# Drivers of growth and decay of Sargassum in the Tropical Atlantic: a Lagrangian approach

Witold Podlejski, Léo Berline, Julien Jouanno, Nicolas Barrier, Christophe Lett

► To cite this version:

Witold Podlejski, Léo Berline, Julien Jouanno, Nicolas Barrier, Christophe Lett. Drivers of growth and decay of Sargassum in the Tropical Atlantic: a Lagrangian approach. Progress in Oceanography, 2024, 229, 103364 [10 p.]. 10.1016/j-pocean.2024.103364. hal-04824357

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# Drivers of growth and decay of *Sargassum* in the Tropical Atlantic: A Lagrangian approach

Podlejski Witold<fnref n="1" />, <fnref n="2" />, *, Berline Léo<fnref n="1" />, Jouanno Julien <fnref n="3" />, Barrier Nicolas <fnref n="2" />, Lett Christophe <fnref n="2" />

## Abstract :

The proliferation of Sargassum in the Tropical Atlantic has occurred almost every year since 2011, but a strong variability of biomass is observed among years. Essential knowledge about the drivers of Sargassum growth and decay is still lacking to explain this interannual variability. Benefiting from accurate basin scale Sargassum detections provided by remote sensing, and from physical and biogeochemical ocean simulations, we developed a Lagrangian drift-growth model to simulate Sargassum distribution over the period 2016–2020. The resulting trajectories and biomass time series of Sargassum aggregates were analyzed to highlight the main limiting factors of growth and decay. The nitrogen and phosphorous concentrations are found to be weakly restrictive compared to physical limiting factors, especially the temperature. In particular, the warm waters found off northern Brazil appear to be instrumental in triggering the end of seasonal growth of Sargassum. The timing of the seasonal warming of this region strongly impacts the quantities of Sargassum simulated each year. This suggests that this region should be monitored to anticipate the development of Sargassum and resulting strandings.

## Highlights

* Nutrients only slightly limit the growth of *Sargassum* in its distribution area. * Temperature is the main factor in the growth of *Sargassum*. * The inter-annual variability of *Sargassum* lies in variations in climatic modes. * High temperatures in northern Brazil are interrupting the annual growth of *Sargassum*. * Temporality of water warming in this zone determines the annual quantity of biomass.

**Keywords** : Lagrangian simulation, Growth model, Tropical North atlantic, Alternative Floating Algae Index, Time series, Nutrients

<footnote n="1">¹ MIO, Aix Marseille Univ, Université de Toulon, CNRS, IRD, Marseille, France</footnote>

<footnote n="2">² MARBEC, Université de Monpellier, CNRS, Ifremer, IRD, Sète, France</footnote>

<footnote n="3">³ LEGOS, Université de Toulouse, IRD, CNRS, CNES, UPS, Toulouse, France</footnote>

<footnote>* Corresponding author : Witold Podlejski, email address : witold@podlejski.fr</footnote>
# 1. Introduction

The *Sargassum* massive proliferation in the Tropical Atlantic observed since 2011 is a profoundly dual phenomenon. It generates a tremendous shelter for biodiversity (Fine, 1970; Martin et al., 2021) and enhances connectivity (Sehein et al., 2014) while fixing the atmospheric carbon (Wang et al., 2018; Gouvêa et al., 2020). But, at the same time, it causes havoc for coastal ecosystems and related human activities (Resiere et al., 2018; Chávez et al., 2020; Merle et al., 2021). Various hypotheses have been put forward to explain this 2011 shift, in particular a strong climatic event occurring in 2010, long-term increase of temperature and eutrophication of large rivers, or changes in upwelling and Saharan winds intensities (Wang et al., 2019; Djakouré et al., 2017; Oviatt et al., 2019; Johns et al., 2020; Marsh et al., 2021; Skliris et al., 2022). However,
disentangling the *Sargassum* growth dynamics remains challenging and there is no consensus on what are the drivers of the seasonal growth and decay, either due to biogeochemical or physical factors, and therefore what determines the interannual variability of *Sargassum* distribution remains to be explored.

The distribution of *Sargassum* is well monitored by satellite observations, allowing the presence of algae to be extracted and biomass to be estimated over time (Gower & King, 2011; Wang & Hu, 2016; Cuevas et al., 2018; Minghelli et al., 2021; Podlejski et al., 2022; Laval et al., 2023; Jouanno et al., 2023). With these observations and complementary *in-situ* data, the drift of *Sargassum* has been quantified and decomposed as a function of currents and wind (Putman et al., 2018; Kwon et al., 2019; Putman et al., 2020; Berline et al., 2020; Johnson et al., 2020). Compared to previous studies, the recent drift measurements of Podlejski et al. (2023) suggest a larger effect of wind (windage) and a reduced effect of currents on *Sargassum* drift. These results bring a possible improvement of drift models that needs to be further tested in large scale simulations.

Many studies have already focused on modelling and forecasting short-term *Sargassum* stranding events (Maréchal et al., 2017; Triñanes et al., 2022; Bernard et al., 2022), but few extend the forecast to a longer timescale (Jouanno et al., 2021a; Marsh et al., 2021; Brooks et al., 2018; Johnson et al., 2020). While short-term forecast only requires accurate model of drift, growth can not be ignored for longer-term forecast.

The growth of *Sargassum* being multifactorial, very few studies have attempted to reproduce it numerically (Brooks et al., 2018; Jouanno et al., 2021a,b, 2023). The most advanced model was developed by Jouanno et al. (2023) using a growth quota approach to model both physical (temperature, salinity, irradiance) and biogeochemical (phosphorous, nitrate) limitation factors. Although accurate in its predictions, this Eule-rian model did not track the history of *Sargassum* aggregates, preventing the detection of delayed effects.

Conversely, Lagrangian models are commonly used to track the history of drifting objects, in particular *Sar-gassum* algae (Franks et al., 2016; Putman et al., 2018; Berline et al., 2020; Johnson et al., 2020), and make it possible to analyze the drivers of dynamics at the individual scale.

Here, the Lagrangian approach and Jouanno et al. (2023) growth modelling approach were combined to simulate *Sargassum* distribution in the Tropical Atlantic over a 5-year period (2016-2020). First, we calibrated the drift model following Podlejski et al. (2023)'s results for the basin scale and then adapted the growth model from Jouanno et al. (2023) to the Lagrangian approach. The simulation results were then analyzed in order to highlight the main limiting factors of growth, the areas of growth and decay and the possible causes of the interannual variability of *Sargassum*.

# 2. Materials and Methods

## 2.1. Satellite observation dataset

The Alternative Floating Algae Index (AFAI) defined by Wang & Hu (2016) was used according to the methodology detailed by Descloitres et al. (2021) in order to detect the presence of *Sargassum* with the Moderate-Resolution Imaging Spectroradiometer (MODIS) sensor. Then the filtering method developed by Podlejski et al. (2022) was applied to remove false detections due to clouds, shadows, sun glint or coastal
waters. The Sargassum Fractional Coverage (FC) was then derived from AFAI using the ratio proposed by Wang & Hu (2016). FC at the native resolution of the two MODIS Aqua and Terra satellites (1 to 8 km²) was projected daily onto a 1 km resolution grid. Monthly FC composites at 50 km resolution were finally calculated by averaging these daily maps (excluding hidden and uncovered pixels in the average). FC was then converted to dry weight biomass estimates using the ratio of 3.34 kg m⁻² (Wang et al., 2018). Alternatively to FC maps, we also used presence maps (p) calculated as the fraction of 1-km pixels detected as Sargassum (Ns) over all unmasked pixels (Nu) inside each box of 50 km² (p = Ns/Nu, Berline et al. (2020)). The smallest presence values (p < 0.003) were excluded to remove remaining isolated false detections due to clouds, shadows or sun glint.

The Sargassum drift model used for the simulation was based on Podlejski et al. (2023)'s model:

$$ \mathbf{U}_S = C_f \mathbf{U} + w * \exp(i\phi)\mathbf{W} \quad (1) $$

where the variables $U_S$, $U$ and $W$ are the Sargassum drift, the local current and the local wind expressed as complex numbers. The parameters $C_f$, $w$ and $\phi$ are respectively the current factor, the drift factor and the deviation angle of the drift. Podlejski et al. (2023) suggested $C_f = 80\%$, $w = 2\%$ and $\phi = 10°$ as the best set of parameters. Given the difference in scale and resolution between the Podlejski et al. (2023)'s approach (3 hours of measurements at 1 km resolution) and the present study, we have tested parameter values around these estimates in order to calibrate the drift in our Lagrangian model (see section 2.5.1 below). The current factor was tested between 70 and 100%, the windage between 0 and 3%, and the deviation angle between 0 and 30°. The model does not take into account the effect of Stokes drift, as Podlejski et al. (2023) has shown that it does not improve the prediction of Sargassum drift.

### 2.3. Sargassum growth model

Based on the best set of parameters given by the drift model calibration (section 2.2), we extended the model to take into account the growth and decay of Sargassum. The growth model is based on Jouanno et al. (2023)'s nutrient quota model adapted from the Eulerian to the Lagrangian approach.

For each particle (aggregate) of Sargassum, three state variables are monitored: the carbon content (C), the nitrogen content (N) and the phosphorus content (P). These variables evolve at each simulation time step, depending on the local conditions that determine the rate of absorption and loss:

$$ \begin{aligned} \frac{\partial C}{\partial t} &= U_C - \Phi_C \\ \frac{\partial N}{\partial t} &= U_N - \Phi_N \\ \frac{\partial P}{\partial t} &= U_P - \Phi_P \end{aligned} \quad (2) $$
where $U_C$, $U_N$ and $U_P$ are the uptake rates for carbon, nitrogen, and phosphorus content, respectively, and $\Phi_C$, $\Phi_N$, $\Phi_P$ are the loss rates.

The uptake of carbon is defined as follows:

$$U_C = \mu_{max} \cdot C \cdot f(T) \cdot f(I) \cdot f(S) \cdot f(Q) \quad (3)$$

where $\mu_{max}$ is the maximum carbon growth rate, and $f(T)$, $f(I)$, $f(S)$ and $f(Q)$ are the limiting functions depending on temperature $T$, irradiance $I$, salinity $S$ and nutrient quotas $Q$ in the tissues, respectively, as detailed below.

$$f(T) = e^{-2 \left( \frac{T-T_{opt}}{T_{ref}-T} \right)^2} \quad (4)$$

with $T_{opt}$ the optimal temperature for Sargassum growth and $T_{ref}$ a parameter equal to the minimal growth temperature $T_{min}$ if $T \le T_{opt}$ or to the maximal growth temperature $T_{max}$ otherwise. Parameters $T_{min}$ and $T_{max}$ are the minimal temperature and maximal temperature for growth, respectively.

$$f(I) = \frac{I - I_{min}}{I_{opt}} e^{\left(1 - \frac{I - I_{min}}{I_{opt}}\right)} \quad (5)$$

with $I_{opt}$ the optimal irradiance for Sargassum growth and $I_{min}$ the minimal irradiance required for growth.

$$f(S) = \alpha_S S + \beta_S \quad (6)$$

with $\alpha_S$ and $\beta_S$ empirical parameters set to reproduce the salinity limitation shown by Hanisak & Samuel (1987).

$$\begin{align*}
f(Q) &= \min(f(Q_N), f(Q_P)) \\
f(Q_N) &= \left( \frac{1 - (Q_{Nmin}/Q_N)}{1 - (Q_{Nmin}/Q_{Nmax})} \right) \\
f(Q_P) &= \left( \frac{1 - (Q_{Pmin}/Q_P)}{1 - (Q_{Pmin}/Q_{Pmax})} \right) \tag{7}
\end{align*}$$

where $Q_N$ and $Q_P$ are the nitrogen and phosphorus quotas defined as $Q_N = N/C$ and $Q_P = P/C$, respectively. The parameters $Q_{Nmin}$, $Q_{Nmax}$, $Q_{Pmin}$, $Q_{Pmax}$ correspond to the minimum and maximum quotas of nutrients in the algae. All limiting functions are restricted to the interval $[0, 1]$, therefore values outside this interval were thresholded.

At each time step, Sargassum takes up nutrients from surrounding waters as follows:
$$U_N = V_{Nmax} \cdot C \cdot \left( \frac{[N]}{K_N + [N]} \right) \cdot \left( \frac{Q_{Nmax} - Q_N}{Q_{Nmax} - Q_{Nmin}} \right) \quad (8)$$

$$U_P = V_{Pmax} \cdot C \cdot \left( \frac{[P]}{K_P + [P]} \right) \cdot \left( \frac{Q_{Pmax} - Q_P}{Q_{Pmax} - Q_{Pmin}} \right)$$

with $[N]$ and $[P]$ the nitrogen and phosphorus concentration in water, $V_{Nmax}$ and $V_{Pmax}$ the maximal uptake rates of nutrients and $K_N$ and $K_P$ the half saturation constants of the absorption functions.

The loss terms in Equ. 2 depend on the mortality designed empirically using a quadratic function to account for high mortality when Sargassum accumulates. The mortality term used here differs from Jouanno et al. (2023)'s model with no constant term and no term due to warm temperature. This simplification allows us to isolate and better interpret the effect of temperature as limiting Sargassum growth only (Eq. 4), while guaranteeing equivalent results as Jouanno et al. (2023) due to our use of a restrictive range of temperatures suitable for growth (24-28°C, Table 1).

$$\begin{align}
\Phi_C &= m \cdot C \cdot \frac{C}{K_m + C} \cdot \alpha_{wind} \nonumber \\
\Phi_N &= \Phi_C \cdot Q_N \tag{9}
\end{align}$$

$$\Phi_P = \Phi_C \cdot Q_P$$

with $m$ the mortality rate, $K_m$ the half saturation constant and $\alpha_{wind}$ a term for mortality due to wind:

$$\alpha_{wind} = 1 - \frac{1}{1 + e^{1.5(W - 5)}} \quad (10)$$

where $W$ is the wind speed at the sea surface. This sigmoid function amplifies mortality in case of low wind due to the absence of vertical mixing and subsequent drying of the Sargassum emerging part. The values of parameters used in the Sargassum growth model are listed in the Table 1.
<table><caption>Table 1: Parameters used in the *Sargassum* growth model. All came from (Jouanno et al., 2023) except temperature parameters and mortality parameters which were adapted to our formulation of mortality, different from (Jouanno et al., 2023).</caption><thead><tr><th>Name</th><th>Description</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>μ<sub>max</sub></td><td>Maximum carbon uptake rate</td><td>0.06</td><td>d<sup>-1</sup></td></tr><tr><td>T<sub>min</sub></td><td>Minimum temperature value</td><td>24</td><td>°C</td></tr><tr><td>T<sub>max</sub></td><td>Maximum temperature value</td><td>28</td><td>°C</td></tr><tr><td>T<sub>opt</sub></td><td>Optimal temperature value</td><td>27.5</td><td>°C</td></tr><tr><td>I<sub>opt</sub></td><td>Optimal irradiance value</td><td>170</td><td>W.m<sup>2</sup></td></tr><tr><td>I<sub>min</sub></td><td>Minimum irradiance value</td><td>30</td><td>W.m<sup>2</sup></td></tr><tr><td>α<sub>S</sub></td><td>Slope of the limitation curve for salinity</td><td>0.0714</td><td>unitless</td></tr><tr><td>β<sub>S</sub></td><td>Origin of the limitation curve for salinity</td><td>-1.5714</td><td>unitless</td></tr><tr><td>Q<sub>Nmin</sub></td><td>Minimum quota value of N/C</td><td>0.014</td><td>mgN.mgC<sup>-1</sup></td></tr><tr><td>Q<sub>Nmax</sub></td><td>Maximum quota value of N/C</td><td>0.025</td><td>mgN.mgC<sup>-1</sup></td></tr><tr><td>Q<sub>Pmin</sub></td><td>Minimum quota value of P/C</td><td>0.001</td><td>mgP.mgC<sup>-1</sup></td></tr><tr><td>Q<sub>Pmax</sub></td><td>Maximum quota value of P/C</td><td>0.0014</td><td>mgP.mgC<sup>-1</sup></td></tr><tr><td>V<sub>Nmax</sub></td><td>Maximum uptake rate for nitrogen</td><td>0.015</td><td>mgN.mgC<sup>-1</sup>.d<sup>-1</sup></td></tr><tr><td>V<sub>Pmax</sub></td><td>Maximum uptake rate for phosphorus</td><td>0.005</td><td>mgP.mgC<sup>-1</sup>.d<sup>-1</sup></td></tr><tr><td>K<sub>N</sub></td><td>Half saturation term for nitrogen uptake</td><td>0.01</td><td>mmol.m<sup>3</sup></td></tr><tr><td>K<sub>P</sub></td><td>Half saturation term for phosphorus uptake</td><td>0.8</td><td>mmol.m<sup>3</sup></td></tr><tr><td>m</td><td>Maximum quadratic mortality rate</td><td>0.004</td><td>d<sup>-1</sup></td></tr><tr><td>K<sub>m</sub></td><td>Half saturation term for mortality</td><td>25.10<sup>6</sup></td><td>mgC</td></tr></tbody></table>

## 2.4. Model inputs: currents, wind, solar irradiation and nutrients

Our drift simulations of *Sargassum* used daily outputs coming from the GLORYS12 reanalysis at 1/12 degree resolution (Lellouche et al., 2021). The physical variables extracted from this daily dataset were: the current velocity (U), the temperature (T) and the salinity (S) (downloaded from https://data.marine.copernicus.eu/). Wind velocity (W) and shortwave radiation (I) were taken from the daily reanalysis ERA5 available at https://cds.climate.copernicus.eu.

The biogeochemical variables [N] and [P] were extracted from daily Mercator Ocean International BIO4 analysis at 1/4 degree resolution, available at https://www.mercator-ocean.eu/. The [N] concentration is computed as the sum of NO₃ and NH₄ while [P] concentration is equal to PO₄.

## 2.5. Simulations setup

### 2.5.1. Drift-only simulations

Simulations were first run to find the best drift parameters set. From monthly *Sargassum* presence maps at 50 km resolution, particles were seeded in each pixel containing detections of *Sargassum*. The particles
115 were evenly distributed inside the 50 km boxes, every 2 km ($N_0$ = 625 particles for each 50 km box). Each particle was associated with a weight derived from the presence of *Sargassum* ($\mu$ = $p/N_0$). This configuration was designed similarly to Berline et al. (2020) and Marsh et al. (2021).

The particles were advected with Ichthyop software v3.3.13 (Lett et al., 2008) using Runge Kutta's 4th order numerical scheme with a 3-hour time step. The drift was purely due to advection (no diffusion term), in accordance with Eq. 1. Simulations started on the 15th of month *i* and lasted until the end of month *i* + 3 (≈ 105 days). Results were saved daily. A coastal 'bouncing'<fnref n="1" /> boundary condition was used to conserve the same quantity of simulated *Sargassum* particles along the simulation. Based on the final location particles, we built a simulated monthly composite for each month: 1) the *Sargassum* particle weights in each 50 km box were summed to create simulated daily maps; 2) the mask (clouds) of the corresponding daily MODIS images was applied to these simulated maps to ensure consistency between the simulation and the satellite observations; 3) maps were averaged monthly and binarized using the threshold $p < 0.003$ to remove weak presence value. A summary of the simulation setup is shown in Fig. 1.

<figure><img src="image_2.png" /><figcaption>Figure 1: Workflow of the simulation setup. The example shown is for 1-month simulations, but an identical approach was used for longer simulations (3 months, 1 year).</figcaption></figure>

### 2.5.2. Assessment of model skill

The comparison between the simulated and the observed composites of *Sargassum* presence maps was performed using the True Skill Statistic (TSS, Allouche et al. (2006); Berline et al. (2020)) in four different oceanic regions between 0°S and 30°N: i) the Caribbean Sea (85°W to 60°W); ii) the Central Atlantic Ocean (60°W to 35°W); iii) the East Atlantic Ocean (35°W to 5°W); iv) the overall region (85°W to 5°W) (see Figure 4). TSS makes it possible to compare presence maps giving equal weight to the absence of *Sargassum* and to

<footnote n="1">¹The coastline acts as a billiard edge and the particle bounces as a billiard ball in case its movement would take it beyond the coastline (Ichthyop documentation).</footnote>
the consistent/inconsistent cases of presence. This simplifies assessment of model skill by focusing on where
the *Sargassum* is without considering its amount of biomass. The TSS value ranges from 0 (no skill) to 1
(perfect match).

The gain brought by the model was evaluated by comparing the TSS values with a reference, called here
“persistence”, which is the TSS calculated between the satellite composites of months i and i+1. TSS values
were computed for all the simulations, i.e. for all different sets of drift parameters (4*4*4=64 sets), starting
each month of the time series (12*5=60 times) and for a simulation period of 1, 2 and 3 months (3 periods).
So the experiment ended up with 64*60*3=11520 TSS values to analyze. As the different sets of parameters
gave slightly different TSS values with no obvious best choice, we choose to aggregate the results for a given
set of parameters, a given region and a given year, and calculated the mean and median TSS values. For each
set of parameters, we added the number of occurrences where these values were the highest to determine the
most appropriate parameters according to each region.

2.5.3. *Drift-growth simulations*

The simulation set-up was identical to the drift simulation experiment, except that the simulation duration
was extended to 1 year to leave sufficient time for *Sargassum* growth. Also, each particle was associated
with a C content derived from the biomass (kg wet weight) of *Sargassum* using the ratio of carbon / dry
biomass of 27% (Wang et al., 2018). The initial content of nitrogen and phosphorus was arbitrarily set
to $C * (Q_{Nmax} - Q_{Nmin})/2$ and $C * (Q_{Pmax} - Q_{Pmin})/2$, respectively. The boundary condition used is
'beaching'<fnref n="2" />: any particle that touches the coast is removed from the simulation. This mimics the stranding
term used in the Eulerian model of Jouanno et al. (2023).

For each simulation, C content was converted back to wet weight to compute monthly simulated images.
The comparison of simulated biomass distribution with satellite composites on the four different ocean regions
was used to assess the quality of the growth model and calibrate *Sargassum* mortality parameters (*K*<sub>m</sub>, Table
1) manually by minimizing the difference over the four regions between simulation and satellite maps.

2.5.4. *Time to double biomass*

The Lagrangian approach enables the fate of a given *Sargassum* aggregate (i.e. a particle) along its
trajectory to be followed. We defined an experiment to assess the time required for an aggregate to double
its biomass given its starting location. We seeded a large area (100°W to 15°E, 5°S to 35°N) with *Sargassum*
particles every 5 km with 1000 kg initial biomass (arbitrary value ensuring a negligible quadratic mortality).
After running the simulation over 1 year, the time to double (in days) was computed and associated to
the starting location to obtain maps over the whole area. With all the simulations starting each month of
the time series, we aggregated the maps of time to double biomass seasonally and compared it with growth

<footnote n="2">²Ichthyop does move the particle inland but “kills” it; from then the particle is removed from the simulation (Ichthyop documentation).</footnote>
limitation factors maps, from biogeochemical and physical variables.

3. Results

Presence maps of *Sargassum* aggregates over the Tropical Atlantic derived from satellite and from our drift model were compared using TSS (True Skill Statistic). An example of TSS values averaged over the whole simulated domain obtained along the simulation time period is shown in Figure 2 for the particular case *C*<sub>*f*</sub> = 100%, *w* = 1%, and *φ* = 0° (blue line). In Figure 2 is also shown the persistence, i.e., the TSS values obtained by comparing the initial and 1-month later satellite-derived presences (orange line). The TSS curve above the persistence curve indicates that using the model prediction of *Sargassum* presence is better than assuming that *Sargassum* does not move at all over a 1-month period, and therefore that the model has some skill to simulate *Sargassum* drift (Figure 2). The assessed TSS values ranged between 30 and 80% with higher values in summer and lower in winter, broadly following the periods of higher and lower amounts of *Sargassum* (assessed by the fractional coverage in Figure 2, red line). The gain brought by the model, assessed by the difference between TSS and persistence, was between 0 and 30% and tended to be higher for the years with low amount of *Sargassum* (Figure 2). Overall, the influence of the deflection angle on the TSS values was small and we therefore decided to set *φ* = 0°. For this value, the values of current and windages leading to the highest average TSS depended on time and on the considered area, being most often *C*<sub>*f*</sub> = 70%, *w* = 1% for the Caribbean area, *C*<sub>*f*</sub> = 100%, *w* = 1% for the Central Atlantic area, and *C*<sub>*f*</sub> = 100%, *w* = 2% for the East Atlantic area (Figure 3). We chose the values *C*<sub>*f*</sub> = 100%, *w* = 1% that lead most often to the highest TSS for the whole area (Figure 3).

<figure><img src="image_3.png" /><figcaption>Figure 2: Drift-only simulations. TSS values computed between simulated monthly composites maps of *Sargassum* presence after 1 month of simulation and corresponding satellite images with windage set to 1%, current to 100% and deviation angle of windage to 0°. The orange curve shows the persistence, i.e. the TSS value computed between the previous satellite composite and the current one. The area between orange and blue curves gives the gain brought by the model. The red curve is the average fractional coverage in percent over of total area.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3: Drift-only simulations. Model skill assessment for different sets of windage and current factors in four oceanic regions. Color and values refer to the number of occurrences where the parameters set was the best performing over simulations aggregated annually. There are 30 values for each plot corresponding to each year (5), each lead (simulation duration of 1, 2 or 3 months) and either the mean or the median (total number of values: 5*3*2 = 30). The deflection angle was here set to 0°.</figcaption></figure>

Simulations of the biomass growth used the best set of drift parameters. Simulations were extended to 1-year with the simulated biomass computed for the four regions. Figure 4 shows an example of a 1-year simulation initialized on January 2017. The model faithfully reproduces the overall biomass dynamics (bottom right panel) with consistent starting and ending biomass values, as well as the local maximum and minimum of biomass found in May and in November, respectively. The simulation accuracy in the Caribbean area (orange curve) is poorer with erroneous linear growth compared to the parabolic growth observed with satellite. This is likely due to inaccurate initialization in January, when biomass is low and concentrated to the east. In contrast, the Central (red curve) and East (green curve) Atlantic biomasses are well predicted by the model. However, there are some spatial discrepancies after 6 months of simulation (top panels), with the biomass located further west and north in the simulations than in the satellite composites. Figure 5 shows the model biomass forecast compared to satellite for different leads (i.e. simulation durations: 2, 4 and 6 months). The biomass forecast is closer to observations in the Central Atlantic and in the Caribbean compared to the East Atlantic region. The annual maxima of biomass, in particular the peak in 2018, are accurately reproduced by 2-month lead simulations and still to some extent with 4-month leads. Yet, forecast quality declines with the longer simulation times (> 4 months), and simulations reproduce the growth and
200 decrease with a time lag of 4-6 months compared with satellite observations. The accuracy of initialization, which is not optimal due to the poor quality of satellite images (mainly due to cloud cover), is likely essential for model predictability and an important source of forecast error.

<figure><img src="image_5.png" /><figcaption>Figure 4: Drift-growth simulations' results starting in January 2017. The first row shows the monthly composites millions of tons per pixel of 50 x 50km from satellite (left) and from the model after 6 months of simulation (right). The time series below show the evolution of *Sargassum* biomass summed over the four areas displayed on the top panel from the satellite (black lines) and the simulation (colored lines).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5: Drift-growth simulations. Comparison between biomass (millions of tons) estimated with satellite observation (black lines) and simulated biomass (colored lines). Each point corresponds to the simulation initialized at *t*-lead. Colors refer to the oceanic regions shown in Fig. 4.</figcaption></figure>

The drift-growth model was used to calculate the time required for a *Sargassum* particle's biomass to double from its starting location at a given time of year, either along its trajectory tracked with the Lagrangian approach, or assuming particles are not transported. The resulting maps and maps of physical and biogeochemical limiting factors at each fixed model cell are shown in Figure 6 for the four seasons. Patterns of time to double biomass were largely consistent across the *Sargassum* distribution area and seasonal cycle. However, the Lagrangian results show more contrasting patterns and allow better identification of areas unsuitable for growth where particles have been trapped or exported outside their habitat zone. For example, in the Gulf of Guinea, particles are transported to the South Atlantic and in the Gulf of Mexico (in summer) where they are trapped or transported to the Sargasso Sea. During the major part of the year, the area of low time to double biomass values for *Sargassum* algae spans from the Gulf of Mexico to 20°W. The areas with high time to double biomass values are restricted to the North of the Atlantic Ocean (above 25°N), to the Brazilian waters and to the Gulf of Guinea. Summer stands out with high time to double biomass values in
the Caribbean Sea and the Gulf of Mexico, whereas the Gulf of Guinea has lower time to double biomass values. As for the physical ($f(T).f(S).f(I)$), see Equations 4,5 and 6) and biogeochemical ($min(f(Q_N), f(Q_P))$), see Equation 7) limiting factors, they are spatially inversely correlated. High values (weak growth limitation) for the physical factor and low values (strong growth limitation) for the biogeochemical factor are located in the tropical Atlantic (around 10 °N) during the first half of the year, with this trend reversing in the second half of the seasonal cycle when these values are found in the southern subtropical and equatorial zones. The physical limitation values are largely more restrictive (0.4, average over the overall area, of Fig. 4) than the biogeochemical limitation (0.8, average over the overall area). Growth limiting factors are presented in more details in Figure 7 with seasonal maps for each physical and nutrient variable. Of the physical variables limiting growth, temperature is the only one to exhibit a contrasting seasonal cycle and spatial variability, with values ranging between 0 and 1. Salinity and irradiance factors are more homogeneous and close to 1 in the tropical Atlantic. The limiting factors associated with phosphorus and nitrogen quotas show significant spatial and temporal variability, with values ranging from 0.4 to 1. The lowest values for these two biogeochemical factors are located around 15 °N during the first half of the year and further north during the second half. The interannual variability of the time to double biomass is illustrated in Figure 8, focusing on the area between northern Brazil and the Gulf of Mexico. High values of the time to double in this zone appeared more or less early in the season and last until the end of summer. They appeared in May in 2016, but more frequently in June as in 2017, 2019 or 2020, and much later, in August, in 2020.

<figure><img src="image_7.png" /><figcaption>Figure 6: Time to double biomass for *Sargassum* particles seeded at that location, in the case particles are tracked with a Lagrangian approach (first column) or considering no transport (second column). The third column is the biogeochemical limitation factor according to the quotas of nitrogen or phosphorus in the tissues (*min*(*f*(*Q*<sub>N</sub>), *f*(*Q*<sub>P</sub>)). The fourth column is the physical limitation factor according to temperature, irradiance, and salinity (*f*(*T*).*f*(*S*).*f*(*I*)).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 7: Spatial and seasonal variability of the five limitation factors to Sargassum growth used in our model. T, I, S, Qn and Qp stand for temperature, irradiance, salinity, nitrogen quota and phosphorus quota, respectively.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8: The time to double biomass for years 2016 to 2020 and months May to August. The low time to double biomass values (yellow) between the North of Brazil and the Gulf of Mexico appeared in early May for 2016, in June for 2017, 2019 and 2020 and in August for 2018 (rounded at the date of appearance).</figcaption></figure>

The seasonal dynamics of Sargassum biomass in the Caribbean Sea and its interannual variability are
studied in more detail using biomass time series of particles crossing the Caribbean arc (Figure 9). In 2016 most of the individual particle biomasses stopped increasing at the beginning of May when the particles entered the Caribbean Sea, and then gradually decreased on their westward trajectory to the Gulf of Mexico. Conversely, in 2018 biomasses kept on increasing until early July, and some particles reached their biomass maximum while off the Yucatán Strait.

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<figure><img src="image_10.png" /><figcaption>Figure 9: Sample of simulated trajectories (a different color for each trajectory, one dot for each daily location) that cross the Caribbean arc (left) and corresponding biomass time series (right) for the years 2016 (top) and 2018 (bottom). The black vertical line indicates the approximate average date of the biomass maximum over all the trajectories and the location of each particle on this date is displayed with a black star on the corresponding map.</figcaption></figure>

# 4. Discussion

240

## 4.1. *Drift parameters variability*

Our simulations have shown that the angle of deviation of the wind effect on the drift has a very small impact on the results, and we were unable to conclude on a preferred value, probably because the Ekman current is already taken into account in the GLORYS12 current. Consequently, setting it to zero for simplicity seems satisfactory. On the other hand, the windage and current factor have a significant impact on simulation performances. The three sub-regions studied each have a different best set of wind and current parameters (Figure 3). The Caribbean region shows the greatest variability, with a weak consensus obtained for 1% wind and 70% current. This could be explained by the high concentrations of *Sargassum* in this area, most likely associated with large *Sargassum* mat sizes, which may induce a drag effect and reduce the current effect. In the central Atlantic Ocean, the windage is estimated at 1% and the current factor at 100% consistently with previous studies (Putman et al., 2018; Kwon et al., 2019; Berline et al., 2020). In the eastern Atlantic Ocean, the best current factor is again 100%, but with a higher windage (2%). This could be due to the

245

250
lower wind speed (4.2 m.s⁻¹ on average in the east versus 5.9 m.s⁻¹ in the central region). In calm wind and sea conditions, *Sargassum* algae likely have a larger emerged fraction (Woodcock, 1993; Ody et al., 2019) and therefore a proportionally stronger wind effect on their drift (Breivik et al., 2012). Despite these local variations, we chose 1% for wind and 100% for current as the best set of parameters over the whole region for the combined drift and growth simulations. The discrepancies between these values and those suggested by Podlejski et al. (2023) (2% wind and 80% current) are likely due to the difference in scales of the two studies and associated resolved physical factors acting on drift. Whereas here we used long-term simulations (several months) with a coarse composites' resolution (50 km) to estimate the drift model parameters, the measurements by Podlejski et al. (2023) were carried out on successive images separated by 3 hours only and at a 1 km resolution. GLORYS12 currents have lower accuracy than drifter-derived currents used by Podlejski et al. (2023). GLORYS12 currents can also underestimate actual currents, artificially resulting in a higher current factor.

## 4.2. Main drivers of growth

The results show a weak biogeochemical limitation (min(f(QN), f(QP)) > 0.8, over the overall area). In particular, the nitrogen does not strongly constrain the growth as the associated saturation term is low (KN=0.01 mmol.m⁻³). Phosphorous is more constraining, but not dominating for the growth dynamics (Figure 7). However, the spatial pattern of the combination of these two factors shows that low values (0.8, averaged over the overall area) are found at the same location as *Sargassum* distribution in the first half of the year, suggesting a slight limitation effect on *Sargassum* growth (Figure 6). These results highlight that biogeochemical factors are likely not primarily restrictive for *Sargassum* growth. This is consistent with recent laboratory experiments showing that *Sargassum* do not respond greatly to nutrient enrichment (Philippi et al., 2023; Magaña-Gallegos et al., 2023). The spatial impact of nutrient enrichment on *Sargassum* distribution, either by Amazonian influx, Sahara deposition or Mauritanian upwelling as proposed in the literature (Wang et al., 2019; Oviatt et al., 2019) are not found critical in our results. In fact, as the limitation factors associated to those enrichment sources are rather stable between years (not shown), they are likely playing a minor role on the current interannual variability of *Sargassum* distribution. It is worth noting that the biogeochemical fields used to force the model obtained from BIO4 simulations may under-represent the amplitude of the interannual anomalies. We considered that the uptake of nutrients by *Sargassum* was negligible compared to the available stock in the surrounding water, therefore the model does not consider the induced decrease in the nutrient concentration in the water. As a result, the model does not conserve nutrients amounts, leading to an artificial increase in the overall stock. However, this error is small.

Regarding the physical limitation of growth in simulations, low salinity can be limiting but rarely where *Sargassum* is observed and solar radiation is always sufficient for *Sargassum* (Figure 7). It is the temperature that highly determines the dynamics of growth, depending on the area and the season. The function used for the temperature limitation was designed to inhibit growth in cold waters and to account for a weakening of the growth rate in too warm waters. In particular, our interval of temperatures favorable for *Sargassum*
growth (24 – 28°C) was adjusted to fit large scale growth observation from satellite data, as in Jouanno et al. (2021a). These values are consistent with the observations from Wang et al. (2019) (Supplementary Materials). At the basin scale, the high temperatures (above 28°C) are the primary limitation factor that prevent *Sargassum* growth in the simulations. This is consistent with the large-scale negative correlation between SST and *Sargassum* concentration found in the literature (Wang et al., 2019; Skliris et al., 2022). However, rather less restrictive temperature limitations were found in laboratory experiments (20 – 31°) (Magaña-Gallegos et al., 2023; Schell et al., 2023). This difference could be due to some environmental factors which are not present in laboratory experiments, such as the biofouling in warm waters. In addition, although *Sargassum* morphotypes have different growth responses to temperature, the extreme temperature values among morphotypes corresponds to our threshold limits (i.e., 24-28°C, Corbin & Oxenford (2023); Schell et al. (2023)).

Mortality is also a key parameter, but we lack data on this particular phenomenon. The quadratic mortality function we used limits the growth for high concentrations of *Sargassum* and improves the robustness of the results by avoiding an exponential and unrealistic growth of *Sargassum*. It performs better than linear mortality, but is insufficient for low biomass particles, leading to steady slow decrease in this case. Furthermore, the role of sinking on *Sargassum* dynamics is not taken into account in our model, such as the effect of hurricanes, for example, even though it may be one of the driving forces responsible for the annual decrease in *Sargassum* (Sosa-Gutierrez et al., 2022).

### 4.3. Identified regions for growth and decay of *Sargassum* algae

As shown in Figure 6, the time to double biomass is heterogeneous at large scale both spatially and temporally, which allows us to retrieve distinct areas for *Sargassum* growth dynamics. In particular, a front is often found between 20-30°N separating the northern zone where *Sargassum* have longer time to double biomass because they growth poorly or decay due to low temperatures. The Gulf of Guinea is generally too warm for growth, except in late summer, and traps particles within it, inducing the long time to double biomass. This index can therefore be interpreted as an indication of whether a location at a given date will be favorable or not to *Sargassum* growth along its future trajectory.

An important feature appearing in our results is the band-like zone of long time to double biomass appearing in June to September from the offshore waters of northern Brazil to the Gulf of Mexico, including the entire Caribbean Sea (Figure 8). It is the high temperatures reached in this zone that prevent the growth of *Sargassum* (see very low values of limiting factor in this area, Figure 7). Interestingly, 2018 differs from the others years on this point, with the long time to double biomass pattern delayed until late August, leading to huge biomasses. Conversely, in 2016, this band-like zone appeared in May, and biomasses remained low (Figure 8). The timing of the water warming in the area could explain the high variability of biomass between years and the resulting quantities of harmful strandings. This seasonal regulation is consistent with the time series of particle biomass crossing the Caribbean arc (Figure 9). The tipping point between growth and decline is reached when warming appears. Thus, its date in the seasonal cycle could play a major role
to determine whether algae continues to grow in the Caribbean Sea, and hence the amount of *Sargassum* reaching the Yucatán coast and entering the Gulf of Mexico. The timing of warming could be linked to climate mode variability, such as the Atlantic meridional mode (AMM) or the North Atlantic Oscillation (NAO) (Wang et al., 2019; Skliris et al., 2022; Marsh et al., 2023). In particular, Skliris et al. (2022) showed that the AMM corresponds to high positive SST anomaly (Sea Surface Temperature) in the area between North Brazil and the Gulf of Mexico and is negatively correlated with *Sargassum* concentration. The value of the AMM appears then promising as a proxy for the long-term forecasting of the *Sargassum* biomass development, and may help to improve the management of *Sargassum* strandings on the beaches.

## 5. Acknowledgments

We acknowledge TOSCA-CNES and IRD for funding the project SAREDA-DA and the production of the MODIS *Sargassum* detection dataset. AERIS-ICARE is thanked for providing processing infrastructure for the production of the dataset. The Ph.D. of Witold Podlejski is funded by ANR FORESEA (FORE-SEA project, grant ANR-19-SARG-0007). The authors acknowledge the Pôle de Calcul et de Données Marines (PCDM) for providing DATARMOR storage, data access, computational resources, visualization, web-services, consultation, support services. URL: http://www.ifremer.fr/pcdm.

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