## 2 Materials and Methods
### Methodology
#### 2.3.3 Inversion of the SRT Model to Retrieve the _Sargassum_ Depth and Fractional Coverage  
The inversion of the SRT model consists of using an optimization method to minimize the Euclidian distance between the sea surface reflectance that is derived from satellite observations and the simulated sea surface reflectance (forward SRT model). The bio-optical parameters (Chl, NAP, CDOM, FC, and z) for which the retrieved error between observations and simulations is minimum are selected.  
The minimization is operated using the least squares method based on a first guess initial values of the bio-optical parameters, and on the range of variation of each parameter. The range of variation of the chlorophyll concentration was set between 0 and 2 mg m\({}^{-3}\) based on the OCC-CI algorithm developed by the CMEMS (Copernicus European community) which provides monthly average of the chlorophyll-a in the Atlantic Ocean. The range of variation of the NAP concentration was set between 0 and 2 g m\({}^{-3}\) and the CDOM absorption coefficient at 443 nm between 0 and 0.1 m\({}^{-1}\). These ranges of variation were set based on the S3W OLCI Level-2 products (distributed by EUMETSAT-CODA service) where the NAP ranged from 0.13 and 0.32 g m\({}^{-3}\) and the CDOM from 0.04 and 0.06 m\({}^{-1}\). The FC ranges between 0 and 1 and z ranges from the surface (i.e., 0 m) to 5 m deep because _Sargassum_ aggregations are known to float between 0 and 5 m [18; 30; 31; 32]. The initial value of the bio-optical parameters was fixed as a first guess as follows: Chl = 0.5 mg m\({}^{-3}\), NAP = 1 g m\({}^{-3}\), CDOM = 0.0005 m\({}^{-1}\), FC = 1 and z = 0 m. The minimization process is stopped when the error between observations and simulations is below a threshold, namely \(10^{-20}\). Such threshold is relevant to overcome the issue of local minima. The five optimum parameters (Chl, NAP, CDOM, FC and z) are then estimated for each pixel of the satellite image. Practically, the MATLAB optimization function \"_Isqcurfit_\" has been used.  
Figure 3: Inputs and output of the SRT model.  
2.3.4. Maximum Chlorophyllll Index (MCI) and Fractional Coverage (FC)  
The Maximum Chlorophyll Index MCI [11; 13] is defined as follows (Equation (8)):  
\[\text{MCI}=\rho^{\prime}(709)-\left[\rho^{\prime}(681)+\left(\rho^{\prime}(754)- \rho^{\prime}(681)\right)\ast\frac{709-681}{754-681}\right] \tag{8}\]  
The MCI background (\(\text{MCI}_{\text{bg}}\)) value corresponds to the noise over _Sargassum_ free waters. It can be estimated using a median filter window, which is efficient provided that a large majority of pixels inside this window is not contaminated by _Sargassum_. Our tests showed that a 167 \(\times\) 167 pixels window (50 km \(\times\) 50 km) is satisfactory to fulfill such a condition. \(\text{MCI}_{\text{bg}}\) is then subtracted from the MCI to derive the so-called MCI deviation, which is defined as \(\delta\text{MCI}=\text{MCI}-\text{MCI}_{\text{bg}}\).  
The fractional coverage can be linked to \(\delta\text{MCI}\) through a linear relationship \(\delta\text{MCI}=\text{K}^{\text{*}}\text{FC}\), where K is a coefficient of proportionality. K can be estimated using the SRT model outlined in Section 2.3.2 for a pixel that is entirely composed of _Sargassum_. K is equal to \(\delta\text{MCI}_{\text{max}}\) where \(\delta\text{MCI}_{\text{max}}\) is \(\delta\text{MCI}\) for a pixel composed only of _Sargassum_ (i.e., FC = 100%) located at the surface (z = 0) [16]. In the current study, the value of K was estimated at 0.0579.