## 4 Discussion
A three-band model obtained the fourth best validation result in the previous study, with an R\({}^{2}\) of 0.85, an RMSE of 41.8 mg/m\({}^{3}\), an RRMSE of 52%, and a bias of 4.77 mg/m\({}^{3}\), while for the C2 XC Rrs validation results, the R\({}^{2}\) was 0.9, the RSME was 50.6 mg/m\({}^{3}\), the RRMSE was 57%, and the bias was 3.22 mg/m\({}^{3}\). This RMSE is similar to that obtained by [PERSON] et al. [48] of 56.9 mg/m\({}^{3}\) in his study using the three-band model, the 6S (Second Simulation of the Satellite Signal in the Solar Spectrum) model for AC, and a Chl_a data range until 600 mg/m\({}^{3}\), and an RMSE slightly higher than that obtained by [PERSON] et al. [49] of 33.5 mg/m\({}^{3}\) for a data range between 2.3 and 306 mg/m\({}^{3}\). It may be that an improved recovery of the Red-edge bands with Polymer will make the three-band model the best Chl_a retrieval algorithm. The best-validated algorithm for PC estimation was based on the Red-edge1/Red ratio (\(R704/R665\)) and applied to C2 XC Rrs. The Red-edge1/Red ratio was the algorithm with the shortest wavelength bands of all tested algorithms, and therefore the bands with the fewest errors in the validation of the Rrs, and it was also the best result in the previous study. The validation results in the previous study were an R\({}^{2}\) of 0.8, an RMSE of 43.7 mg/m\({}^{3}\), an RRMSE of 55%, and a bias of 14.64 mg/m\({}^{3}\) for a data range between 0.7 and 1040 mg/m\({}^{3}\). The results improved in this work with an R\({}^{2}\) of de 0.9, an RMSE of 38.9 mg/m\({}^{3}\), an RRMSE of 39%, and a bias of 5.45 mg/m\({}^{3}\) for a data range between 0 and 751.1 mg/m\({}^{3}\). This demonstrates the band ratio applicability in S2-MSI images, which is a band ratio used in the previous study and in the drone and aircraft studies of [PERSON] et al. [50] and [PERSON] et al. [51]. The calculated RMSE is similar to the standard error of 45.5 mg/m\({}^{3}\) obtained by [PERSON] et al. [2] for a PC higher than 50 mg/m\({}^{3}\), using samples from the same climatic region. The application of water quality algorithms developed from in situ reflectances, using reflectances obtained after an AC process, may lead to different errors than those calculated in the development of the algorithms. Algorithms with the shortest wavelength bands had better results if their validation results in the previous study were not very high. Only three algorithms were coincident and showed similar error statistics. However, the results demonstrate the applicability of the algorithms developed from in situ reflectances to satellite S2-MSI imagery after the correction of atmospheric and sun specular effects, a step that was missing in other works. Indeed, there is always some difficulty to obtain general algorithms to cover a wide range of data. One solution to obtain a good retrieval algorithm for each different bio-optical variable is to obtain specific algorithms for each different water type according to a pre-established classification based on their optical spectrum (optical water types), as it has been performed in several studies (e.g., [PERSON] et al. [52]; [PERSON] et al. [53]; [PERSON] et al. [19]; [PERSON] et al. [42]). If the same problem exists for AC, the results would probably be more accurate if the optical water type differentiation was defined before applying the AC.