## 2 Materials and Methods
### Methodology
#### 2.3.2 Sargassum Radiative Transfer (SRT) Model  
As mentioned Section 1, the adaptation of the Lee semi-analytical radiative transfer model [20] proposed by [PERSON] et al. [21] to account for the immersion of _Sargassum_ aggregations is used here; such a model is further called _Sargassum_ Radiative Transfer (and noted SRT). Similar to the [PERSON]'s model, SRT can simulate the above surface reflectance using the bio-optical properties of the water column, the bottom depth and bottom composition as inputs (forward model). More precisely, the inputs typically consist of the chlorophyll concentration (Chl), the Non-Algal Particles (NAP) concentration, and the Colored Dissolved Organic Matter (CDOM) absorption coefficient. These parameters determine the Inherent Optical Properties (IOP) of the water such as the absorption (a(\(\lambda\))) and backscattering (b\({}_{\text{b}}\)(\(\lambda\))) coefficients that are used to model the deep-water reflectance \(\rho_{\text{rs}}^{\text{dp}}\)(\(\lambda\)). [PERSON]'s model also considers the seabed reflectance and depth (z). In addition to [PERSON]'s model, SRT is also able to consider the depth and the fraction coverage (FC) of _Sargassum_ as inputs [21]. To do that, the _Sargassum_ aggregation is assumed as an opaque layer at a given depth z (at the surface or in-water). Such an opaque layer can be optically considered as a seafloor that would be solely composed of _Sargassum_. The seabed reflectance used in the [PERSON]'s model can, thus, be considered as a linear mixing between the immersed _Sargassum_ reflectance (\(\rho_{\text{sargassum}}(\lambda)\)) and the _Sargassum_-free water reflectance (\(\rho_{\text{w}}(\lambda)\)). The seabed reflectance in [PERSON]'s model is replaced by the composite reflectance of the immersed _Sargassum_ aggregation, noted \(\rho_{\text{c}}\)(\(\lambda\)) (Equation(4)):  
\[\rho_{\text{c}}(\lambda)=\text{FC}\ \times\rho_{\text{sargassum}}(\lambda)+(1- \text{FC})\times\rho_{\text{w}}(\lambda) \tag{4}\]  
The reflectance of the water column for the layer that is in between the surface and the _Sargassum_ aggregations at the depth z is noted \(\rho_{\text{rs}}\)W and the reflectance of the _Sargassum_ aggregations that are located at the depth z is noted \(\rho_{\text{rs}}\)C. These reflectances are expressed in Equations (5) and (6):  
\[\rho_{\text{rs}}\text{W}\big{(}0^{-},\lambda\big{)}=\rho_{\text{rs}}^{\text{ dp}}\big{(}\lambda\big{)}\Bigg{(}1-\text{e}^{-(\frac{1}{\alpha\cos(\theta_{\text{w}})} +\frac{\text{D}_{\text{r}}^{\text{W}}(\lambda)}{\cos(\theta_{\text{r}})})}K_{ \text{d}}(\lambda)\text{z}\Bigg{)} \tag{5}\]  
\[\rho_{\text{rs}}\text{C}\big{(}0^{-},\lambda\big{)}=\frac{1}{\pi}\rho_{\text{ c}}(\lambda).\text{e}^{-(\frac{1}{\alpha\cos(\theta_{\text{w}})}+\frac{\text{D}_{ \text{r}}^{\text{C}}(\lambda)}{\cos(\theta_{\text{r}})})}K_{\text{d}}(\lambda) \text{z} \tag{6}\]  
where Du\({}^{\text{W}}\) and Du\({}^{\text{C}}\) are the optical path-elongation factors for photons scattered by the water column and _Sargassum_ aggregations respectively. \(\theta_{\text{w}}\) and \(\theta_{\text{v}}\) are the solar and viewing zenith angle, respectively, and K\({}_{\rm d}\) is the diffuse attenuation coefficient. The sea water reflectance just beneath the surface (\(\rho_{\rm rs}(0^{-},\ \lambda)\)) is then the sum of \(\rho_{\rm rs}\)W and \(\rho_{\rm rs}\)C. Finally, the above water reflectance \(\rho_{\rm w}^{+}\)(\(\lambda\)) is derived as follows (Equation (7)):  
\[\rho_{\rm w}^{+}(\lambda)=\frac{0.52\ \rho_{\rm rs}(0^{-},\ \lambda)}{1-1.56\ \rho_{\rm rs}(0^{-},\ \lambda)}\ \times\ \pi \tag{7}\]  
The components of the SRT model that include the water parameters (Chl, NAP and CDOM) and the Fractional Coverage and depth of the _Sargassum_ aggregations are presented in Figure 3.