## 2 Materials and Methods
### Image Processing  
Images processed in this work correspond to the S2-MSI mission, inside the Copernicus program of ESA. The S2-MSI mission is a two-satellite constellation: S2-MSI-A (launch date: 23 June 2015) and S2-MSI-B (launch date: 7 March 2017). Each satellite has the MSI (Multispectral Instrument) sensor, which measures the Earth's reflected radiance in 13 spectral bands from visible to VNIR and SWIR, with spatial resolutions of 10, 20, and 60 m [28]. Table 1 shows the MSI bands' spectral characteristics and their spatial resolution. A total of 41 S2-MSI images were downloaded from the Copernicus Open Access Hub, an ESA site to provide Sentinel missions imagery. Cloud-free images were coincidental to field campaigns in a great percentage (80%, 33 images), two with one day's difference, two with two days' difference, two with four days' difference, and two with ten days' difference. The images with ten days' difference were from two stable water bodies, Valdecarfas reservoir with four months of residence water time and Cazalegas reservoir with five months of residence water time. For this reason, the number of data used to validate the water quality algorithms does not coincide with the number of data used to validate the ACs, for which were used in situ reflectance measurements coinciding with the satellite pass only. To process the AC, the C2-Nets available for the S2-MSI imagery in the SNAP program and the Polymer program were used (POLynomial-based approach applied to MERIS data) because, as mentioned in the introduction, they are the ones that have given good results in previous Case 2 waters studies: [PERSON] and [PERSON] [18], [PERSON] et al. [12], [PERSON] et al. [19], [PERSON] et al. [20], [PERSON] et al. [21], and [PERSON] et al. [29]. SNAP software (v8.0; Brockmann Consult GmbH) in the image processing inverts the top-of-atmosphere full spectrum by a neural net processing to obtain water-leaving reflectance in the VIS and NIR bands [30]. The inversion of the water signal and satellite signal is performed by different processors (C2-Nets) which differ in the NN training ranges of inherent optical properties (IOPs). A characterization of optically complex waters through its IOPs is used, along with the coastal atmospheres to parameterize radiative transfer models for the atmosphere over the water body [12]. The C2 RCC-Net (C2 RCC) is \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Band Number** & **Name** & **Spectral Region** & **Central Wavelength (nm)** & **Bandwidth (nm)** & **Spatial Resolution (m)** \\ \hline
1 & \(R\)443 & Coastal aerosol & 442.7 & 21 & 60 \\
2 & \(R\)492 & Blue & 492.4 & 36 & 10 \\
3 & \(R\)560 & Green & 559.8 & 31 & 10 \\
4 & \(R\)665 & Red & 664.6 & 31 & 10 \\
5 & \(R\)704 & Red-edge1 & 704.1 & 15 & 20 \\
6 & \(R\)740 & Red-edge2 & 740.5 & 15 & 20 \\
7 & \(R\)783 & Red-edge3 & 782.8 & 20 & 20 \\
8 & \(R\)833 & NIR & 832.8 & 106 & 10 \\
8a & \(R\)865 & NIR narrow & 864.7 & 21 & 20 \\
9 & \(R\)945 & Water vapor & 945.1 & 21 & 60 \\
10 & \(R\)1373 & SWIR/Cirrus & 1373.5 & 31 & 60 \\
11 & \(R\)1614 & SWIR1 & 1613.7 & 91 & 20 \\
12 & \(R\)2202 & SWIR2 & 2202.4 & 175 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Spectral information and spatial resolution of MSI sensor (ESA, 2012). the original normal net, covering typical ranges of coastal IOPs. C2 RCC was complemented with the Coast Colour dataset to extend the range for coastal waters including extreme cases [30], resulting in the C2X-Net (C2X). C2X-COMPLEX-Net (C2 XC) was trained with intermediate ranges of IOPs, larger than C2 RCC and tighter than C2X [31]. C2-Nets do not include specific corrections for land adjacency [29]. The principle of the Polymer algorithm is a spectral matching method based on: (1) a polynomial used to model the spectral reflectance of the atmosphere and sun glint, (2) a water reflectance model, and (3) the use of the whole spectral range from the blue to the near-infrared [16].