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# Numerical investigation of seasonal wind-wave responses to severe seagrass decline in a coastal lagoon

Arnaud Le Pevedic<sup>a,b,*</sup>, Paul Bayle<sup>a,c,1</sup>, Alexandre Nicolae Lerma<sup>c</sup>, Aldo Sottolichio<sup>b</sup>, Florian Ganthy<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Wind wave
WAVEWATCH-III
Intertidal zone
Seagrass decline
Zostera noltei
Seasonality
Arcachon lagoon

## ABSTRACT

The intensification of environmental stressors and anthropogenic pressures has resulted in significant seagrass loss worldwide, reducing the capacity of vegetation to damp hydrodynamic energy. While the broad-scale impact of seagrass decline on wind waves has been partially investigated in coastal lagoons, the role of seasonal variations in seagrass characteristics in influencing these responses remains not fully understood. We propose to explore the seagrass-wave interaction through the implementation of a novel coupled wave-flow-vegetation model, which considers deflected canopy height in WAVEWATCH-III, and applied to the Arcachon lagoon. We perform a scenario analysis using different wind conditions and various maps of seagrass coverage (from 1989 to 2016) to provide new insights into how seasonality affects wind wave responses to *Zostera noltei* decline. Our results reveal that during the summer, when seagrasses are fully developed, seagrass decline significantly reduces the ability of *Z. noltei* to dissipate wave energy, leading to a wave height increase (reaching 30 %, for $H_{m0}$ between 0.05 m and 0.35 m) in the areas where seagrass coverage is most reduced. However, during the winter, when canopy height and density are low, no significant changes in wave dissipation are observed due to *Z. noltei* decline. This study also shows that modifications of the ambient current within the canopy further decreases the capacity of *Z. noltei* to attenuate waves, as the intensification of flow conditions due to seagrass decline reduces canopy height.

## 1. Introduction

Coastal vegetation is increasingly integrated into coastal risk management strategies (Temmerman et al., 2013; Arkema et al., 2017) and often promoted has a Nature Based Solution able to mitigate erosion and submersion hazard. Halophytic plants have been recognized for their ability to limit beach erosion and mudflat scouring (Guannel et al., 2015) through their network of roots and rhizomes, which stabilize the substratum (Gacia et al., 1999; Ganthy et al., 2011). Additionally, their foliage can reduce suspended sediment concentration in the water column by trapping freshly suspended sediment (Neumeier and Ciavola, 2004; Hendriks et al., 2010). Vegetation also has a buffering function for coastal areas by dissipating hydrodynamic energy through current (e.g. Peterson et al., 2004) and wave (e.g., Fonseca and Cahalan, 1992)

attenuation.

Dissipation of wave energy by vegetation occurs through diverse mechanisms, including skin friction, form drag, and the transfer of energy from waves to vegetation that sets plants in motion (Paul et al., 2012). As a result of these processes, significant reductions in wave energy have been measured within seagrass meadows compared to bare sediments, with reductions reaching 70 % both in the field and laboratory; considering waves under 10 cm in the laboratory (Luhar et al., 2017) and waves ranging from 5 to 18 cm in the field (Hansen and Reidenbach, 2012).

Wave damping by vegetation is highly dependent on wave characteristics (e.g., Rupprecht et al., 2017), as well as vegetation characteristics (e.g., Bradley and Houser, 2009; Manca et al., 2012; Anderson and Smith, 2014). Contrasting results showed that wave height and wave

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<footnote><sup>a</sup> Ifremer, LITTORAL, Quai du Commandant Silhouette, F-33120, Arcachon, France</footnote>

<footnote><sup>b</sup> Univ. Bordeaux, CNRS, Bordeaux INP, EPOC, UMR 5805, F-33600, Pessac, France</footnote>

<footnote><sup>c</sup> Brgm Direction Régionale Nouvelle-Aquitaine, Pessac, France</footnote>

<footnote>* Corresponding author. Univ. Bordeaux, CNRS, Bordeaux INP, EPOC, UMR 5805, F-33600, Pessac, France.
E-mail address: alepeved@ifremer.fr (A. Le Pevedic).</footnote>

<footnote n="1">¹ Present address: Delft University of Technology, Faculty of Civil Engineering and GeoSciences, Department of Hydraulic Engineering, Stevinweg 1, 2628CN, Delft, The Netherlands.</footnote>
period can either enhance (e.g. Anderson and Smith, 2014) or reduce (e. g. Maza et al., 2015) wave dissipation by vegetation. Wave attenuation is positively correlated with the leaf length (Garzon et al., 2019), as an increase in leaf length increases the drag force exerted on the plant stands (He et al., 2019). Consequently, a taller canopy results in higher energy dissipation rates (Paul et al., 2012). The drag force exerted on vegetation is also highly dependent on plant rigidity and decreases with its flexibility (Mullarney and Henderson, 2010), to the extent that wave attenuation can be up to 70 % lower for flexible vegetation in compar- ison with rigid vegetation (van Veelen et al., 2020). Wave attenuation is also positively correlated with leaf density (e.g. Ozeren et al., 2014), and it was shown that flexible seagrass featuring large densities (or bio- masses) can reach rates of wave attenuation comparable to, or higher than, the rates observed for rigid species (Bouma et al., 2010). It was estimated that the short and flexible seagrass species *Zostera noltei* re- quires a Leaf Area Index (LAI = leaf length × leaf width × density; m²· m⁻³) four times higher than that of a rigid meadow to achieve similar wave attenuation (Paul et al., 2012). Spatial extent also constitutes a key parameter in the damping capacity of the meadows, as waves propa- gating over wide areas colonized by flexible species can be significantly attenuated (Houser et al., 2015). In this regard, Infantes et al. (2012) observed a 50 % reduction in the root mean square wave height by a 1-km long meadow of *Posidonia Oceanica*. Therefore, flexible seagrass meadows featuring high densities and colonizing broad areas can effi- ciently dissipate wave energy.

Seagrasses have been declining at the global scale (Waycott et al., 2009). In Europe, it is estimated that one-third of the seagrass popula- tion was lost between 1869 and 2016 (de los Santos et al., 2019). Sea- grass decline has been particularly important in shallow coastal areas, where intertidal species are especially vulnerable to environmental stresses (Valle et al., 2014). As a result of their decline, seagrasses can no longer provide the same ecosystem services, to the extent that hydro- dynamic conditions, including current and wave conditions, as well as erosion rates can be drastically modified.

Waves are one of the primary drivers of sediment transport, and even in sheltered areas where waves are locally wind-generated, they can remobilize a significant amount of sediment (Contti Neto et al., 2022). To characterize the effect of seagrass loss on sediment dynamics, it is first necessary to gain better understanding of the response of wave conditions to seagrass coverage.

Previous studies (Vu et al., 2017; Donatelli et al., 2019) showed that seagrass losses reduce the capacity of the meadows to attenuate waves. Although the impact of the evolution of vegetation on wave height in a shallow coastal lagoon was studied by Donatelli et al. (2019), their study was only conducted for submerged aquatic vegetation and neglected the impact of seasonality due to a lack of data available at their study site. Nevertheless, the processes involved are highly season-driven since seagrass undergoes significant seasonal variations (Auby and Labourg, 1996) and wind-waves depend on the seasonal climate conditions. Therefore, beyond the influence of vegetation decline, the wave atten- uation capacity, which depends on wave and vegetation characteristics, is very likely to vary seasonally.

The Arcachon lagoon (Nouvelle-Aquitaine, France), is a sheltered and shallow coastal lagoon, extensively colonized by *Zostera noltei*. *Zostera* meadows has severely declined, losing 33 % of their population between 1989 and 2008 (Plus et al., 2010), through density as well as spatial extent losses. Simultaneously, significant morphological evolu- tions have been observed inside the lagoon, suggesting a direct influence of seagrass decline on sediment remobilization and redistribution.

The seagrasses in the Arcachon lagoon have been extensively monitored (Auby and Labourg, 1996; Ganthy et al., 2011; Cognat et al., 2018), providing a comprehensive dataset of their characteristics, which enables the study of both their decadal and seasonal evolutions. This site is therefore a privileged location to study the response of wind wave characteristics to the decline of intertidal seagrass at different times of the year.

To account for the high variability of vegetation and wind regime, numerical modeling is used to conduct a scenario analysis, considering the most common wind events and the corresponding seasonal devel- opment of the meadows in the Arcachon lagoon. For this purpose, we implement a novel coupled wave-flow-vegetation model, incorporating the influence of energy dissipation by vegetation in the wave model WAVEWATCH-III (WW3; Roland and Ardhuin, 2014), similar to the approach used by Abdolali et al. (2022). New coupling fields relative to vegetation are also added in WAVEWATCH-III for the model to consider spatially varying vegetation characteristics. WAVEWATCH-III is cali- brated and validated for the Arcachon lagoon using *in situ* field obser- vations. A particular attention is paid to the calibration of the wave-vegetation drag coefficient through a procedure involving field- work and 1D numerical modeling.

## 2. Study area

Located on the French South-West coast, the Arcachon lagoon (Fig. 1) is a sheltered environment separated from the open ocean by the Cap Ferret sandpit. In its southwest corner, a 3-km wide opening allows for the tide to propagate inside the lagoon and the water mass exchange between the open ocean and the lagoon. This environment is meso-tidal with a semi-diurnal tide ranging from 0.8 m during neap tide to 4.6 m during spring tide. Large swell waves do not generally enter the lagoon (Parisot et al., 2008) as wave energy is rapidly and strongly dissipated across numerous sand banks in the inlet, hence waves in the lagoon are mainly locally wind-generated (Nicolae Lerma et al., 2024).

Wide intertidal flats make up 70 % of the lagoon's surface and are separated by a dense network of channels. This site is characterized by a complex bathymetry with steep slopes on the channel banks and very mild slopes on the mudflats. Intertidal areas are extensively colonized by *Zostera noltei* meadows, yet seagrass coverage has significantly declined over the past three decades.

## 3. Methods

This study utilizes the spectral wave model WAVEWATCH-III, which is widely used to study wave conditions in lagoon-like environments (Jouon et al., 2009; Chevalier et al., 2015; Rute Bento et al., 2015; Manawasekara et al., 2019). The first three parts of the methods (Section 3.1 to 3.3) describe the model calibration approach detailed in Fig. 2 and the fourth part presents the scenario analysis performed to study the influence of seagrass decline on wave conditions in the Arcachon lagoon.

A first calibration of the model without vegetation (hereafter referred to as calibration n°1) was performed during the winter at Tr1-B (Fig. 3b), a site almost completely devoid of vegetation in this season. This allows a first calibration of the model without taking into account vegetation; hence no wave-vegetation drag coefficient ($C_D$). The effect of wave energy dissipation by vegetation was then implemented in WAVEWATCH-III (Section 3.2), using an empirical wave-vegetation drag coefficient. Calibration of this coefficient was performed in WAVEWATCH-III through a 1D numerical analysis (Section 3.3). Finally, the model (including the effect of vegetation) was re-calibrated for this study area (Section 4.1). An additional set of data from Cognat (2019) was used at some steps of the model calibration (Fig. 2).

### 3.1. Measurement campaign

Wave and vegetation data were collected monthly throughout one year (between November 2020 and November 2021) at the center of the lagoon (location Bourrut, Fig. 1). Two transects were instrumented with SP2T pressure sensors (NKE Instrumentation®; Fig. 3a) to obtain free surface elevation from pressure variations over 3'30" bursts every 16'30" at an acquisition frequency of 4Hz. Transect orientations were chosen based on an analysis of the prevailing and most energetic wind di- rections and adjusted depending on the terrain (flat surface with a
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Map of the Arcachon lagoon with its general localization (top left) and the sites of interest. The red dots represent the calibration sites and the yellow star is the site where model validation and calibration of the drag coefficient are performed. The yellow dot marks the location of the weather station where winds are measured.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Schematic representation of the calibration approach. The field data used for each step are mentioned in bracket in italic font.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Instrumentation and survey sites at Bourrut (see Fig. 1 for location). (a) SP2T pressure sensors (NKE Instrumentation®). (b) Instrumented sites for wave measurements (red dots) and vegetation sampling sites (red and green dots).</figcaption></figure>

uniform slope) and meadow characteristics (homogenous meadow). Two communicating transects oriented North-West and South-East were instrumented with synchronized pressure sensors (5 sensors in total), providing a spatial discretization of approximately 50 m (Fig. 3b). An Acoustic Doppler Current Profiler (ADCP, Signature 1 000 from Nortek) was also set in point Tr1-A (Fig. 3b) to measure current velocities and directions for reconstruction of the free surface from pressure. Free surface was reconstructed using an ‘automatic’ cutoff frequency, the determination of which has been the topic of additional investigation as detailed in Appendix A.

Samples of *Zostera* meadows were collected monthly at the locations of the pressure sensors and halfway between two sensors (5 samples per transect; Fig. 3b). Seagrass samples consisted of sediment cores with a diameter of 10 cm taken within the meadow. These samples were then analyzed in the laboratory to determine seagrass characteristics. After careful rinse, the number of shoots was counted to obtain the shoot density. Ten shoots, representative of the samples, were selected and used for measuring leaf length, leaf width, and counting the number of leaves per shoot.

## 3.2. Numerical modeling

WAVEWATCH-III is a phase-averaged wave model that gives the evolution of the wave action density spectrum $N(k, \theta)$, defined as:

$$N(k, \theta) = F(k, \theta)/\sigma \qquad (\text{Eq. 1})$$

where $F$ is the energy density spectrum, $\sigma$ is the relative radian frequency, $k$ is the wavenumber and $\theta$ is the wave direction. This model is based on a spectral decomposition of the sea state as a function of the wavenumber and wave direction, based on the wave action balance equation:

$$\frac{\partial N(k, \theta)}{\partial t} + \nabla_x [(C_g + U)N(k, \theta)] + \frac{\partial}{\partial k} c_k N(k, \theta) + \frac{\partial}{\partial \theta} c_{\theta} N(k, \theta) = \frac{S_{tot}(k, \theta)}{\sigma} \qquad (\text{Eq.2})$$

with $C_g$ the group velocity, $U$ the depth- and time-averaged current velocity, $c_k$ and $c_\theta$ the propagation velocity in wavenumber $k$ and direction $\theta$ spaces, respectively. $S_{tot}$ is the total energy source term defined as the sum of all the source and sink terms modifying wave energy. An overview of model settings is presented in Appendix B.

While the effect of vegetation could be considered as a simple increase in bottom roughness length, such a representation cannot prop-

erly account for all the physical processes associated with vegetation and oscillatory flow interactions (Jacobsen et al., 2019; van Veelen et al., 2021), and is not able to accurately represent the strong seasonality of *Zostera noltei* in the Arcachon lagoon. To account for these processes, Infantes et al. (2012) emphasized the importance of using a parameterization based on leaf geometry. Therefore, a new sink term ($S_{veg}$) was implemented in the model (in $S_{tot}$) in a similar manner as Abdolali et al. (2022) and Pillai et al. (2022). This sink term is based on Mendez and Losada’s (2004) formulation of energy dissipation of random waves by vegetation, which has been adapted as a sink term for the spectral wave model SWAN by Suzuki et al. (2012; Eq. (14)) and reads:

$$S_{veg} = -\sqrt{\frac{2}{\pi}} \frac{\sigma^2 \tilde{C}_D b_v N(\tilde{k})^3 \sinh^3(\tilde{k}l_D) + 3 \sinh^3(\tilde{k}l_D)}{3\tilde{k} \cosh^3(\tilde{k}h)} \sqrt{E_{tot} E(\sigma, \theta)} \qquad (\text{Eq. 3})$$

where $E$ is the energy density spectrum, $E_{tot}$ is total wave energy, $\tilde{C}_D$ is the bulk drag coefficient for wave-vegetation interactions, $h$ is water depth and $g$ is acceleration due to gravity. $\tilde{\sigma}$ and $\tilde{k}$ are the mean frequency and mean wavenumber, respectively, and are computed as in Suzuki et al. (2012). This parameterization also considers vegetation parameters that are shoot density $N$, leaf width $b_v$ and the deflected plant height $l_D$ (as in Losada et al., 2016, Eq. (10)). The specificity of this implementation (in comparison to Abdolali et al., 2022; Pillai et al., 2022) is the addition of a new vegetation coupling field in WW3 that allows the wave model to directly receive the vegetation characteristics ($N$, $b_v$ and $l_D$) from a hydrodynamic model (MARS3D; Lazure and Dumas, 2008), in which flow-vegetation interactions were added (Kombiadou et al., 2014). This feature is particularly important for very flexible species colonizing a tide-dominated environment like the Arcachon lagoon, as currents can maintain the vegetation in a streamlined position, thereby reducing the canopy height and the wave attenuation capacity of the meadows. For this reason, it is key in this analysis to take into account the deflected canopy height ($l_D$), which is directly computed in the hydrodynamic model MARS3D.

The $S_{veg}$ sink term (Eq. (3)) is based on a Morison equation (Morison et al., 1950) that neglects swaying motion and inertial forces (Dalrymple et al., 1984). As a result, Eq. (3) only accounts for straight and rigid plant stands. Using the deflected plant height thus provides a better approximation of the wave energy dissipation capacity of flexible seagrass
species than the full leaf length.

In parallel, it was shown that a thorough calibration of the wave-vegetation drag coefficient ($\tilde{C}_D$) can implicitly account for the effects of plant swaying (Infantes et al., 2012; van Veelen et al., 2020) and provide a good approximation of the effect of flexible vegetation on the oscillatory flow (Bradley and Houser, 2009). The calibration of the drag coefficient is therefore also performed in this study, and is presented in the next section.

The novelty of this model lies in the recent integration of vegetation in our hydrodynamic model (MARS3D) and its state-of-the-art representation of current-vegetation interactions. This includes an iterative method applied at each time step (Abdelrhman, 2007) to account for the feedback mechanism between currents and vegetation, as current intensity affects leaf bending, while leaf bending, in turn, alters the current profile. As a result, the model provides a detailed representation of both currents and vegetation position in the water column. It is important to note that the computation of leaf bending in our flow model neglects elasticity, assuming the blades to be completely flexible. This assumption appears valid for highly flexible species, such as Zostera leaves, for which buoyancy is the primary restoring force acting on the blades, rather than elasticity (Abdelrhman, 2007).

### 3.3. Drag coefficient calibration

A 1D numerical modeling approach using WW3 (not coupled with the hydrodynamic model, Fig. 2) was implemented to represent wave evolution along the two transects (Fig. 3) and to establish a parameterization of $\tilde{C}_D$. This approach involves forcing the model with an input wave spectrum obtained from measurements at one end of the transect (depending on the wave direction) and comparing the significant wave height at the other end of the transect with the one measured by the pressure sensors at the corresponding location.

Transects were surveyed with a Differential Global Positioning System (DGPS) at a 10-m resolution and used as bathymetries in WW3 for the numerical analysis. Seagrass characteristics were spatially and temporally interpolated to account for the seasonal variations and spatial heterogeneity of vegetation along the transects. Meteorological conditions, currents and water level corresponding to the date of the chosen input spectra were used to force the model.

To ensure that the relationship between the spectra at both ends of the transect is correct, only bursts characterized by a wave direction (equals to the wind direction in this environment) collinear to the transect orientation (with a tolerance of $\pm 5^\circ$) were selected. Additionally, to ensure that the two spectra measured at both ends of the transect have consistent shapes and peak frequencies, these spectra were first normalized by their maximum amplitude and then compared using a Pearson correlation coefficient (PCC). Only spectra considered to be analogous (PCC >0.9) were retained for the determination of $\tilde{C}_D$.

For the drag coefficient parameterization to be valid in every condition encountered in the lagoon, the selected bursts were sorted into different bins, namely bins of significant wave height, bins of Leaf Area Index (LAI) and bins of current direction (following or opposing current), for both transects. One representative spectrum was selected for each combination of bins and used as input spectrum for the numerical modeling analysis.

The analysis was conducted with a constant drag coefficient ranging from 0 to 4 with a step of 0.1 and was thus repeated 41 times for each input spectrum. The drag coefficient of the run providing the most accurate significant wave height at the end of the transect was saved. Repeating this procedure for each input spectrum gave a set of the best values of $\tilde{C}_D$ in contrasting conditions, on which a fitted line with the following equation was defined:

$$ \tilde{C}_D = \alpha + \left(\frac{\beta}{X}\right)^{\gamma} \qquad (\text{Eq. 4}) $$

<figure><img src="image_6.png" /><figcaption>Fig. 4. Drag coefficient parameterization. Parameterization of the drag coefficient relation (black curve) fitted on the drag coefficient value obtained from numerical modeling (red squares).</figcaption></figure>

With $\alpha$, $\beta$, $\gamma$ calibration coefficients and $X$ a hydrodynamic parameter, often the Reynolds number $Re$ (Kobayashi et al., 1993; Bradley and Houser, 2009; Möller et al., 2014), the Keulegan-Carpenter number $KC$ ($KC = u_{max}T_p/bv$, with $u_{max}$ the maximum horizontal velocity and $T_p$ the peak period; Ozeren et al., 2014; van Rooijen et al., 2016; van Veelen et al., 2020) or $Q_{Re}$ and $Q_{KC}$ (Mendez and Losada, 2004; Anderson et al., 2011; Garzon et al., 2019):

$$ Q_{KC} = \frac{KC}{(l_D/h)^{\gamma}} \qquad (\text{Eq. 5.1}) $$

$$ Q_{Re} = \frac{Re}{(l_D/h)^{\gamma}} \qquad (\text{Eq. 5.2}) $$

With $\psi$ a calibration coefficient. In this specific calibration analysis, WW3 is not coupled to the hydrodynamic model thus the deflected height $l_D$ needs to be directly computed in the wave model adopting Ganthy et al.'s (2015) formulation:

$$ l_D = l \exp(-c_h \bar{u}) \qquad (\text{Eq. 6}) $$

Where $l$ is the unbent leaf length, $c_h$ is a calibration coefficient (3.6 for seagrass Z. noltei, Ganthy et al., 2015), and $\bar{u}$ is the depth-averaged free-stream velocity. Comparing the results given by the different hydrodynamic parameters, the best fit is provided by $Q_{KC}$ for $\alpha = 0.05$, $\beta = 95$, $\gamma = 4$ and $\psi = 0.05$ ($r^2 = 0.977$ and RMSE = 0.14; Fig. 4).

### 3.4. Scenario analysis

To look into the response of wind waves to the decline of Zostera noltei coverage, a scenario analysis is carried out over a low neap- and high spring-tidal cycle, considering the period March 29th, 2020 to April 13th, 2020. This period is representative of the contrasting tide conditions occurring in the lagoon and provides insights into the influence of water level and current velocities on wave damping by vegetation. The corresponding water levels and tidal currents used as forcing in WW3 are obtained from the hydrodynamic model MARS3D, using the FES2012 tide solution (Carrère et al., 2013). This study focuses on wind waves only, so no swell forcing is applied at the domain's boundaries and waves are studied over a restricted frequency range stretching from 0.2 Hz to 1 Hz.

The influence of the variation in seagrass coverage on wind waves is analyzed through significant wave height ($H_{m0}$), extracted from WW3 at
a 15-min time step. To focus this analysis on significant waves, only wave heights greater than 0.05 m are considered for data post-processing. The modification of wave characteristics between the pre- and post-decline scenarios is computed as a percentage change in $H_{m0}$, mean ($\Delta H_{m0,mean}$), computed over the simulation period and defined as:

$$ \Delta H_{m0,mean} = 100 \frac{H_{m0,mean post-decline} - H_{m0,mean pre-decline}}{H_{m0,mean pre-decline}} \quad (\text{Eq. 7}) $$

Every simulation is run with identical modeling parameters and only the vegetation characteristics and wind conditions vary as described in the following two subsections. The bathymetry used to represent the study area is based on 2016 data from the Arcachon Lagoon District Organization (SIBA) and has been adapted into a Cartesian grid with a 65-m resolution for numerical modeling in both MARS3D and WW3.

### 3.4.1. Wind scenarios

Previous studies (He et al., 2019; Garzon et al., 2019) have shown that water level plays a significant role in the wave attenuation capacity of vegetation. In the meso-to macro-tidal environment of this study, significant differences in the impact of seagrass decline on wave conditions can be expected between high and low tides, as well as between neap and spring tides. In this context, the consideration of variable wind conditions would make it difficult to clearly distinguish the effect of seagrass decline on wind waves at different tidal stages, as wind speed and directions typically vary between neap and spring tides. For this reason, it was decided to use constant wind speed and direction, defining representative scenarios based on typical wind conditions observed in the Arcachon lagoon. An analysis of the wind data measurements conducted at the Cap Ferret weather station (Fig. 1) since 1985 (not shown) revealed three distinctive wind regimes used as scenarios for this study: a summer sea breeze, a winter anticyclone and a winter storm.

- A summer sea breeze is defined as a wind event occurring between June and September, for which there is a mild wind (<5 m s⁻¹) in the morning (between 6 a.m. and 12 p.m.) and a north-west wind (between 290° and 340°N) in the afternoon (between 12 p.m. and 9 p.m.

m.), blowing for more than 3 h over a threshold value of 7.7 m s⁻¹. This threshold value is defined to take into consideration the most energetic sea breeze. Among the events that meet these conditions, the one having the median wind velocity is selected: a wind of 9.0 m s⁻¹ with a direction of 314.13°N is used to represent the summer sea breeze.

- A winter anticyclone is defined as a wind event occurring between November and February, with a direction between 0° and 90°N, a wind speed above 5 m s⁻¹, and lasting for more than four consecutive days. The median event selected to represent a winter anticyclone is an 8 m s⁻¹ wind, oriented 43.41°N.

- A winter storm is represented as an event occurring between November and February and having a peak wind speed exceeding 20 m s⁻¹. The median event selected to represent a winter storm is characterized by a speed of 22.3 m s⁻¹ and a direction of 262.10°N.

Note that these wind events are simulated as constant winds over the whole duration of the simulation and used to force both the current and wave models.

### 3.4.2. Seagrass scenarios

To represent the reduction in Z. noltei coverage, each wind scenario is simulated using two historical maps of seagrass coverage, namely the 1989 and 2016 coverage maps (Fig. 5), corresponding to the pre- and post-decline periods, respectively. These maps are the oldest and most recent maps in our possession and were created following the methodology described in Plus et al. (2010). For consistency, the wind events are simulated with vegetation characteristics corresponding to the season in which they occur, obtained from Cognat et al. (2018) who defined summer and winter characteristics for Z. noltei in the Arcachon lagoon. Ultimately, four vegetation scenarios are defined (Table 1), namely the pre-decline scenario (Fig. 5a) with summer and winter seagrass characteristics: Summer 1989; Winter 1989, respectively; and the post-decline scenario (Fig. 5b) with summer and winter seagrass characteristics: Summer 2016; Winter 2016, respectively.

<figure><img src="image_7.png" /><figcaption>Fig. 5. Coverage of Zostera noltei meadows in their (a) pre-decline configuration (1989) and (b) post-decline configuration (2016).</figcaption></figure>

Table 1

Definition of the simulations and associated vegetation characteristics obtained from averaging field measurements from Auby and Labourg (1996), Ganthy et al. (2013) and Cognat et al. (2018).

<table><thead><tr><th rowspan="2">Wind event</th><th colspan="2">Seagrass scenarios</th><th colspan="4">Z. noltei characteristics</th></tr><tr><th>Pre-decline</th><th>Post-decline</th><th>Leaf Length (m)</th><th>Leaf Width (m)</th><th>Leaf Thickness (m)</th><th>Leaf Density (m<sup>-2</sup>)</th></tr></thead><tbody><tr><td>Sea Breeze</td><td>Summer 1989</td><td>Summer 2016</td><td>0.126</td><td>0.00113</td><td>0.0002</td><td>73706</td></tr><tr><td>Anticyclone</td><td>Winter 1989</td><td>Winter 2016</td><td>0.036</td><td>0.00034</td><td>0.0002</td><td>16295</td></tr><tr><td>Storm</td><td>Winter 1989</td><td>Winter 2016</td><td>0.036</td><td>0.00034</td><td>0.0002</td><td>16295</td></tr></tbody></table>
# 4. Results

## 4.1. Model results

Model calibration and validation (last step in Fig. 2) is performed in terms of significant wave height ($H_{m0}$) using wave measurements collected during the ReZoEnv (November, 2015–November, 2016; Cognat, 2019) and ARCADE (November, 2020–November, 2021; this study) field campaigns, for calibration and validation, respectively. Both field campaigns used NKE SP2T pressure sensors with the same characteristics, sampling approach (described in Section 3.1) and data

treatment (Appendix A). Calibration and validation are both performed using variable wind forcing corresponding to the simulated period and obtained from wind hindcast data generated by the AROME meteorological model (Meteo-France).

### 4.1.1. Model calibration

Model calibration is conducted in terms of wave height and carried out at 2 sites (ILE and GARR; Fig. 1), over two 10-day periods, from January 3rd, 2016 to January 13th, 2016 (Fig. 6a to 6d) and from June 5th, 2016 to June 15th, 2016 (Fig. 6e to 6h), referred to as the winter and summer periods, respectively. These two time-spans are selected

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Model calibration conducted in terms of zero-moment wave height presented as time series (a., c., e., g.) and scatter plots (b., d., f., h.) at the calibration sites ILE and GARR (see Fig. 1 for locations) for the winter (blue lines) and summer (red lines) periods. In the time series, solid lines are the modeling results and grey dashed-dotted lines are the measurements. In the scatter plots, the black line is the identity line and the colored line is the trend line.</figcaption></figure>
<caption>**Table 2**</caption>

Calibration results at ILE and GARR during the winter period (January 03, 2016–January 10, 2016) and summer period (05/06/2016-15/06/2016). Validation results at Bourrut (see Fig. 1 for location) during the winter period (December 27, 2020–January 02, 2021) and summer period (21/05/2021-31/05/2021). Statistical estimators used for calibration and validation are root mean square error (RMSE) and BIAS.

<table><thead><tr><th rowspan="2">Calibration</th><th colspan="2">Summer</th><th colspan="2">Winter</th><th rowspan="2">Total</th></tr><tr><th>ILE</th><th>GARR</th><th>ILE</th><th>GARR</th></tr></thead><tbody><tr><td>RMSE (m)</td><td>0.042</td><td>0.058</td><td>0.098</td><td>0.126</td><td>0.081</td></tr><tr><td>BIAS (m)</td><td>-0.001</td><td>0.001</td><td>0.000</td><td>-0.029</td><td>-0.007</td></tr><tr><td>Validation</td><td>Summer</td><td>Bourrut</td><td>Winter</td><td>Bourrut</td><td>Total</td></tr><tr><td>RMSE (m)</td><td>0.050</td><td></td><td>0.090</td><td></td><td>0.07</td></tr><tr><td>BIAS (m)</td><td>-0.019</td><td></td><td>0.008</td><td></td><td>-0.0055</td></tr></tbody></table>

because they present contrasting seagrass characteristics and both encompass energetic wind events; that is to say they cover a suitable range of conditions for model calibration in addition to account for the seasonal variations of *Z. noltei*.

In winter, when seagrass biomass is at its lowest, simulated wave heights show a good agreement with the measurements at ILE and GARR (Fig. 6a to 6 d), with the slope of the trend lines of 0.82 and 0.84, respectively, and data homogeneously scattered around the identity line (Fig. 6b and 6d), as evidenced by the low BIAS of 0.000 m and -0.029 m (Table 2). Discrepancies can be observed between the observations and the model at both sites on January 9th, which can be explained by the gusts of wind that are not well represented by the 1-h discretization of the wind forcing used in WAVEWATCH-III. Additionally, the model overestimates wave heights at GARR on January 11th (Fig. 6c), certainly due to the presence of tidal creeks close to the measurement points that could have affected the channelization of the flow and induced rapid and strong current shifts that are not well represented in the flow model

MARS3D and its 65-m grid resolution.

Summer calibration (Fig. 6e to 6 h) is conducted over a period characterized by well-developed seagrass meadows and milder wind conditions, with waves not exceeding 0.4 m. For this calibration period, very satisfactory RMSEs of 0.042 m at ILE and 0.058 m at GARR are obtained. The model is able to correctly reproduce the distribution of $H_{m0}$, as indicated by the slope of the trend lines of 0.85 at ILE and 0.75 at GARR (Fig. 6f and 6 h), despite occasional underestimations noticeable at both sites.

Despite the challenging configuration of the study site, consisting of wide intertidal flats and a dense network of channels with steep banks, thorough model calibration provides highly satisfactory performance at a broad scale. The model successfully reproduces the distribution of observed $H_{m0}$ under both calm and energetic conditions, considering winter as well as summer vegetation characteristics.

Additionally, the Arcachon lagoon is a hotspot of oyster farming with numerous oyster farms scattered throughout the lagoon, which are expected to have a significant impact on wave damping, since oyster tables were shown to have an important influence on wave dissipation (Kervella et al., 2010). However, these macro-structures are not represented in the model and likely degrade model performances.

### 4.1.2. Model validation

Model validation is conducted approximatively at the center of the domain (Bourrut location, Fig. 1) over two periods: from December 27th, 2020 to January 2nd, 2021 (Fig. 7a and 7b) and from May 21st, 2021 to May 31st, 2021 (Fig. 7c and 7d), characterized by low-density and well-developed meadows, respectively. Validation results exhibit excellent performance for both periods, as evidenced by a trend line slope of 0.98 and data grouped very closely around the identity line (Fig. 7b and 7d), with a low RMSE of 0.090 m and BIAS of 0.008 m during the winter, and a RMSE of 0.050 m and a BIAS of -0.019 m during the summer.

The validation site being the same as for calibration of the drag coefficient $\tilde{C}_D$, the better capacity of the model to reproduce the observations at Bourrut than at GARR and ILE shows that the wave-vegetation

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Validation results at Bourrut during the winter period (a. and b.) and the summer period (c. and d.). Modeling results (blue and red) are compared to measurements (grey) and presented as time series (a. and b.) and scatter plots (c. and d.). In the scatter plots, the black line is the identity line and the colored line is the trend line.</figcaption></figure>
drag coefficient calibrated in section 3.3 likely varies throughout the lagoon, underlying the very strong site-dependence of this coefficient.

Note that before calibrating our model using a drag coefficient derived from a 1D numerical analysis, model calibration was attempted using constant drag coefficients ($C_D$ = 1, 0.5, and 0.1), as is commonly done in large scale studies (Beudin et al., 2017 a,b; Donatelli et al., 2019), as well as drag coefficients from the literature (Paul and Amos, 2011; Garzon et al., 2019). However, these coefficients, even Paul and Amos' (2011) formulation specifically developed for *Zostera noltei* under wind wave conditions, failed to reproduce the seasonal dynamics of wave conditions in this environment. While the drag coefficient calibrated through 1D modeling using data collected at *Bourrut* may not perfectly represent conditions across the entire lagoon, it performs very well at the lagoon scale and provides significantly better results than those obtained using a constant drag coefficient or a drag coefficient from the literature.

## 4.2. Wave attenuation by vegetation

### 4.2.1. Significant wave height

Fig. 8 presents the percentage change in mean significant wave height computed over the full neap-spring tidal cycle ($H_{m0,mean}$) in response to seagrass decline for the different simulated scenarios (Fig. 8b,c,d) against the percentage change in seagrass coverage between 1989 (pre-decline) and 2016 (post-decline; Fig. 8a). Fig. 8a shows an overall decrease in vegetation coverage, with large vegetated intertidal areas experiencing seagrass loss, which exceed 80 % in the southwest of the lagoon, while sparse areas, such as the northwest corner of the lagoon and the *Leyre* delta (southeast corner), exhibit slight seagrass development.

The percentage change in $H_{m0,mean}$ for the summer sea breeze (Fig. 8b) exhibits a clear intensification of wave heights over the majority of the tidal flats following the reduction in seagrass coverage. The tidal flats of the west and center of the lagoon are characterized by a moderately higher $H_{m0,mean}$ of about 15 %, while the eastern tidal flats feature larger differences of 20 %. The percentage increase even exceeds 30 % very locally along the eastern coastline and in the southeast corner, with $H_{m0,mean}$ rising from 0.22 m to 0.29 m (Figures C.1.a and C.1.b).

Although *Z. noltei* is only present on the tidal flats, the decrease in seagrass coverage in these areas also leads to changes in $H_{m0,mean}$ within the channels. In the shallow inner channels of the southeastern part of the lagoon (Fig. 1), the variations in $H_{m0,mean}$ are almost identical to those observed on the surrounding tidal flats, with an increase of 20 %. In contrast, the increase in $H_{m0,mean}$ is much lower in the secondary channels (*Teychan* and *Girouasse* channels; ~5 %), and almost negligible in the rest of the deeper channels (<2 %).

Unlike the trend observed in the rest of the lagoon, the wave attenuation capacity of the meadows increases in certain areas due to higher seagrass coverage (see Fig. 8a). In the northern part of the lagoon, $H_{m0,mean}$ differs by 10 %–25 %, dropping from 0.07 m to 0.05 m (Fig. 8b). $H_{m0,mean}$ is reduced by 20 % in the *Leyre* delta, going from 0.26 m to 0.21 m, and by 10 % along the southern coastline. Conversely, some areas featuring higher seagrass coverage exhibit an increase in $H_{m0,mean}$ as a consequence of the significant intensification of wave conditions in their surrounding areas. For instance, West of *Ile aux Oiseaux* (IO; Fig. 8a), $H_{m0,mean}$ increases by approximately 10 % in spite of the increase in *Z. noltei* coverage, due to the reduction in seagrass coverage North and West of this area.

In the *Leyre* delta and along the southern coastline where seagrass coverage also increases, wave height is highly attenuated despite wave intensification in the neighbor areas. This shows that despite the increase in wave height within the lagoon, significant development of seagrass meadows in very shallow areas, even over a short distance, are effective in attenuating waves reaching the coast.

The highest percentage change in $H_{m0,mean}$ (>30 %) observed in the southeast of the lagoon is first explained by the important loss of

seagrass coverage that occurs in this area. Second, considering a summer sea breeze characterized by a northwest wind, the southeast region corresponds to the end of the fetch, meaning that waves reaching this area have been affected by the vegetation from the rest of the lagoon. Therefore, the reduction in wave attenuation capacity associated with the reduction in seagrass coverage accumulates over the distance of propagation and results in a maximum increase in $H_{m0,mean}$ in the southeastern part of the lagoon. These results show that vegetation-induced wave damping efficiency can become significant when dissipation occurs over long distances, as pointed out by Fonseca and Cahalan (1992). This demonstrates the high potential of short-stature species like *Zostera noltei* to efficiently attenuate local wind-waves when dense meadows colonize broad areas.

The intensification in $H_{m0,mean}$ due to the reduction in *Z. noltei* coverage observed in this study (20 %–30 % in the southeastern part) exceeds the total attenuation capacity reported for the same species (20 %) by Paul and Amos (2011; hereafter referred to as PA). The significant influence of seagrass coverage on wave height at this study site can be explained by a combination of factors. First, because of the much longer fetch, reaching up to 15 km in the Arcachon lagoon against 300 m in PA. Then, the large shoot density in the Arcachon lagoon, reaching 22,000 shoots·m⁻² at our study site (Auby and Labourg, 1996) leads to loss of shoot density higher than the density of *Z. noltei* in PA (4 600 shoots·m⁻²). Finally, due to the larger mean significant wave height in our study (comprised between 0.05 m and 0.35 m; Figure C.1.a) than in PA (comprised between 0.05 m and 0.07 m), since larger waves are more efficiently attenuated (Anderson and Smith, 2014; Luhar et al., 2017; Garzon et al., 2019).

Fig. 8c and 8d shows the percentage change in significant wave height for the winter scenarios, considering an anticyclone and a storm, respectively. For the anticyclone scenario (Fig. 8c), only a slight decrease in $H_{m0,mean}$ occurs along the east coast of the lagoon (5 %, with $H_{m0,mean}$ going from 0.085 to 0.090 m; Figures C.1.c and C.1.d), due to the reduction in seagrass coverage along the coast for a north east event, while no significant change is observed in the rest of the lagoon. In the case of the storm scenario (Fig. 8d), *Z. noltei* coverage loss does not yield to any significant change $H_{m0,mean}$.

In the Arcachon lagoon, *Z. noltei* experiences strong seasonal variations (Auby and Labourg, 1996), characterized by much smaller leaf length, leaf width, and lower leaf density during the winter, resulting in considerably smaller leaf biomass in winter than in summer (Auby and Labourg, 1996, Table 1). These seasonal variations in *Z. noltei* characteristics are responsible for the divergent responses in wave dissipation to the reduction in seagrass coverage, highlighting the positive correlation between biomass and wave attenuation, as already reported in numerous studies (e.g. Bouma et al., 2010; Koftis et al., 2013; He et al., 2019). In conclusion, these results show that seagrass decline, represented through the reduction in seagrass coverage, leads to contrasted responses in $H_{m0,mean}$ depending on the season, with a much more significant impact during the summer when *Z. noltei* is fully developed than during the winter.

## 4.3. Influence of seagrass on tidal current

Fig. 9a and 9b represent the time series of water level and tidal current velocities averaged over canopy height, respectively, extracted at *Bourrut* in the case of the summer sea breeze scenario. The time series of tidal velocities (Fig. 9b), given for the pre- and post-decline scenarios, show that current velocities are consistently larger in the post-decline configuration (brown line). This illustrates the capacity of seagrass to attenuate current velocities (Peterson et al., 2004), as well as the influence of vegetation loss on the canopy ambient current, as demonstrated in previous studies focusing on the influence of seagrass decline on tidal hydrodynamics (Vu et al., 2017; Donatelli et al., 2019).

Current velocities have a high influence on seagrass blade pronation and can change the configuration of the canopy in the water column
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** (a) Percentage change in Z. noltei meadow coverage between 1989 (pre-decline) and 2016 (post-decline). Green areas represent seagrass development and brown areas represent seagrass loss. Percentage change in mean significant wave height between 1989 (pre-decline) and 2016 (post-decline) for scenarios of summer sea breeze (b), winter anticyclone (c) and winter storm (d). Red values represent an increase in wave height (i.e., lower attenuation capacity of vegetation), and blue values represent a decrease in wave height (i.e., higher attenuation capacity of vegetation).</figcaption></figure>

(Luhar and Nepf, 2011; Ganthy et al., 2015). In this regard, Fig. 9c shows the evolution of canopy height ($H_{can}$) and exhibits a constant reduction in this parameter in the post-decline scenario. Because an identical leaf length is used in the pre- and post-decline scenarios (Table 1), the reduction in $H_{can}$ is attributed solely to leaf bending by currents. As current velocities increase due to the reduction in seagrass coverage, higher hydrodynamic stress is exerted on the flexible canopies, constraining the seagrass blades lower in the water column and thus reducing the canopy height. This reduction appears more pronounced during the neap tide, when current velocities are lower than during the spring tide. Under the highest current velocities during a spring tide (Fig. 9b), the leaves are streamlined lower in the water column and the canopy height is reduced during both the pre- and post-decline scenarios

(Fig. 9c), with little difference between them.

Seagrass, acting as macro-rugosity on the seabed, influences wave dissipation, which is also highly dependent on the water level. For this reason, its impact on waves is often regarded as a ratio of seagrass height to water level (Anderson and Smith, 2014; Garzon et al., 2019; van Veelen et al., 2020), referred to as the relative canopy height ($H_{rel}$). Fig. 9d provides a representation of $H_{rel}$ and shows that a lower seagrass coverage yields to a reduction in $H_{rel}$ during a neap tide, mainly during the flood, while milder changes are observed during a spring tide. The contrasted responses of this parameter to the tidal cycle lie in the fact that during a spring tide, the canopy is maintained low in the water column for both the pre- and post-decline configurations (Fig. 9c), while absolute water levels are higher (Fig. 9a).
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Time series of (a) water level, (b) tidal current velocities averaged over canopy height, (c) canopy height, (d) relative canopy height (computed as the ratio of canopy height to water level) and (e) significant wave height extracted at Bourrut (yellow star in Fig. 1); for a summer sea breeze scenario in the pre-decline (green curves) and post-decline (brown curves) scenarios. In panel e., the values at the top are the mean $H_{m0}$ over a tide in the pre-decline (green values) and post-decline (brown values) scenarios; the values at the bottom correspond to the indices of the tides.</figcaption></figure>

Finally, a comparison of the time series of significant wave height ($H_{m0}$) is provided in Fig. 9e and depicts a higher $H_{m0}$ in the post-decline scenario throughout the entire tidal cycle, with the mean $H_{m0}$ (calculated over each tide) going from 0.18 m in the pre-decline scenario to 0.23 m in the post-decline scenario (28 % increase). This increase in $H_{m0}$ exhibits a contrasted pattern depending on the tidal cycle. During a neap tide, $H_{m0}$ undergoes significant changes, as the mean $H_{m0}$ computed over a tide increases by up to 7 cm, going from 0.09 m to 0.16 m for tide n°9 and from 0.13 m to 0.20 m for tide n°11, namely a 78 % and 53 % increase, respectively. During a spring tide, the changes in mean $H_{m0}$ over a tide are less significant. Although these changes can reach up to 6 cm, with the mean $H_{m0}$ rising from 0.23 cm to 0.27 cm for tide n°15, it only represents a 26 % increase. As relative canopy height is reduced, the hydrodynamic drag exerted on the plant stands decreases (Kobayashi et al., 1993; Freeman et al., 2000). Additionally, with increasing depth, the drag force exerted on the plant decreases and wave energy is less attenuated (Mendez and Losada, 2004; Jacobsen et al., 2016). Therefore, during a spring tide, when water level is higher and the seagrass leaves are streamlined lower in the water column, wave attenuation by vegetation is less important, and the changes in $H_{m0}$ induced by the reduction in seagrass coverage are milder.

The dependence of wave height on canopy height can be observed

through corresponding asymmetries between ebb and flood tides in both $H_{m0}$ (Fig. 9e) and $H_{rel}$ (Fig. 9d). This is evident from the minimum in $H_{rel}$ reached after high tide slack, at the beginning of the ebb, and the corresponding pattern in $H_{m0}$, which also reaches a maximum after the onset of the ebb. It is clear that during the flood, $H_{m0}$ is significantly smaller in the pre-decline scenario than in the post-decline scenario, while $H_{m0}$ peak is reached during the ebb, with lower changes between the pre- and post-decline scenarios. These results confirm the prominent role of vegetation height on wave attenuation, in agreement with prior studies (e.g. Manca et al., 2012; Maza et al., 2015; He et al., 2019). Nevertheless, it must be noted that the intensity of these changes is also highly dependent on the variation of canopy density, as demonstrated for this species (Paul et Amos, 2011) and other species (e.g. Bradley and Houser, 2009; Koftis et al., 2013).

Results from Fig. 9 reveal that during a neap tide, there is a positive correlation among the intensification of tidal currents due to seagrass decline, the reduction in canopy height and the increase in wave height. Therefore, beyond the direct effect of tidal currents to enhance or reduce wave height whether they are following or opposing (Hu et al., 2014), they also affect the ability of flexible vegetation to dissipate wave energy by bending the seagrass blades.
# 5. Discussion

## 5.1. Modeling the deflected canopy height

A new wave-flow-vegetation model was developed within the scope of this study, with the specificity of considering feedback between leaf bending and the profile of current velocity in the flow model (Kombiadou et al., 2014), and using this deflected canopy height in the wave model. This approach of using the deflected canopy height instead of the leaf length was defined by Losada et al. (2016), and to the author's knowledge, this study constitutes the first implementation of this method at the scale of a coastal lagoon. Although the consideration of the deflected canopy height was shown to provide more accurate results than the full leaf length (Losada et al., 2016), the lack of accuracy regarding the influence of the flow on leaf bending in many numerical models has limited the use of this approach.

Another approach to address the lack of knowledge regarding the deflected canopy height has consisted in the definition of an effective leaf length, defined as the length of a rigid blade that results in the same drag as the corresponding flexible blade length (Luhar and Nepf, 2011). Parameterizations of effective leaf length were developed for unidirectional currents (Luhar and Nepf, 2011), pure waves (Luhar and Nepf, 2016), and combined wave-currents (Lei and Nepf, 2019).

In the Arcachon lagoon, mean current velocities on the tidal flats are on average at least twice as large as the mean orbital velocities. In a tide-dominated environment like this one, Lei and Nepf (2019) showed that the effective leaf length is best represented by the parametrization only accounting for unidirectional currents (Luhar and Nepf, 2011). Under such conditions, we can expect the use of a deflected leaf length computed in our flow model through a comprehensive force balance equation to provide better results than the effective leaf length, but this assumption must be verified. However, during storms, the influence of oscillatory flow on leaf bending can be non-negligible, and using the effective leaf length in combined wave-current conditions could offer a better representation of the drag exerted on flexible vegetation. Comparison of both approaches in reproducing wave energy dissipation remains to be tested under different conditions in this intertidal environment to determine the most appropriate modeling strategy for the computation of wave energy dissipation by vegetation.

## 5.2. Uncertainties regarding drag coefficient calibration

The wave-vegetation drag coefficient is highly dependent on hydrodynamics and meadow characteristics, such as size, density, coverage and plant stand arrangement, making this coefficient highly site-specific.

Density is one of the main factors influencing the wave dissipation capacity of seagrass meadows and the wave-vegetation drag coefficient (He et al., 2019). The drag coefficient of a cylinder field is higher than that of individual, isolated cylinder-like plant stands due to interactions among the cylinders (Tanino and Nepf, 2008; Ozeren et al., 2014). The interaction between flow and a plant stand generates a wake and produces turbulence, which in turns interact with lateral and downstream plant stands; provided that the flow excursion amplitude is larger than the spacing between the plant stands (Etminan et al., 2019).

The drag coefficient also depends on canopy length, as wave dissipation by vegetation is influenced by the propagation of waves through the canopy. Most wave energy is dissipated within the first few meters of the canopy (Riffe et al., 2011), and the rate of wave dissipation decreases exponentially with the distance traveled through it (Sánchez and González, 2011).

In the Arcachon lagoon, seagrass meadows occur in patches of varying sizes, coverages and arrangements, causing the drag coefficient to fluctuate significantly throughout the lagoon. Ideally, a drag coefficient should be calibrated for each site and set of vegetation characteristics and wave conditions, but this is not realistically feasible. To obtain a drag coefficient adapted to the range of vegetation characteristics and hydrodynamic conditions present in the Arcachon lagoon, the data were sorted into distinct sets of conditions. An equal number of samples was selected from each set to perform the calibration. This approach ensures that the various conditions found in the Arcachon lagoon are equally represented in the calibration of the drag coefficient. Without this method, the calibration would have been biased toward the low KC values, which are more frequently encountered in this environment.

Given the amount of data available for calibration, we are confident that this parameterization of $\tilde{C}_D$ is the most suitable for the Arcachon lagoon. While it may not perfectly fit every seagrass meadow – given their variation in size, coverage and density – our various calibration tests indicate that this formulation is the most appropriate for modeling wave conditions in the presence of the meadow characteristics found in this environment. It performs better than both a constant drag coefficient and existing parameterizations from the literature (Paul and Amos, 2011; Garzon et al., 2019). Nevertheless, our results highlight the need for a more universal definition of the wave-vegetation drag coefficient, which does not rely on calibration parameters, as calibration is not adapted to capture the variability in meadow characteristics and wave conditions.

## 5.3. Incapacity to model wave period transformation

Previous studies investigating wave spectrum dissipation by vegetation (Lowe et al., 2007; Koftis et al., 2013; Jacobsen et al., 2019) have evidenced that wave energy dissipation by vegetation is non-uniform across the frequency range. The main limitation of Suzuki et al.'s (2012) formulation lies in its assumption of uniform energy dissipation across the entire frequency range. This implies that vegetation-induced energy dissipation results in a downshift of the wave energy spectrum, with its shape remaining unchanged. As a result, the change in mean wave period ($T_{m02}$) is insignificant. Consequently, this formulation is not suitable for studying wave period transformation induced by variations in seagrass coverage and does not allow for drawing quantitative conclusions regarding this parameter.

Such a study would require a parameterization that considers a frequency-dependent drag coefficient (Jadhav et al., 2013) or a frequency-dependent parameterization of wave dissipation, such as the one developed by Jacobsen et al. (2019). However, the latter was developed for the spectral wave model SWAN, which uses frequency-direction discretization, and implementing this parameterization in WW3, which uses wavenumber-direction discretization, is not straightforward and should be the subject of further work.

## 5.4. Implications for sediment resuspension and seagrass survival

In sheltered environments like the Arcachon lagoon, local wind-induced waves have been identified as an important cause of sediment erosion (Contti Neto et al., 2022). Erosion flux, as a function of bottom shear stress, evolves with the square of near-bed orbital velocities (Soulsby, 1997, Eq. (57)). To provide insights into the influence of the reduction in seagrass coverage on the potential reinforcement of erosion in the Arcachon lagoon, the percentage change in mean near-bed orbital velocities is presented in Fig. 10. Orbital velocity being linearly
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Percentage change in mean near-bed orbital velocity between 1989 (pre-decline) and 2016 (post-decline) for a summer sea breeze scenario. Red values represent an increase in mean near-bed orbital velocity and blue values a decrease in this parameter.</figcaption></figure>

correlated with wave amplitude, very similar patterns of change can be observed for both parameters (Fig. 8b and 10). Seagrass loss leads to an increase in mean near-bed orbital velocities ($U_{orb, mean}$) on all the tidal flats, except in the northern corner of the lagoon and Leyre Delta (Fig. 1), where vegetation coverage increases. $U_{orb, mean}$ is characterized by a percentage increase comprised between 15 % and 30 % on most of the tidal flats (going from 6.7 cm s⁻¹ to 9.0 cm s⁻¹), and comprised between 50 % and 100 % in the eastern part of the lagoon where the decline is the most severe (intensifying from 7.1 cm s⁻¹ to 13.8 cm s⁻¹; Figures C.2.a and C.2.b).

The increase in $U_{orb, mean}$ on most of the mudflats (Fig. 10) and constant amplification in $H_{m0}$ over a tide (Fig. 10e) are expected to have accentuated sediment remobilization throughout the tidal cycle. This trend is all the more expected considering that vegetation also significantly contributes to soil stabilization (Gacia and Duarte, 2001) and this function is hindered by seagrass loss. Therefore, a significant increase in the suspended sediment stock can be expected during the summer period. It is also worth noting that, although there are no significant changes in wave conditions following seagrass decline during the winter, the reduction in sediment stability caused by seagrass decline may also lead to additional sediment resuspension during this season.

The pattern of change in $U_{orb, mean}$ presented in Fig. 10 is expected to modify sediment transport, leading to a redistribution of sediment classes and changes in seabed elevation. In the southern part of the lagoon, and more specifically in the southeastern region, $U_{orb, mean}$ increases suggesting enhanced resuspension, likely causing seabed erosion and coarsening of the substratum, as fine sediments are more easily eroded. In contrast, in the northern part of the lagoon where $U_{orb, mean}$ decreases, increased deposition is expected, leading to seabed accretion and a muddier substratum due to the accumulation of fine sediments. This expected trend aligns with observations made by the local authorities (Ifremer, Ganthy, pers. com.), who reported muddification and infilling of the northeastern inner channels, which has hindered navigation in some areas and increased the need for dredging.

Seagrass decline is also responsible for the modification of tidal

hydrodynamics (Donatelli et al., 2019), through changes in tidal asymmetry and intensification of current velocities on the tidal flats, both highly influential on sediment transport (Quaresma et al., 2007). Therefore, the cumulative influence of the modification of wave conditions and tidal hydrodynamics is very likely to have restructured the sediment fluxes in the Arcachon lagoon.

Intensification of hydrodynamic energy can also directly affect the vegetation meadows through uprooting or mechanical leaf destruction (Koch, 2001; Balke et al., 2014; Arkema et al., 2017), threatening the survival of the remaining plant stands. These additional losses are expected to accelerate the feedback mechanisms between the intensification of hydrodynamic conditions and seagrass loss (Bouma et al., 2009), and may destabilize the ecosystem.

## 6. Conclusion

A coupled wave-flow-vegetation model was developed to study the influence of seagrass decline on wave conditions in a sheltered coastal lagoon. For this purpose, the effect of vegetation on wave energy dissipation was implemented in the spectral wave model WAVEWATCH-III, with the specificity of using the deflected canopy height computed in the flow model, and provided to the wave model through the addition of novel coupling fields in WAVEWATCH-III. Thorough calibration of the wave model was performed at our study site (Arcachon lagoon) using *in situ* field measurements, with a special attention paid to the calibration of the wave-vegetation drag coefficient through an approach involving field measurements and 1D numerical modeling.

The definition of three typical wind events in this environment, namely a summer sea breeze, a winter anticyclone and a winter storm, allowed us to study the influence of vegetation coverage on wave height, accounting for the seasonality of *Z. noltei* characteristics and wind conditions.

This study highlights the significant role of leaf density, leaf length and surface colonized by seagrasses (*Zostera noltei*) in modifying wave characteristics inside the lagoon and underlines the severe consequences of the seagrass decline that occurred over the last decades on wave parameters. Results reveal that the reduction in seagrass coverage is responsible for the intensification of wave conditions during the summer, characterized by a mean significant wave height increase reaching 30 % (about 6 cm) in the regions where seagrass meadows declined the most. The modification of wave conditions was twofold: an increase in the mean wave height over the tidal cycle, rising from 0.18 m in the pre-decline scenario to 0.23 m in the post-decline scenario (28 % increase), and an increase in the maximum wave height. Conversely, during the winter, when seagrass biomass is at its lowest, no significant changes in wave characteristics were observed following the reduction in seagrass coverage, regardless of the intensity of the wind event. This study also highlights a clear contrast between neap and spring tides, as seagrass coverage loss caused significant changes in wave conditions during neap tides but milder ones during spring tides, when the water level is much higher.

In addition to the reduction in seagrass coverage that amplified wave energy in the lagoon, the intensification of current velocity induced by seagrass loss is found to reduce the capacity of *Z. noltei* to attenuate waves. Due to the higher current velocities, seagrass blades are streamlined lower in the water column, and canopy height is reduced, thus limiting the efficiency of the meadows to dissipate wave energy.

The loss of *Zostera noltei* also significantly intensified near-bed orbital velocity, with increases ranging from 50 % to 100 % in the areas where seagrasses severely declined, further to which additional erosion can be expected. Future work should evaluate the influence of vegetation loss and subsequent increase in current velocity and wave energy on sediment dynamics in the Arcachon lagoon.
### CRediT authorship contribution statement

**Arnaud Le Pevedic:** Writing – original draft, Software, Methodology, Investigation, Formal analysis, Conceptualization. **Paul Bayle:** Writing – original draft, Investigation, Formal analysis. **Alexandre Nicolae Lerma:** Writing – review & editing, Investigation, Funding acquisition. **Aldo Sottolichio:** Writing – review & editing, Supervision, Investigation, Funding acquisition, Conceptualization. **Florian Ganthy:** Writing – review & editing, Supervision, Investigation, Funding acquisition, Conceptualization.

### Funding sources

This work was supported by Nouvelle-Aquitaine region, SIBA (Arcachon Lagoon District Organization), PNMBA (Arcachon Basin Marine Nature Park), and AEAG (Water Agency Adour-Garonne).

### 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

A. Le Pevedic is supported by a PhD fellowship from SIBA (Arcachon Lagoon District Organization), PNMBA (Arcachon Basin Marine Nature Park), Nouvelle-Aquitaine region and AEAG (Water Agency Adour-Garonne). This study is part of the ARCADE project which aims at studying geomorphological, hydrodynamic and bio-sedimentary evolutions in the Arcachon lagoon. Authors acknowledge the French Research Institute for Exploitation of the Sea (IFREMER) for providing infrastructures and instrumental support, and PCDM (Pole de Calcul et de Données Marines) for providing DATARMOR (storage, data access, computational resources, visualization, web-services, consultation, support services). We would like to thank M. Paul, D. Idier, M. Herrmann, F. Grasso, X. Bertin and N. Senechal for their insightful comments and suggestions, which helped improve this work. We would like to thank the two reviewers for their very constructive comments, which undoubtedly helped improve our manuscript.

## Appendix A. Wind wave reconstruction

### A.1 Free surface reconstruction method

The hydrodynamics of the Arcachon lagoon is dominated by strong tidal currents and wind-generated short waves. Tidal currents are alternatively in the direction of and opposite to wind waves, and as such, strong non-linear interactions take place (Longuet-Higgins and Stewart, 1960). Through these interactions, the wavelength and amplitude change may lead to breaking in the form of white-capping (Longuet-Higgins and Stewart, 1961). Although the presence of non-linear interactions in such environment is well known, previous studies using pressure sensors to measure wind-generated short waves in similar environments (e.g., Jones and Monismith, 2007; Parisot et al., 2008; Paul and Amos, 2011) have used the linear theory to reconstruct the free surface from pressure data. This choice is ascribed to the fact that there are no other published methods of free surface reconstruction (other than the hydrostatic and linear method) for this type of hydrodynamic environment, in comparison with nearshore zones where other methods accounting for non-linearity have been developed: fully dispersive (Bonneton and Lannes, 2017), weakly dispersive (Bonneton et al., 2018; Mouragues et al., 2019; Martins et al., 2020) and ‘moderately’ dispersive (Martins et al., 2021). Nonetheless, one of the advantages of the linear theory is that the pressure signal can be corrected from Doppler effects caused by the ambient current (this is not the case for the nearshore methods mentioned before), and it is known that not correcting for this Doppler effect can lead to significant errors when strong currents are present (Svendsen, 2005). For all these reasons, in this paper the linear theory is used as a base to reconstruct the free surface from pressure data.

The procedure to convert raw pressure data into free surface elevation went as follows. Absolute pressure data were transformed into relative pressure data by correcting for sea level atmospheric pressure using data collected at the nearby meteorological station (Cap Ferret, Fig. 1). Free surface elevations were obtained from the hydrostatic reconstruction of the detrended relative pressure signal and then corrected using the linear transfer function $K_p$ (from the linear theory, to correct from non-hydrostatic effects; Svendsen, 2005) given as:

$$K_p = \frac{\cosh(kh_0)}{\cosh(k\delta_m)} \qquad (\text{Eq. A.1})$$

where $k$ is the wavenumber, $h_0$ is the mean water depth (m) and $\delta_m$ the distance between the sensor and the bed (m). The wavenumber $k$ was calculated for each spectral discrete frequency using the dispersion relation accounting for currents (i.e., Doppler effects; Svendsen, 2005), given as:

$$\omega_a - kU\cos\mu = \omega_r \qquad (\text{Eq. A.2})$$

$$\omega_r = \pm \sqrt{gk \tan h(kh_0)} \qquad (\text{Eq. A.3})$$

$$\omega_a = 2\pi/T_a \qquad (\text{Eq. A.4})$$

where $\omega_a$ is the absolute angular frequency (rad.s⁻¹) calculated with the absolute (i.e., measured) wave period $T_a$, $\omega_r$ the relative (to the current) angular frequency (rad.s⁻¹) which is the unknown, $U$ the mean current (m.s⁻¹), $\mu$ the angle between the wave and the current propagation direction (rad) and $g$ the acceleration due to gravity (m.s⁻²). Note that $\omega_r$ is negative (positive) when the current is in the same (opposite) direction as (to) the wave.

Variance density spectra were computed from the reconstructed free surface elevation using a fast Fourier transform, with a Hamming window of 32 s with 50 % overlap. This gives 27 equivalent degrees of freedom which allows sufficient accuracy on the spectral estimate at a 95 % confidence level (Priestley, 1981). The minimum frequency (or maximum resolution) that can be determined is 1/32 = 0.032 Hz; nevertheless, the frequency cutoff ($f_c$) between infragravity and gravity band was taken as 0.04 Hz to match the one used in the model. The high-frequency cutoff is discussed in the next section, A.2. The use of these frequency cutoff is explained in section A.3.
## A.2 High-frequency cutoff

Wind-generated short waves, characterized by wave periods shorter than 4 s (i.e., frequency >0.25 Hz), have their spectral energy concentrated in the high-frequency band (Jones and Monismith, 2007) with the frequency peak generally comprised between 0.3 and 0.7 Hz. As a consequence, it is important to reconstruct the signal to a frequency sufficiently high to encompass the energy peak, in order to get accurate bulk parameters. However, if the cutoff frequency is too high, the signal amplification at relatively high frequency caused by the linear theory might be included in the calculation of the bulk parameters (see section A.3). This yields more energy than there is actually, resulting in an erroneous (too large) values for bulk parameters. Note that with a sampling frequency of 4 Hz, the Nyquist frequency is 2 Hz, which is large enough to avoid aliasing effects at the frequencies of interest. Jones and Monismith (2007) used a high-frequency cutoff of 0.6 Hz, while Bradley and Houser (2009) and Paul and Amos (2011) used 1 Hz.

To choose an adequately high-frequency cutoff, an Acoustic Doppler Current Profiler (ADCP, Signature 1 000 from Nortek) equipped with an Acoustic Surface Tracking (AST) system was deployed in point Tr1-A (Fig. 3) for two weeks. The AST provides a direct measure of the free surface, and can thus be used as a reference to test the reconstruction. Figure A.1 shows a wave density spectrum recorded during low-moderate energetic conditions (weak wind-generated waves), and compares the AST spectrum (used as a reference) with other reconstructions. Beyond showing that the hydrostatic reconstruction is, as expected, not performant, it also highlights the fact that a high-frequency cutoff of 0.6 Hz is too low to encompass the entirety of the energy peak. For the burst presented in Figure A.1, the significant wave height ($H_{m0}$) is about 50 % under-estimated. Overall, the ADCP test showed that the reconstruction could be done most of the time up to at least 0.6 Hz (in some exceptional cases, the high-frequency cutoff should be lower), and sometimes up to 0.9 Hz (0.83 Hz in Figure A.1). However, these variations in frequency cutoff (from one burst to another) are due to multiple factors that cannot be predicted (e.g., the instrument noise and the non-linearity, among others).

To face this issue, a simple method was developed to automatically identify the suitable high-frequency cutoff based on the high-frequency 'noise' tail of the hydrostatic signal ($\zeta_H$). This method consists in finding the slope change between the 'signal' and the 'noise' (intersection between the two blue secant lines in Figure A.1). Note that this method is inspired by pioneer studies that used a 'noise' threshold (Jones and Monismith, 2007) to determine the high-frequency cut. However, the 'noise' of the instrument is not always well defined, and can vary over time if non-linearities are part of it. Therefore, the current method allows for variability in the 'noise' tail between bursts and is performed on the hydrostatic signal. Figure A.1 shows an example of this 'secant method'. Note that some spectra can have a very coarse shape, in which case this method cannot assess accurately the cutoff frequency. To prevent unrealistic cutoff frequency from being chosen, the selection is bounded between 0.5 and 0.9 Hz, with a default value of 0.6 Hz if it falls outside those boundaries. This method is assessed in the next section, A.3.

<figure><img src="image_13.png" /><figcaption>Fig. A.1. Wave density spectrum during low-moderate conditions, obtained from the AST ($\zeta_{AST}$, black solid line), the hydrostatic reconstruction ($\zeta_H$, black dashed line), the linear reconstruction ($\zeta_L$, red solid line). The dashed vertical black line marks the separation between the infragravity and gravity bands, and the dashed green line marks the 0.6 Hz frequency cutoff usually used in the literature. The blue lines represent the 'secant method' used to determine the high-frequency cutoff, referred to as 'automatic' frequency cutoff and represented by the dashed red line. Note that other non-linear methods (see Section A.1) derived for nearshore zones were also tested, but as expected, they did not give a better solution than the linear theory for this type of environment. The 95 % confidence interval is shown as the magenta dot with the vertical bars.</figcaption></figure>
### A.3 Bulk parameters and assessment of the ‘secant method’

For calibration of WAVEWATCH-III, the spectral wave height of zero order moment ($H_{m0}$) and spectral mean wave period ($T_{m02}$) are calculated for the gravity frequency band only, using the following equations:

$$m_i = \int_{f_c}^{f_{c-auto}} f^i E(f) \cdot df \qquad (\text{Eq. A.5})$$

$$H_{m0} = 4\sqrt{m_0} \qquad (\text{Eq. A.6})$$

$$T_{m02} = \sqrt{m_0/m_2} \qquad (\text{Eq. A.7})$$

Where $m_i$ is the moment of order $i$ (m$^2$), $f_c$ is the frequency cutoff (Hz) between gravity and infragravity band (Section A.2), $f_{c-auto}$ is the high frequency cutoff using the ‘secant method’ (Section A.2) and $E(f)$ is the energy (m$^2$.Hz$^{-1}$) associated with each discrete frequency $f$ of the density spectrum.

Figure A.2 shows a comparison between the wave parameters ($H_{m0}$ and $T_{m02}$) measured with the AST and the linear theory with different high-frequency cutoff. This figure shows that while most of the bulk energy is encompassed within 0.6 Hz, especially during high energetic events where the peak is around 0.3–0.4 Hz, this frequency cutoff is not high enough to describe the bulk energy during low-moderate energy events. In contrast, the ‘secant method’ shows a slight amelioration of the bulk energy calculation, which can be significant for some low-moderate energy events. Nonetheless, it provides good representation of the AST signal on average with RMSEs of 0.044 m for $H_{m0}$ and 0.564 s for $T_{m02}$, against 0.060 m for $H_{m0}$ and 0.656 s for $T_{m02}$ with the fixed 0.6 Hz high-frequency cutoff, which is a significant enough improvement to be presented here.

<figure><img src="image_14.png" /><figcaption>Fig. A.2. (a.) Water depth, (b.) Spectral significant wave height, $H_{m0}$ and (c.) mean wave period, $T_{m02}$, obtained with the AST (black line), the linear reconstruction with a 0.6 Hz high-frequency cutoff (green line) and the automatic cutoff high frequency obtained with the ‘secant method’ (red line), over the two weeks of ADCP measurements.</figcaption></figure>
## Appendix B. Model Settings

<caption>**Table B.1**</caption>

Overview of the main model settings.

<table><thead><tr><td>Parameter</td><td>Option/Value</td></tr></thead><tbody><tr><td>Time stepping scheme</td><td>Static</td></tr><tr><td>Global time step</td><td>6 s</td></tr><tr><td>Frequency discretization</td><td>18 frequencies</td></tr><tr><td>Direction discretization</td><td>15 directions</td></tr><tr><td>Wind Input source term</td><td>Ardhuin et al. (2010)</td></tr><tr><td>Bottom friction</td><td>SHOWEX bottom friction (Ardhuin et al., 2003)</td></tr><tr><td>Depth-induced breaking</td><td>Battjes and Janssen (1978) including the parameterization of the breaking coefficient as a function of the local bottom slope, following Pezerat et al. (2021)</td></tr><tr><td>Nonlinear wave-wave interactions</td><td>Activated</td></tr><tr><td>Triad nonlinear interactions</td><td>Activated</td></tr><tr><td>Shoreline Reflection</td><td>Activated</td></tr></tbody></table>
## Appendix C. Wave characteristics

<figure><img src="image_15.png" /><figcaption>**Fig. C.1.** Spatial representation of mean significant wave heights (Hm0,mean) computed over the tidal cycle for the three simulated wind scenarios: a summer sea breeze considering the zostera meadows with their pre-decline (a) and post-decline (b) characteristics; a winter anticyclone considering the zostera meadows with their pre-decline (c) and post-decline (d) characteristics; and a winter storm considering the zostera meadows with their pre-decline (e) and post-decline (f) characteristics.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. C.2. Spatial representation of mean orbital velocities (Uorb,mean) computed over the tidal cycle for the three simulated wind scenarios: a summer sea breeze considering the zostera meadows with their pre-decline (a) and post-decline (b) characteristics; a winter anticyclone considering the zostera meadows with their pre-decline (c) and post-decline (d) characteristics; and a winter storm considering the zostera meadows with their pre-decline (e) and post-decline (f) characteristics.</figcaption></figure>

Data availability

The data that has been used is confidential.

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