## 2 Materials and Methods
### Methodology  
#### 2.3.1 Atmospheric Correction Procedure over Sargassum Dominated Waters  
The first requirement for the detection of in-water _Sargassum_ aggregations is to derive the water leaving reflectance at the sea surface level from satellite data. Thus, the top of the atmosphere (TOA) reflectance (\(\rho_{\rm TOA}\)) needs to be corrected for the atmospheric effects such as the Rayleigh (i.e., molecular) and aerosols scattering and sun/sky glint. While the Rayleigh atmospheric scattering is known from theory, the estimation of the aerosol reflectance remains challenging due to the high variability in their spatial and optical properties [24]. The POLYMER atmospheric correction algorithm [25] could be used to retrieve the above water reflectance over open ocean waters. POLYMER was first applied to ENVISAT/MERIS data and more recently to Sentinel-2/MSI and Sentinel-3/OLCI data [26; 27]. POLYMER atmospheric correction approach firstly consists in normalizing the TOA radiance by the cosine of the solar zenithal angle (\(\theta_{\rm w}\)) and the extraterrestrial solar irradiance (Es) to obtain the TOA reflectances (\(\rho_{\rm TOA}\)). \(\rho_{\rm TOA}\) can then be decomposed as follows (Equation (1)):  
\[\rho_{\rm TOA}=\ \mathsf{t}_{\rm oz}\mathsf{t}_{\rm NO2}\Big{(}\rho_{\rm mol}+ \mathsf{T}\rho_{\rm gli}+\rho_{\rm aer}+\rho_{\rm coupl}+\mathsf{t}_{\rm w}^{+} \Big{)} \tag{1}\]  
where \(\mathsf{t}_{\rm oz}\) and \(\mathsf{t}_{\rm NO2}\) are, respectively, the transmittance of the ozone and the nitrogen dioxide, \(\rho_{\rm mol}\) accounts for the Rayleigh molecular scattering, \(\rho_{\rm gli}\) is the sunlight reflectance, \(\mathsf{T}\) is the direct transmittance, \(\rho_{\rm aer}\) is the reflectance of the aerosols, \(\rho_{\rm coupl}\) represents various coupling terms between the sunlight, the molecules and the aerosols, \(\mathsf{t}\) is the total (i.e., direct and diffuse) transmittance for atmospheric scattering, and finally, \(\rho_{\rm w}^{+}\) is the sea surface reflectance (i.e., above water reflectance). The top of the atmosphere reflectance is first corrected for the ozone transmittance, the Rayleigh scattering effects and most of the sunlight reflectance ([PERSON] and [PERSON] (1954, [28]) which are known from theoretical calculations. The derived reflectance is called \(\ \rho^{\prime}\). The reflectance \(\ \rho^{\prime}\) can be expressed from Equation (1) as follows Equation (2) where \(\rho_{\rm ag}\) includes the aerosols reflectance, the coupling term. \[\rho^{\prime}(\lambda)=\ \rho_{\rm ag}(\lambda)+\mathsf{t}(\lambda)\rho_{\rm w}^{ +}(\lambda) \tag{2}\]  
POLYMER then relies on the expression of the term \(\rho_{\rm ag}\) as a polynomial function of \(\lambda\) and \(\rho_{\rm mol}\) (Equation (3)):  
\[\rho_{\rm ag}(\lambda)=\ \mathsf{t}_{\rm o}\mathsf{c}_{0}+\ \mathsf{c}_{1} \lambda^{-1}+\mathsf{c}_{2}\rho_{\rm mol} \tag{3}\]  
A least square fitting approach on the satellite measurements is then applied to estimate \(\rho_{\rm ag}\). The intrinsic _Sargassum_ reflectance exhibits a strong increase in the near infra-red (NIR) (see Figure 2 in [10]). Such an increase remains significant enough to influencethe overall oceanic reflectance although the fractional _Sargassum_ coverage that is usually encountered in the ocean is weak; typically lower than 5% based on MODIS data [13]. However, since the _Sargassum_ intrinsic reflectance is not considered by the POLYMER algorithm, the _Sargassum_ optical signature on the top of atmosphere reflectance is wrongly identified as an aerosol signature. This leads to an overestimation of the reflectance \(\rho_{\text{ag}}\) in the NIR domain and the subsequent loss of the _Sargassum_ signature on the total surface reflectance (\(\rho_{\text{w}}^{+}\)) (see Figure 4 in [29]). [PERSON] et al. [29] recently addressed the issue of correcting \(\rho_{\text{TOA}}\) for atmospheric effects over _Sargassum_ dominated waters by adjusting the POLYMER algorithm, hereafter noted POLYMER\({}_{\text{ext}}\), to the presence of _Sargassum_.