back to the lagoon during the decay of the swell when the offshore significant wave height reduces to 1.95 m in the early morning of January 5. The model captures the slight increase of wave setup from A2 to A1 in the lagoon because of the correct depiction of energy dissipation due to bottom roughness. The rapid water-level build-up over the reef slope and a gradual increase in the lagoon are unique to tropical coastal environments.

The transformation of the observed spectrum across the reef provides insights into the triad interactions and the ability of the LTA parameterization in describing these processes in natural reef environments. We selected two distinct records for this purpose and present the results in Fig. 12. The first record at 2:34 pm on January 1 corresponds to the peak of the swell event and the second one represents less energetic conditions toward the end of the case study on January 8, 6:34 am. Both events reveal similar trends albeit the large difference in energy level. The model reasonably reproduces the observed spectra from buoy 51201 to A4, while discrepancies between the observed and computed spectra are evident at A2 and A1 in the back-reef region. The broadening of the spectra to low frequencies is not reproduced by the

model. The LTA parameterization transfers energy to the superharmonics during shoaling and breaking and accounts for some of the high-frequency energy in the lagoon. Even though the energy levels are much lower at A1 and A2, the recorded data clearly shows a dominant sub-harmonic component that is not captured by SWAN due to the lack of appropriate parameterization. Infragravity waves are of primary importance in nearshore processes, as they drive currents and transport sediment, and need special attention in spectral wave modeling.

## 5. Conclusions and recommendations

Spectral wave models rely on parameterizations of nonlinear coastal processes such as wave breaking, bottom friction, and wave interaction on gentle-sloping beaches. Recorded data from a laboratory experiment and a field study allows examination of these parameterizations for fringing reef environments. The comparison of model data from SWAN with the laboratory data demonstrates that the default wave-breaking parameterizations are not able to capture the sharp build-up and decay

<figure><img src="image_68.png" /><figcaption>**Fig. 12.** Comparison of recorded and computed wave spectra for high and low-energy waves at Mokuleia. Black line: observed spectra; red dotted line: computed spectra using LW05 with $K_w = 0.16$ and 0.5 m.</figcaption></figure>
of the wave height associated with the energetic breaking process at the reef crest. An ad hoc calibration of the parameterization of Battjes and Janssen (1978) improves the overall model performance. The NRMSE decreases by 39% with the use of the optimal parameters $B = 1.09$ and $\gamma = 0.94$. The improved description of wave attenuation provides a better estimate of the wave setup on the reef flat.

The field data covers two north swell events with breaking and non-breaking wave conditions for examination of bottom-friction parameterizations. The results highlight the importance of bottom roughness in wave transformation over fringing reefs. Published parameterizations for bottom friction can adequately describe the dissipation over most of the reef slope, but underestimate the effects over the nearshore reef, where the surface is observed to be highly irregular. Calibration of the parameterization of Lowe et al. (2005) gives a roughness scale of 0.5 m in the nearshore region in comparison to the adopted value of 0.16 m over the reef slope. This works well with the optimal wave-breaking parameterization of Battjes and Janssen (1978) to reproduce the wave height and setup across the fringing reef for a full range of wave conditions and to provide a framework for calibration of spectral wave models using data from other PILOT project sites.

Both the laboratory and field data shows transfer of energy from the spectral peak to the sub and super-harmonics as the waves propagate across the reef. The LTA triad parameterization of Eldeberky (1996) describes the transfer of energy to the super-harmonics associated with increasing wave nonlinearity during the shoaling phase. However, the transfer of energy to the infragray band is, by construction of SWAN, not taken into account. This leads to omission of an important wave component in the inner reef region that might for instance produces seiches and other coastal hazards. With recent advances in fully nonlinear, triad interaction models, future research should be directed toward a complete parameterization of the triad wave-wave interactions for spectral wave modeling.

## Acknowledgment

The Department of Energy supported this research through Grant No. DE-FG36-08G018180 via the National Marine Renewable Energy Center at the University of Hawaii. The authors would like to thank Dr. Okey Nwogu for the laboratory data, Dr. Jane Smith for the field data from the PILOT project, Prof. Mark Merrifield, Prof. Janet Becker, and Mr. Justin Stopa for their assistance with this study, and the two anonymous referees for their comments and suggestions on the paper. SOEST Contribution No. 8543.

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Further reading

Ardhuin, F., Herbers, T.H.C., O'Reilly, W.C., 2002. A hybrid Eulerian-Lagrangian model for spectral wave evolution with application to bottom friction on the continental shelf. J. Phys. Oceanogr. 31, 1498–1516.

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Tolman, H.L., 1994. Wind waves and moveable-bed bottom friction. Journal of Physical Oceanography 24 (5), 994–1009.
4.C Paper from Varing & al. (2021b)
<figure><img src="image_69.png" /></figure>

# Spatial distribution of wave energy over complex coastal bathymetries: Development of methodologies for comparing modeled wave fields with satellite observations

Audrey Varing<sup>a</sup>, Jean-François Filipot<sup>a, *</sup>, Matthias Delpey<sup>b</sup>, Gilles Guitton<sup>c</sup>, Fabrice Collard<sup>c</sup>, Paul Platzer<sup>a, d, e</sup>, Volker Roeber<sup>f</sup>, Denis Morichon<sup>f</sup>

<figure><img src="image_70.png" /></figure>

## ARTICLE INFO

**Keywords:**

Satellite observation

Spectral wave model

Phase-resolving wave model

Coastal area

Refraction

## ABSTRACT

In this study we show that spectral and phase-resolving wave models, used for coastal engineering applications, can provide significant differences in the local wave heights and wave power magnitude in the presence of strong bottom-induced refraction. We present here methodologies to compare, in a consistent manner, model outputs to an alternative source of spatial data derived from Synthetic Aperture Radar (SAR) satellite images. Normalized amplitude-derived data are computed from SAR images, compared to both normalized amplitude-derived map from a phase-resolving model outputs and normalized significant wave height-derived map from a spectral model. Two methodologies of SAR images analysis are developed in this paper. While one appears unsuitable due to stochastic wave group modulations, the second methodology provides encouraging similarities between the SAR data and the phase-resolving model outputs.

## 1. Introduction

Surface ocean waves play a major role in coastal and nearshore processes. As a consequence, the accurate characterization of waves over the continental shelf is crucial for numerous coastal engineering activities (e.g. coastal defence, port design, navigation, Marine Renewable Energy planning) and environmental issues (e.g. sediment transport, erosion, flooding, nearshore dispersion). At the same time, the spatial variability of the wave field increases across the coastal area due to the intensification of wave interactions with the sea bottom and with hydrodynamic currents. These interactions result in a set of specific processes that typically activate for depth lower than half the wavelength and that will finally dominate wave evolution in the nearshore. These processes include wave refraction, shoaling, non-linear wave-wave interactions (triads) and eventually depth-induced breaking (Holthuijsen, 2007). Over heterogeneous bathymetries, bottom-induced refraction is expected to result in a large spatial variability of the wave

field over small length scales. In presence of intense water depth variations, locally steep gradients of wave energy may occur between focusing points and neighbouring areas [e.g. 2, 3]. Such steep gradients may be similarly obtained in the presence of strong heterogeneity in surface currents (Arduuin et al., 2012).

In most coastal studies, the spatial distribution of wave properties is provided by a numerical model, whose reliability is supported by a comparison against (a set of) point measurement(s). Among available wave modeling approaches for such applications, spectral modeling as offered by reference models such as SWAN (Booij et al., 1999) or WAVEWATCH III (Tolmanet al.; Arduuin et al., 2010), is probably the most widely used tool in applied research and engineering studies. A number of coastal wave characterization works based on spectral models can be found in the literature, especially during the last decade for the purpose of wave energy resource assessment. Several of these numerical studies have suggested the presence of very steep wave energy gradients in the nearshore (Iglesias and Carballo, 2009, 2010a, 2010b). However,

<footnote><sup>a</sup> France Energies Marines, Bâtiment Cap Océan, 525 Avenue Alexis de Rochon, 29280, Plouzané, France</footnote>

<footnote><sup>b</sup> SUEZ, Smart & Environmental Solutions, Center Rivages Pro Tech, Bidart, France</footnote>

<footnote><sup>c</sup> OceanDataLab, Locmaria-Plouzané, France</footnote>

<footnote><sup>d</sup> Laboratoire des Sciences Du Climat et de L'Environnement, Saclay, France</footnote>

<footnote><sup>e</sup> IMT Atlantique, Lab-STICC, UMR CNRS 6285, F-29238, Plouzané, France</footnote>

<footnote><sup>f</sup> Université de Pau et des Pays de l'Adour, E2S-UPPA, Chair HPC-Waves, SIAME, Anglet, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: audrey.varing@ite-fem.org, audrey.varing@gmail.com (A. Varing), jean.francois.filipot@france-energies-marines.org (J.-F. Filipot).</footnote>
spectral modeling of wave transformation in shallow water is still a large
challenge and an active field of research. Strong wave refraction over
steep slopes is still hardly capture (Roland and Ardhuin, 2014). Dis-
crepancies with point observations may be hard to reduce in high res-
olution applications to nearshore areas with complex bathymetries [e.g.
12]. Moreover, the contribution of non-linear triad interactions, which
may significantly modify the wave spectrum in shallow water (Hassel-
mann, 1962), require phase information to be computed explicitly. It is
parameterized in spectral models (Eldeberky, 1996; Becq-Girard et al.,
1999) but still represents a largely approximated representation of the
full triad interactions. Finally, the parameterization of wave breaking
dissipation in spectral models is another major difficulty (Thornton and
Guza, 1983; Filipot et al., 1029).

An interesting alternative modeling approach to address some of
these limitations is provided by phase-resolving models. These models
solve different simplified versions of the Navier-Stokes equations and
provide the instantaneous non-linear evolution of the free surface
elevation and of the fluid velocity at one or several levels in the water
column. Models built around phase-resolving dispersive equations
(Boussinesq-type or non-hydrostatic) have experienced an increasing
popularity in recent years due to improved computer performances. In a
report released in 2015, (IEC-TS Committee) recommends the use of
phase-resolving models to analyze the wave conditions for wave farms
to be installed in nearshore areas. Many studies for practical applications
with phase-resolving models are based on one-dimensional horizontal
cross-shore transects [e.g. 19–22]. But even without the use of super-
computers, it is nowadays possible to obtain high-quality solutions for
numerical grids with millions of cells equivalent to computational do-
mains of several square kilometers and resolutions of a few meters. Thus,
several studies have suggested that phase-resolving models can provide
realistic spatial distribution of complex nearshore wave processes over
complex bathymetry including the generation of infragravity waves [e.g.
23–25]. When studying a potential wave energy onshore site (Varing
et al., 2017), used the phase-resolving model BOSZ (Roeber et al., 2010)
to characterize the nearshore wave field and reported encouraging re-
sults regarding the capabilities of such a phase-resolving approach in
reproducing propagation on a complex bathymetry. Here again, results
suggested the presence of very large gradients in wave heights on
reduced length scales in the nearshore, due to combined wave refrac-
tion, shoaling, and/or breaking.

However, in both spectral and phase-resolving applications to
coastal sites, the proper validation of obtained spatial wave patterns is
hard to achieve. Indeed, observations available for coastal wave model
validation are usually point measurements collected by *in situ* sensors
such as wave buoys, pressure gauges or current profilers. It does not
provide spatial distribution of the wave field characteristic but a limited
number of control points for the model [e.g. 12, 28, 29]. In cases with
large bathymetric heterogeneity, local cross-shore and longshore vari-
ability of the wave energy may be hardly described by a limited number
of point measurements. Actually, very little is known on the accuracy of
the wave models in representing the detailed spatial distribution and
especially the wave field alongshore variability in coastal areas. A
proper sampling of the wave field spatial variability would require a
very dense and expensive array of point *in situ* sensors. Consequently,
the spatial density of sensors used for validation is generally not suffi-
cient to verify the consistency of small-scale modeled energy gradients
without ambiguity. This emphasizes the need for alternative measure-
ments providing a spatial information about wave parameters in the
coastal and nearshore areas, with a space resolution that is fine enough
to capture most local steep gradients.

To address the limitation related with point *in situ* deployments,
remote sensing observations may represent an interesting option.
Remote sensing techniques are being used with increasing frequency to
study wave field properties. Techniques such as stereo imagery [e.g.
(Benetazzo et al., 2017; Gallego et al., 2011; Leckler et al., 2015; Filipot
et al., 2019; De Vries et al., 2011)], X-band radar [e.g. (Lund et al., 2014;

Nieto Borge et al., 2004; Atkinson et al., 2018)], polarimetric imaging [e. g. (Zappa et al., 2008)], airborne LIDAR surveys [e.g. (Coleman et al., 2011; Wedding et al., 2008; Hwang et al., 2000; Romero and Melville, 2010; Sutherland and Gascard, 2016)], video imagery [e.g. (Gemmrich et al., 2008; Kleiss and Melville, 2010; Schwendeman and Thomson, 2017; Vousdoukas et al., 2014)] or infrared imagery [e.g. (Sutherland and Melville, 2013)] were experimented to study ocean waves in deep and shallow water conditions. The quantity and quality of wave data available from space-borne instruments offer also an attractive perspective, with the swath of the satellite allowing access to the wave field spatial distribution. For instance, altimeter data are used to validate the wave field variability [e.g. (Delpey et al. Chapron; Filipot and Ardhuin, 1978; Stopa et al., 2013)]. These satellite data have been used to calibrate wave models and improve global or regional phase-averaged model outputs [e.g. (Cavaleri and Sclavo, 2006; Mazas et al., 2015)]. However, this source of observations can not be used in coastal area due to the corruption of the data by the land signal and also because the spatial resolution (O(10km)) is too large and would not be appropriate to capture the nearshore wave field variability (O(10m)). Alternatively, among the sources of wave information collected with remote sensing instruments, the Synthetic Aperture Radar (SAR) images provide maps of sea surface roughness that can be processed to access a variety of small and mesoscale ocean characteristics, including oceanic waves in coastal waters. Observations of ocean waves can be derived from SAR images since their orbital motion modulates the Bragg waves and their underlying slope that scatters back the SAR electromagnetic signal. By analyzing this signal alteration, SAR data provides a unique view of the spatial variability of the wave amplitude, direction and wavelength. The ability of SAR to retrieve this spatial variability at about 2km scale has been demonstrated in (Collard et al., 2005). This study showed that high-resolution SAR instruments (O(10m)) can reveal detailed spatial variability of ocean waves integrated parameters, including wavelength and direction. Thus, SAR data are potentially useful to capture strong refraction patterns in coastal areas (before surf zone) in water depths typically between 10 and 30m. However, to our knowledge, SAR data analysis has not been performed nor confronted to wave modeling at such smaller scales so far.

In this context, this paper investigates the capabilities of SAR data to
provide valuable information for the assessment of the spatial distri-
bution obtained from wave models in the nearshore. First, significant
discrepancies are highlighted in the spatial distribution produced by two
different numerical wave modeling approaches, when applied to a
stretch of the southwestern French Atlantic coastline. This finding
motivated the definition of a new methodology to use SAR images, with
the aim of assessing the wave field spatial variability in coastal/near-
shore areas, at a relevant scale (0–10 m) to capture potential steep en-
ergy gradients suggested by the implemented models. Hence, this paper
establishes the first milestones to a methodology aiming to (i) extending
the wave amplitude analysis from SAR data to smaller scales/depth and
(ii) comparing this SAR-derived information to nearshore wave
modeling. The application to MRE, which is of interest for the chosen
application site off Biarritz and Anglet towns, is taken as an example to
illustrate the implication of local features in the wave field, in the
perspective of e.g. a further site assessment or wave climate analysis.

The present study starts with a brief description of the two wave
models used, based on spectral and phase-resolving approaches
respectively, which is given in section 2. Observation means are also
presented in this section, especially SAR data used for the study. Then, in
section 3, wave models are applied to a demonstration site in the
southwestern French coastal area and differences between modeled
spatial distributions of wave energy are discussed. This leads to the
introduction of two methodologies to derive consistent wave informa-
tion from SAR images, which are confronted to both wave models in
section 4. Finally, section 5 presents a discussion and the conclusion of
the paper.
## 2. Models and observations

### 2.1. Models

#### 2.1.1. Spectral model SWAN

Spectral wave models are commonly used for numerous applications in open ocean, coastal and nearshore areas, from coastal engineering studies to operational wave forecasting. In the present work, the third generation spectral wave model SWAN is used (Booij et al., 1999; Ris et al., 1999) in its version 41.10. SWAN is a state-of-the-art model widely used in coastal applications for various purposes. It allows to simulate the evolution in time and space of the wave energy spectral density $E(f, \theta)$ by solving the following wave action balance equation:

$$ \frac{dA}{dt} = \frac{S}{\sigma} \qquad (1) $$

where $A = E/\sigma$ denotes the wave action density, $\sigma = 2\pi f$ is the wave pulsation with $f$ and $\theta$ the frequency and direction of the spectral wave component respectively, $d/dt$ denotes material derivative and $S$ is a source/sink term (Gelci et al., 1957). In third generation spectral wave models such as SWAN, the spectrum can describe multi-modal sea states and the source term $S$ contains parameterizations of physical processes that include energy input by wind, non-linear energy transfers by wave-wave interactions (quadruplets and triads), and dissipation through wave breaking (both whitecapping and depth-induced) and bottom friction [e.g. (Booij et al., 1999; Tolman, 2008; Komen et al., 1996; Zijlema, 2010)].

#### 2.1.2. Boussinesq-type model BOSZ

Although their computational cost is much more demanding for realistic applications, numerical models based on the Boussinesq-type (hereinafter noted BT) formulations have proven their usefulness to accurately represent nearshore processes (Rusu and Soares, 2012). In the present study, the Boussinesq Ocean and Surf Zone model (BOSZ) developed by (Roeber and Cheung, 2012) is used. This model is based on a conservative formulation of the depth-integrated BT equations of (Nwogu, 1993). Details about BOSZ numerical formulation can be found in (Roeber et al., 2010; Roeber and Cheung, 2012; Roeber, 2010). A comprehensive validation of BOSZ with laboratory and field data was provided by (Roeber and Cheung, 2012). The BOSZ model has been applied to continental shelf configurations in Brittany, France (Varing et al., 2017; Filipot et al., 2013), and Aquitaine, France (Bellafont et al., 2018), where it provided encouraging capabilities in reproducing nearshore wave transformation over complex bathymetries. BOSZ has also proven to be a stable and accurate option for the representation of wave processes at locations with irregular bathymetry and extreme wave conditions (Li et al., 2014, 2018).

### 2.2. Observations

#### 2.2.1. In situ

To force the different models with incident wave conditions, measurements from the Anglet wave buoy (06402) are used. This directional wave buoy is moored off the study site at a depth 50 m (location 1°36,9'W 43°31,93'N, see Fig. 1). Frequency-directional spectra are computed with resolution $df = 0.005Hz$ and $d\theta = 5°$ from the buoy heave, pitch and roll measurements on 30 min time windows and used as an input offshore boundary condition for both wave models.

#### 2.2.2. Satellite

The Copernicus program of the European Space Agency is providing free and open access to the Sentinel-1 SAR acquisitions over the entire European coastline. Sentinel-1 constellation (Sentinel-1A and Sentinel-1B) produces SAR acquisitions over the French coasts in Interferometric Wide (IW) swath mode around 06 h and 18 h UTC time and with an average revisit time less than two days. In order to cover one year of observations over our study site, 201 Level-1 IW Ground Range Detected (GRD) products were collected. Standard IW GRD maps offer a spatial resolution around 10 m.

SAR data provide a map of the normalized radar cross section (NRCS or $\sigma_0$) of the sea surface (see illustration in Fig. 2). The modulation of the NRCS by waves is induced by several imaging mechanisms among which the velocity bunching and the tilt as described in (Collard et al., 2005). In moderate wave steepness conditions, these imaging mechanisms provide a quasi-linear relationship between NRCS modulations and wave modulations (Engen and Johnsen, 1995). In a first approximation, we therefore estimate the relative variability of the wave amplitude by analyzing the relative variability of the NRCS modulation signal.

## 3. Case study

### 3.1. Study site

The study site for the present work is a coastal area located in the southeastern Bay of Biscay, off the South-West French Atlantic coastline (Fig. 1). The area is a cultural and touristic hotspot in France and local authorities are long committed to a proactive coastal management, which involves many issues from marine flooding and beach erosion to the preservation of water quality and marine life. More recently, the region is also exploring opportunities in the MRE sector motivated by an interesting wave energy resource. Along this coastline, Saint-Jean-de-Luz and Bayonne cities have been especially spotted as potential wave energy conversion sites in the frame of the EMACOP and WAKE projects, which investigated the local resource and the opportunity of equipping breakwaters with wave energy converters (Michard et al., 2015; Lastiri

<figure><img src="image_71.png" /><figcaption>Fig. 1. Geographic location of the study (left panel) along with the bathymetry used as input of the wave models (right panel). The red square on the right panel indicates the Anglet wave buoy location. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
<figure><img src="image_72.png" /><figcaption>**Fig. 2.** Normalized Radar Cross Section, $\sigma_0$, from Sentinel-1 above our study site identified in the red square on the 20180131 17:55 UTC in geographic coordinates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

et al. Roeber). In the present work, investigations are focused on Biarritz/Anglet/Bayonne nearshore, a shallow area with complex bathymetric features that are typical of the region.

The studied coastal environment is mostly exposed to wave systems generated in the North-East of the Atlantic Ocean. The local wave climate is moderately to highly energetic with offshore annual mean significant wave height, peak period and peak direction ($H_s$, $T_p$, $\theta_p$) = (1.6 m, 9.6 s, 302°) respectively (Abadie et al., 2005). Storm conditions with $H_s > 4m$ are found 7.5% of the year and correspond to winter energetic swells with $T_p > 12.5s$ from W-NW sector. The region is dominated by a semi-diurnal and mesotidal regime with a tidal range of about 4.5m at spring tides around a mean tide level of 2.5m (above Chart Datum).

Moreover, the southwestern French coast is at the boundary between a straight sandy coastline in the North and a complex mix of rocky-sandy pocket beaches in the South like e.g. Biarritz main beach (Morichon et al., 2018). Among the numerous bathymetric heterogeneities, the presence of a steep rocky reef can be noticed in the study site, at around 20–25m depth off Biarritz (see Fig. 1). This rocky formation is an important local feature that strongly affects the wave field, as it will be discussed later in the paper.

## 3.2. Studied wave event

In the present study, a series of model computations were conducted on different wave events encountered during winter 2017–2018. Despite some variability induced by the different incident wave conditions, strong similarities in the wave energy focusing and defocusing patterns were obtained that seems mainly controlled by the wave refraction induced by the remarkable local bathymetric features. In this section, we selected one particular wave event as an illustration, which occurred on 1st of February 2018 at 16:30. It corresponds to an energetic winter swell event with ($H_s$, $T_p$, $\theta_p$) = (3.96m, 14.3 s, 315°) measured by the Anglet wave buoy. Numerical simulations of these wave conditions are used here as a test case to describe the specific wave patterns obtained on the study site and to compare the solution provided by the two models presented above. The major long swell contribution to the event should be favorable for the two modeling approaches. It is also expected to activate strong wave refraction patterns over the local bathymetric features, which are at the core of the present study.

## 3.3. Models setup

### 3.3.1. Common setup

The computational grid is common to both models. The modeled domain extends about 8km offshore (cross-shore, x-direction) up to a depth close to 50m (Fig. 1) and covers a region of approximately 10km wide (long-shore, y-direction). The bathymetry is derived from the combination of global data from the French Naval Hydrographic and Oceanographic Service (SHOM) and a high-resolution nearshore survey performed as part of the POCTEFA MAREA project. Spatial steps of the computational grid $\Delta x = \Delta y = 7.5m$ were used for BOSZ and SWAN. For both models, incident wave energy is obtained from the frequency-directional spectrum measured by the Anglet wave buoy, which is used to prescribe the offshore boundary condition homogeneously all along the North-West side of the domain. A mean tide level $\bar{\eta} = 4.5m$ (above Chart Datum) is applied for the studied test case, as prescribed by measurements of the Socoa tide gauge (SHOM). It corresponds to a spring high-tide.

### 3.3.2. SWAN specific setup

SWAN is run in stationary mode with an exponential frequency discretization using 25 frequencies, $f_i$, from 0.04 to 0.5Hz so that $f_{i+1} = 1.1f_i$. The directional grid is regular with a 5° resolution. Wave generation by wind and quadruplets wave-wave interactions are not considered in the simulation because of the rather small extension of the domain considered. Triads are included through the LTA formulation proposed by SWAN with default parameters. Bottom friction is considered through the (Madsen et al., 1988) parameterization using an equivalent bottom roughness length scale of 0.085. Depth-induced breaking is accounted for using (Battjes and Janssen, 1978) formulation with a breaker index $\gamma = 0.73$. The BSBT numerical scheme is used with convergence required on 99.5% of the grid points. After preliminary tests (not shown), the numerical scheme for refraction was forced to be centered in order to minimize numerical diffusion (using the SWAN parameter cdd = 0, see (SWAN Team, 2019)). For the specific event studied, this numerical parameterization of refraction appeared to give the most comparable results with BOSZ model, especially compared to the default SWAN setup (i.e. cdd = 0.5).
<figure><img src="image_73.png" /><figcaption>Fig. 3. Significant wave height distribution $H_s$ from the SWAN and BOSZ models on the studied test case (1st of February 2018 at 16:30 UTC). The vertical dashed lines indicate two longshore transects that are analyzed in Fig. 4.</figcaption></figure>

### 3.3.3. BOSZ specific setup

Individual waves are generated along the South-West boundary by an internal wavemaker. To avoid recycling of the input time series arising from the superposition of individual monochromatic waves with a random phase, the input wave spectrum is re-sampled to narrow frequency bins down to 0.00011 Hz (Roeber and Bricker). To comply with the wavemaker theory framework, the water depth off the 50m-isobath is assumed be uniform and equal to 50m. Sponge layers are used on all sides of the domain to absorb possible outgoing wave energy. These sponge layers cover 50 cells around the perimeter of the computational domain. The corresponding parts of the computational grid will not be shown in the figures presented in this paper. Dissipation by bottom

friction is taken into account using a Manning coefficient of 0.02, which is typical for a seabed with coarse sand or smooth rocks (Arcement and Schneider, 1989). Dissipation by depth-induced wave breaking is accounted for, using a momentum gradient limitation criterion combined with dispersion terms cut-off (Roeber et al., 2010). The numerical procedure uses a Courant number of 0.5 preventing the fastest waves from traversing more than half a grid cell within a time step. Together with a second order accurate time stepping scheme (Runge-Kutta), the solution is stable under breaking and non-breaking wave conditions (Roeber and Cheung, 2012). The total computed time is 2.5 h to allow for a fully developed sea state and to provide sufficiently long time series for further analysis of wave statistics. The first 30 min are dedicated to

<figure><img src="image_74.png" /><figcaption>Fig. 4. Significant wave height distribution $H_s$ of SWAN and BOSZ along the two longshore transects identified in Fig. 3. The green squares highlight four (A to D) focusing/defocusing zones. Variations of $H_s$ between the minimum (blue markers) and maximum (red markers) of each focusing/defocusing area are described in Table 1. The circle markers are used for SWAN and square markers for BOSZ. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
<caption>**Table 1**</caption>

$H_s$ variations relative to the longshore distance, $\Delta H_s/\Delta y$ (in m/100 m), for SWAN and BOSZ at the main focusing zones (A, B, C, D) identified in Fig. 4.

<table><thead><tr><th>X = 4.125 km</th><th>SWAN</th><th>BOSZ</th></tr></thead><tbody><tr><td>A</td><td>0.55</td><td>1.58</td></tr><tr><td>B</td><td>0.29</td><td>0.72</td></tr><tr><td>C</td><td>0.24</td><td>0.39</td></tr><tr><td>D</td><td>0.06</td><td>0.11</td></tr></tbody><thead><tr><th>X = 5.250 km</th><th>SWAN</th><th>BOSZ</th></tr></thead><tbody><tr><td>A</td><td>0.16</td><td>0.35</td></tr><tr><td>B</td><td>0.22</td><td>0.46</td></tr><tr><td>C</td><td>0.18</td><td>0.52</td></tr><tr><td>D</td><td>0.09</td><td>0.11</td></tr></tbody></table>

the solution spin up and only the last 2 h of the computation are then analyzed. The BOSZ model allows for an OpenMP parallel processing. It was run on the *Datarmor* high performance computing and data processing infrastructure for marine sciences.

### 3.4. Model outputs

Both model results shown in Fig. 3 highlight remarkable wave patterns in the nearshore with large variations in $H_s$ over short cross-shore and longshore distances. In the offshore part of the domain, the wave field is rather homogeneous up to roughly the 40m-isobath (see Fig. 1). Then, from 40m to 20m depth, refraction (and shoaling to a lesser extend) over the many bathymetric accidents results in a strong spatial variability of wave energy, with intense focusing areas alternating with pronounced shadowing areas. The $H_s$ in focusing zones may easily increase of + 50% compared to offshore incident wave height. Wave heights in defocusing areas are of the order of half the focusing heights, resulting in important longshore $H_s$ gradients. In the shallow region above 20m-isobath, despite a more homogeneous bathymetry in the longshore direction, longshore variability seems to propagate up to the surf zone.

However, despite the overall qualitative consistency, Fig. 3 also reveals that the intensity and exact localization of refraction patterns vary significantly between the two models. To examine these differences in more details, two longshore transects are extracted at $X = 4.125km$ and $X = 5.250km$ respectively (dashed black lines in Fig. 3) and plotted in Fig. 4. Four major focusing/defocusing zones are indicated by green squares along the transects (A, B, C, D). Fig. 4 shows that $H_s$ focusing and

shadowing spots were generally well captured by both models. However, SWAN produces overall refraction patterns that are remarkably smoother than BOSZ. The $H_s$ variance along both offshore and onshore transects is about 3 times higher in BOSZ (0.38 and 0.41 respectively) than in SWAN (0.11 and 0.14 respectively). To complement the analysis, Table 1 gives the $H_s$ variations relative to the longshore distance, $\Delta H_s/\Delta y$ (in m/100 m), for the four focusing/defocusing patterns (A,B,C,D) in Fig. 4. Although longshore variations appear important on short length scales in both models, it confirms the previous diagnosis: along the examined transects, $\Delta H_s/\Delta y$ is about 2 times higher in BOSZ than in SWAN. Highest differences are obtained in zone A (ratio = 2.2) and zone C (ratio = 2.9) respectively for the offshore and onshore transect.

The obtained discrepancies can lead to a strong impact on coastal and nearshore areas in terms of e.g. wave height, direction, power and infragravity wave content. As an illustration, the wave energy flux $P_w = \rho g \int_0^\infty C_g(f, d)E(f)df$ (with $\rho$ the sea water density $g$ the gravity, $d$ the local water depth and $C_g$ the wave group velocity) computed from both models is plotted in Fig. 5. Because of the large computational effort required to compute $P_w$ at each mesh node from the phase-resolved free surface elevation provided by BOSZ, a focus is made on one illustrative focusing/defocusing pattern located in the southern half of the domain (zone A). As expected, the wave energy flux is even more affected by the differences in the model representations. In the wave energy focusing patch, maximum $P_w$ obtained from BOSZ is 250 kW/m, while is around 150 kW/m only in SWAN.

These results reveal important discrepancies between the two models, with differences in the wave patterns that seem to be mainly related to the representation of bottom-induced refraction and to a lesser extend shoaling. The different physics and numerics involved in the models are eligible candidates for these discrepancies, although respective contributions of physics and numerics would require additional investigations to be assessed. However, in case of very heterogeneous $H_s$ fields like those obtained on our study case, it seems that only proper observations of the wave field spatial distribution could help to decide which model provides the most accurate representation. *In situ* measurements could also contribute to this evaluation, but a quite large and dense array would be required to distinguish over-/under-estimations of focusing, as well as to accurately assess steep gradients in wave energy. Thus, the configuration studied in this paper illustrates the need for alternative observations providing information on the wave field spatial variability. In the following section, we propose a methodology to derive wave amplitude maps from SAR images. This will provide a

<figure><img src="image_75.png" /><figcaption>**Fig. 5.** Comparisons of wave energy flux $P_w$ distribution obtained from SWAN (left) and BOSZ (right) on the studied test case (1st of February 2018 at 16:30 UTC). Focus on an illustrative focusing/defocusing pattern.</figcaption></figure>
<figure><img src="image_76.png" /><figcaption>**Fig. 6.** SAR Normalized Radar Cross Section $\sigma_0$ (left panel), BOSZ filtered free surface elevation $\eta$ (center panel) and BOSZ non-filtered free surface elevation $\eta$ (right panel) maps for the event on the 20180131 17:55 UTC.</figcaption></figure>

new source of information that we shall use to assess the discrepancies between the different modeling approaches.

# 4. Methodologies for consistent comparisons of numerical models and SAR wave information

## 4.1. Wave amplitude maps

A succession of processing steps are necessary to obtain wave amplitude maps from SAR images. A first spectral isolation of the wave signal from all other signatures in the SAR image is performed by a spectral analysis followed by a filtering of all spectral components away from the wave related spectral peak. The filtered Normalized Radar Cross Section (NRCS) modulations are then reconstructed. The amplitude of the wave related filtered NRCS modulations, hereinafter referred to as the wave amplitude map, is then estimated by measuring the difference between the local consecutive minima and maxima of the filtered NRCS modulation map.

For consistency, we apply to BOSZ free surface elevation map the same spectral filtering as in the SAR data. Applying the filter allows to focus on the dominant wave field of SAR and BOSZ. Hereinafter, the raw data will be mentioned as “non-filtered”. In this study, both the filtered and non-filtered BOSZ wave fields will be used: the filtered BOSZ information is consistent for a comparison with the SAR data. Obtaining a consistent information from SWAN would require to output the direction-frequency wave energy spectra at grid point and perform a spectral filtering around the peak frequency and direction to compute the wave height from the dominant wave partition only. As this is not doable in practice for obvious computer memory reasons, we shall use the non-filtered SAR and BOSZ information for a consistent comparison with SWAN output. This will further allow to put into perspective the comparison between the SWAN and SAR data, as it will be seen later in the paper.

Fig. 6 gives a comparison between the NRCS $\sigma_0$ (filtered) map obtained from a SAR image available on January 31, 2018 17:55 UTC, and a snapshot of the filtered and non-filtered wave elevation $\eta$ maps produced from the corresponding numerical simulation with BOSZ. A first qualitative examination reveals that the filtered $\sigma_0$ and $\eta$ maps show significant similarities in terms of dominant wavelength and direction. This will be further supported by the spatial spectrum comparison presented in the next paragraph.

The non-filtered map from BOSZ simulation indicates the presence of oblique wave components, starting at approximately $X = 3.5\,km$ (on the steep rocky reef in 20–25m depth) with energy travelling close to the longshore direction. The nearshore area ($X > 6\,km$) is characterized by wave shortening due to the wave-bottom interaction. The modulation by infragravity waves can be also guessed from BOSZ results. These different contributions are removed while applying the SAR spectral filtering method. This information must be kept in mind for the comparison

of the SAR images and numerical model outputs. In the following, the areas corresponding to wavenumbers 1.1 higher than the highest wavenumber involved in the spectral filtering procedure are masked for clarity (white areas in the wave field figures), since no energy is expected (due to spectral filtering) in these regions.

## 4.2. Methodology #1: comparison of SAR-derived amplitude map with snapshots of the modeled wave field

### 4.2.1. Spatial spectrum comparison

As a first step in the comparison of observed and modeled spatial distributions, 2D spatial $\sigma_0$ spectrum derived from SAR images available on 20180131 17:55 UTC are compared to that obtained from the free surface elevation maps produced by BOSZ for the same date (see Fig. 7). This date corresponds to a relatively moderate wave event with a dominating long swell, with incident significant wave height $H_s = 1.30\,m$, peak period $T_p = 12.5\,s$ and peak direction $\theta_p = 300^\circ$. In this relatively low wave steepness case, the non-linearities in the SAR wave imaging can be neglected and the wave spectrum considered as a linear transformation of the SAR intensity spectrum. The domain considered for the spectral analysis is the one in Fig. 6. It covers a range of wavelengths and directions due to the frequency-direction spreading of the incident wave field and the further modifications due to wave-bottom interactions inside the domain.

In this approach, two similar wave spectra would not indicate a perfect match between the two wave fields. For example, similar wave patterns in terms of wavelength, amplitude and direction but shifted in space in the same domain, would virtually lead to the same spectrum. But conversely, a mismatch in the spectral content necessarily leads to discrepancies between the wave fields. In other words, a reasonable match between SAR and model spectra is a necessary but not sufficient condition for the agreement between model and observation. Then, the spectral content comparison over the domain can be considered as a prerequisite to the consistency between the SAR-derived observation and BOSZ output.

Fig. 7 shows the SAR and BOSZ spectra computed from the non-filtered $\sigma_0$ and $\eta$, respectively, along with the filter contour applied to compare SAR and BOSZ amplitude maps. For this event, the filter removes the energy outside the directional range [280, 325]$^\circ$ and the wavenumber range [0.026, 0.053]$\,m^{-1}$, the latter corresponding to wavelengths in the range [240, 118]$\,m$. For the SAR spectrum, these components mainly corresponds to noise. The SAR and BOSZ spectra displayed in Fig. 7 show a good agreement in the range of wave numbers present in the dominant wave field (area inside the filter contour). The comparison suggests that the distribution of wave energy among the different wavelengths is generally reasonable, with a peak wavelength and peak wave direction of ($L_p, \theta_p$) = (180m, 300$^\circ$) for the SAR and ($L_p, \theta_p$) = (190m, 305$^\circ$) for BOSZ model. The directional spreading is narrower in BOSZ than in the SAR. Both the SAR and BOSZ data suggest
<figure><img src="image_77.png" /><figcaption>Fig. 7. SAR $\sigma_0$ spectrum (left panel) and BOSZ free surface elevation spectrum (right panel) for the event on the 20180131 17:55 UTC. The black lines indicate the filter contour applied to compare SAR and BOSZ amplitude maps.</figcaption></figure>

that other wave components from other wavelengths and directions contribute to the wave field as well. There is a contribution of oblique waves in the South-West sector that are clearly visible in Fig. 6 though the associated spectral density is small and are outside the filter contour. We note that the low level of energy of these obliques waves is likely due to the spectrum computation method that consider the entire elevation map, while the contribution of these waves is restricted to only a portion of the domain. The short wave scales inherent to the incoming wave field or generated by wave shortening in shallow water and the infragravity wave in the inner surf zone, are also filtered.

### 4.2.2. Direct comparison of wave amplitude fields from SAR and BOSZ

In this paragraph, we shall pursue our exploration of the SAR images potential and go more into the details of the spatial distribution of the wave field in the coastal area. The aim of the following method is to compare amplitudes computed from the filtered SAR $\sigma_0$ data and from filtered BOSZ $\eta$ wave fields. These amplitudes are derived from different variables but we shall assume here that once normalized (with the maximum value of the selected area) their relative variations can be compared. An additional difficulty to compare these data principally resides in the presence of wave groups that are different in BOSZ and SAR outputs since BOSZ wavemaker randomly picks the phase of the incident spectral components. This means that even with a statistically identical wave field (i.e. with the same wave energy spectrum), the chance is limited of observing the same wave groups arrangement in the

SAR image taken at one single instant and in a given free surface elevation map from BOSZ. In an attempt to circumvent this problem, the hypothesis will be tested that when performing a sufficiently long BOSZ simulation, the multiplication of random phase arrangements offers a chance to find a particular time step in which the wave groups are close to those in the SAR snapshot. In other words, we try to identify a correct BOSZ analog of the SAR amplitude map.

To illustrate the methodology, the same previously examined wave event on 20180131 17:55 UTC is considered. A 10-h BOSZ simulation is performed. BOSZ uses a numerical wavemaker that produces a wave field from spectral components spanning over 4241 uniformly-spaced frequencies (re-sampled to avoid recycling of input time series) and 120 directions equally spaced on the sector ($\theta_p - 60^\circ, \theta_p + 60^\circ$). The computed free surface elevation snapshots are then saved every 10 s of the simulation. For each saved time step (3600 in total), we compute the filtered wave field amplitude following the same methodology as described in paragraph 4.1. Fig. 8 recalls the model computational domain along with the corresponding significant wave height $H_s$ map for the selected event. Two sub-domains (black rectangles) are identified in this figure: they represent two control sub-domains that will be used for comparison in the following description. The left sub-domain corresponds to a deeper area (average depth $D \approx 45m$ and $k_p D = 1.34$, with $k_p$ the peak wave number), where we expect the wave field spatial variability to be dominated by wave groups randomness. The right sub-domain corresponds to a shallower area with average depth $24m$ and

<figure><img src="image_78.png" /><figcaption>Fig. 8. BOSZ bathymetry (left panel) and significant wave height map for the event on the 20180131 17:55 UTC (right panel). Two sub-domains (black squares) are highlighted.</figcaption></figure>
<figure><img src="image_79.png" /><figcaption>**Fig. 9.** BOSZ free surface elevation snapshot (left panel) and derived amplitude map (right panel) for a simulation time step. The most nearshore area is masked as the filtering process removes wave components that might visually disturb the reader.</figcaption></figure>

$k_p D = 0.88$, where the effect of bottom irregularities may start to impose more deterministic, refraction-forced, wave amplitude patterns. Fig. 9 gives an example of a free surface elevation snapshot from BOSZ simulation (left panel) and the corresponding amplitude map (right panel).

To compare observations- and model-derived amplitude fields, BOSZ and SAR data are interpolated on the same grid. Moreover, a Gaussian filter with a footprint of 200m is applied to BOSZ and SAR amplitudes in order to smooth small scales random contributions and ease the comparison of main patterns. The smoothed BOSZ and SAR amplitudes are then normalized by the respective maximum value in each sub-domain. Finally, a linear correlation between the smoothed filtered SAR and BOSZ amplitudes is computed based on the Pearson product-moment correlation coefficient on each sub-domain, applied to each of the 3600 BOSZ amplitude maps. Fig. 10 displays the time series of correlation coefficients for each sub-domain, and Fig. 11 shows SAR and BOSZ amplitude maps at the time step of the maximum correlation.

For this wave event, the maximum correlation coefficients are 0.43 for the deeper sub-domain (Fig. 10, top panel) and 0.52 for the shallower sub-domain (Fig. 10, bottom panel). We noticed that the correlation values are strongly dependent on the size of the control sub-domains, larger sub-domains providing lower correlation values due to the randomness of the wave groups (not shown here). These results show slightly higher correlation between SAR and BOSZ in the shallower sub-domain. This could support a larger control of the wave amplitude by the bottom topography in the onshore sub-domain compared to the more offshore wave groups-dominated sub-domain, although the correlation difference remains limited. It is also to be noticed that the time steps of the maximum correlation are different for each sub-domain (red circles in Fig. 10).

Finally, the smoothed amplitudes of each sub-domain at the maximum correlation time are displayed in Fig. 11. This result suggests possible similarities between both fields. However, it seems difficult to conclude that the model representation is consistent with SAR

<figure><img src="image_80.png" /><figcaption>**Fig. 10.** Time series of correlation coefficients between observation- and model-derived amplitude maps. Red markers indicate the time step the correlation is maximum for the left sub-domain (top panel) and right sub-domain (bottom panel). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
<figure><img src="image_81.png" /><figcaption>**Fig. 11.** SAR-derived amplitude map from $\sigma_0$ (left panel) and BOSZ-derived amplitude map from free surface elevation (right panel) on the control sub-domains plotted on top of the bathymetry in grey scale. The correspondence between the sub-domains are associated to different time steps of the BOSZ simulation.</figcaption></figure>

<caption>**Table 2**</caption>

Set of BOSZ input parameters used as part of the sensitivity analysis. $H_s$ is the significant wave height, $T_p$ is the peak period and $\theta_p$ is the peak direction. The mean tide level is $\bar{\eta}$. One parameter at a time (identified in bold characters) is modified from the reference simulation (REF).

<table><thead><tr><th></th><th>H<sub>s</sub>(m)</th><th>T<sub>p</sub>(s)</th><th>θ<sub>p</sub>(°)</th><th>η̄(m)</th></tr></thead><tbody><tr><td>Simulation 1<sup>a</sup></td><td>3.8</td><td>12</td><td>300</td><td>2.5</td></tr><tr><td>Simulation 2</td><td><b>6</b></td><td>12</td><td>300</td><td>2.5</td></tr><tr><td>Simulation 3</td><td>3.8</td><td><b>15</b></td><td>300</td><td>2.5</td></tr><tr><td>Simulation 4</td><td>3.8</td><td>12</td><td><b>290</b></td><td>2.5</td></tr><tr><td>Simulation 5</td><td>3.8</td><td>12</td><td><b>310</b></td><td>2.5</td></tr><tr><td>Simulation 6</td><td>3.8</td><td>12</td><td>300</td><td><b>4.5</b></td></tr><tr><td>Simulation 7</td><td>3.8</td><td>12</td><td>300</td><td><b>0.25</b></td></tr></tbody></table>

observation at this point.

To further interpret these findings, we can make a rough estimate of the minimum BOSZ simulation duration that would be necessary to allow the identification of a BOSZ amplitude map *analog* that is strongly similar to the SAR amplitude map. Applying the method described by (Van den Dool, 1994), the minimum number of independent BOSZ time steps *M* that need to be simulated to find at least one correct *analog* of the SAR amplitude map is defined as:

$$M = - \ln(1 - p) / \alpha^N \quad (2)$$

*N* is the number of independent and identically distributed (IID) random variables that represent the global amplitude map. Assuming that the global map can be well represented by *N* IID amplitude points is reasonable in the deeper area of the domain. Therefore we will preferably focus our following discussion on the deeper sub-domain. *p* is the probability that we indeed find one correct *analog* of the SAR amplitude map. *α* is the probability that an amplitude point ranges within a confidence interval *ε*. Thus *ε* controls the quality of the *analog* we are looking for (smaller *ε* means better *analog*). In the deeper sub-domain, we can reasonably make the hypothesis that the *N* IID amplitude points follow a Rayleigh distribution with a shape parameter *s*, such that *α* = 1 - exp(- *ε*² / (2*ε*²)).

In our configuration, we set *s* = 0.25 (suitable for normalized amplitude ranging between 0 and 1) and *ε* = 0.2 (authorising a confidence interval of ±20%), hence *α* ≈ 0.1. We further choose *p* = 95%. To estimate *N*, we consider that the size of a wave group is a good approximation to evaluate the average distance between two IID amplitude points. From visual inspection, we estimate that a reasonable

wave group size is 1km and considering a sub-domain size of approximately 2km by 6km, we find *N* = 12. Therefore according to (Van den Dool, 1994), the minimum number of amplitudes maps that would be required is ≈ 3 × 10¹². With BOSZ amplitude maps saved every 10s, to identify one correct *analog* of the SAR amplitude map would require a BOSZ simulation of at least 10 million years.

Though this first analysis produces interesting insights into BOSZ model-SAR comparison, the wave group stochastic nature makes difficult any quantitative use of the SAR information for a direct comparison to numerical model outputs. To overcome this problem, in the next section we propose to explore a second methodology aiming at filtering out the wave group signature in the SAR wave information.

### 4.3. Methodology #2: comparison of BOSZ output with averaged SAR-derived amplitude maps

#### 4.3.1. Main steps of the methodology

Satellite data provide instantaneous information about the wave field amplitude, which is modulated by wave group effects and depends of the immediate phase shift between the different spectral components. As demonstrated in the previous section, these random wave group modulations prevent direct comparison between a single SAR image - or snapshot - and any instantaneous free surface elevation map from a model as soon as this model is forced at its offshore boundary by a superposition of spectral components which has not exactly the real phases distribution.

An alternative option, which is further explored in this section, is to attempt to filter this unknown amplitude modulation due to wave groups by averaging several SAR images grouped into similar conditions. To identify which images can be averaged, it is first necessary to determine a range of parameters that define these similar conditions. For that purpose, we first performed a sensitivity analysis of the study site to the incident sea state conditions (wave height, period, direction) and to the mean tide level, using BOSZ output as a first guess for this exercise.

Based on these considerations, the methodology proposed can be decomposed into the following main steps:

1. Define ranges of parameters that can be considered as similar conditions based on a site sensitivity analysis;

2. Collect historical SAR images and classify them into ensembles corresponding to similar conditions; Then for each ensemble of SAR images:

3. Compute the normalized averaged SAR-derived amplitude map;

4. Compute the averaged offshore incident wave spectrum for the ensemble and run the corresponding wave model simulation;

<footnote><sup>a</sup> Reference case (REF).</footnote>
<figure><img src="image_82.png" /><figcaption>**Fig. 12.** Normalized significant wave height along the two longshore transects for the different simulations performed for the sensitivity analysis (input parameters summarized in Table 2). Panel (a) corresponds to the transect in the deeper waters ($X = 4.125\,km$) and panel (b) corresponds to the transect in the shallower waters ($X = 5.250\,km$).</figcaption></figure>
<figure><img src="image_83.png" /><figcaption>Fig. 13. SAR images classified as function of the mean wavelength and mean wave direction. The color is related to the normalized energy of each event. The three circles indicate relevant ensembles selected for the following study. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

5. Compute the normalized averaged wave model amplitude map (spectral filtered and non-filtered) if phase-resolving model, or the normalized wave model $H_s$ map if spectral model;

6. Compare the obtained SAR-derived and model-derived maps.

The next paragraphs present an application of these different steps on our study site.

### 4.3.2. Sensitivity study of the site of interest

The sensitivity analysis was performed on the following parameters: incident wave height $H_{s,0}$, wave period $T_{p,0}$, wave direction $\theta_{p,0}$, and mean tide level $\bar{\eta}$. For simplicity, parametric input spectra were used as an input of BOSZ, fitting the so-called TMA spectral shape on the incident sea state bulk parameters. The two longshore transects identified in Fig. 3 are examined again in this analysis.

The relevant ranges to be tested for each parameter have been determined based on a 1 year dataset of Anglet wave buoy measurements (year 2018). We choose to focus our interest on moderate to energetic swell events since they are more favorable for the SAR - model comparison. Hence, only cases with $H_{s,0} > 3m$ are considered. Conditions used as reference case (hereinafter referred to as REF) are ($H_{s,0}$, $T_{p,0}$, $\theta_{p,0}$) = (3.8m, 12 s, 300°) with a mean tide level $\bar{\eta} = 2.5m$ (above Chart Datum). Then, simulations are conducted introducing variations of these parameters, as summarized in Table 2.

The normalized significant wave height $H_s/H_{s,0}$ extracted from BOSZ simulations along the two longshore transects is plotted in Fig. 12 (a) and (b) for the different sets of parameters considered. Results obtained suggest that wave conditions at the two transects are quite sensitive to the incoming peak wave direction and to a lesser extent to peak period and significant wave height changes. The mean tide level influence on the longshore variability is limited over the two transects. Small differences due to $\bar{\eta}$ modifications are visible in shallower waters ($X = 5.250km$) but they are marginal. Significant differences only happen closer to the coast, near and inside the surf zone (not shown), but this area is not our focus here as SAR images does not provide information about breaking waves amplitude.

Therefore, we can conclude on the range of variation authorized to identified similar events. No significant differences are seen between $T = 12s$ and $T = 15s$. It corresponds to a wavelength difference of 50m (in water depths ≈ 25m). In the following methodology, for the SAR images ensembles analysis, we authorize a direction range of 20° and a wavelength variation of ±10m around the characteristic wavelength. This is a trade-off between the sensitivity of the wave field to the offshore parameters, and the need for a sufficiently large number of SAR images to suppress the random wave groups contributions in an ensemble.

### 4.3.3. Comparison between SAR-derived and BOSZ-derived averaged normalized amplitude maps

Combining conclusions of the sensitivity analysis with the available historical SAR images database (201 Level-1 IW GRD), three ensembles of SAR images are finally selected, which we shall assume to represent statistically comparable wave conditions for the site of interest. The total available SAR images data set is represented in Fig. 13 according to the corresponding incident wavelength, direction and energy, together with three selected ensembles (circles), hereinafter referred as # in the figures. #1, #2 and #3 contain respectively 29, 21 and 19 events. This step is constrained by a trade-off between the sensitivity of the wave field and the need for a large enough number of SAR images to smooth the wave groups modulations. It can be noticed here that the increase in SAR images quantity in the coming years should support a more accurate statistical representation of a given wave situation. As explained in the previous paragraphs, based on this classification of SAR images into consistent wave event ensembles, the averaged normalized SAR amplitude map is computed for each ensemble. Here the mean amplitude over half the offshore domain is used to normalize the amplitude map. Maps obtained for the three ensembles are given in Fig. 14 (a).

Then, wave model conditions corresponding to each ensemble are simulated to compare them to the SAR-derived maps. To run the corresponding model simulations, the equivalent incident spectrum of each ensemble is computed by averaging the Anglet wave buoy spectra of all the events in each ensemble. Three averaged spectra are thus obtained and used as an input for the corresponding numerical simulations with both BOSZ and SWAN models. The input parameters are summarized in Table 3.

Three BOSZ model runs were performed corresponding to the three incident conditions in Table 3. Free surface elevations maps are saved every 10 s and wave amplitude maps (filtered and non-filtered) are computed, normalized and averaged. Results obtained are plotted in Fig. 14(b) and (c). Finally, in the case of SWAN, which does not provide free surface elevations $\eta$, the $H_s$ field is used instead of the amplitude. Computed $H_s$ field are normalized by their mean offshore value (we verified in the course of the study that this is a reasonable approximation for the normalized amplitude). Maps consequently obtained from SWAN are given in Fig. 14 (d) for the three ensembles.

First examining the SAR-derived maps (Fig. 14-a), a significant variability of the wave field is obtained in the offshore half of the domain ($X < 3.5km$). We believe that this variability is due to wave groupiness that controls this deeper part of the area and which is still not properly filtered by the ensemble average. It is even more pronounced for ensemble #3 which contains the smallest number of events. In the nearshore area ($X \ge 4km$), several patterns seem to appear more clearly. This is especially the case for ensemble #3 in the area of Biarritz Grande Plage ($3km < Y < 6km$). In this area, wave propagation is highly
<figure><img src="image_84.png" /><figcaption>Fig. 14. SAR normalized amplitude (ā) map derived from the average of the events in each ensemble (a) and the corresponding BOSZ-derived normalized amplitude (ā) (spectral filtered (b) and non-filtered (c)) and SAR-derived normalized significant wave height (Hs) maps of each ensemble (d).</figcaption></figure>
<caption>**Table 3**</caption>

Set of parameters of the three ensemble used as input of BOSZ and SWAN defined from the Anglet wave buoy. $H_s$ is the significant wave height, $T_p$ is the peak period and $\theta_p$ is the peak direction. The mean tide level is $\bar{\eta}$.

<table><thead><tr><th></th><th>$H_s(m)$</th><th>$T_p(s)$</th><th>$\theta_p(\circ)$</th><th>$\bar{\eta}(m)$</th></tr></thead><tbody><tr><td>#1</td><td>2.07</td><td>11.11</td><td>305</td><td>2.5</td></tr><tr><td>#2</td><td>2.28</td><td>13.33</td><td>310</td><td>2.5</td></tr><tr><td>#3</td><td>2.54</td><td>15.38</td><td>295</td><td>2.5</td></tr></tbody></table>

influenced by local bathymetric features and the SAR #3 map reveals a remarkable shadow area around $Y = 4.5km$, neighbours by two higher energy areas in the South ($Y = 3.5km$) and in the North ($Y = 5km$). Steep longshore gradients of wave amplitude separate these areas generated by bottom-induced refraction. Remarkably, looking at the filtered BOSZ map (Fig. 14 (b)) for ensemble #3, the focusing/defocusing pattern described above off Biarritz Grande Plage appears rather consistent with the SAR information in terms of both location and intensity.

The input peak direction of ensemble #3 is oblique and because BOSZ model wavemaker generates wave at the offshore boundary (and not along the lateral sides), it artificially creates a shadow area on the most southern area of the domain. This is the reason why strong discrepancies are observed between the SAR and BOSZ data (both spectral filtered and non-filtered) at this location. Ensembles #1 and #2 also provides interesting similarities between SAR and BOSZ filtered maps regarding the defocusing area in front of Biarritz Grande Plage ($3km < Y < 6km$), while the agreement is less appreciable in the remaining of the domain. Reasons for this discrepancy are still unclear at this stage.

The non-filtered BOSZ map (Fig. 14 (c)) indicates more intense focusing areas than the filtered BOSZ maps. This is due to the non-filtered data containing the converging oblique waves of short and infragravity wave scales, which lie in a directional and/or wavelength sector that is outside the spectral filter. Therefore, the filtered data appear generally smoother than the non-filtered one.

SWAN normalized $H_s$ maps (Fig. 14 (d)), contains in theory the contribution of these oblique and short waves but not the contribution of infragravity waves, since the non-linear transfer toward the low frequency band is not parameterized in the triad interaction source term. The application of the same filtering approach to make SWAN output directly comparable to the filtered SAR and BOSZ amplitude maps is in theory feasible, but it would require access to the frequency-directional wave energy spectrum at each grid point which is out of reach in practice, as already stated earlier. If we were able to apply the same spectral filtering to SWAN, we would most likely obtain smoother focusing patterns, since the oblique and short waves generated by the refraction and shoaling would be dampened. Since the bottom-induced refraction patterns are already less intense in SWAN than in BOSZ non-filtered data, filtered SWAN data would likely show larger discrepancies than filtered BOSZ compared to filtered SAR data.

## 5. Conclusion

The present study site is a region with strong spatial heterogeneity in the wave field in both the cross-shore and longshore directions, which is mostly due to depth-induced refraction in the coastal zone. The present work suggests that different numerical approaches, including the spectral modeling approach from SWAN, routinely used for coastal engineering applications, may lead to significant differences in the local wave heights, wave power magnitudes and location of focusing areas. In general, remarkably steep longshore gradients in wave heights are provided by the implemented phase-resolving approach, while smoother variations are suggested by the spectral model. However, there is a lack of observation to confirm or not such patterns, which can hardly be assessed from *in situ* point measurements. Assuming that SAR images

contain relevant coastal wave information, this paper proposes several methodologies to compare it consistently with wave model outputs.

The first methodology consists in comparing instantaneous amplitude wave fields obtained from SAR images to snapshots of simulations done with the phase-resolving model BOSZ. To account for modulation by wave groups, similarities between BOSZ and SAR amplitude maps were searched among a series of BOSZ results corresponding to various random phases realizations. Though some similarities in the wave patterns are obtained, the effects of wave group modulations prevent a rigorous comparison with the phase-resolving model. We conclude that the random phase procedure used as part of the BOSZ wavemaker would require a non-affordable number of simulations to get a correct analog of the SAR snapshot.

Pursuing from this conclusion, an attempt to filter the wave group modulations was performed by averaging amplitude-derived maps from SAR images grouped into similar wave conditions ensembles. This second methodology shows encouraging similarities between filtered BOSZ and SAR data, at our site of interest that features very pronounced focusing/defocusing patterns. The associated comparison appears to support the wave refraction representation of the phase-resolving model, over the situations considered.

Although further research are required to validate the accuracy of the wave information extracted from SAR images, we believe that this study reveals a potential of SAR images for the investigation of the wave field spatial variability, as well as its representation by wave models, which is still very hard to assess from traditional *in situ* point measurements. The main drawback of SAR data is its intermittent and instantaneous nature. In addition, the empirical transfer function between $\sigma_0$ and wave amplitude would need further investigation to clarify its reliability. Dedicated validation with instruments providing accurate measurements of the phase-resolved wave amplitude spatial distribution, such as stereo-video systems [e.g. 33] would be valuable in this objective. The accumulation of SAR images over the coming years will also likely improve the accuracy and robustness of the statistical estimation provided by the proposed methodology. Thus, we believe that SAR imagery has the potential to become an important asset in the evaluation of wave models skills, allowing to capture essential information regarding the wave field spatial variability in coastal areas.

## CRediT authorship contribution statement

**Audrey Varing:** Writing – original draft, Investigation, Conceptualization, Methodology, Validation. **Jean-François Filipot:** Conceptualization, Methodology, Investigation, Supervision, Funding acquisition. **Matthias Delpey:** Software, Conceptualization, Methodology, Investigation, Funding acquisition. **Gilles Guitton:** Investigation, Methodology. **Fabrice Collard:** Conceptualization, Methodology, Funding acquisition. **Paul Platzer:** Formal analysis, Investigation. **Volker Roeber:** Software, Investigation. **Denis Morichon:** Investigation.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgment

This work has been done in the framework of the DiMe and CAR-AVELE projects, which benefit from French government support managed by the Agence Nationale de la Recherche (ANR) under the program ‘Investissements d’Avenir’ ANR-10-IEED-0006-14 and ANR-10-IEED-0006-26. Also, this study was part of the COASTWAVE project, winner of the 3rd numerical challenge CADO-Satellite data driven by the Pôle Mer Bretagne Atlantique via the MORESPACE initiative. The nearshore bathymetric and Anglet buoy data were collected as part of
the MAREA project (2016–2019), which is an INTERREG POCTEFA research program funded by FEDER and led by Communauté d'Agglomération Pays Basque. Anglet buoy (06402) is operated by CEREMA with the support of Université de Pau et des Pays de l'Adour as part of the CANDHIS network. Offshore bathymetric data were provided by the French Navy Hydrographic and Oceanographic Service (SHOM) through the web service data. shom.fr. Volker Roeber acknowledges financial support from the Isite program Energy & Environment Solutions (E2S), the Communauté d'Agglomération Pays Basque (CAPB) and the Communauté Région Nouvelle Aquitaine (CRNA) for the chair position HPC-Waves. The numerical simulations were performed on the High Performance Computing (HPC) cluster Datarmor of the “Pôle de Calcul Intensif pour la Mer” (PCIM) (http://www.ifremer.fr/pcim).

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.coastaleng.2020.103793.

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# Chapter 5

Interaction between breaking waves
and offshore structures: field
experiments

**5.1 Introduction**

Slamming load on bottom-fixed offshore wind turbines has triggered a corpus of industry-driven research projects (e.g. the joint industry projects WIFI and BREAKING, for instance) and papers [e.g. *Wienke and Oumeraci, 2005; Bred-mose et al., 2013; Lian, 2018; Paulsen et al., 2019*] because breaking waves occur frequently in the intermediate to shallow water conditions of the corresponding farms.

In the typical water depths (> 50m) targeted by the floating offshore wind
industry, the interaction of waves with the sea bottom are weak, hence, so are the
shoaling effects that enhance the likelihood of large breaking waves. However,
wave group interactions may lead to large breaking waves even in deep water.
As an example, the superstructure of the Jean Nicoli passenger ship (200m long,
40m high) was severely damaged by a large breaking wave during a storm in
the Mediterranean Sea. A video record of Principle Power WINDFLOAT float-
ing offshore wind turbine in storm conditions off the Portuguese coast shows a
striking example of a large breaking wave impacting a semi-submersible platform
deployed in deep water. Impact of large breaking waves on offshore platforms has
been a concern for the oil&gas industry for decades. Hurricane conditions during
Ivan, Rita and Katrina caused the destruction of 126 oil&gas offshore platforms
and severe damages to 186 others in the Gulf of Mexico [Kaiser et al., 2009], with
likely an important contribution from large breaking waves. In December 2015,
a crew member of an oil&gas platform deployed West of Bergen, Norway, was
killed when a large breaking wave impacted and then flooded the living quarters
of the platform. Lighthouse keepers at La Jument lighthouse, Brittany, France,
<figure><img src="image_85.png" /><figcaption>Figure 5.1.1: Top panels : a sequence of a massive wave slamming La Jument lighthouse on February 6, 2014. The lighthouse is 48m-high and the substructure 14m-high. The wave is approximately 20m-high from trough to crest, similar to "wave1" in Filipot et al. [2019]. Credit : Air, Vide et Eau. Bottom panel : Côme and Gauthier experiencing a slamming load. The kids are 1m(10)-high and the wave approximately 0.25m-high, from trough to crest. Picture taken at Portez beach, Brittany, France on November 11, 2021.</figcaption></figure>

known as the "hell of the hells", reported earthquake-like breaking wave impacts (see 5.1.1) that often caused the mercury tank supporting the lense to overflow. Equally well documented in the Oil&Gas or fixed offshore wind turbine literature, large breaking waves may excite the first structural modes, cause damage by vertical water excursion (run-up), water over deck (green water), or local mechanical damages. The IEC 61400-3 (2005), one of the most widely applied certification document for the design of offshore wind turbines, recommends to amplify by a factor 1.35 the 50-year loads on the structure, to ensure an acceptable balance between risk and economic viability. The conservativeness of this safety factor is one of the main motivation for the present research effort. From observations collected at a bottom mounted offshore wind turbine (Blyth wind farm, UK), Hallowell et al. [2016] reported that slamming loads were underestimated by the engineering approach proposed in the certification documents. The same statement was made by Vestbøstad et al. [2017] for the ULS slamming loads on the Heidrun oil rig moored in deep water (350m), off the Norway coast.

One important knowledge gap regarding slamming loads on offshore wind turbines is the lack of observations in the field of the parameters of interest. This
includes the geometry and fluid kinematics of the impacting wave, the pressure field at slamming and the dynamic response of the structure. We introduce below a synthetic state of the art of the past studies investigating slamming loads in the field and then present a research effort dedicated to the development of a measurement protocol that intends to collect decisive information on slamming loads on full scale offshore structures.

## 5.2 Past field experiment on slamming on coastal and offshore structures

Among the pioneers, De Rouiville [1938] equipped the Dieppe breakwater (France) with pressure sensors, and recorded a peak pressure of 6.90 bars. More recently, Bird et al. [1998] deployed sensors on the Alderney breakwater (Jersey, UK) and captured a peak pressure of 3.96 bars. In France, Larroque et al. [2018], Poncet et al. [2019] and d'Amico et al. [2020] investigated the slamming loads on the Artha detached breakwater (Saint Jean de Luz France) which lies in 10-15m water depth and captured a peak pressure of 4.47 bars. In the frame of the OWTES project one of the 2MW turbines deployed at the Blyth (UK) wind farm was equipped with sensors during sixteen months to study the wave loads and associated structural response under the action of shallow water breaking waves. The turbine was equipped with a wave radar to record the water elevation at the monopile, current and wave sensors moored 40m up-wave of the turbine and several strain-gauges to capture the bending moments of the pile foundation and turbine mast. The dataset was exploited by Hallowell et al. [2016] to study the breaking wave loads on the Blyth turbine. They were able to identify that the breaking waves were the only waves able to excite the second mode of oscillation of the structure. They report a maximum moment of 14.9 MN/m caused by a rather small breaking wave and concluded that the source of variability of the breaking wave loads could be attributed to the distance of the breaking onset relatively to the offshore wind turbine, the actions of other environmental forcing such as wind and the variability in the geometry and orbital velocities of the breaking waves.

## 5.3 Development of a measurement protocol to study slamming loads on offshore structures

This section introduces an experiment deployed from a rock-lighthouse in the frame of the DiMe project, that is about to be deployed on a floating offshore wind turbine in the scope of the DIMPACT project.

To illustrate further the motivation of the study, let us start by presenting
the generic law used by engineers to account for slamming loads on offshore or coastal structures. For a cylinder of Radius R impacted by a breaking wave, the resulting force can be expressed, based on Goda and Kakizaki [1966] and recalled in Wienke and Oumeraci [2005] by:

$$F_I = \pi \rho R \lambda \eta_b c^2, \qquad (5.1)$$

where λ is the so-called "curling factor" that gives the proportion of the crest height that is active in the slamming loads (i.e., that is vertical), η_b is the crest elevation of the breaking wave and c the crest phase speed that approximates the fluid velocity in the breaking crest. Although the relevance of this simple formulation can be discussed (see Chapter 6), equation 5.1 probably contains the parameters of interest for the problem at hand.

The main difficulty to validate equation 5.1 is hence to correctly capture the wave parameters η_b, c and λ. None of the past studies provided such level of information and therefore the material required to validate the engineering approach in the field.

In the frame of the DiMe project, an original experiment was conducted from La Jument lighthouse [see Appendix 5.A Filipot et al., 2019], one of the most iconic lighthouse in the world, thanks to the spectacular wave impacts it undergoes every winter. La Jument lighthouse, built at the beginning of the 20th century, is located over a shallow rocky platform, preceded by a steep bottom slope, diving under 80m depth only 500m offshore, to the West of the lighthouse. It is exposed to severe sea states associated with intense low pressure systems sweeping the North East Atlantic during the winter months. The scientific effort, carried out by FEM, Cerema, Ifremer, HZG and Shom, focused on the deployment of an integrated observational system able to capture synchronously and in a deterministic way the geometric and kinematic properties of the individual incoming waves together with the slamming induced-pressure field applied on the lighthouse and the response of the structure. To achieve this the following instruments were deployed in December 2017 (at the exception of the pressure sensors) and are running since then, for systems 1 to 4:

1. A stereo-video system consisting of 2 BM-500GE JAI cameras, installed at the altitude of the lantern, hence about 42m above the chart datum

2. Five pressure sensors (installed in summer 2018 and not exploited in Filipot et al. [2019]), one on the substructure and four on the tower,

3. Four RECOVIB-IAC-A03 accelerometers were deployed inside the lighthouse at four different heights: 20.6, 31.1, 38.7 and 45.6m above the chart datum,

4. An X-band radar was running from the top of the lighthouse to capture the larger (compare to the stereo-video system) scale current and wave field
<figure><img src="image_86.png" /><figcaption>Figure 5.3.1: Illustration of some of the instruments deployment of La Jument lighthouse. Panel a): one of the two cameras of the stereo-video system, b) X-band radar operated by HZG, c) one of the pressure sensors deployed on the tower wall, d) one of the accelerometers installed inside La Jument.</figcaption></figure>

5. An AWAC current profiler, able to record wave information was installed in 59m water depth

6. A datawell wave buoy, moored in 92m depth, 3km offshore of the lighthouse.

Filipot et al. [2019] presents the exploitation of the winter 2017-18 with a focus on a particular storm event, that occurred on January 3, 2018. This event, associated with a typical wind low pressure system, generated waves with significant wave height nearing 10.5m with peak periods of about 14s carrying extreme individual waves reaching 24.2m high for one of them. The choice of this particular event follows the so-called "Response-based design" approach, hence starting with the analysis of the acceleration records over the experiment period that showed an extreme acceleration peak measured by the highest sensor (see figure 5.3.2), on January 3, 2018 at 09:41:22 UTC. The exploitation of the stereo-video record at the time of this remarkable impact, highlighted the existence of a giant breaking wave (hereinafter wave1) with a wave height of 19m and a crest elevation of 13m above the mean sea level (see figure 5.3.3). Further investigations showed the presence of other large breaking waves, with crest elevation nearing that of wave1. Still, none of these other waves induced a structural acceleration comparable to that caused by wave1. This nonlinear behaviour triggered further examination of the relative altitude of the wave crest, with regards to the lighthouse structure. The analysis suggests that wave1's crest elevation exceeded the top of the substructure that was added shortly after La Jument commissioning to limit the lighthouse vibrations. Surprisingly, our hypothesis was further supported by two pictures of wave1 taken by accident from Ushant island by two different observers. These images are presented in Denarié and Fady [2019] and clearly demonstrated that wave1 crest reached La Jument tower that is more flexible than the substructure which explains the intense vibrations sensed by the
<figure><img src="image_87.png" /><figcaption>Figure 5.3.2: Acceleration along the horizontal and vertical axes measured by the highest sensor, on January 3, 2018 around 09:41:22 UTC. The left panel shows that the acceleration peak occurred suddenly after several minutes of calm. The right panel provides a zoomed version of the same acceleration event.</figcaption></figure>

top accelerometer.

## 5.4 Database of the geometry and kinematics of breaking waves

As shown by equation 5.1, the magnitude of slamming loads is controlled by the crest velocity, the slope of the front face and the elevation of the crest. Regarding the crest elevation, the recommendation of certification documents [DNV, 2014] for the design of floating offshore wind turbines, is to use a crest elevation of 1.4 the significant wave height of the design sea state. The robustness of this proposition may be questioned. To address this, the stereo video system could be useful since it is a powerful tool to characterize the shape and kinematic of breaking waves.

On a related topic, for practical reasons, the wave tank and numerical experiments reproducing slamming loads on offshore structures often rely on focused or chirped wave packets [e.g. Hildebrandt et al., 2013]. However, one may wonder whether the type of wave packets studied share similarities with those carrying large breaking waves at sea. First the shape of the breaking front face, hence the severity of the breaking, should be further investigated at sea. Also, the wave group structure should be examined since it may control the dynamical response of a floating offshore wind turbine that would then further modify the relative floater-fluid motion and consequently the slamming loads. The observations of 4D (3D in space + time) wave reconstruction provided by Guimarães et al. [2020] (Appendix 5.B) are a first database that should be exploited to address the above-cited challenges. Further efforts are required to accumulate more observations in the most severe conditions. This is one of the main objective of the ongoing field
<figure><img src="image_88.png" /><figcaption>Figure 5.3.3: Stereo-video reconstruction of "wave1" (19m-high, crest elevation of 13m), the giant wave that impacted La Jument lighthouse on January 3, 2018, 09:41:22 UTC.</figcaption></figure>
experiment, perpetuated at La Jument lighthouse in the frame of the DIMPACT project. Careful examination of the observations will be carried out to provide guidance for the definition of the wave characteristic to be inputed in the slamming load formulas. They will also help guiding more realistic wave tank and numerical experiments attempting to reproduce slamming loads on offshore wind turbines.

## 5.5 Discussions & Conclusion

Although wave tank experiments and numerical models can provide insightful information regarding the design loads associated with breaking wave impact on offshore wind turbines, the inherent limitations (e.g.: scaling issues, numerical schemes accuracy), field observations appear to be an important step in reducing the uncertainties in the slamming loads estimation needed for the design of offshore wind turbines. One of the major difficulty, lies in defining a proper measurement protocol to capture all the parameters of interest. This was precisely the objective of La Jument experiment that served as a demonstrator for a deployment on the former Hywind Demo wind turbine, to be achieved through the DIMPACT project (see Chapter 6). Still, the question of the ability of the pressure sensors to render a reliable estimation of the loads remains open. Indeed, the study of Filipot et al. [2019] did not exploit the pressure records (since the sensors where not deployed for the first winter). Further numerical investigations (conducted in the DIMPACT project) should help understanding whether relevant load information can be inferred by point measurements of the pressure field, known to be highly variable in space. In addition to provide ground truth for validating engineering approaches to assess slamming loads, these experiments should also provide guidance on the characteristics of the breaking waves to be considered. This question is particularly critical in intermediate or deep water where no observations of large breaking waves exists, with the exception of mariners testimonies.
# Appendix

5.A Paper from Filipot & al. (2019)
Research

<figure><img src="image_89.png" /></figure>

Check for
updates

**Cite this article:** Filipot J-F et al. 2019 La Jument lighthouse: a real-scale laboratory for the study of giant waves and their loading on marine structures. *Phil. Trans. R. Soc. A 377:* 20190008.

http://dx.doi.org/10.1098/rsta.2019.0008

Accepted: 8 June 2019

One contribution of 14 to a theme issue
'Environmental loading of heritage structures'.

**Subject Areas:**

oceanography, ocean engineering, structural
engineering, fluid mechanics

**Keywords:**

extreme wave, wave breaking, wave loading

**Author for correspondence:**

J.-F. Filipot

e-mail: jean.francois.filipot@ite-fem.org

Electronic supplementary material is available
online at https://doi.org/10.6084/m9 figshare.
c.4567532.

La Jument lighthouse:
a real-scale laboratory for
the study of giant waves
and their loading on
marine structures

J.-F. Filipot<fnref n="1" />, P. Guimaraes<fnref n="2" />, F. Leckler<fnref n="2" />, J. Hortsmann<fnref n="3" />,
R. Carrasco<fnref n="3" />, E. Leroy<fnref n="4" />, N. Fady<fnref n="4" />, M. Accensi<fnref n="5" />,

M. Prevosto<fnref n="5" />, R. Duarte<fnref n="1" />, V. Roeber<fnref n="6" />, A. Benetazzo<fnref n="7" />,

C. Raoult<fnref n="2" />, M. Franzetti<fnref n="8" />, A. Varing<fnref n="1" /> and N. Le Dantec<fnref n="4" />

<figure><img src="image_90.png" /></figure>

J-FF, 0000-0003-0875-8791

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

<footnote n="1">¹France Energies Marines, Plouzané, Bretagne, France</footnote>

<footnote n="2">²Service Hydrographique et Oceanographique de la Marine, Brest,
Bretagne, France</footnote>

<footnote n="3">³Helmholtz-Zentrum Geesthacht HZG Campus Teltow, Geestacht,
Germany</footnote>

<footnote n="4">⁴CEREMA Direction territoriale Ouest, Plouzané, Bretagne, France</footnote>

<footnote n="5">⁵Ifremer, Plouzané, Bretagne, France</footnote>

<footnote n="6">⁶University of Pau and Pays de l'Adour, Bidart, France</footnote>

<footnote n="7">⁷CNR-ISMAR, Venice, Italy</footnote>

<footnote n="8">⁸IUEM-LGO, Plouzané, Bretagne, France</footnote>
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'.

# 1. Introduction

## (a) La Jument lighthouse: context

Offshore lighthouses at sea represent examples of engineering marvels, by overcoming challenges of constructing robust structures to withstand the extreme environmental loading they have to face for decades or even centuries. Among these environmental forcings, the wave loading generally dominates by far the winds or current actions on the structure. Indeed, because the lighthouses at sea are constructed upon shallow rocky platforms they are exposed to breaking waves responsible for intense and transient forces, also known as ‘slamming’ impacts. During the most extreme storms, breaking waves impacts threaten the lighthouses’ structural integrity, which raises the question of the remaining lifetime of these fascinating monuments. Among the threatened offshore lighthouses, La Jument, located offshore of Ushant island, Western Brittany, France (figure 1) is one of the most iconic. A series of pictures taken from a helicopter by Jean Guichard, showing the lighthouse keeper opening the door while a giant wave engulfs the substructure is famous worldwide. La Jument’s photogenic quality is tightly related to its extreme exposure to North East Atlantic storm waves. These waves that shoal over the very steep foreshore bathymetry may violently break over the lighthouse and generate sea spray that can run up well over the lighthouse lantern (see the helicopter video recording available as electronic supplementary material).

La Jument was completed in 1911 after 8 years of construction. The final structure, 48 m high above chart datum (CD), underwent worrying vibrations during the first strong winter storms. In 1911 and 1916, two storms were responsible for vibrations so intense that they caused the lantern glass to break and the mercury tank (supporting the Fresnel lens rotation) to overflow, forcing the lighthouse keepers to retrieve the toxic liquid with their bare hands [1]. These incidents pushed the engineers to propose and provide reinforcement of the lighthouse substructure (figure 1). This did not completely stop the waves from damaging the lighthouse. In 1934, three holes were drilled from the substructure to 30 m down to anchor La Jument directly into the underlying rocky platform.

Today, La Jument still faces storm waves and the question of the remaining lifetime of this iconic heritage monument is open. The same question, applicable to English rock lighthouses sparked interest in the scientific community. Considerable efforts were conducted through the STORMLAMP project (e.g. [2,3]) to improve the knowledge of the current mechanical response and health status of different British lighthouses exposed to high seas. Regarding La Jument [4] has addressed the complex question of the remaining lifetime of the structure and the possible reinforcements required to extend it. This in-depth study examined the mechanical structure's response to impacts of large breakers and showed that the lighthouse behaviour in terms of accelerations, displacements, strains and failures was highly correlated to the characteristics of the breaking waves hitting the lighthouse. However, knowledge of the wave field around La Jument was insufficient at the time of Loraux's work and he had to rely on wave climatology produced by a phase averaged spectral wave model to define the geometric and kinematic characteristics of the breaking waves for his extreme loading cases on La Jument. He concluded that dedicated field measurements would be valuable to support his results; this statement was part of the motivation for the experiment that will be described in this paper.
<figure><img src="image_91.png" /></figure>

**Figure 1.** La Jument lighthouse, Brittany France (48°25′20.00″ N, 5°8′2.28″ W). (a) in calm wave conditions but with intense spring tide currents causing eddies in the wake of the lighthouse. The substructure added to the lighthouse to solve its early-life stability issues is well visible. (b) La Jument in storm conditions. Picture courtesy of Jean Guichard. (c) Historical plan of La Jument, before the addition of the final substructure. The current elevation above chart datum of the substructure is virtually shown here (14 m) as it is a key element for the paper. (d) Wave rose from the wave climatology presented in the paper (location of the extraction: 48°25′35″ N, 5°7′50″ W, i.e. about 1.2 km in the northwest of La Jument).

## (b) Lighthouses design and breaking waves

The design of any marine structure, such as offshore oil platforms, offshore wind turbines, breakwaters or offshore lighthouses, relies among other parameters on knowledge of the most extreme sea states that the structure will possibly face over its lifetime. The corresponding characteristic 100 or 50 year wave is then used to compute inertia and drag forces based on Morison theory [5]. It is now well acknowledged that in the presence of breaking waves, an additional impact or slamming force should be added. Indeed, at breaking onset, the horizontal fluid velocities at the wave crest reach or even exceed the wave phase speed. At breaking onset, the wave crest (or at least part of it) behaves as a wall of water moving at the wave crest phase speed and its encounter with a marine structure results in a violent impact, yielding a large impulsive force. This breaking wave impact force must be considered in the marine structure design since it can be several times greater than the magnitude of the combined drag and inertia forces, though over a very short time interval [6]. The severity of the breakers and hence the magnitude of their induced force on the structures depends on the type of breaking (e.g. [7]): the most gentle ones, known as spilling breakers are initiated by a modest jet located in the direct vicinity of the wave crests, while plunging breakers are characterized by a much larger and more intense jet, enclosing an air pocket during the process of breaking. In addition, irrespective of the breaking type, the stage of the breaking process at impact is an important parameter, namely a broken wave with its highly aerated front face will cause a lower impact force than a wave at breaking onset, featuring a non-turbulent, non-aerated, vertical front face with high fluid velocities in the wave propagation direction (e.g. [8–10]).

When and why waves are breaking remains an open question because the understanding of wave breaking physics is still poor. For instance, until recently there was no consensus regarding an universal breaking onset criterion for irregular waves. Among the pioneers in this field, Miche [11] demonstrated that regular waves over a flat bottom are stable until $kH/\tanh(kd) = 0.88$, where k is the wavenumber, H is the wave height and d is the water depth. In deep water, this leads to the familiar $H/L = 1/7$ threshold in which $L = 2\pi/k$ the wavelength of an individual wave. In shallow water the Miche breaking limit becomes the so-called 'breaker index' $H/d = 0.88$, while the most widely used value is 0.78 [12]. Miche theory is not directly applicable to irregular waves propagating over a possibly varying bottom. A paper from Barthelemy et al. [13] suggests that any deep or intermediate water wave with a ratio orbital velocity at the crest over phase speed greater than 0.85 will inevitably and quickly break (within a fraction of wave period). Preliminary results
from Varing et al. [14] indicate that this breaking limit could be valid in shallow water as well. Shallow water breaking waves have been widely discussed in the literature and as mentioned above, it is well known that breaking onset can be related to the breaker index $H/d$. Thornton & Guza [15] showed that at a given location (or water depth) the probability density function of breaking wave height was not a Dirac function but a rather broad distribution. This is due to the stochastic nature of the breaking occurrence and probably to measurement technique that detects breakers at different stages. In addition to the height of the breakers, the type of breaking controls the magnitude of the wave loads on marine structures. The well-known Iribarren or surf similarity parameter [16], $\zeta = \tan \beta / \sqrt{S_0}$, with $\beta$ being the bottom slope and $S_0$ being the deep water wave steepness, provides an empirical breaking type classification. For storm waves at La Jument, $\zeta$ takes values between 2 and 3, typical of plunging waves. This is further consistent with visual observations of storm waves in the vicinity of La Jument. As explained in this paragraph, the knowledge regarding breaking waves statistics and type is still empirical and its application to complex and extreme hydrodynamic conditions found at La Jument is somewhat cumbersome. This stresses the importance of collecting direct and detailed observations of breaking waves on this site.

Because of the associated short impulsive force, breaking waves can excite specific structural modes of marine structures including lighthouses or offshore wind turbines. For instance, Hallowell et al. [17] noted that only breaking waves were able to excite the second mode of oscillations of a 2 MW fixed offshore wind turbine deployed at the Blyth wind farm (UK). Chella et al. [18] reported that the large remaining uncertainties in the design of offshore wind turbines are connected to our lack of knowledge of the breaking waves loading. The pioneering work from Von Karman [19] assimilated the effect of a breaking wave to the impact of a cylinder falling and hitting the water surface. Later, Goda & Kakizaki [20] concluded that the breaking-induced wave force on a vertical cylinder is due the change in momentum in the water mass. More recently, Wienke & Oumeraci [21] proposed the following expression for the time evolution of the slamming force induced by a breaker over a vertical cylinder:

$$F(t) = \lambda \eta_c \rho_w R V^2 \left( 2\pi - 2\sqrt{\frac{V}{R}} t \tanh^{-1} \sqrt{1 - \frac{V}{4R}} t \right), \quad (1.1)$$

for $0 \le t \le R/8V$,

$$F(t') = \lambda \eta_c \rho_w R V^2 \left( \pi \sqrt{\frac{V}{6Rt'}} - \left(\frac{8V}{3R}t'\right)^{1/4} \tanh^{-1} \sqrt{1 - \frac{V}{R}t' \sqrt{\frac{6V}{R}t'}} \right), \quad (1.2)$$

for $(R/8V) \le t' \le (12R/32V)$, with $t' = t - R/32V$.

The parameters controlling the intensity and time distribution of the impact force are therefore $\eta_c$ the elevation of the crest above the mean sea level, $\lambda$ the curling factor that gives the portion of the crest impacting the structure, $V$ the orbital fluid velocity in the crest, $\rho_w$ the water density and $R$ the radius of the cylinder. This formulation was carefully validated with a number of wave flume experiments reproducing the impact of breaking waves on a cylinder and is used in design standards for offshore marine structures (see, for instance, [22] for application to offshore wind turbines). Though the relevance of considering breaking waves for design purpose, the impact forces might also be considered for fatigue computations especially in shallow water environment (such as La Jument) where breaking waves are frequent [23]. From equations (1.1) and (1.2), it appears that the geometric and kinematic properties of the breaking waves (i.e. the parameters $\eta_b$, $\lambda$ and $V$) determine the magnitude and time evolution of the slamming force. Unfortunately, it is very difficult, if not impossible, to infer the characteristics of the breaking waves at the moment of their impact from a typical wave climatology that usually provides integrated wave parameters computed at several hundreds metres away from the structure.
<table><caption>**Table 1.** Extreme Wave/Wind/Current statistics from HOMERE database, $H_s$ is the significant wave height, $U_{10}$ and $U_{10,d}$ are the 10 m-high wind speed and direction, respectively; $T_p$ and $D_p$ are the peak period and direction of waves, respectively; $C_s$ and $C_d$ are the current speed and direction, respectively.</caption><thead><tr><th rowspan="2"></th><th colspan="4">return values</th><th colspan="7">most severe event</th></tr><tr><th>10y</th><th>20y</th><th>50y</th><th>100y</th><th>$H_s$ (m)</th><th>$T_p$ (s)</th><th>$D_p$ (°)</th><th>$U_{10}$ (m s<sup>-1</sup>)</th><th>$U_{10,d}$ (°)</th><th>$C_s$ (m s<sup>-1</sup>)</th><th>$C_d$ (°)</th></tr></thead><tbody><tr><td>$H_s$ (m)</td><td>11.8</td><td>12.7</td><td>13.9</td><td>14.7</td><td>12.7</td><td>17</td><td>-66</td><td>21.3</td><td>-78</td><td>0.79</td><td>146</td></tr><tr><td>$U_{10}$ (m s<sup>-1</sup>)</td><td>27.2</td><td>28.3</td><td>29.4</td><td>30.0</td><td>9.9</td><td>13.5</td><td>-82</td><td>29.4</td><td>-70</td><td>0.33</td><td>131</td></tr><tr><td>$C_s$ (m s<sup>-1</sup>)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.92</td><td>323</td></tr></tbody></table>

### (c) Objectives of the paper

In this paper, we shall try to provide a description of the hydrodynamic conditions at La Jument with a focus on the breaking waves impacting the lighthouse during storm events. The first part of the paper describes the storm waves, current and structure acceleration observations and bathymetric data collected from or around this lighthouse during winter 2017–2018. The second part of the paper focuses on a particular storm event on 3 January 2018 marked by a strong and transient acceleration and displacement peak in the lighthouse at 9:42:07 UTC, induced by a giant breaker slamming over La Jument. A discussion follows on the characteristics of this wave to elucidate why it produced considerably higher accelerations and displacements of the structure compared to the other large waves of the same storm event.

## 2. Hydrodynamic climate around La Jument

The lighthouse is located in a macro-tidal environment. Tidal observations were recorded in 2013 by SHOM in the Lampaul bay (5°06' W, 48°27' W) and were analysed in [24]. The tidal range is 7.68 m and mean level is 4.13 m CD. Harmonic analysis on water elevation was also computed and tidal predictions from them are used in the paper. The tidal currents around La Jument can exceed 2 m s⁻¹ and have a complex horizontal distribution (figure 3). An analysis of the extreme statistics at La Jument was produced based on the 23 years (1994–2016) of the hindcast database HOMERE [25]. The selected model point (48°25'35" N, 5°7'50" W) for the extreme statistical analysis is located northwest of La Jument, about 1260 m away from the lighthouse. At that location the water depth is 39 m with a tidal range of 6.8 m. A blockmax method with a block duration of one month was used to estimate the distribution of the yearly maximum water level. The fit on the monthly maxima by a Gumbel distribution gives 11.8 m for a return period of 10 years. The significant wave height, $H_s$ and current speed, $C_s$ (only tidal current in HOMERE) are not correlated. The dominant directions of waves for $H_s > 9$ m are 250°–300° (approx. WSW to WNW; table 1).

## 3. Description of the field experiment

### (a) La Jument experiment

#### (i) Context

This experiment was performed within the frame of the DiMe project dealing with the characterization of extreme breaking waves for the purpose of survivability design of marine renewable energy devices such as fixed or floating wind turbines or wave energy converters. Because the observation of extreme sea states is cumbersome due to the obvious hazards faced by any instruments deployed in stormy seas, little is known about their characteristics and especially
regarding their breaking properties (e.g. statistics of occurrence, breaking type). This motivated
the acquisition of oceanic storm wave observations with a focus on the breaking waves.

La Jument lighthouse was chosen for the study of extreme breaking sea states for the following reasons:

(i) The lighthouse lies over a rocky platform that drops abruptly on its western boundary.

(ii) The upper deck of the lighthouse is located at about 42 m above the CD, making possible the observation of very high sea states in intermediate to shallow waters with a large field of view and a minimal shadowing effect.

(iii) Its high location provides a (relative) shelter from the extreme sea states for onsite remote sensing instruments.

(iv) An analysis of the HOMERE database [25] shows that the 10 year significant wave height at La Jument (in 50 m depth) is equal to or larger than the 100 year significant wave height of most of the French Channel and Atlantic coastline.

(v) In the meantime, a parallel experiment had been planned to measure the acceleration of the lighthouse under storm wave impacts, based on the recommendations of [4].

The connection between the storm waves field experiment and the acceleration measurements
appeared to be relevant and motivated the writing of the present paper.

(ii) Instruments deployment

The deployment of an X-band radar, Stereo-Video Imagery system (SIS) and four accelerometers on La Jument took place on 5 and 6 December 2017. Because the access to the lighthouse by sea is hazardous, especially in winter, we relied on the civilian security helicopter to reach La Jument. Previously, a wave buoy and a current profiler were moored during the winter by the French Naval Hydrographic and Oceanographic Service (Shom) to independently measure the offshore wave field and current vertical profile. Finally, a bathymetric survey was performed in July 2018 to improve the knowledge of the water depth around the lighthouse. In the next section, we will be described the instrumental set-up involved in this field experiment.

(iii) Stereo video system

The stereo-video cameras were mounted on each side of a hut located just below the lantern and looking approximately 246° N. SIS used in this experiment consists of a pair of synchronized 5 megapixel (2048 × 2456 pixels) BM-500GE JAI cameras, with a 5 mm and wide angle lens. The cameras synchronization was done by a trigger inside of the left camera case, the maximum difference between the two cameras records were of the order of O(10⁻⁵) s. The configuration of the lighthouse imposed a maximum camera separation (baseline) of 5.44 m. The stereo images acquisition rate was set at 10 Hz and time stamped thanks to a GPS time server. The cameras were deployed at about 42 m above the CD and equipped with sprinklers and wipers enabling them to be cleaned before each acquisition and during extreme sea states conditions. This system collected 7 TB of storm waves, corresponding to about 35 h of observations between 6 December 2017 and January 15 with significant wave height reaching 10.5 m. The sea surface reconstruction method used follows the methodology presented by Fedele [26], Benetazzo [27] and Leckler [28] implemented in the WASS (waves acquisition stereo system) code version 1.4, from [29].

The sea surface area covered by the stereo video images and the surface resolution mostly depend on the experimental set-up, local brightness and sea level position. The expected accuracy of the stereo observations was derived using the formulations of the quantization error from [30]. For the present stereo set-up, the expected quantization error is represented by the root-mean-squared (RMS) errors along the x-, y- and z-axes. This set-up allowed one to capture the wave field at 50 m from the base of the tower up to 250 m offshore, with a RMSx = 0.14 m, RMSy = 0.35 m and RMSz = 0.09 m.
<figure><img src="image_92.png" /><figcaption>**Figure 2.** Bathymetry around La Jument. (a) Global view, La Jument position is marked by the red dot. The blue and green squares display the location of the Datawell wave buoy and AWAC current profiler. The red circle indicates the domain covered by the X-band radar. The bold black line shows the area covered by the bathymetric survey conducted in the project and the black straight line corresponds to the profile presented in the lower panel. (b) Zoom on La Jument bathymetry. The green square is the AWAC position and the dashed yellow line encloses the stereo video reconstruction domain. The blurred area corresponds to pre-existing bathymetric data. (c) A schematic bathymetric profile between lighthouse (red vertical bar on the right) and Datawell buoy (blue square on the left). The yellow line on the surface represents the stereo video field of view and the green square is the AWAC position. The profile is in Lambert93 coordinate system, in a metric scale.</figcaption></figure>

The main source of error observed in the system was related to the correlation around the breaking events. Breaking waves form bright patches over darker surface water, sometimes resulting in strong brightness gradients that disturb the reconstruction process. The correlation around the foam patches was improved by Leckler [28]; however, this is still one of the main restrictions in the stereo-video reconstruction. Therefore, the analysis of the wave field in the direct vicinity of the lighthouse was performed with extra care because of the presence of larger breakers.

### (iv) X-band marine radar

All radar data used within this study were acquired by a 12 kW marine radar, operating at X-band (9.3 GHz) with vertical polarization in transmit and receive modes (VV-pol). The radar was mounted at a height of about 43 m.a.s.l. and run in a rotational mode covering a range of roughly 3260 m at 0.5 Hz around the lighthouse (red circle in figure 2). The radar was operated with a pulse length of 50 ns, which resulted in a range resolution of 7.5 m. The antenna had a vertical beam opening of 21° and a width of 7.5 feet (2.3 m) giving an azimuthal resolution of approximately 0.9°. The radar was run with a pulse repetition frequency of 2 kHz and the backscattered signal operated through a linear amplifier and then was digitized with 13 bits.

Within this experiment, the X-band marine radar was used to observe ocean waves in space and time. This allows the measurement of the two-dimensional wave spectra from which parameters such as the peak wave direction and peak wave period can be determined [31,32]. In
addition, the radar data give surface wave properties such as wavelength and phase velocity, which in turn enable one to retrieve the surface current vector [33,34]. The surface currents measurements result from the difference between the observed phase velocity and that given by the linear dispersion relation of surface gravity waves, which is given by

$$ \omega(\mathbf{k}) = \sqrt{gk \tanh(kd)} + \mathbf{k} \cdot \mathbf{U} = \omega_0(\mathbf{k}) + \mathbf{k} \cdot \mathbf{U}, \qquad (3.1) $$

where **k** is the wavenumber vector, $\omega$ and $\omega_0$ the relative and absolute wave pulsation, $g$ the gravitational force, $d$ the water depth and **U** the two-dimensional near-surface current. A detailed description of the methodology used in this study to extract the surface current fields is described in [35]. An in-depth validation of surface currents retrieved by marine radars showed an RMSE of less than 0.04 m s⁻¹ [36].

## (v) Accelerometers

The four RECOVIB-IAC-A03 accelerometers were firmly mechanically fixed inside the lighthouse at four different heights: 20.6, 31.1, 38.7 and 45.6 m above the CD. The highest one is installed on the steel structure that supports the lens close to the top of the lighthouse while the three remaining are mounted on the inside masonry of the lighthouse. These accelerometers are able to measure accelerations in the range ±2g (with g the gravity acceleration) outputting a current of 4–20 mA. They embed a low-pass filter of first order with an upper frequency limit of 1000 Hz (–3 dB). The accelerometers were wired to a data acquisition system which is independent of the one used for radar and cameras but synchronization with the wave observations was still possible thanks to GPS time stamping. The power consumption of these systems was very low compared with the other devices deployed for the experimentation so that it was possible to record all the data throughout the winter. The data acquired at 5 kHz were stored in the lighthouse in a dedicated hard drive and transferred on an hourly basis to the mainland to allow preliminary analyses without physical access to the lighthouse.

## (vi) Bathymetric campaign

Bathymetric information was lacking in the immediate vicinity of La Jument, even though it was critical for understanding and modelling wave propagation and wave breaking around the lighthouse. Water depth close to the lighthouse is beyond bathymetric Lidar capabilities due to the steep seabed slope near the lighthouse, and the strong tidal currents and high waves make this zone of rocky shoals very difficult for marine navigation (numerous shipwrecks). To fill the lack of high-resolution bathymetric data in the vicinity of La Jument, we conducted a field campaign in July 2018, with the research vessel (R/V) ‘Albert Lucas’. The hydrographic survey was carried out with a shallow-water multibeam echosounder (MBES) Kongsberg EM3002 (high-resolution 300 kHz MBES system) coupled with a hull sound velocity sensor (H-SVS) Valeport miniSVS, an inertial measurement unit IxSea Octans3000 and a global navigation satellite system (GNSS) Astech ProFlex500. Sound velocity profiles were carried out with an AML BaseX equipped with sound velocity and pressure sensors of model Xchange. The GNSS navigation was processed according to the post processed kinematic method with Novatel GrafNav software and the multibeam soundings were edited with QINSy software, in order to provide a 2 m grid digital terrain model.

## (vii) Wave and current in situ measurements

To complete the field campaign, one directional Datawell waverider wave buoy and an acoustic wave and Nortek AWAC current profiler were deployed in the vicinity of the lighthouse on 27 November 2017. The wave buoy was located about 3 km away from the lighthouse (5°10.410' W, 48°25.131' N) in the western direction, at 92 m depth and at the limit of the radar coverage (figure 2). The wave buoy was deployed on 27 November 2017 and recorded until 3 March 2018. The current profiler was deployed at 59 m depth CD, about 300 m away from the
<figure><img src="image_93.png" /><figcaption>**Figure 3.** Marine radar retrieved current maps of 3 January 2019 between 08.15 and 10.30 UTC (left to right). The colour coding gives the current magnitude and the unit vectors represent the current directions. Each map was generated from 15 min of marine radar data.</figcaption></figure>

lighthouse (5°08.196′ W, 48°25.284′ N) in the southwest direction, at the limit of the video-system reconstruction area (figure 2). The AWAC stopped its acquisition on 1 February 2018 and was found to be seriously damaged on the inter-tidal area on the north shore of Ushant island two months later. The analysis of the data revealed that the instrument was not stable on the bottom with tilt values of up to 40° due to ebb currents. Accordingly, we kept only the data acquired in the tilt validity range given by the instrument manufacturer. More than 60% of the AWAC records were removed, mainly during ebb tides.

# 4. Results

## (a) Bathymetry

Figure 2 shows the bathymetry surrounding La Jument. The lighthouse stands on a promontory that is always submerged except during low spring tides. Our high-resolution bathymetry reveals with greater details the densely fractured bedrock on the barren platform that is extending 2–3 km away to the west and south of the lighthouse. Except for the area north of La Jument, as well as in the bedrock fractures, there is no sediment cover on the granitic bedrock, consistent with high-energy hydrodynamic conditions. Secondary fractures also occur oblique to the main fault orientation. The dense network of fractures yields a rather chaotic seabed relief with large blocks separated by deep incisions. The waves that we will describe in the rest of the paper are propagating approximately from west nowest, hence will advance towards the lighthouse over this indented topography. The bathymetry data collected here are therefore of primary importance when examining the wave physical processes (refraction, shoaling and breaking) that will control wave loads on La Jument.

## (b) X-band radar observations

The marine radar, which retrieved current fields from 3 January 2018 between 08.15 and 10.30 AM UTC, are shown in figure 3. Each current map results from approximately 15 min of radar data. The window size for the retrieval of each current vector is 480 × 480 m and adjacent cells are overlapping by 50%, which leads to one current vector every 240 m. For the current field retrieval only wavelengths between 15 and 100 m were considered, which give access to the mean current in the upper 7 m. Figure 3 shows the current field at different instants close to the time of the waves and accelerations records that are discussed in detail in the rest of the paper. It reveals a complex horizontal distribution of the current field with velocity magnitude reaching 1.8 m s⁻¹ over the
<figure><img src="image_94.png" /><figcaption>**Figure 4.** Time series of the significant wave height *H*<sub>s</sub>, peak period, *T*<sub>p</sub> and peak wave direction, *D*<sub>p</sub> measured by the offshore wave buoy moored during winter 2017–2018.</figcaption></figure>

domain of interest and about 1 m s⁻¹ in the area covered by the SIS of La Jument at the time (09:47:30 UTC, third panel of figure 3) close to the wave event considered in the rest of the paper.

### (c) Wavebuoy observations

The wavebuoy provided wave spectra every 30 min from which integrated wave parameters were extracted. Strong currents caused the buoy to malfunction episodically, the corresponding data were filtered out for the analysis. Figure 4 displays the time history of the significant wave height *H*<sub>s</sub> which shows intense storm waves with *H*<sub>s</sub> values close to 10 m as for instance the storm event of 3 and 4 January 2018 that is studied in the present paper. During storm events, typical peak period and wave direction values are about 15 s and 270° N, respectively.

### (d) Stereo video observations

Owing to technical issues, the SIS stopped working from 15 January 2018. During its operation phase, the SIS captured several wave records in storm conditions with significant wave height ranging from 7.5 to 10.5 m (table 2).
<table><caption>**Table 2.** Summary of the storm records captured by the SIS during the field experiment. The date marks the time when the SIS acquisition starts (duration: 30 min each). The significant wave height ($H_s$) and peak wave period ($T_p$) for each event is measured by the stereo video system, the peak wave direction ($D_p$) is that of the Datawell (i.e. without the bathymetry effect), the mean current speed $C_s$ is measured from the X-band radar and the wind speed at 10 m height ($U_{10}$) is estimated using the wind hindcasts from European Centre for Medium-Range Weather Forecasts (ECMWF) for La Jument location.</caption><thead><tr><th>date</th><th>H<sub>s</sub> (m)</th><th>T<sub>p</sub> (s)</th><th>D<sub>p</sub> (°)</th><th>C<sub>s</sub> (m s<sup>-1</sup>)</th><th>U<sub>10</sub> (m s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>3 Jan 2018 09.39</td><td>10.03</td><td>13.3</td><td>279</td><td>0.77</td><td>17.9, W</td></tr><tr><td>3 Jan 2018 10.30</td><td>10.51</td><td>15.4</td><td>278</td><td>0.69</td><td>15.5, W</td></tr><tr><td>3 Jan 2018 11.09</td><td>8.33</td><td>12.5</td><td>282</td><td>0.36</td><td>15.5, W</td></tr><tr><td>3 Jan 2018 11.54</td><td>9.63</td><td>12.5</td><td>281</td><td>1.08</td><td>15.5, W</td></tr><tr><td>4 Jan 2018 09.40</td><td>7.34</td><td>11.1</td><td>279</td><td>0.65</td><td>15.0, W</td></tr><tr><td>4 Jan 2018 10.45</td><td>7.18</td><td>10.5</td><td>286</td><td>0.79</td><td>14.7, W</td></tr><tr><td>4 Jan 2018 11.43</td><td>7.52</td><td>11.1</td><td>274</td><td>0.52</td><td>14.7, W</td></tr></tbody></table>

An analysis of the SIS surfaces for the record of 09.39 on 3 January 2018 (which will be analysed in more details later) revealed some interesting features about rogue wave occurrence in the vicinity of the lighthouse. For this analysis, only wave components of frequency higher than 0.5 Hz were selected, thus removing sparse spikes close to the poorly matched areas. Following the standard procedure, the dataset was analysed by splitting the sea surface region and the time interval in adjacent and non-overlapping subrecords [37]. To this end, we have selected 14 space-time regions $V_s$ (with $s = 1, 2, ..., 14$) of same area $A_s = 12920 \text{ m}^2$ and duration $D_s = 50 \text{ s}$ in order to produce independent realizations of the random variable maximum crest height defined as $C_m = \max(z(x, y, t) | (x, y, t) \in V_s)$. As a result, the observed values of $C_m$ range between 1.04 $H_s$ and 1.76 $H_s$ (on average $C_m = 1.31 H_s$), and seven individual waves can be classified as rogue as they meet the classic criterion $C_m > 1.25 H_s$ [38]. Two single waves exceeded 1.7 $H_s$ (for comparison, the Draupner wave reached 1.55 $H_s$), the highest one, observed at about 80 m in the southwest of the lighthouse, peaked at 17.7 m.a.s.l. and had crest-to-trough height of about 24 m. Compared to typical open ocean waves, all crests are very steep (the crest-to trough half-period is about 0.4 $T_p$) and are accompanied by rounded and shallow troughs; the ratio between the lowest trough and the highest crest is 0.3, on average. These analysis performed on the SIS surfaces indicate that the occurrence rates of rogue waves at La Jument were higher than expected for deep water waves, possibly due to wave interaction with the bottom and or with the current field.

### (e) Accelerometer observations

The goal of our experiment was to investigate the relationship between the incoming wave field and the mechanical loading felt by the tower in a wave-by-wave framework. To achieve this, we focused our efforts towards a deterministic comparison between the waves captured by our SIS and of the accelerations measured inside the lighthouse. One particularity of this experiment is the synchronization of the acceleration and SIS acquisition system (through the use of a time server, Galleon NTS-6002-GPS time server, accuracy 1 µs) that enabled us to connect a peak in acceleration to a wave captured by the SIS. Because of the slender geometry of the lighthouse, the accelerations induced by waves are larger at the top than near the base of the lighthouse hence the signal-to-noise ratio of the highest accelerometer is more favourable to examine the effect of waves on La Jument's mechanical response. For this accelerometer, the x-axis is pointed 214° N and the y-axis 124° N.

Figure 5 presents a sample of synchronized elevation and accelerations time series that were collected on 3 January between 09:39:38 and 10:09:38 UTC, containing the largest acceleration peak captured during the 3 and 4 January 2018 event. For our analysis, we extracted the
<figure><img src="image_95.png" /><figcaption>**Figure 5.** First panel, 30 min elevation time series for 3 January 2019 (starting at 09:39:38 UTC) extracted from point (X = 99 250 m, Y = 6844 500 m) in the stereo images of figures 7 and 8, the horizontal dashed line show the 8 m elevation threshold used to select the individual waves studied in the paper. Second and third panel: accelerations along x- and y-axes for the same record measured by the highest accelerometer in the tower. The signal noise was filtered out using a Butterworth filter with a cut-off frequency of 50 Hz.</figcaption></figure>

wave elevation data from $P_{SIS}$ the nearest point from the lighthouse, located at $X = 99 250$ m, $Y = 6844 500$ m (figures 7 and 8) hence about 50 m away, southwest of La Jument. Unfortunately, the white waters generated by breaking waves at the base of the lighthouse prevent any reliable stereo reconstruction closer to the structure due to a lack of texture in the images.

The horizontal displacements of the tower can further be computed from the acceleration records by double integration in time and is a better proxy to measure the possible structural damages since it is related to the strains in the structure as reported in Loraux's [4] study on La Jument. For the largest acceleration peak (about $3 \text{ m s}^{-2}$ in the x-direction and $2 \text{ m s}^{-2}$ in the y-direction) measured around 9:42:07 on 3 January the horizontal displacement reached a peak value of about 45 mm, a value several time higher than the other acceleration events presented in figure 5. This acceleration and displacement peak is related to an extreme wave (hereinafter referred to as 'wave1'), 19 m high with a crest elevation reaching 12.9 m at location $P_{SIS}$. In the next section, we will explore why this particular wave induced such an intense impact on La Jument.

### (f) Focus on one extreme slamming wave

Video images of wave1, show a water vertical excursion consecutive to the wave slamming on the lighthouse that washed up the video cameras located about 41 m.a.s.l. (at that instant). This is illustrated by figure 6 showing the evolution of wave1 before and during the breaking process. Unfortunately, the stereo-video images do not give access to the impact zone of the wave on the structure as the video images do not cover the base of the lighthouse and because the white waters in the immediate vicinity of the lighthouse make stereo reconstruction inaccurate. A careful visual
<figure><img src="image_96.png" /><figcaption>**Figure 6.** Examples of stereo video three-dimensional surface elevation map *z*(*i*R, *j*R, *t*) plot over its corresponding right camera bitmap image in the pixel reference system. The colourbar shows the sea surface elevation and ranges from —15 m (blue) to +15 m (red) above the mean sea level computed at the time of the record. The sequence of images shows an extreme breaking event (referred to as wave1 in the paper, corresponding wave height: 19.0 m). The reconstruction area was reduced in this illustration to highlight the breaking areas.</figcaption></figure>

analysis of the other video records (table 2) revealed that no other wave caused such water runup. In the following section, we compare wave1 to seven over waves from the same SIS record, whose crest elevations exceed a threshold set at 8 m.a.s.l. We chose to select our subset of high waves based on their crest elevation, η_c, instead of their trough-to-crest height because η_c appears to be a key parameter in the formula of [21] used to compute wave impact forces on slender bottom-mounted vertical-cantilever type marine structures (see equations (1.1) and (1.2)).

### (i) Spatial wave properties analysis

Here we shall use a combination of the video images and of the stereo-video reconstruction to obtain a better description of the high waves of interest at the base of the lighthouse. The strength of the stereo-video system compared to other traditional point in situ wave instruments is of course its ability in providing spatio-temporal information on the wave field. Figures 7 and 8 display snapshots of the sea surface capturing the spatial signature of the eight high waves selected above. The photographs of these waves (figures 7 and 8, left panels) indicate that they were all breaking at the base of the lighthouse. Compared to the others, wave1 appears to have strong variation of the along-crest elevation, with high elevations concentrated close to the lighthouse. Snapshots of wave1's nonlinear evolution towards breaking is available in figure 6, and animations of the wave surfaces overlaid over the video images can be analysed to further understand the breaking process at the base of the lighthouse (these videos are available as electronic supplementary material; the reconstruction area was reduced in these videos to highlight the breaking areas). It reveals that when the wave crest is approaching the structure, a fast flow towards the crest appears and seems to be associated with the birth a secondary jet just below the main crest. Finally, both crests merge into one that violently overturns. Figure 8.6.a also shows a good illustration of the secondary jet generation.
<figure><img src="image_97.png" /><figcaption>**Figure 7.** Description of the eight high waves selected for our study (four in this figure and four in figure 8). Left panels: video images, middle panel reconstructed wave surfaces projected in a Lambert93 geographic system overlaid over iso-contours of water depths (the black dots show the extraction point of the time series analysed in the paper) right panels: time series of the high waves elevation, collected at x = 99 250 m, y = 6844 500 m from the stereo video reconstruction.</figcaption></figure>

## (ii) Time-series analysis

We analysed the same surface by extracting a 30 min time series of the sea surface elevation recorded at *P*<sub>SIS</sub>, for the same SIS acquisition (starting at 09:39:38 UTC). With this elevation time series, we pursue our investigations of the eight high waves properties. Superposing the
<figure><img src="image_98.png" /><figcaption>**Figure 8.** Same as figure 7 but for the four remaining high waves.</figcaption></figure>

individual waves on a single plot shows time profile similarities between the eight high waves selected in terms of vertical and horizontal asymmetries. Some of the characteristics of these waves are listed in table 3.

Such similarities in the wave profile of high waves were already discussed for deep water waves by Bocotti [39], Phillips et al. [40,41], who proved that for Gaussian sea states, the profiles of the highest waves were self similar and follow the shape of the auto-correlation function of the full wave field. The eight high waves studied here are all skewed: the crests being much higher
<table><caption>**Table 3.** Crest, $\eta_c$ and trough $\eta_t$ elevation, wave height $H$ and half period $T_{1/2}$ (duration between front trough and crest) for the eight individual waves studied in the paper.</caption><thead><tr><th>wave</th><th>η<sub>c</sub> (m)</th><th>η<sub>t</sub> (s)</th><th>H (m)</th><th>T<sub>1/2</sub> (s)</th></tr></thead><tbody><tr><td>wave1</td><td>12.9</td><td>-6.1</td><td>19.0</td><td>2.0</td></tr><tr><td>wave2</td><td>8.5</td><td>-4.1</td><td>12.6</td><td>4.6</td></tr><tr><td>wave3</td><td>8.3</td><td>-3.4</td><td>11.7</td><td>2.9</td></tr><tr><td>wave4</td><td>11.2</td><td>-4.0</td><td>15.2</td><td>2.8</td></tr><tr><td>wave5</td><td>9.2</td><td>-4.0</td><td>13.2</td><td>2.9</td></tr><tr><td>wave6</td><td>8.9</td><td>-3.7</td><td>12.6</td><td>2.2</td></tr><tr><td>wave7</td><td>10.3</td><td>-5.3</td><td>15.6</td><td>2.4</td></tr><tr><td>wave8</td><td>8.0</td><td>-3.2</td><td>11.2</td><td>3.5</td></tr></tbody></table>

than the troughs and asymmetric: the front face being significantly steeper than the back face. Most of them are followed by a secondary crest. Table 3 and figure 9 demonstrate that wave1 has the highest crest (12.9 m) with a shallow preceding trough (-6.1 m) and the largest individual wave height (19.0 m). The second highest wave (wave7) has a wave height reaches 15.6 m but with a lower wave trough (-5.3 m) and lower crest (10.3 m) than wave1. At the studied location ($P_{SIS}$), the time separating the preceding trough and the crest of wave1, which can be linked to the front face geometric steepness, is only 2.0 s, the lowest value among the different waves. The record of the back trough of wave1 is dominated by noise because of the water spray induced by the wave slamming that blinded the video cameras and corrupted the reconstruction for a short period of time. In figure 9, the grey bar indicates the elevation of the top of the lighthouse substructure, the bar thickness quantifies the water-level variation over the time period of the wave record, namely the water level dropped by 42 cm during the 30 min wave record considered. Measurements of a tide gauge from Shom collected at Le Conquet harbour (25 km ESE of La Jument) show storm surge values around 0 cm at 10.00 UTC the same day. We assumed here that the storm surge at La Jument can be neglected in our analysis. Figure 9 indicates that the crest elevation of wave1 measured at $P_{SIS}$ is the only one crossing the substructure elevation level. We advance that this is a plausible explanation for the acceleration peak found for wave1 only. Since La Jument's tower is much more flexible than the substructure itself [4] the mechanical response to wave slamming impacts on the tower may be significantly more intense and may translate into much larger accelerations and displacements than those due to waves impacting the substructure only. This would explain why waves with slightly lower crest elevations, such as wave7, produced horizontal accelerations and displacements of the top of the structure one order of magnitude lower than wave1. Of course, it is difficult to be fully conclusive regarding the actual elevation of the crest right at the lighthouse, from considerations derived from observations collected at 50 m away from the structure. As reported earlier in the paper, the elevation can change significantly along the crest over distances of O(50 m) (figures 7 and 8, central panels). Because of the white water the near wave field (closer to 50 m in the up-wave direction) was not accessible from the SIS data. To fill the gap between the lighthouse and the edge of the SIS surface we operated BOSZ, a phase-resolving Boussinesq-type model for the computation of near-shore waves (e.g. [42–45]) that solves the equations based on a conserved variable formulation of [46]. Animations of the wave transformation in the vicinity of the lighthouse are available as electronic supplementary material. The computation of the wave field around the lighthouse of La Jument is based on a 2.7 km by 2.5 km domain composed of a Cartesian grid of uniform 7.5 m by 7.5 m. The input wave spectrum comes from the wave buoy at the time of interest, i.e. 3 January 2017 at 9.30.

As shown in figure 10, the wave field shows strong convergence in close proximity to the lighthouse with $H_s$ values 50% higher than the observed offshore conditions. This suggests that, statistically speaking, wave height may be higher at the base of the lighthouse than at $P_{SIS}$, though
<figure><img src="image_99.png" /><figcaption>**Figure 9.** Comparison between wave1 (black) and the seven other high waves for the record of 3 January 2018 at 9.39 UTC. The grey bar indicated the altitude of the lighthouse substructure (figure 1) above the sea level at the time of the wave record. The vertical extent of the bar corresponds to the water level change over the 30 min of the record.</figcaption></figure>

<figure><img src="image_100.png" /><figcaption>**Figure 10.** Significant wave height map obtained from the BOSZ model for the simulation corresponding to the wave event of 09.39 on 3 January.</figcaption></figure>

the reflection of the wave field on the substructure likely contributes to this local wave height increase. However, even with this additional information, it is not possible to draw definitive conclusions regarding the elevation of wave1's crest on the structure since there is no guarantee that the observed statistical increase in $H_s$ systematically results in higher individual wave crests.

Fortunately, a series of pictures of wave1 taken from Ushant Island supports our findings. These improbable but highly valuable pictures are available in [47] and present the details of wave1's impact on La Jument (for the review stage, a picture is available as electronic supplementary material). These pictures confirm that wave1 crest elevation was high enough to cause an impact above the substructure, i.e. directly on the tower. Two pieces of evidence match to relate the pictures to wave1: the correspondence of the time stamps is less than 2 min (probably due to inaccuracies in the camera clock) and wave1 was the only wave in our records of 3 January 2019 that caused sea spray up to the stereo-system. This finding confirms the numerical results
of Loraux, who reported that breaker impacts on the substructure alone do not produce any significant accelerations on La Jument (see fig. 46 in [4]). The substructure built several years after the lighthouse’s erection plays therefore a double role: it adds stiffness to the initial lighthouse tower and protects it from the assaults of most of the breaking waves.

## 5. Discussion

The paper introduces a broad spectra of observational and model data that we used to provide a better understanding of the complex hydrodynamics in the vicinity of La Jument. However, the coming discussion will focus on the wave-acceleration study performed in the previous section.

The first analysis presented here examined a particular stereo-video record featuring a large breaking wave (wave1) that induced significant horizontal accelerations and displacements in the tower and caused water spray that reached up to the video cameras. As mentioned in the Introduction, the mechanical response of La Jument under extreme waves was addressed in detail by Loraux [4], who simulated the loading of a series of three waves with characteristics based on the estimation of 50–100 year return period waves, combined with varying tidal level. The horizontal acceleration and displacement caused by wave1 (looking at the x-axis) is of the same order or magnitude as the values reported by Loraux’s [4] numerical experiment, though his largest numerical wave (22 m high with crest elevation of 18 m) combined with a 8.5 m CD tidal level (50 cm above the highest astronomic tide and 6.5 m below the substructure top) yields a horizontal acceleration peak above $20 \text{ m s}^{-2}$. Loraux further found that the horizontal displacements (up to 2 cm) were highly correlated to the duration of the impact pressure load.

We should stress here that the waves studied in our paper correspond to a severe but not extreme storm: indeed the significant wave height of 10.5 m is a wave event with a 2 year return period. In addition, the tide level was low (1.15 m CD in average over the 30 min record) which places the water level 12.85 m below the top of the lighthouse substructure. Even in these ‘adverse’ conditions, our instruments captured a wave able to hit the lighthouse’s upper tower causing notable vibrations (double integration in time yields horizontal displacements of about 45 mm at the top of La Jument). This advocates for more observations in stronger sea states with different water levels to accumulate more acceleration data synchronized to wave observations. This would further help understanding the relation between the wave characteristics in terms of wave height, period and direction, the water level and the tidal currents on the impact magnitude on the structure. A larger subset of high waves reaching the tower would be necessary to examine what other properties (e.g. breaking type, breaking stage, angle of attack, fluid velocities in the crest) are important, beyond the crest elevation. In addition, since the stereo-video domain does not cover the last 50 m of wave propagation, additional sensors would be helpful in capturing the elevation of the wave impact on the structure. Numerical efforts to represent the three-dimensional geometry and fluid velocities of the impacting crest would also help in the cross interpretation of the wave characteristics especially regarding the distribution of the orbital velocities and their role in the impact process.

The acceleration records have only been briefly addressed in the paper and served just as markers of the wave slamming severity. These observations deserve a dedicated study, especially regarding their spectral contents that would provide important information about the stiffness of La Jument, hence its structural health and remaining lifetime.

We hope to further investigate the scientific questions raised in this discussion thanks to the extension of the field experiment over several winters and the addition of five pressure sensors, one on the substructure and four on the lighthouse tower, spread over three faces of the octagonal structure. We hope they will provide further information regarding the relation between impacting wave properties and the magnitude and time history of the pressure loads.
## 6. Conclusion

In this paper, we present observations from a field campaign designed to improve the description of the extreme wave loads on one of the most iconic lighthouse in France, if not in the world. The dataset, collected during winter 2017–2018, contains storm waves and wave-synchronized acceleration data together with tidal current measurements and high-resolution bathymetry. The dataset features several records with significant wave heights about 10 m for two of them and giant waves reaching 24 m high.

In the paper, we focused our analysis around an intense and isolated horizontal acceleration and displacement burst and showed that it is due to a 19 m high breaking wave. Our work suggests that this particular wave (wave1) carried a crest high enough to pass above the substructure and reach the lighthouse tower. A series of photographs of wave1 taken from Ushant island support that the crest hits the concrete belt covering the lower part of the tower [47]. This indicates that the water level during storm events controls the frequency of strong acceleration peaks since the lighthouse substructure acts as a high-pass filter for the wave crests. We hope that this ongoing field work will help in quantifying the remaining lifetime of La Jument through a finer description of the incoming waves and of their effect in terms of mechanical loading on the structure. This experiment could further bring insight regarding the loads of breaking waves on other marine structures installed on top of a steep slope such as breakwaters.

La Jument is a heritage iconic structure, part of Brittany's culture and known all over the world. Putting aside its role in the navigation safety, it is wise to wonder whether we should spend large amounts of money to maintain a monument that is not accessible to the public. Our scientific experiment demonstrates that this lighthouse is a unique laboratory to study extreme waves and the loading they induced on marine structures. We believe that its privileged location at the edge of a steep shoal overseeing the open ocean makes it a favourable site for many other fields of research including wave-current interactions, wave breaking or air-sea interface processes. This opportunity could offer a second operational life to La Jument and may justify maintaining this fascinating monument in good condition.

**Data accessibility.** This article does not contain any additional data.

**Authors' contributions.** J.F.F. drafted the manuscript and analysed the accelerations and stereo-video times series. P.G., F.L., M.A. and R.D. produced and analysed the stereo-video surfaces; E.L., N.F. and A.V. contributed to the accelerations analyses; M.P. did the hydrodynamic climatology study; J.H. and R.C. were in charge of the X-band investigations; C.R. was in charge the datawell and AWAC observation study; A.B. performed the rogue wave analysis; V.R. was responsible for the BOSZ modelling; M.F. and N.L.D. carried out the MBS field survey and analysed the bathymetric data.

**Competing interests.** We declare we have no competing interests.

**Funding.** This work benefited from government support managed by the Agence Nationale de la Recherche under the program Investissement d'Avenir with the reference ANR-10-IEED-0006-14 and ANR-10-IEED-0006-26 related to the projects DiMe and CARAVELE. Numerical simulations were performed on HPC facilities Datarmor of 'Pôle de Calcul Intensif pour la Mer' (PCIM) (http://www.ifremer.fr/pcim). Finally, the fundings from the filière Mer, Crédit Agricole contributed to the success of the experiment.

**Acknowledgements.** We acknowledge the contribution of Peter Sutherland and (Ifremer) to the deployment of the stereo-system and assistance in the SIS data acquisition. We thank Lucia Pineau-Guillou (Ifremer) for her assistance in the storm surge data analysis. We are grateful to Phares et Balises who allows us to work on La Jument and provides significant support in the preparation and realization of the deployment. We would like to thank the reviewers whose comments have significantly improve the manuscript.

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5.B Paper from Guimaraes & al. (2020)
SCIENTIFIC DATA

<figure><img src="image_101.png" /></figure>

<figure><img src="image_102.png" /></figure>

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DATA DESCRIPTOR

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# A data set of sea surface stereo images to resolve space-time wave fields

Pedro Veras Guimarães<fnref n="1" />,⁸✉, Fabrice Ardhuin²✉, Filippo Bergamasco ID³, Fabien Leckler⁴, Jean-François Filipot<fnref n="1" />, Jae-Seol Shim⁵, Vladimir Dulov⁶ & Alvise Benetazzo ID⁷,⁸✉

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 ~$10^4$ 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.

## Background & Summary

Stereo imaging measurement of the sea surface elevation is based on single snapshots or time records captured by a pair of synchronized and calibrated cameras. The first projects to prospect the stereo photography use to measure sea surface topography was presented by<fnref n="1" />,². However, the significant computational time required to extract the three-dimensional (3-D) elevation maps from a pair of images have limited the use of this technique until late 70s and early 80s with the works of³,⁴. In 1988⁵, used a pair of cameras mounted on an oceanographic offshore tower to measure the 3-D sea surface elevation to observe the directional distribution of short-scale ocean waves. Later on⁶, applied similar stereographic measurement techniques to study the 2-D wavenumber spectrum of short gravity waves.

More recently⁷, describe a stereo vision technique to measure the water surface topography. They used a conventional stereographic technique algorithms to survey geodetic surfaces and static objects. Based on that⁸, proposed a partially supervised technique (Wave Acquisition Stereo System, WASS) to estimate the 3-D shape of water waves using video image analysis with high spatial and temporal resolutions. Despite the basic principle remains more or less the same⁹, optimized the⁸ technique and presented the first open source code version of WASS (http://www.dais.unive.it/wass/).

Since the work by⁸, WASS and others similar stereo imaging systems have been widely used for different investigation purposes on ocean waves. For example¹⁰⁻¹²: used the foam footprint in the surface reflection to identified wave breaking in the video records, with that is possible observe the space and time evolution of breaking waves and investigate different properties of wave energy dissipation¹³⁻¹⁵,¹⁶ used stereo data to study the shape and likelihood of the highest waves, including maximum and rogue waves¹⁷,¹⁸; used the 3-D spectrum to explore non-linear waves properties like bound waves, second-order and harmonics, wave-current interactions

<footnote n="1">¹France Energies Marines, Plouzané, France. ²Univ. Brest, CNRS, IRD, Ifremer, Laboratoire d'Océanographie Physique et Spatiale (LOPS), IUEM, Plouzané, France. ³DAIS – Università Ca' Foscari, Venice, Italy. ⁴Service hydrographique et océanographique de la Marine (SHOM, HOM, REC), Brest, 29200, France. ⁵KIOST – Korea Institute of Ocean Science and Technology, Busan, South Korea. ⁶Marine Hydrophysical Institute, Sebastopol, Russia. ⁷Institute of Marine Sciences, Italian National Research Council (ISMAR-CNR), Venice, 30122, Italy. ⁸These authors contributed equally: Pedro Veras Guimarães, Alvise Benetazzo. ✉e-mail: pedro.veras.guimaraes@france-energies-marines.org; Fabrice.Ardhuin@ifremer.fr; albise.benetazzo@ve.ismar.cnr.it</footnote>
<figure><img src="image_103.png" /><figcaption>**Fig. 1** Example of stereo imaging system. Left: Geometric configuration of the stereo camera systems. Right: System installed on the Socheongho Ocean Research Station (Yellow Sea). The two cases holding the digital cameras are seen in the horizontal position used for alignment, before being inclined down-looking in their operative position.</figcaption></figure>

and bi-modality. Stereo video system were also tested with certain level of success mounted over a moving vessels¹²,¹⁹,²⁰ and²¹ also investigated its application in the surf zone.

As a general principle, stereo imaging results in a surface elevation map $ζ(x, y, t)$ in the horizontal physical 2-D space $x = (x, y)$ and time $t$. The coverage area, accuracy, and resolution depend mostly on the experimental setup (e.g. the distance between the cameras), camera specifications, and lenses⁸,²². See later in the paper a discussion about the expected errors for stereo observations. One of the greatest advantage of having the space-time elevation field $ζ(x, y, t)$ is to compute the 3-D wavenumber/frequency spectrum without the need of invoking any (e.g. linear) wave theory for background noise removal and signal selection. This is most important for the short wave components, for which nonlinear contributions are more significant⁶,¹⁷.

This observation technique is very powerful to investigate many different process related to the sea surface and it brings a new perspective to investigate ocean waves, specially at mid to short scales. Stereo imaging connects the missing information between large to small-scale ocean observations (e.g., 10 m pixel resolution by SAR images) or a single point high frequency observation (wave gauge, moored buoys and others). In this context, stereo video have been prof to be useful to explore different aspects of ocean waves.

In this paper, for the first time, we aim at presenting a valuable stereo-image data set, free available for the scientific community. This data set contains original records, calibration files, configuration files for processing, and examples of post-processed surface elevation maps collected during several oceanic campaigns, at different locations around the world ocean and under different sea state conditions. All this makes this data set especially useful to explore a common framework to investigate ocean waves and the sea surface dynamics.

## Methods

The data set contains two main assets. First, we provide several raw stereo-image acquisitions, that consists in about 30 min of pair of images sequences of the sea surface, for different locations in the world oceans and met-ocean conditions. Such images are captured with two cameras, temporally synchronized and optically calibrated, to allow the 3-D geometrical analysis of the observed scene. Second, we processed the stereo sequences with the currently available state-of-the-art WASS tool to obtain space-time fields of wave elevation data that can be conveniently used for further analysis.

Due to their different nature, the two assets deserve a separate discussion on what concerns their description. The stereo images represent the *raw data* directly acquired from the observed phenomenon. Consequently, we will focus on the hardware side, describing the imaging technologies involved and, even more importantly, on the optical characteristics of the camera-lens system. On the other hand, the operations we performed to get the final space-time field is a pure algorithmic process that could potentially be improved in the future. As such, we will summarize what tools were used to process the data together with the raw stereo images. So any researcher is welcome to reprocess them based on its one personal interest and convenience, for example, by choosing a finer/larger interpolation grid, a different range of the gridding domain and technique to interpolate the data, or outlier filtering scheme. Therefore, we'll concentrate on the kinds of errors that should be kept under observation at each stage of the processing, to guarantee that the final elevation model is an accurate measurement of the real imaged sea surface.

**Stereo images.** Image data is grouped in several acquisitions (records), each one composed by a sequence of images (namely a *stereo sequence*) captured by two cameras. The two cameras are temporally synchronized such that, for each image acquired by the first, there correspond an image acquired by the second with a maximum delay in the order of microseconds. The synchronization is ensured by a cable connecting the two devices and a *hardware trigger* generating electrical impulses at a predefined frequency. The final result is, for each record, a sequence of several image pairs, acquired at a given rate (usually around from 10 to 15 Hz).

Cameras are placed side-by-side, with parallel optical axes, both down-looking at the sea surface. The baseline (i.e. the vector connecting the two optical centers) spans the x-axis of the camera reference frames as shown in Fig. 1 (Left). The geometric setup is “loose”, in a sense that no mechanical solution was used to enforce it. For example, the optical axes were manually aligned just by visual inspecting the resulting images. We must stress, however, that each camera position must not be known precisely a-priori for the success of the reconstruction.
<figure><img src="image_104.png" /><figcaption>**Fig. 2** Example of stereo camera calibration. Left: chess board corners detection for intrinsic cameras calibration. Right: Chess board corners reconstruction in a real world coordinate system.</figcaption></figure>

Thus, the ideal arrangement in Fig. 1 should be considered as a guideline for a successful setup more than a strict operational requirement. The two cameras are referred as *Camera 0* and *Camera 1*, regardless their spatial configuration. Usually the *Camera 0* is placed at the right-hand side of *Camera 1* but this is not mandatory for the tools used for reconstruction (the spatial configuration can be automatically inferred from the extrinsic calibration performed directly on the acquired images).

In all the records we used a pair of BM-500GE JAI cameras, producing gray-scale images with a spatial resolution of 2048 × 2456 pixels (5 Megapixels) and intensity levels quantized to 8 bits (i.e. 256 different shades of gray). Exposure time was set to a value less then 0.005 s to avoid motion blurring and, if necessary, compensated by the analog gain control of the camera to obtain images in which the average intensity level of the pixel in a central Region of Interest (ROI) is ~110. Care was taken to ensure that both the stereo images exhibit the same average intensity level in their own ROI to maximize the photometric consistency of corresponding points (see next section for details).

To reconstruct the metric properties of the observed scene, the optical model of each camera must be taken into account. We considered the common pinhole camera model with a 5-degrees polynomial radial distortion, resulting in a total of 9 parameters, namely: the *focal length* (2 parameters, to account for non-square pixels), the position of the *principal point* (2 parameters) and the 5 parameters used to model the *radial and tangential distortion*. To estimate them, the *intrinsic calibration* was performed on each camera before installation consisting in the acquisition of a known chessboard target in dozens of different poses (Fig. 2). We used the Camera Calibration Toolbox for Matlab, provided by Jean-Yves Bouguet (www.vision.caltech.edu/bouguetj), implementing the method described in²³.

**3-D Reconstruction and Wave Field estimation.** Each record of the data set is composed by a sequence of stereo frames and the intrinsic calibration data for each camera-lens system. The process used to reconstruct the spatio-temporal wave field is divided in three subsequent steps. First, the relative spatial position of the two cameras (ie. the *extrinsic calibration*) is recovered automatically by analyzing a subset of stereo frames. Second, each stereo pair is processed to reconstruct a dense 3-D point cloud of the observed sea surface. Finally, each point cloud is filtered, cleaned and interpolated on a regular grid to produce a *data cube* containing the spatial surface elevation over time. We used the WASS pipeline⁹ for the first two-steps and Matlab® scripts for the last one.

The principle of stereo reconstruction is easy to understand. It is based on the assumption that we geometrically know the imaging model of the two cameras (*intrinsic parameters*) and their relative poses described by a rotation matrix **R** and a translation vector **T** (known as *extrinsic parameters*). In this scenario, once a pixel-to-pixel correspondence is established between a point on one camera and the same point on the other (i.e. the two projections of the same 3-D feature on a scene), the exiting rays of the two cameras can be intersected to recover the 3-D position of the point. This process is known as *triangulation* (See Fig. 3, Left). Stereo reconstruction algorithms usually exploit the *epipolar constraint* to limit the search space of corresponding points. A pre-processing step called *rectification* warps the two frames such that corresponding points lie on the same scan-line of each image as described in²⁴.

Extrinsic parameters are estimated on the stereo images itself with a procedure known as auto-calibration. The idea is to find the best rigid motion (**R**, **T**) such that a set of point-to-point correspondences (determined by any robust matching function) satisfy the resulting epipolar constraint. Since the resulting epipolar lines are invariant with respect to the norm of **T**, the camera pose can be estimated up to an unknown baseline distance that has to be measured in other ways. The *wass_match* and *wass_autocalibrate* programs are used to perform robust point matching and auto-calibration respectively. At the end of this step, the WASS pipeline provides the estimated (**R**, **T**) together with some statistics useful to evaluate the accuracy of the output. In particular, two parameters are important to be monitored: (i) the number of point-point matches that are considered inliers (i.e. valid) with respect to the estimated pose; (ii) the average epipolar error of the inlier matches (ie. how coherent are the inliers