## 2 Materials and Method
### Sentinel-2 Images Processing and Validation  
The twin satellites of Sentinel-2 (S2A and S2B) carry on board the MultiSpectral Instrument (MSI) optical sensor, which acquires images in the visible-near-infrared (VIS-NIR: 13 bands from 442 to 2202 nm) spectrum, with a spatial resolution of 10, 20, and 60 m (depending on the band), at a frequency of about 5 days were used in this study to assess the spatiotemporal dynamics of the macrophyte community's colonization. A total of 34 images available between 2015 and 2020 were downloaded from the Copernicus Open Access Hub [51] or from the ONDA catalogue [52] (Table 1). In detail, for each year except 2015 (the S2 mission began in July 2015), six images were chosen: two for each season characterized by macrophyte presence (from spring to autumn). For this work, the first seven bands were used: from 442.7 to 782.8 nm for S2A and from 442.3 to 779.7 nm for S2B. The bands of each image were then resampled to the spatial resolution of 10 m. All images were chosen without clouds and cloud-shadows, without sun-glint and other radiometric noise. Figure 1: Sentinel-2 image of Lake Garda in true color (23/03/2019). Above on the left is the location of Lake Garda in Italy. The blue and green rectangles represent the two areas analyzed to extract turbidity values (NTU). The red box represents the study area (Sirmione Peninsula). Below on the right shows an enlargement of the Sirmione Peninsula (grey): the yellow area represents the mask used to create the bottom coverage maps (3.97 km\({}^{2}\)), while the lines with black squares represent the transects used for assessing the macrophytes gradients from the coast. All images were downloaded as Level 1 (L1); consequently, the first processing step was the conversion of top of atmosphere (TOA) reflectances into TOA radiances, through the SNAP tool \"ReflectanceToRadianceOp\" for allowing the atmospheric correction to be performed. To this aim, the Second Simulation of the Satellite Signal in the Solar Spectrum code vector version (6 SV ver. 2.1) [53] was adopted in agreement with previous validating studies [54; 55]. The 6 SV was parametrized with aerosol values (AOD\({}_{550}\)) referring to the acquisition dates and collected from a nearby AERONET station [56] or from NASA data [57] when AERONET data were not available. The 6 SV-derived atmospherically corrected products were converted into remote sensing reflectances (Rrs) dividing by \(\pi\). The robustness of the atmospheric correction performed by 6 SV on S2 images, already demonstrated in [PERSON] et al. (2018) and [PERSON] et al. (2019) [54; 55], was further tested over land. To this aim, an evergreen wooded area, a sandy beach, and some rooftops were selected as invariant reflectance targets. The 6 SV-derived reflectances of the targets were compared for the 34 atmospherically corrected images. Three regions of interests (ROIs; of a 2 \(\times\) 2 pixel size) were created, one for each invariant surface (Figure S1), for computing the average reflectances for each of the 34 S2 images. Rrs products were then used as input for the BOMBER bio-optical model (Bio-Optical Model-Based tool for Estimating water quality and bottom properties from Remote sensing images) [58] for estimating the substrate coverage. BOMBER parameterization was based on the in situ inherent optical proprieties (IOP) of the water column and reflectances of bottom substrate collected in Lake Garda and previously used and validated in different work [54; 59; 60; 61]. The BOMBER code was applied in shallow water mode for each pixel included in the predefined mask of 3.97 km\({}^{2}\) (Figure 1), defining the shallow waters of Sirmione Peninsula reaching a maximum depth of 10 m. This mask was created to avoid areas too close to the coast that might contain mixed pixels (water-land interface). The BOMBER outputs provide the fractional cover of bottom substrates through three classes: sand (b0), rocks (b1), and rooted macrophytes (b2), and in addition produce the optical closure error maps.