BS_2011/2011-10-01_16-18-00_15 Hz. The following data are publicly available there:

1. The raw uncompressed images (8 bit gray scale Tagged Image File TIF or Portable Network Graphics PNG formats) for the synchronized left and right stereo cameras. These images are stored in "input" folder. "NNNNNNN_01.tif, .png" correspond to left camera images, "NNNNNNN_02.tif, .png" correspond to the right camera images and NNNNNN is the sequential image number since the record start.

2. The WASS stereo processing configuration files used to analyse images are stored in "config" folder: distortion_00.xml and distortion_01.xml contains the lens distortion; intrinsics_00.xml and intrinsics_01.xml correspond to the intrinsic cameras calibration parameters; matcher_config.txt and stereo_config.txt are the WASS pipeline configuration files. For more detail information on how to modify and use these files see$^9$.

3. A subset of post-processed sea surface elevation space-time fields bi-linearly interpolated on a regular 2-D horizontal uniform grid is stored as NetCDF 4 format file inside the "nc" folder. Decoding information and metadata are included in each file.

Here we provide a full dataset for twelve stereo video records, including examples of post-processed Netcdf outputs, the raw images and the link to the codes repository. So the users can either work with the surface elevation map samples or download the images and reprocess it according to their needs.

## Code availability

All the data processed in this dataset used the WASS ("An open-source pipeline for 3-D stereo reconstruction of ocean waves") code version 1.4 provided by$^9$ and available at http://www.dais.unive.it/wass (the WASS is a full-frame and dense-matching evolution of the previous stereo code developed by$^{8,26}$ and further refined by$^{10}$). This tool is able to (i) reconstruct the sea surface by means of a dense cloud of 3-D points from stereo images, (ii) compute the extrinsic parameters of the stereo rig without the need of tedious calibration on-the field, and (iii) provide the parameters necessary to transform the wave data to a local geographical reference system. The fast 3-D dense stereo reconstruction is based on the OpenCV library$^{29}$ and analyzes the photometrically distinctive features of the water surface to eventually provide the 3-D surface elevation map. When the stereo images are processed by WASS, the generated 3-D point cloud is re-sampled in a uniform grid and the final space-time surface elevation is stored in a standard NetCDF4 file.

We developed an additional tool (https://github.com/fbergama/wassncplot) that provides the mapping between each image pixel (either from left or right camera) to the 3-D geographical reference frame of the grid stored in the NetCDF4 file. This way, any further processing can take into account both the luminance of each pixel and its 3-D location onto the sea-surface. Possible applications include the analysis of white-capped areas, the 3-D tracking of floating objects and measuring the shape and extent of individual waves. Note that this mapping is in general one-way (ie. from image to 3-D space) since cameras are angled with respect to the sea-surface and some 3-D points in the back-side of the waves are occluded by the crests. In this context, the *wassncplot* tool computes the correct intersection between the 3-D ray in space passing through the camera center and a pixel *p* with the gridded surface. Since multiple intersections may occur, only the one nearest to the camera is considered for the mapping. Operatively, the operation is performed by projecting each triangle of the grid to the image plane corresponding to one of the two stereo cameras. The coordinate of each grid vertex is interpolated considering the barycentric coordinates within each triangle corrected by the depth of the point. A Z-buffer is used to discard occluded points and produce the final mapping as a 3-dimensional data cube *D* of size (*W* × *H* × 3) in which the first two dimensions spans the image space and the third the 3-D coordinates of a point (ie. *D*<sub>*i*,*j*,0</sub>, *D*<sub>*i*,*j*,1</sub>, *D*<sub>*i*,*j*,2</sub> are the *x*, *y*, *z* coordinates of the 3-D point corresponding into the pixel *i*, *j* in the image). Optionally, the tool can produce a rendering of the 3-D surface grid on top of the original images for a qualitative evaluation of the reconstructed data (See Fig. 6).

Received: 13 February 2020; Accepted: 9 April 2020;
Published online: 15 May 2020
## References

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## Acknowledgements

This work has been done in the framework of the DiMe, CARAVELE projects, which benefit from French government support managed by the Agence Nationale de la Recherche under the program Investissement d'Avenir ANR-10-IEED-0006-14, ANR-10-IEED-0006-26. YS data collection was supported by the project "Construction of Ocean Research Stations and their Application Studies", funded by the Ministry of Oceans and Fisheries, Republic of Korea. AA data collection was funded by the Flagship Project RITMARE— The Italian Research for the Sea—coordinated by the Italian National Research Council and funded by the Italian Ministry of Education, University and Research within the National Research Program 2011–15. This work has been partially 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.

## Author contributions

P.V.G. and A.B. equally contributed to the manuscript and shared first authorship. F.A., A.B., F.B., J.-F.F., F.L. and P.V.G. wrote the manuscript and analysed the results, J.Y. contributed to the setting up the J.-S.S. experiment and V.D. contributed in the BS experiment and provided additional wind and wave data. F.B. developed and maintains the code used to process stereo images.

## Competing interests

The authors declare no competing interests.
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© The Author(s) 2020
# Chapter 6

## Perspectives

This chapter presents perspectives of research activities, that for some of them directly follow the work introduced in the previous chapters and for others, constitute new research topics. They span from the definition of the slamming loads on offshore wind turbines, to the characterization of breaking waves effects on satellite wind measurements and air-sea interactions.

### 6.1 Modeling waves in extreme conditions

Being able to simulate extreme sea states with spectral models is crucial to define the design sea state and the corresponding design breaking wave used to determine the ULS slamming loads. Here we shall continue our efforts in developing further the WW3 model by exploring new parameterizations for the wave breaking source term and investigating new observational means to characterize breaking waves and their spatial distribution. Also, because wind and (breaking) waves are highly coupled in storm conditions, the development of air-sea coupled models should be intensified at FEM in the coming years (see section 6.3.2).

#### 6.1.1 Deep and intermediate water wave breaking dissipation parameterization

Efforts are undergoing in the DiMe and CASSIOWPE projects with F. Leckler (FEM) to implement in WW3 the new wave breaking statistics framework presented in Chapter 3 [Stringari et al., 2021b], extended to the full wave energy spectrum. The approach relies on the Phillips [1985] and Duncan [1981] findings showing that the spectral wave dissipation source term could be formulated as:

$$S_{ds}(c) = bg^{-1}c^5\Lambda(c)dc \qquad (6.1)$$

Here b is a tuning constant reflecting the breaking severity. Such type of wave breaking source term has been recently proposed by Romero [2019] in WW3.
His model for $\Lambda(c)$ is based on empirical considerations related to the spectral saturation introduced by *Banner et al.* [2002]. Our main contribution compared to the latter work, will be to introduce a theoretical formulation for $\Lambda(c)$ using the same Gaussian field model as in *Stringari et al.* [2021b], i.e., accounting for the joint statistics of crest fluid velocities and phase speeds. This is done jointly with the validation of the linear-equivalent breaking criterion of *Stringari et al.* [2021b], currently explored by F. Hulin, PhD student in the DIMPACT project, (see section 6.2.2), since this concept is at the center of the new source term. Our objective will be first to validate our parameterization for $\Lambda(c)$ with field observations. Then, the only free parameter to tune, will be the breaking strength, $b$. Future research will focus on the parameterization of $b$ based on physical consideration. In this regard, the recent effort published by *Derakhti et al.* [2018] is inspiring. They suggested, from numerical simulations, that $b$ is correlated to the breaking severity parameter:

$$ \Gamma = T_b \frac{(du_c/c)}{dt}, \qquad (6.2) $$

with $T_b$ the breaking wave period. Further recent and unpublished progresses by M. Prevosto (in the DIMPACT project), to obtain $\Gamma$ from Gaussian field theory also offer promising perspectives of improvements for the parameterization of eq. 6.1.

Still the lack of $\Lambda(c)$ observations remains a major difficulty to achieve the objectives presented above. The perpetuation of La Jument real scale lab is aiming to fill this gap. This winter, the deployment of our stereo-video system will aim at capturing storm breaking waves in deep-to-intermediate water (80m depth), representative of the floating offshore wind turbines environment. They will help validating our $\Lambda(c)$ parameterization and gathering detailed observations of the severity of field breaking waves in storm conditions.

### 6.1.2 Shallow water wave breaking dissipation parameterization

The applicability and relevance of equation 6.1 in shallow water should also be explored. Because waves become non-dispersive in shallow water, it may require to be adjusted. It seems also relevant to revisit the strategy proposed by *Thornton and Guza* [1983] who developed a wave breaking dissipation parameterization based on two physical components: a breaking wave height distribution and a theoretical dissipation rate per unit crest length, inspired from the bore model [*Le Mehaute*, 1962].

Accurate observations of breaking waves in the surf zone will be useful to develop new breaking wave height distributions, extending the work of *Thornton and Guza* [1983]. Preliminary tests performed in the surf zone at Biarritz beach
in the frame of the MARLIT project<fnref n="1" /> (see Figure 6.1.1), suggest promising capabilities of stereo-video systems through a comparison with pressure observations transferred to elevation using Bonneton et al. [2018] method. Cross-comparison with other instruments, such as lidars [Martins et al., 2020] or single camera systems [e.g. Almar et al., 2012] would be helpful in further assessing the limitation of the instruments. One important challenge will be to assess the ability of the sensors to capture the elevation of foamy breaking crests.

These efforts may contribute to further improve shallow water breaking source terms for WW3 but also to provide the industry with information about the statistics of breaking crest height, $\eta_b$, intervening in the slamming loads (and corresponding moment of force) to validate and/or improve the theoretical distributions available in the literature [e.g. Wu et al., 2016]. For this latter research axis, the incorporation of bottom slope effects in the crest heights distribution models could bring significant improvements [Zhang et al., 2019]. These perspectives should finally help to refine the characteristics of the design breaking wave used to assess the design loads, (see section 6.2).

Regarding the dissipation rate per unit length of breaking crest, $\epsilon$, it seems relevant to investigate the progresses brought by Grasso et al. [2012] and more recently by Martins et al. [2020] on the dissipation rate of shallow water breaking waves and to attempt to incorporate them into a new wave breaking source term. Wave tank experiments following the continuous PIV efforts deployed at IRPHE (Marseille France) [e.g. Branger et al., 2007; Kimmoun and Branger, 2007] could also provide more insights on the turbulent and dissipative wave breaking processes.

### 6.1.3 Characterization of the spatial variability of coastal wave fields

Bottom-fixed offshore wind turbines will likely be exposed to breaking waves. Still, if the up-wave bathymetry is uneven, the occurrence rate and possibly the severity of the breaking wave can be different across a given offshore wind farm. Informing the wind farm developers on the areas exposed to high breaking waves could help them optimizing the turbine siting on one hand and the maintenance plan on the other hand.

Still, relevant observations are required to progress in the assessment of the spatial wave energy variability. In the present document we have presented an original approach (see Chapter 4 and Varing et al. [2021b]) to evaluate the numerical models skills in conditions featuring sharp gradients of wave energy using SAR information. Still, the SAR images processing assumes a quasi linear relation between the normalized radar cross section and the wave field amplitude which

<footnote n="1">¹The MARLIT project, led by the foundation AZTI, was co-funded by the European Union through the POCTEFA program.</footnote>
<figure><img src="image_114.png" /><figcaption>Figure 6.1.1: Top panel : stereo-reconstruction of the sea-surface elevation in the surf zone at Biarritz Beach, France, on March 30, 2021. The color gives the sea surface elevation above the mean sea level. Bottom panel: comparison between the wave elevation signals derived from a stereo-video system (dashed lines) and pressure sensors (solid line) deployed at two different depth in the surf zone. The results are from F. Leckler and R. Duarte (FEM). This work was conducted as part of a collaboration between FEM and the center Rivages Pro Tech of SUEZ in the framework of the MARLIT project.</figcaption></figure>
can be questioned. Other instrumental solutions should be explored to evaluate
the validity of this assumption. X-band radar could represent a potential solution
but the transfer function between the radar signal and the wave information, es-
pecially in a wave-by-wave framework is quite empirical and the same questions
raised for the SAR solution also apply. The stereo-video system used in the DiMe
project offers an interesting alternative, as discussed in section 6.1.2. The scale
of the stereo-video observed area (O(100m)) is however smaller than that of the
SAR images (O(100km)) and to a lesser extent than that of the X-band radar
(O(1km)), but cross-comparisons performed at small (stereo-video) scale should
bring valuable insights on the capabilities of the different instruments.

Statistical downscaling of low resolution wave fields from spectral models, using artificial intelligence and different sources of higher resolution wave data (from SAR or phase-resolving models), also carries an interesting potential for innovation. As a starting point, the approach deployed by He et al. [2015] for wind fields statistical downscaling by could be followed.

The Guérande bank (France) bottom-fixed offshore wind farm seems a good candidate to apply new observational tools able to capture wave focusing areas. The farm is being deployed over a shoal preceded by a rather steep and uneven slope susceptible to cause wave energy focusing inside the farm. Because the construction is in progress, the observations will not be useful to optimize the farm layout but could be employed to identify the offshore wind turbines that will be more exposed to intense wave/slamming loads and therefore possibly requiring a tighter monitoring and maintenance plan.

## 6.2 Estimation of slamming loads on offshore wind turbines

Slamming loads on offshore wind turbines still concentrate a number of chal-
lenges that need to be faced to reduce the safety factors applied during the ULS
design. Here we shall address the question of the breaking severity and of its
parameterization and the development of engineering methods based on linear
wave theory.

6.2.1 Determining the severity of breaking waves

As mentioned is section 6.1.1, recent efforts by Derakhti et al. [2018] have demon-
strated that the breaking-induced dissipation parameter *b* was correlated to the
severity parameter Γ given in eq. 6.2. It seems relevant to evaluate whether
these findings could be useful to progress on the definition of simple engineering
formula. More precisely, the classical engineering slamming load formula pre-
sented in equation 5.1 relies on the curling factor λ that, in theory, represents
the portion of the wave crest that is vertical. In practice, λ cannot be accurately
measured, since, at breaking onset (and after) the wave face is only locally vertical. Applying the strict definition of $\lambda$ then lead to values tending toward the vertical resolution of the observed or model elevation data. The estimation must then rely on some arbitrary threshold slopes, making $\lambda$ more a tuning parameter than a physical variable carrying the severity of the wave.

In the DIMPACT project, Computational Fluid Dynamic simulations will be implemented by M. Batlle Martin (postdoc, DIMPACT project) and J. Harris (ENPC) to investigate with F. Hulin the relation between $\Gamma$ and the $\lambda$ parameter and possibly elaborate new strategies to improve equation 5.1. Further work by M. Prevosto (FEM) are conducted to estimate $\Gamma$ and $\lambda$ for linear wave using similar Gaussian approaches as in Stringari et al. [2021b]. If this effort is successful, combined with the linear-equivalent breaking criterion introduced by Stringari et al. [2021b] and currently investigated by F. Hulin, this would offer a complete framework to estimate slamming loads in global simulations of floating offshore wind turbines usually performed with linear waves, as further developed in the next section.

### 6.2.2 Linear-Equivalent breaking criterion and severity

Varing et al. [2021b]'s breaking onset criterion is able to detect breaking onset of nonlinear waves and can be applied to numerical models able to simulate such type of waves. However, for the design of floating offshore wind turbines, the industry employs numerical hydro-aero-elastic codes, also known as "global models", to simulate the turbine motions and loads on the structure. Because of computational power limitation, the waves are represented using the linear wave theory. Disregarding the linear wave theory limitations, it could be convenient to detect breaking onset in these linear waves simulations to account for slamming loads along the turbine design process.

The first step to apply slamming loads to the structure is to capture breaking onset of the waves passing through the structure. Current efforts are ongoing in the DIMPACT project to incorporate the linear-equivalent breaking criterion presented in [Stringari et al., 2021b] in global models of floating offshore wind turbines.

F. Hulin, is also currently applying a numerical wave maker in the Fully Nonlinear Potential Flow Model from Grilli and Subramanya [1996] to simulate focused wave packets in deep water. The joint analysis of the nonlinear wave packets and of their linear "twins" demonstrates that the linear-equivalent breaking onset threshold is close to 0.3, with a rather low spread around this value, for the limited number of simulations examined so far.

To go further, the numerical approach developed by F. Hulin will be replicated in Ifremer's wave tank to confirm his preliminary results with observations and different types of breaking waves.

The next step will be to verify that the actual slamming loads magnitude
can be evaluated knowing the linear wave properties, only. This will especially requires to infer the severity of the "linear" breaking waves, currently expressed by the curling factor $\lambda$ in equation 5.1. As discussed in the previous section, it seems that the $\Gamma$ parameter (eq. 6.2) from Derakhti et al. [2018] could be a more robust way to track the breaking severity, in place of the curling factor $\lambda$.

Current work from M. Prevosto provides a theoretical way to assess $\Gamma$ from dynamic properties of the linear waves and the validity of the approach is currently being examined.

Field observations of the geometry of the storm breaking waves will also help progressing in the definition of the breaking wave to consider for the ULS design. The 2021-22 experiment conducted from La Jument lighthouse in the frame of the DIMPACT project aims exactly at providing the required information. The stereo-video images will be processed to obtain statistical information on the shape and slope of breaking waves, replicating the study from Schwendeman and Thomson [2017] but with a focus on large storm breaking waves.

If all these efforts are confirmed, and the road is still long, the DIMPACT project would have bring a significant contribution to the development of more accurate engineering tools to account for slamming loads on offshore wind turbines.

## 6.3 Application to wind characterization

The offshore wind industry requires a finer estimation of the wind resource and wind design conditions to continue decreasing its $L_{CoE}$. Any improvement in the wind characterization indeed results in large cost reduction. For instance, a reduction of 0.1 m/s in the wind resource uncertainty resulted in a gain of 10 million pounds a year for a commercial wind farm, with a 25-year lifetime, in United Kingdom [Hasager et al., 2013]. Large CAPEX gain may also be expected with finer information on the extreme wind and wave conditions taken as input of the offshore wind turbines ULS design. Such conditions are prone to high uncertainties due to the obvious lack of observations needed to progress on the understanding of the peculiar physical processes governing the atmosphere and ocean and their coupling.

This section presents research perspectives linking wave breaking to high-wind retrieval from space and to the parameterization of the heat and momentum fluxes at the air-sea interface. They will aim to provide reliable winds observations together with more accurate numerical simulations of the wind fields, with a focus on extreme conditions where the air-sea coupling reaches its apex.
### 6.3.1 Wave breaking and wind retrieval from space

Satellite measurements are sometimes the only source of information regarding wind at sea, especially in presence of extreme conditions such as hurricanes that often destroy any sensors deployed at sea. The Synthetic Aperture Radar (SAR) measurements collected, for instance, by the European Space Agency with the Sentinel constellation, allow to capture the entire wind field of hurricanes crossing the satellite track, with a high resolution (O(100-1000m)). This kind of information is crucial for the offshore wind industry that is targeting areas exposed to hurricanes whose extreme winds and shear may exceed the design standards [Worsnop et al., 2017]. This question will likely become more and more critical with the foreseen effect of climate change on the hurricanes intensification.

Surface winds can be obtained from radar measurements taken from space through the interpretation of the normalized radar cross section (NRCS) that is affected by the Bragg scattering mechanism [Donelan and Pierson Jr, 1987; Romeiser et al., 1994] and non-Bragg scattering effects including impact of the breaking waves [Phillips, 1988]. Hence the total NRCS of the surface $\sigma_0^p$ can be written as [Kudryavtsev et al., 2003a]:

$$ \sigma_0^p(\theta) = \sigma_0^{br}(\theta) + \sigma_{sp}(\theta) + \sigma_{wb}(\theta) \quad (6.3) $$

With $\sigma_0^{br}(\theta)$ the Bragg scattering contribution, $\sigma_{sp}(\theta)$ the specular reflection contribution and $\sigma_{wb}(\theta)$ the breaking waves contribution.

Kudryavtsev et al. [2003b] express then the breaking wave contribution for a radar incidence $\theta$ as $\sigma_{wb}(\theta) = q\sigma_{0wb}(\theta)$ with $q$ the fraction of the sea surface covered by breaking waves and $\sigma_{0wb}(\theta)$ the NRCS of the breaking foam patches given by:

$$ \sigma_{0wb}(\theta) = (\sec^4\theta/s_{wb}^2) \exp(-\tan^2\theta/s_{wb}^2) + \epsilon_{wb}/s_{wb}^2 \quad (6.4) $$

Here, $\epsilon_{wb}/s_{wb}^2$ is a breaking wave self-similarity parameter proportional to the ratio of the breaker thickness to its length and $s_{wb}^2$ is the mean square slope of the breaker surface.

Finally, $q$ is the fraction of the sea surface covered by breaking patches, parameterized by:

$$ q = C_b \int_{c_{min}}^{\infty} c\Lambda(c)dc \quad (6.5) $$

with $C_b$ a constant to be determined and $c_{min}$ the phase speed of the shorter breaking wave influencing the NRCS. Kudryavtsev et al. [2003b], applying their model showed that the effect of breaking waves should be considered to correctly parameterize the radar modulation transfer function and infer surface wind speeds with accuracy.
Here we review the efforts conducted in the DiMe and CARAVELE projects to refine all the parameters of interest here, i.e., $s_{wb}$, $q$, and $\epsilon_{wb}$ and the perspectives to provide all the information required to assess the NRCS associated with breaking waves, $\sigma_{wb}$ given by 6.4.

As shown in Chapter 3 the DiMe project has brought a breaking statistics parameterization for the dominant waves [Stringari et al., 2021b]. With F. Leckler (FEM) we are currently trying to extend this approach to the entire spectrum and provide a solution for $\Lambda(k)$ and $q$ (see section 6.1.1).

Other efforts conducted in the CARAVELE project, with P. Guimaraes addressed the self-similarity of the breaking waves ($\epsilon_{wb}$) through an analysis of very large number of breaking waves collected in the black sea. The study did not allow to identify any breaking wave self similarity. We hypothesize that this is the result of the narrow range of wave conditions considered. To explore this assumption, the database will be extended by adding larger/longer breaking waves observed from La Jument over the coming winter 2021-22.

Improvement and validation of models for $s_{wb}^2$, the mean square slope of the breaker surface requires lab experiments. Ericson et al. [1999] explored the effect of breaking area on X-band backscatter, through laser sheet measurements of a stationary breaking wave generated by a hydrofoil. Although of great interest, the representativeness of the standing breaker roughness can be questioned since the breaking waves that will affect the radar backscatter at sea are wind-generated, irregular, non-stationary and 3-dimensionnal. This has motivated a research effort conducted at the SUSTAIN facility at the RSMAS. Two experiments (September 2019 and 2021) were conducted in the frame of the CARAVELE project. The experiments involved the SUSTAIN team led by B. Haus (RSMAS) and a FEM team made of P. Guimaraes and myself.

The first experiment consisted in the deployment of stereo-video system, a polarimetric camera, an infra red camera and a wave wire (see figure 6.3.1) to explore the mean square slope of the breaking areas $s_{wb}^2$ under high wind conditions (from 11 to 33m/s in the wave tank). The data analysis performed by P. Guimaraes, suggested that the breaking patches exhibit an higher roughness and therefore a higher mean square slope than non breaking areas. The work is unpublished, waiting for a proper validation of the stereo-video signal with a wave probe (that malfunctioned during the first experiment). The second experiment reproduced the instrumental setting of the first one but with the addition of a C-band radar. The objective will be to qualify the effect of the breaking patches on the radar backscatter and attempt to validate and/or refine the model proposed by Kudryavtsev et al. [2003b]. The dataset remains to be explored, and this effort will require to setup a new research project, since the CARAVELE project that has supported the experiments is coming to its end. To make the best of the observational dataset, the future research effort should involve contribution from specialists of the radar measurements and satellite observations.
<figure><img src="image_115.png" /><figcaption>Figure 6.3.1: Top: side view of SUSTAIN tank during an acquisition, with a sonic anemometer mounted next to the stereo-video area. Bottom left : instrumental setup. Bottom right: Lightning conditions used during the stereo-video record.</figcaption></figure>
## 6.3.2 Air-sea coupled modeling

During storms and hurricanes, the coupling between the ocean and the atmosphere must be considered as shown by Larsén et al. [2003]; Bouin and Lebeaupin [2020]; Pineau-Guillou et al. [2020] to properly capture the variables of interest for the offshore wind (e.g. peak wind speed at hub height, wind shear or wave height). In such severe conditions, breaking waves play a key role in the momentum, latent and sensible heat flux at the air-sea interface.

### 6.3.2.1 Effect of breaking waves on the momentum flux at the air-sea interface through air flow separation

The shape of the sharp breaking crests causes an air-flow separation revealed and confirmed by wind-wave tank experiments performed by Banner and Melville [1976] and Reul et al. [1999]. The latter demonstrated the existence of strong recirculating air-flow over the downwind face of the breaking wave, carrying intense vortices. Further numerical experiments by Suzuki et al. [2013, 2014] have shown the influence of the dominant breaking on different atmospheric parameters, including the drag coefficient and mean wind vertical profile. An impressive lab experiment study carried out by Buckley et al. [2020] revealed that this air-flow separation occurs for any type of wave, breaking or not, but was largely increased over breaking wave crests. These lab observations of air-flow separation led to the development of sea drag parameterizations to incorporate this effect in atmospheric models. Makin and Kudryavtsev [2002a] formulated the separation stress as:

$$ \tau_s = 0.5 \int_0^\infty u_s^2 \cos \theta \Lambda(c) dc \qquad (6.6) $$

where $u_s$ is the reference wind speed.

Recent efforts brought by Fernandes et al. [2021], in the frame of the CAR-AVELE project have led to a parameterization of the air-flow separation effect above breaking wave. It seems to reproduce the observed decrease of the wind drag at high wind speed, translating the fact the "detached" wind feels a smoother surface. Again it is obvious that finer parameterization of $\Lambda(c)$ (see section 6.1.1) may lead to improved formulation for the air flow separation wind stress which we hope will reflect into more reliable atmospheric forecasts, especially at high wind speeds. Still, breaking waves induce other important heat and momentum fluxes because of the sea spray droplets they eject in the atmosphere as will be further discussed in the next section.

### 6.3.2.2 Effect of breaking waves on the momentum and heat flux at the air-sea interface through sea spray generation

Because of its importance in the physics of hurricanes, the effect of sea sprays on the heat and momentum fluxes have motivated an important corpus of pa-
pers [e.g. Andreas, 1992; Bao et al., 2000; Perrie et al., 2004; Fairall et al., 2009; Soloviev and Lukas, 2010; Bao et al., 2011]. The different parameterizations developed to account for the sea spray effects on the heat and momentum turbulent fluxes at the air-sea interface [Veron, 2015] are beyond the scope of the present document and beyond my current expertise. Still, it is interesting to note that the droplet source function, that is at the center of the sea-spray mediated heat and momentum fluxes is generally expressed as [Fairall et al., 2009; Laussac et al., 2018]:

$$S_n(r, U_{10}) = W(U_{10})f_n(r) \qquad (6.7)$$

With $W(U_{10})$ being the area coverage by breaking foam and $f_n(r)$ the size distribution representing the production of a fully whitecap covered sea. This formulation can be questioned, first because whitecap coverage accounts, indistinctly, from the active breaking foam, attached to the breaking crests and to passive breaking foam that remains in the wake of the breaking crests. This results in large uncertainties, since the most important droplets in the heat and momentum fluxes [Veron, 2015] are the largest one that are released by the actively breaking crests, whose effects are diluted in the $W(U_{10})$ parameterizations. Indeed, $W(U_{10})$ contains both active and passive foam, and foam persistence depends on many environmental parameters [e.g. Wu, 1988].

In the CASSIOWPE project, efforts are conducted to accommodate for the effect of the actively breaking crests in the sea spray generation function. The work carried out by S. Brumer (FEM-LOPS) to develop new heat and momentum flux parameterization in a Ocean-Wave-Atmosphere model, will incorporate the new $\Lambda(c)$ parameterization under development with F. Leckler (FEM), and extending the work by Stringari et al. [2021b] (see section 6.1.1). Continued efforts, from La Jument lighthouse, will provide the material for validation of our $\Lambda(c)$ parameterization under high wind conditions. Potential findings regarding the severity of breaking waves and the $\Gamma$ parameter (section 6.2.1 and eq. 6.2) could also be useful in refining the source function (eq. 6.7). Indeed, the quantity and size of droplets ejected by breaking waves possibly depending on their severity.

We further note that the knowledge that will be accumulated through the CASSIOWPE project, may be of interest, not only for wind resource or design conditions characterization but also for the corrosion of the offshore wind turbines, since sea spray and therefore salt can be transported at altitudes high enough to impact hub components.

## 6.4 Development of real scale laboratories

Although this is not strictly a research axis, it seems important to stress that real scale labs are valuable tools to provide the observations required to face
the research challenges presented in this chapter. Deploying, developing and perpetuating them will also require intense efforts.

### 6.4.1 Perpetuation of La Jument laboratory

La Jument lighthouse has proven to be an appropriate spot to study extreme breaking waves and their interactions with offshore structures [Filipot et al., 2019]. Its location over a rocky platform rapidly plunging eastward, reaching depth of about 80m at about 500m away from the tower, allows to cover a range of water depth relevant for both the bottom fixed and floating offshore wind turbines. The altitude of the lantern further warranties some protection for the onsite remote sensing instrumentation, to survive the worst winter storms. These storms generate waves with a 10-year return period significant wave height of 11.8m which is well above most of the design (50 year-) significant wave heights found along the French coastline. This means that useful information regarding the properties of the extreme waves can be collected over a short period of time (typically a few winters). As an illustration, during a "moderate" storm (January 3, 2018, $H_s \approx 10$m) a 24.2 m-high wave was captured by our stereo-video system. It also benefits from onboard electricity generator, with enough power to deploy a large range of sensors.

On top of gathering valuable wave observations, La Jument enabled us to develop and test an instrumental protocol to study the interaction of large breaking waves with offshore structures. We demonstrated [Filipot et al., 2019] that this protocol provides relevant information to further understand extreme structural responses by tracking back the impacting wave and dissect it.

Our current field experiment (winter 2021-22) focuses on the observations of large breaking waves in the far field, i.e. in about 80m depth, 500m to the west of lighthouse. The main application is to obtain information on the statistics of occurrence and geometric-kinematic properties of large breaking waves for the design of floating offshore wind turbines.

### 6.4.2 Implementation of a monitoring system on a real scale offshore wind turbine

The experience accumulated from the lighthouse drove us to setup the DIMPACT project that is supporting the deployment of the same experimental protocol on the Zefyros floating offshore wind turbine (former Hywind Demo deployed in Norway). The objective is to collect information on the slamming loads on the spar-type turbine in order to validate the engineering methods that are being developed in the project. Replicating La Jument setting, a stereo video system deployed from the main deck will collect information on the geometry of the incoming slamming waves, 9 pressure sensors, hosted in steel boxes attached to
the hull will provide information on the hydrodynamic loads, while 9 accelerometers deployed by MORPHOSENSE from the hull to the nacelle will record the slamming induced structural vibrations. An inertial motion unit has been added to correct the stereo-video images and to provide information on the wave-to-structure motion that needs to be accounted to properly understand slamming loads on a moving structure.

The Zefyros turbine, developed by Equinor (former Statoil), is now property of Unitech. They passed an agreement with the Norwegian government to support the exploitation of Zefyros that is now fully dedicated to R&D activities, open to any team in the world. This global initiative supported by the Norwegian government, will certainly result in important progresses for the floating offshore wind industry. Similar efforts could be deployed in France as well, to support the growth of the offshore wind industry.
# Chapter 7

## Conclusion

This manuscript has presented a spectrum of research works intended to bring further understanding and quantification of breaking waves effects on the offshore wind industry.

They relied on theoretical and numerical tools, supported by field, satellite and laboratory observations to progress on the definition of a new breaking onset criterion and of new wave breaking statistics models, the development of spectral wave models and the characterization of the interaction of breaking waves with offshore structures.

The application of these efforts to the offshore wind, primarily concerns the production of more reliable information for the extreme design of offshore wind turbines when slamming loads have to be considered. Because breaking waves influence the heat and momentum fluxes at the air-sea interface, the same tools and results should also find their application in the numerical modeling of the wind conditions at offshore wind sites, with stronger effects expected in storms conditions.

These research works have been carried out, mostly through 2 industry-driven research projects (DiMe and DIMPACT). They involved several postdocs, PhD students and permanent scientists whose contributions to the work introduced here is significant.

Future research projects will be dedicated to improving the knowledge and tools presented in the first part of this manuscript, with my FEM colleagues and other French and international colleagues. The focus will be directed toward breaking waves and extreme conditions that concentrate scientific challenges, industrial impact and lack of observations.

As a concluding word, I would like to stress how privileged I feel to work on such exciting research topics applied to the offshore wind sector.
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# Appendix A

## Curriculum Vitae