## 2 Study Area and Dataset  
The Lake Trasimeno in Central Italy is selected as our case study (Figure 1). It is the fourth largest Italian lake (124 km\({}^{2}\)) which is shallow (\(<\)6 m), turbid (mean Secchi depth 1.1 m), and counts as a eutrophic lake [9]. There is an open bay colonized by aquatic vegetation in the southeast of the lake [9; 62]. We exclude the inversion results over this region to avoid uncertain retrievals through statistical analyses. The lake is subject to the occurrence of seasonal algal blooms including toxic cyanobacteria mostly from July to September. The agricultural activities, tourism, and recreation along with climate change are the main stressors of the lake [9; 62]. We use hyperspectral imagery from the PRISMA satellite to map the in-water constituents. PRISMA was launched in March 2019. After a commissioning phase, access to the data has been granted to the users in early June 2020. PRISMA is an on-demand mission and the available data in the archive are limited. It carries an imaging spectrometer that captures images in a continuum of spectral bands within 400 to 2500 nm at a spatial resolution of 30 m. In total, 66 bands are located in the visible near-infrared (VNIR) portion of the spectrum (400-1010 nm) and 173 bands in the shortwave infrared (SWIR) within 920-2500 nm. The spectral sampling intervals and widths are \(\leq\)12 nm. A panchromatic camera is also onboard PRISMA that provides a single band (400-700 nm) image at 5 m spatial resolution. Here, we rely on VNIR bands only as the water-leaving signal over SWIR bands is negligible with no useful information on the biophysical parameters [63]. We consider four level 2D products from the PRISMA archive with minimal cloud cover. The atmospheric correction of the level 2D products is based upon inverting the radiative transfer model, i.e., minimizing a cost function representing the difference between the simulated spectrum and the measured one. The simulations are performed by the MODTRAN model and they are stored as a lookup-table (LUT) to speed up the inversion. Further details about the mission and products are available in the PRISMA products specification document [50]. Consistency analyses and cross-sensor comparisons are performed by considering images from PRISMA and Sentinel-2 overpasses with a maximum time gap of \(\pm 1\) day (Table 1). A thematic illustration of the PRISMA and Sentinel-2 spectral bands and spatial resolutions are shown in Figure 2.  
The atmospheric correction of Sentinel-2 images is performed using the Case-2 Regional/Coast Colour (C2 RCC) processor which provided highly accurate estimates of surface reflectance in previous studies [64; 65; 66]. The quality flags produced by the C2 RCC processor are investigated to assure the reliability of the input data to the inversion model [64]: (i) Rosa_OOS: the input spectrum out of the scope of the training range of the neural net associated with the atmospheric correction, (ii) Rosa_OOR: the input spectrum out of training range of the atmospheric correction neural net, (iii) Rhow_OOS: the Rhow input spectrum to the inherent optical properties (IOP) neural net is probably not within the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**PRISMA** & 4 June 2019 & 26 July 2019 & 23 April 2020 & 3 June 2020 \\ \hline
**Sentinel-2** & 5 June 2019 & 25 July 2019 & 23 April 2020 & 2 June 2020 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PRISMA and Sentinel-2 acquisitions over Lake Trasimeno. Figure 1: True color images of Lake Trasimeno (**a**) PRecursore IperSpettrale della Missione Applicativa (PRISMA) (641.55 nm, 546.66 nm, 471.12, nm), (**b**) PRISMA resampled to Sentinel-2B (664.9 nm, 559 nm, 492.1 nm), and (**c**) Sentinel-2B (664.9 nm, 559 nm, 492.1 nm) acquired on 23 April 2020. The in-situ stations (St1, St2) are located on the left image. The open bay colonized by aquatic vegetation is highlighted by a red box [9]. Figure 2: Thematic representation of the PRISMA and Sentinel-2 spectral bands and spatial resolutions.