## 3 Method
### Adaptation of WASI for Processing PRISMA and Sentinel-2 Imagery
Then, the forward model simulates the reflections at the water surface based on a three-component model for the sky radiance \(L_{sky}(\lambda)\) reflected in the viewing direction [59; 74]:  
\[ \begin{split}& R_{\text{rs}}^{\text{surf}}(\lambda)=\rho_{L}( \theta_{v})\times\frac{L_{sky}(\lambda)}{E_{dd}(\lambda)+E_{dsr}(\lambda)+E_{ dsu}(\lambda)},\\ & L_{sky}(\lambda)=g_{dd}E_{dd}(\lambda)+g_{dsr}E_{dsr}(\lambda) +g_{dsa}E_{dsa}(\lambda).\end{split}  \tag{6}\]  
where \(\rho_{L}(\theta_{v})\) is the Fresnel reflection for a viewing angle of \(\theta_{v}\)[75]. Direct downwelling irradiance from the sun disk, diffuse downwelling irradiance caused by Rayleigh scattering, and diffuse downwelling irradiance caused by aerosol scattering are indicated by \(E_{dd}(\lambda)\), \(E_{dsr}(\lambda)\), and \(E_{dsa}(\lambda)\), respectively. Figure 3: The specific absorption spectrum of phytoplankton \(a_{\text{phy}}^{*}(\lambda)\) measured in Lake Trasimeno [62]. These three components can be parametrized in terms of aerosols, water vapor, and ozone [76; 77]. The intensities of these irradiance components reflected in the sensor direction are given by the weighting factors \(g_{dd}\), \(g_{dsr}\) and \(g_{dsa}\). The weights can be variable on a pixel-by-pixel basis depending on the water surface status (roughness of the surface). We assume fractions of sky radiance due to molecule and aerosol scattering \(g_{dsr}=g_{dsa}=1/\pi\) as per a hypothetic isotropic sky. The fraction of sky radiance due to direct solar radiation \(g_{dd}\) is treated as a fit parameter. The forward modeling (i.e., simulation of \(R_{rs}(\lambda)\) using Equation (1) is performed in an iterative process by varying the fit parameters. At each iteration, the agreement between the simulated spectrum \(R_{rs}^{simulated}(\lambda)\) and the measured spectrum \(R_{rs}^{measured}(\lambda)\) is assessed using a cost function. The process stops when the cost function reaches a minimum. Thus, the fit parameters minimizing the cost function are considered as output retrievals. Here, a least-square cost function (\(\Delta\)) is considered to minimize the difference between the simulated and observed spectrum:  
\[\Delta\ =\ \frac{1}{N}\sum_{i=1}^{N}\bigl{|}R_{rs}^{measured}\bigl{(}\lambda_ {i}\bigr{)}-R_{rs}^{simulated}\bigl{(}\lambda_{i}\bigr{)}\bigr{|}^{2}. \tag{7}\]  
where \(\lambda_{i}\) is the central wavelength of band number \(i\). and \(N\) is the total number of spectral bands. WASI is flexible in parametrization and a variety of parameters can be iterated through the inversion. However, it is necessary to limit the number of fit parameters as much as possible to enhance the reliability of the retrievals by reducing spectral ambiguities. This is because some combinations of parameters may exhibit similar spectral characteristics. Thus, only the parameters with major impacts on the water-leaving spectra should be iterated. The choice of parameters and their initial values can be assisted by a pre-knowledge about the study area and/or a pre-fit analysis. The pre-fit analysis can be done by performing the inversion for a few representative pixels with different parametrization/initialization [78].