## 1 Introduction
A lot of the ACs to obtain water reflectance from S2-MSI images have been developed by the European Space Agency (ESA) and are provided in the freely available SNAP (SeNtinel Application Platform) program toolkit. Initially, there was only the C2 RCC (Case 2 Regional Coast Colour) processor, which was developed from the original Case 2 regional processor [15] and adapted to different multi and hyperspectral sensors (e.g., S2-MSI and Sentinel-3-OLCI). Currently, a set of three different neural networks (NN) are available for S2-MSI imagery, trained with different databases to perform the AC on different water types and named here as C2-Nets: C2 RCC, C2X (Case2 eXtreme), and C2X-COMPLEX (C2 XC). Another algorithm is Polymer; with its generic approach, it has been applied to many sensors, including S2-MSI and S3-OLCI. The Polymer approach is a physical model based on a spectral optimization method called spectral matching which is aimed at recovering the radiation scattered and absorbed by water from the measured signal by satellite sensors in the visible spectrum [16; 17]. One of the strengths of this algorithm is the ability to recover water radiation in the presence of sun glint, achieving a spatial coverage higher than other products. With Polymer and the C2-Nets, the best S2-MSI radiation validation results have been obtained, as published in previous studies for Case 2 waters, such as those carried out by [PERSON] and [PERSON] [18], [PERSON] et al. [12], [PERSON] et al. [19], [PERSON] et al. [20], and [PERSON] et al. [21]. Once the AC has been applied and the water leaving reflectance has been obtained, the next step is obtaining the retrieval algorithms to estimate the different bio-optical variables, either empirically or analytically. In this sense, the objective is always to obtain a general algorithm, but the great difference in waters with respect to their OAC greatly conditions the results, as in the case of the AC step. The problem with validating the AC algorithms lies in the need to measure the in situ reflectance coinciding with the satellite pass, having a cloud-free image, good wind conditions, and all the involved costs of performing the sampling. Thus, an alternative is to use in situ reflectance data from previous studies, even if they are not coincidental with the satellite pass or even before its launch, to develop the algorithms, which will be validated with different ACs applications and with in situwater quality measurements. In this way, the database can be much larger, giving greater consistency and the water quality retrieval algorithms obtained more robust. In this way, the work elaborated and published by [PERSON] et al. [6] (previous study) was developed, in which five retrieval algorithms using in situ spectrometry were implemented to estimate five water quality variables such as transparency (Secchi disk depth, SDD), total suspended solids (TSS), CDOM, chlorophyll concentration (Chl_a), and phycocyanin concentration (PC), for both S2-MSI and S3-OLCI. This provides us with accurate and robust algorithms developed with in situ reflectance and not specific to a given AC. However, the obtained in situ spectrometry water quality algorithms need to be assessed using different ACs water reflectance because the application with reflectances obtained after an AC process may lead to unexpected results. It is necessary because, in the case of water, the validation of the reflectance resulting from the atmospheric correction is very difficult (the error could be of the same order as the surface reflectance itself). That is why the idea of validating the final products on water quality is the right approach, in particular for water. After all, the interest is not so much in the reflectance of the water itself but in its properties. Therefore, the article is the second part of a previous study to complete the applicability step that was missing in other works, where only in situ reflectances were used to develop algorithms.