For the physical component of the simulation, we use the regional NEMO-based configuration described in Hernandez et al. (2016, 2017) and Radenac et al. (2020) that covers the tropical Atlantic between 35∘ S and 35∘ N and from 100∘ W to 15∘ E. The resolution of the horizontal grid is 1/4∘ and there are 75 vertical levels, 24 of which are in the upper 100 m of the ocean. The depth interval ranges from 1 m at the surface to about 10 m at 100 m depth. Interannual atmospheric fluxes of momentum, heat, and freshwater are derived from the DFS5.2 product (Dussin et al., 2016) using bulk formulae from Large and Yeager (2009). Temperature, salinity, currents, and sea level from the Mercator global reanalysis GLORYS2V4 (Storto et al., 2018) are used to force the model at the lateral boundaries. This configuration has proven to properly represent many aspects of the tropical Atlantic dynamics such as the Amazon plume extent (Hernandez et al., 2016), the large-scale circulation (Kounta et al., 2018) or the surface salinity variability (Awo et al., 2018).

The physical model is coupled to the PISCES (Pelagic Interaction Scheme for Carbon and Ecosystem Studies) biogeochemical model (Aumont et al., 2015) that simulates the biological production and the biogeochemical cycles of carbon, nitrogen, phosphorus, silica, and iron. We use the PISCES-Q version with variable stoichiometry described in Kwiatkowski et al. (2018), with an explicit representation of three phytoplankton size classes (picophytoplankton, nanophytoplankton, and microphytoplankton) and two zooplankton compartments (nanozooplankton and mesozooplankton). The model also includes three non-living compartments (dissolved organic matter and small and large sinking particles). The biogeochemical model is initialized and forced at the lateral boundaries with dissolved inorganic carbon, dissolved organic carbon, alkalinity, and iron obtained from stabilized climatological 3-D fields of the global standard configuration ORCA2 (Aumont and Bopp, 2006), and nitrate, phosphate, silicate, and dissolved oxygen from the World Ocean Atlas (WOA; Garcia et al., 2010) observation database. The model is run from 2006 to 2017, and daily physical and biogeochemical fields are extracted to force the Sargassum model.

Particular care has been given to the prescription of the atmospheric and riverine fluxes of nutrients. The river runoffs are based on daily fluxes from the ISBA-CTRIP reanalysis (Decharme et al., 2019), which has proven to accurately reproduce the interannual variability of the large rivers of the basin (e.g., see Giffard et al., 2019, for the Amazon River). The riverine nutrient fluxes concentrations are from the GLOBAL-NEWS2 dataset, corrected with in situ observations from the Amazon basin water resources observatory database (HYBAM, https://hybam.obs-mip.fr/, last access: 1 February 2020) for the Amazon, Orinoco, and Congo rivers. As in Aumont et al. (2015), we consider an atmospheric supply of P, Fe, and Si from dust deposition. Here, these fluxes are forced using monthly dry-plus-wet deposition products (DUDPWTSUM) from the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) data available on the NASA Giovanni website (http://disc.sci.gsfc.nasa.gov/giovanni, last access: 3 April 2020). Comparison with in situ observations of dust fluxes in Guyana and in Barbados leads to an excellent match with MERRA2 fluxes (Prospero et al., 2020). A climatological deposit of N is obtained from global climate simulations carried out with the ARPEGE-Climate model (Michou et al., 2020). An interactive aerosol scheme including nitrate and ammonium particles (Drugé et al., 2019) is included in ARPEGE-Climate, allowing us to produce fields of wet and dry deposition of nitrogen, ammonium, and ammonia. Figure 2 illustrates that dust and nitrogen fluxes to the ocean are strong in our region of interest, and most particularly in the ITCZ region where atmospheric convergence may focus the wet fluxes.

The modeled chlorophyll for the year 2017 is compared with GlobColour satellite estimates of chlorophyll for the same year (Fig. 3a, b). Model NO3 and PO4 concentrations for 2017 are compared with historical in situ measurements (Fig. 3c–f) from the GLODAPV2 database (Olsen et al., 2016). The model reproduces the major chlorophyll structures and in particular the contrast between the oligotrophic subtropical gyre and productive coastal and equatorial upwellings (Fig. 3a, b). As many other models (e.g., see the CMIP6 model evaluation by Séférian et al., 2020), it struggles to reproduce the offshore extent of the large river plumes and Guinea Dome productivity. Moreover, coastal upwellings tend to be too productive offshore or downstream (for the equatorial upwelling). But above all, it represents realistically the chlorophyll distribution in the region of the ITCZ (∼ 0–10∘ N) and in the Caribbean Sea. As observed, nitrate concentrations are high in the upwelling areas (Fig. 3c, d) but weaker than observed off these regions. It is worth noticing that historical observations of surface nitrate concentrations in the tropical band show very heterogeneous and contrasted values between cruises, so the reliability of a nitrate climatology in this area remains uncertain (Fig. 3c). The model reproduces realistically the observed interhemispheric gradient of surface phosphate concentrations even though it likely overestimates areas of high phosphate content (Fig. 3e, f).

The Sargassum model relies on the strategy used to represent the distribution of other macroalgae species and their transport by 2-D advection–diffusion equations (e.g., Martins and Marques, 2002; Solidoro et al., 1997; Perrot et al., 2014; Ren et al., 2014; Ménesguen et al., 2006; Bergamasco and Zago, 1999). Here, we also consider sink due to stranding at the coast. Growth is modeled as a function of internal reserves of nutrients, dissolved inorganic nutrients in the external medium, irradiance, and sea temperature. As the eco-phycological features are species dependent, the actual knowledge on the three morphotypes of holopelagic Sargassum does allow us to discriminate between them. Following the formalism given in Ren et al. (2014), the physiological behavior is described from three state variables: the content in carbon (C), nitrogen (N), and phosphorus (P), with local variations reflecting the difference between uptake and loss rates. ∂C∂t=UC-ϕC∂N∂t=UN-ϕN∂P∂t=UP-ϕP, where UC, UN and UP are the uptake rates of carbon, nitrogen, and phosphorus, respectively, and ΦC, ΦN, ΦP the loss rates.

The rate of carbon uptake reads as follows: UC=C⋅μmax⁡⋅fT⋅fI⋅fQN⋅fQP, with μmax⁡ the maximum net carbon growth rate, and the four subsequent terms standing for uptake limitation by temperature (T), solar radiation (I), N quota (QN), and P quota (QP), respectively. N and P quotas represent the ratios of nitrogen and phosphorus to carbon in the organism and are computed as N/C and P/C, respectively. The C content (C) can be directly converted to dry biomass considering a mean carbon-to-dry-weight ratio of 27 % (Wang et al., 2018).

The temperature dependence is adapted from Martins and Marques (2002): fT=e-12⋅T-ToptTx-T2, with Tx=Tmin⁡ for T≤Topt; Tx=Tmax⁡ for T>Topt. Topt is the optimum temperature at which growth rate is maximum, Tmin⁡ is the lower temperature limit below which growth ceases, and Tmax⁡ is the upper temperature limit above which growth ceases. Such a function aims at representing a broad optimal temperature range as suggested by experiments in Hanisak and Samuel (1987). The dependence on light is expressed as follows in order to mimic results from Hanisak and Samuel (1987): fI=11+e-0.1IIopt. We have very little information on the response curve relating the nutrient quota to Sargassum growth but experiments for brown seaweed suggest a hyperbolic relationship (e.g., Hanisak, 1983). So, the dependence on the internal nitrogen and phosphorus pools is computed as a hyperbolic curve controlled by the minimum and maximum cell quotas: fQN=1-QNmin/QN1-QNmin/QNmaxfQP=1-QPmin/QP1-QPmin/QPmax. The nitrogen and phosphorus uptake rates depend on the nitrogen (VNmax) and phosphorus (VPmax) maximum uptake velocities, a Monod kinetic that relates uptake to nutrient concentrations in the water, and a function of quota which aims at representing downregulation of the transport system for N and P when approaching the maximum quotas (Lehman et al., 1975): UN=VNmax⋅C⋅NKN+N⋅QNmax-QNQNmax-QNminUP=VPmax⋅C⋅PKP+P⋅QPmax-QPQPmax-QPmin. The carbon loss aims at representing mortality, stranding, and sinking: ϕC=C⋅(me-λm⋅(T-30∘C)+δland⋅αgrnd+mLCe-λmLC⋅HLC-100m). The mortality term depends on m the mortality rate, λm a mortality coefficient, and temperature T. We thus represent thallus senescence and bacterial activity as a growing function of temperature (Bendoricchio et al., 1994; Ren et al., 2014).

The stranding is a function of αgrnd which is a rate of Sargassum stranding per unit of time, and δland which is defined as follows: δland=1if model grid cell is adjacent to two ormore pixels of land,δland=0otherwise. The sinking rate of Sargassum is estimated as a function of the Langmuir cell length scale HLC and a sinking coefficient mLC. The aim is to reproduce possible Sargassum loss by Langmuir cell, as hypothesized by Johnson and Richardson (1977) or Woodcock (1993) to explain large amounts of Sargassum observed at the sea floor (Schoener and Rowe, 1970; Baker et al., 2018). Following, Axell et al. (2014), we estimate HLC as the depth that a water parcel with kinetic energy us2/2 can reach on its own by converting its kinetic energy to potential energy. This corresponds to -∫-HLC0N2z⋅z⋅dz=12⋅us2, with us the Stokes drift and N2 the Brunt–Vaisala frequency. We fixed a 100 m depth threshold as Sargassum becomes massively negatively buoyant at these depths (Johnson and Richardson, 1977).

Losses of nitrate and phosphate are function of the loss of biomass and internal N and P quotas: ϕN=ϕC⋅QN,ϕP=ϕC⋅QP. The transport of C, N, and P is resolved using 2-D advection–diffusion equations discretized on a grid at 1/4∘ resolution with a single vertical layer representing a surface layer of water of 1 m depth. The surface velocities used for the transport account for surface currents, windage effect, and wave transport by Stokes drift: ϕtransport(Nutrient)=-U⋅∂Nutrient∂x-V⋅∂Nutrient∂y+Kh⋅∇h2Nutrient,with(U,V)=(uNEMO,vNEMO)+αwin⋅(u10m,v10m)+(uStokes,vStokes), where (uNEMO,vNEMO) are the horizontal velocity obtained from the physical–biogeochemical model, αwin is a windage coefficient, (u10m,v10m) the components of the wind field at 10 m above the sea level, (uStokes,vStokes) the Stokes velocity, and Kh a diffusion coefficient.

The model simulations are performed for the year 2017 because basin-scale Sargassum fractional coverage observations from MODIS were available (Berline et al., 2020), with concurrent observations carried out during two cruises in the tropical Atlantic (Ody et al., 2019).

The observed and model seasonal distributions of Sargassum in 2017 are shown in Fig. 4. Model distribution is obtained from the ensemble mean of the 100 simulations with the lowest L. Hereafter, this ensemble will be referred to as Ω100. Averages over selected areas are shown in Fig. 5. At this stage, it is worth recording that the selection of the ensemble simulations is performed without constraints on the spatial distribution, the only constraint being on the basin-scale seasonal biomass average (L).

Initialized in January, the model reproduces the seasonal distributions of Sargassum fairly closely. It simulates the Sargassum drift toward the Caribbean Sea, with a summer peak of biomass followed by a decrease until the end of the year, although the increase of biomass comes a little too early in February–March. In the Caribbean Sea, the largest abundance of Sargassum in the northern part of the basin near the Greater Antilles compared to the south of the Caribbean is consistent with observations. Despite a bloom that is occurring too early (May–June) near the Lesser Antilles, the modeled seasonal cycle is also consistent with the observations in this area (Fig. 5b). This is encouraging from the perspective of predicting strandings on the Caribbean islands. It also succeeds in maintaining the biomass in the Eastern part of the tropical North Atlantic below the ITCZ (Figs. 4 and 5d). In the Sargasso Sea area (Fig. 5c), simulations and observations consistently show an increase at the end of the year. The model tends to reproduce heavy proliferations in March–June which seem not to be observed. Given current knowledge, it is difficult to determine the causes of such a bias. It could be due to a bias in the nutrient content simulated by PISCES-Q at this period. Moreover, error in the Sargassum initial conditions (January) and in the transport parameterization can lead to this production too far north during March–June. An observation bias cannot be ruled out either since this area is very cloudy and presents very contrasted Sargassum aggregation properties.

The distribution of parameters for the ensemble Ω100 is given in Fig. 6. There is a significant dispersion of most of the parameters, suggesting either low sensitivity to the parameters in question (as discussed below) or interdependency between them. The analysis shows that there are very different sets of parameters, within the prescribed ranges, that lead to similar seasonal biomass distribution (Fig. 5). Having said that, we observe that the mortality parameters m and λm minimizing L are biased toward low and high values, respectively. This highlights the key importance of this mortality function in representing the seasonal distribution. The half-saturation constants (KN and KP) and the maximum uptake rates of nutrients (VNmax and VPmax) are also distributed toward low and high values, respectively, suggesting some sensitivity of the Sargassum distribution to nutrient resources. These parameters are poorly constrained by observations, and such exercise will allow us to refine the optimization ranges for future studies.

The relative mean deviation of the Sargassum seasonal biomass to 10 % variations in model parameters shown in Fig. 7 confirms findings from the analysis of parameter dispersion in Fig. 6. The most influential parameters are the growth rate, the optimal irradiance, mortality dependence on temperature, and parameter controlling the nitrogen uptake VNmax. It also highlights the influence of the minimum N quota (QNmin). There is moderate dependence on temperature which is in good agreement with measurements from Hanisak and Samuel (1987). In agreement with previous Lagrangian studies (Berline et al., 2020; Putman et al., 2020), we find some sensitivity to the windage parameter.

The simulated stranding from the ensemble Ω100 is shown in Fig. 8. At the scale of the tropical Atlantic, these strandings sum to 1.05 million tons of dry weight for the whole year. The predicted strandings in the Caribbean, northern Brazil, French Guiana, and Sierra Leone correspond to our current knowledge of Sargassum invasions (Bernard et al., 2019; Louime et al., 2017; Oviatt et al., 2019; Sissini et al., 2017; Oyesiku and Egunyomi, 2014; Smetacek and Zingone, 2013). Nevertheless, there are no available large-scale coastal observations or estimates of stranding to go further in the validation of these simulated strandings.

A peculiarity of our modeling strategy is to consider the Stokes drift. The Stokes drift induces a displacement of material parallel to the direction of wave propagation which directly transports the Sargassum. An ensemble of 100 simulations without Stokes drift (“NoStokes”), considering the set of physiological parameters from Ω100, has therefore been conducted. Anomalies of annual Sargassum distribution with respect to Ω100 are shown in Fig. 9a. Sargassum coverage is significantly increased in the central Atlantic but decreases sharply in the Caribbean and the southwestern part of the domain. This highlights the influence of waves, most probably due to the trade winds, in shaping the seasonal distribution, and transporting the algae southward.

We now use the Sargassum model to explore how and to which extent continental nutrient sources (riverine nutrient fluxes, dust deposition, atmospheric N deposition) could participate in the proliferation and may shape the seasonal distribution of Sargassum. First, TATL025BIO simulations were run by deactivating the river sources (simulation “noriver”), atmospheric deposition of P, Si, and Fe (simulation “nodust”), or atmospheric deposition of N (simulations “noNdepo”). We choose to distinguish between dust and N deposition because they do not have the same origin and because spatial, seasonal, and long-term variability is not necessarily the same. The simulations were produced from 2006, so the long-term influence of these forcings on the biogeochemical content is considered there. These simulations were then used to force three ensembles of 100 simulations which used the sets of parameters from Ω100.

As expected for the noriver ensemble, the tropical western Atlantic, which is under influence of the Amazon and Orinoco rivers, is experiencing a decrease in nutrient concentrations (Fig. 10b). Nutrients also show a decrease in the equatorial Atlantic. But for other regions, such as the Sargasso Sea or the Guinea Dome, the long-term equilibration results in an increase in nitrogen concentration. The resulting Sargassum coverage shows a negative anomaly in the Caribbean Sea, in the Gulf of Mexico, and in the region of the ITCZ, with an annual mean basin-scale biomass decrease (Fig. 9a). For this ensemble, strandings are decreased from 0.65 to 0.56 Mt (-13 %).

The nodust ensemble Sargassum distribution shows a slight positive anomaly over most of the domain (Fig. 9c), particularly in the central Atlantic and off western Africa, with a slight decrease in the Caribbean Sea and the Gulf of Mexico. Cumulative strandings sum to 0.72 Mt, and so, are slightly increased compared to the baseline ensemble (+10 %). This sensitivity can be explained by the large-scale phosphorus increase and regional increases in nitrogen and phosphorus concentrations (Fig. 10) in the biogeochemical simulation. This sensitivity is expected to be produced by the reduced iron concentrations, which limit the phytoplankton growth and thus the nutrient uptake.

The removal of atmospheric nitrogen deposition (noNdepo) leads to a global decrease in surface nitrogen concentration and an increase in surface phosphorus concentrations across the entire domain (Fig. 10). The resulting Sargassum coverage is significantly decreased over the whole domain, and the annual averaged stranding decreases by 1 % (Fig. 9d).