## 4 Discussion
The results are in agreeance with [PERSON] el al. 's [42] study, using TOA, C2 RCC, and C2 XACs according the optical water type. The other variable with two algorithms was Chl_a, but this time, the algorithms were not coincidental for concentrations above and below 5 mg/m\({}^{3}\). The threshold value was 5 mg/m\({}^{3}\) because waters with high Chl_a (above 3-5 mg/m\({}^{3}\)[43]) produce discernible spectral features in the red and NIR regions of the reflectance spectrum [44]. The best algorithm for values below 5 mg/m\({}^{3}\) was the same as that obtained in the previous study, the \(\log_{10}\) of the ratio between the band with a maximum value among the \(R443\) and \(R492\) bands as the numerator and \(R560\) as the denominator using C2 XC Rrs, the bands with the fewest errors in the validation of the Rrs. The validation results in the previous study were an R\({}^{2}\) of 0.55, an RMSE of 0.94 mg/m\({}^{3}\), an RRMSE of 43%, and a bias of 0.09 mg/L, similar values to that obtained in this work, where the validation results enhance the RMSE of 0.93 mg/m\({}^{3}\) and the bias of 0.01 mg/m\({}^{3}\). The second-best result was obtained with Polymer Rrs, with the AC having the better validation results for the used bands, obtaining an RMSE of 1.04 mg/m\({}^{3}\), only 0.1 mg/m\({}^{3}\) higher than the previous study validation results but with a very high RRMSE of 64%. The RRMSE is higher as the number of data below 2 mg/m\({}^{3}\) increases, with 72% of the data points in the Polymer validation in front of the 66% in the C2 XC validation and the 56% in the previous study. These results are in agreement with the study carried out by [PERSON] et al. [12], obtaining an absolute error of 0.89 mg/m\({}^{3}\). The results corroborate the applicability of the algorithm developed by [PERSON] and [PERSON] [5] for hyperspectral sensors using in situ radiometry in multispectral sensors using atmospherically corrected MSI Rrs. The best algorithm for values above 5 mg/m\({}^{3}\) was the Green/Red ratio (\(R560/R665\)) applied to Polymer Rrs, although in the previous study, the validation results of this algorithm using in situ Rrs were bad, with an R\({}^{2}\) of 0, an RMSE of 144 mg/m\({}^{3}\), an RRMSE of 156%, and a bias of 43 mg/m\({}^{3}\). However, the algorithm generated with 144 data points in the previous study applied to the 42 data used in the Polymer validation provided the best validation results, an R\({}^{2}\) of 0.9, an RMSE of 28.1 mg/m\({}^{3}\), an RRMSE of 50%, and a bias of 1.35 mg/m\({}^{3}\). This result may be due to two factors, (1) the data range and (2) the used bands. Regarding data range, only 4 of the 42 data used were higher than 100 mg/m\({}^{3}\), and in the previous study, the RMSE for the \(R560/R665\) ratio would be 34.72 mg/m\({}^{3}\) using only values lower than 100 mg/m\({}^{3}\). Regarding the used bands, the \(R560/R665\) ratio was the one that used the shortest wavelength bands of all the tested algorithms using concentrations higher than 5 mg/m\({}^{3}\), the wavelengths for which Polymer gives the best results in the validation of the Rrs. The band relation corresponds to the ratio between reflectances at the minimum absorption at the green region between 550 and 555 nm, to reflectances at the second peak absorption at the red region between 670 and 675 nm, used by [PERSON] et al. [45] in S2-MSI images using the empirical line method as an AC and obtaining a standard error of 0.14 mg/m\({}^{3}\) for a data range of 1.58-6.00 mg/m\({}^{3}\). The same equation was used by [PERSON] et al. [46],obtaining an RMSE of 21.9 for a larger data range of 4.14-76.44 mg/m\({}^{3}\), increasing the RMSE with the data range. It is noted that for C2X and C2 XC, using only 13 and 17 data, respectively, the best algorithm obtained was the three-band model of [PERSON] et al. [47], using the \(R740\), \(R704\), and \(R665\) bands, for which C2X and C2 XC were the ACs with the best validation results.