## 3 Results  
### Performances of the SRT Inversion Retrieval Process Using Synthetic Data  
A synthetic dataset was generated to evaluate the performances of the SRT model inversion for retrieving particularly FC and z. For this purpose, the forward SRT model is used to simulate the surface reflectances for clear waters (i.e., Chl = 0.3 mg m\({}^{-3}\), NAP = 1 g m\({}^{-3}\), CDOM = 0.01 m\({}^{-1}\)), with a depth z varying between 0 m and 5 m, and a fractional coverage varying between 0 and 1. The atmospheric effects are added to simulate the top of the atmosphere radiance using MODTRAN [33]. The OLCI instrumental features (i.e., spectral resolution and SNR) are then applied. In addition, an error representing the imperfect correction of atmospheric effects is taken into account. The minimization of the cost function is used to retrieve the water constituents, namely, Chl', NAP', CDOM', FC', and z'. The desired input parameters that were used to simulate the initial OLCI-like sea surface reflectances are then considered as the reference data to determine the error of the inversion approach. The performances of the SRT inversion retrievals are determined following the approach outlined in Figure 4.  
The root mean square error (RMSE) and the relative RMSE (RRMSE) obtained between the parameters retrieved by the SRT inversion and the desired reference values of each parameter are reported Table 1. The retrieval error could be considered as satisfactory when the Relative RMSE is lower than 20% based on the current inversion algorithms performances [34]. Chl, NAP, and CDOM are retrieved with a weak RMSE. However, the retrievals of the Chl and CDOM parameters are not satisfactory as shown by their high RRMSE, which is greater than 45% and 70% for Chl and CDOM, respectively. The RRMSE estimated for the FC parameter is lower than 3%, thus indicating its good retrieval. Note  
Figure 4: Flowchart describing the procedure used to determine the performances of SRT inversion retrievals. that a RMSE value for FC lower than 1% can be considered satisfactory even though it should be noted that _Sargassum_ contaminated pixels typically show FC values lower than 5% [13]. The RRMSE value of 14.7% that is found for the parameter z, and its RMSE of 0.7 m are satisfactory. Figure 5 shows the distribution of the relative RRMSE errors as a function of FC and z. In Figure 5, FC varies from 0 to 100% along the horizontal axis and z varies from 0 to 5 m along the vertical axis. Two large red bands could be observed in Figure 5d,e (one left vertical band and one top horizontal band, respectively) because the division by 0 (reference value) leads to infinity for RRMSE. The high values in Figure 5e in the left are due to the difficulty to estimate the depth for the case where there is no _Sargassum_ occurrence (FC = 0). Figure 5 reveals that the deeper the _Sargassum_ aggregation, the more difficult to correctly derive the fractional coverage and the depth (Figure 5d,e). Thereby, the inversion model performs better when the _Sargassum_ aggregation is located close to the surface. Similarly, it is observed that the retrieval of FC parameter is more challenging (RRMSE > 15%, Figure 5d) when the depth is higher than 4 m (Figure 5d). The contribution of Chl, NAP, and CDOM is difficult to estimate for the case where the pixel is both covered by 100% of _Sargassum_ (FC = 100%) and located near the surface (z = 0). This is because the surface reflectance is not influenced by hydrosols for such conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **RMSE=\(\sqrt{\frac{1}{8}\sum\left(\textbf{C}_{\textbf{method}}-\textbf{C}_{\textbf{reference}}\right)^{2}}\)** & **RRMSE=100\(\cdot\)RMSE\(\sqrt{\textbf{C}_{\textbf{method}}}\)** \\ \hline Chl (mg m\({}^{-3}\)) & 0.14 mg m\({}^{-3}\) & 48.1\% \\ NAP (g m\({}^{-3}\)) & 0.13 g m\({}^{-3}\) & 13.4\% \\ CDOM (m\({}^{-1}\)) & 0.0078 m\({}^{-1}\) & 78.4\% \\ FC (\%) & 1.51\% & 2.9\% \\ z (m) & 0.74 m & 14.7\% \\ \hline \hline \end{tabular}
\end{table}