## 3 Method
### Sentinel-2 Consistency Analyses  
Since the launch of the first MSI onboard Sentinel-2A (2015), there has been significant interest in analyzing water quality parameters in inland waters due to its suitable spatial (10-20 m), temporal (2-3 days with twin MSIs), spectral (13 bands), and radiometric (12 bit) characteristics. In this  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fit Parameter** & **Initial Value** & **Min** & **Max** & **Units** & **Description** \\ \hline \(C_{NAP}\) & 7 & 0 & 100 & g m\({}^{-3}\) & Concentration of NAP \\ \hline \(C_{phy}\) & 5 & 0 & 1000 & mg m\({}^{-3}\) & Concentration of phytoplankton \\ \hline \(a_{CDOM}(440)\) & 0.2 & 0 & 50 & m\({}^{-1}\) & Absorption coefficient of CDOM at 440 nm \\ \hline \(g_{dd}\) & 0.02 & \(-1\) & 10 & sr\({}^{-1}\) & Fraction of sky radiance due to direct solar radiation \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fit parameters and associated initial values for water quality inversion using Water Color Simulator (WASI).  
context, we perform consistency analyses to gain more insights into the agreement between the water quality products (\(R_{rs}\) and constituents) derived from Sentinel-2 images with those derived from the newly available hyperspectral images from PRISMA. In this context, we synthesize Sentinel-2 images by spectral convolution of the hyperspectral PRISMA images with MSI spectral response function. Therefore, the PRISMA and synthesized Sentinel-2 images differ only in terms of the spectral resolution. We use also real Sentinel-2 images with the closest overpasses for the agreement analyses. We perform a spatial resampling (from 20 m to 30 m) of the Sentinel-2 images and co-registered them with those derived from PRISMA to enable the comparison. The comparisons of the \(R_{rs}\) or constituent products are performed based on averaging the values within windows of 10 \(\times\) 10 pixels. This averaging reduces the effect of co-registration mismatches and the noise [28]. The extracted values from two corresponding constituent maps or \(R_{rs}\) images are regressed against each other to compute agreement statistics. The agreement analyses are performed based on several metrics including the correlation coefficient (R), root mean square difference (RMSD), bias, and mean absolute difference (MAD) [79]:  
\[RMSD=\left(\frac{\sum_{i=1}^{n}\left(E_{i}^{h}-E_{i}^{k}\right)^{2}}{n}\right) ^{1/2} \tag{8}\]  
\[bias=10\frac{\sum_{i=1}^{n}\left(log_{10}(E_{i}^{Sens-1})-log_{10}(E_{i}^{Sens- 2})\right)}{n} \tag{9}\]  
\[MAD=10^{\frac{\sum_{i=1}^{n}\left[log_{10}(E_{i}^{Sens-1})-log_{10}(E_{i}^{Sens -2})\right]}{n}} \tag{10}\]  
\(E_{i}^{h}\) and \(E_{i}^{k}\) are the estimates obtained from sensors \(h\) and \(k\). \(h\) and \(k\) can be PRISMA, synthesized Sentinel-2, and Sentinel-2 in different combinations. \(n\) is the number of image samples. Note that aquatic products are log-transformed for estimation of bias and MAD and these two metrics are dimensionless [79]. For instance, a bias of 1.3 indicates that the estimates of \(h\) are 30% greater than those of \(k\) on average. MAD always exceeds unity and indicates a relative difference of the estimates from two sensors (e.g., MAD = 1.5 indicates a relative difference of 50% between the estimates of \(h\) and \(k\)). Note that the retrievals over the open bay (Figure 1a), i.e., affected by the aquatic vegetations, shoreline pixels, and cloud-shadow pixels are excluded from the statistical analyses since they are less reliable. Boxplots are used to compare the distribution and range of the parameters.