## 2 Materials and Methods
### Performance Metrics  
Correlation was assessed using Pearson's \(r\) and Spearman's \(\rho\) coefficients. The former was calculated as  
\[r=\frac{\sum\Bigl{[}\left(l-\overline{l}\right)\left(\log(chla_{meas})-\overline{ \log(chla_{meas})}\right)\Bigr{]}}{\sqrt{\sum\Bigl{[}\left(I-\overline{l}\right)^ {2}\Bigr{]}\times\sum\biggl{[}\left(\log(chla_{meas})-\overline{\log(chla_{meas })}\right)^{2}\biggr{]}}} \tag{1}\]  
where \(l\) is the spectral index (i.e., the independent variable or predictor) and \(chla_{meas}\) is the measured in situ Chl-\(a\) concentration (i.e., the dependent variable or response). [PERSON]'s \(\rho\) coefficient was given by  
\[\rho=1-\frac{6\sum d^{2}}{n(n^{2}-1)} \tag{2}\]  
where \(d\) is the difference between a pair of ranks and \(n\) is the number of data. For both correlation coefficients, the values range from \(-1\) to \(1\). Statistically, a significant correlation exists when the absolute values of \(r\) and \(\rho\) fall within the range \(0.5\) to \(1\).  
Regression analysis is often used to assess the performance of semi-empirical RS-derived models against the water-truth parameters. Here, we employed the following metrics to assess the models' predictive capability [26; 51; 82]:  
\[RMSLE=\sqrt{\frac{1}{n}\sum\Bigl{\{}\left[\log(chla_{meas})-\log(chla_{mod}) \right]^{2}\Bigr{\}}} \tag{3}\]  
\[RMSE\ (\mu\text{g/L})=\sqrt{\frac{1}{n}\sum\Bigl{[}(chla_{meas}-chla_{mod})^{2} \Bigr{]}} \tag{4}\]  
\[Bias=10^{\lceil\frac{1}{n}\sum\left[\log\left(\frac{chla_{meas}}{chla_{mod}} \right)\right]\rceil} \tag{5}\]  
\[MAE=10^{\lfloor\frac{1}{n}\sum\left[\log\left(\frac{chla_{meas}}{chla_{mod}} \right)\right]\rceil} \tag{6}\]  
\[MAPE\ (\%)=100\times\frac{1}{n}\sum\Bigl{[}\frac{chla_{meas}-chla_{mod}}{chla_{meas }}\Bigr{]} \tag{7}\]  
\[MDAPE\ (\%)=100\times\widetilde{r} \tag{8}\]  
where \(\widetilde{r}\) is the median of \(\frac{\left|chla_{mod}(i)-chla_{meas}(i)\right|}{chla_{meas}((i))}\) where \(i=1,\ldots,n\)  
\[\varepsilon\ (\%)=100\times\left(10^{Y}-1\right) \tag{9}\]  
where \(Y\) is the median of \(\left|\log\Bigl{(}\frac{chla_{meas}}{chla_{mod}}\Bigr{)}\right|\)  
\[\beta\ (\%)=100\times\left(10^{Z}-1\right)\times sing(Z) \tag{10}\]  
where \(Z\) is the median of \(\left[\log\Bigl{(}\frac{chla_{meas}}{chla_{mod}}\Bigr{)}\right]\)  
\[R^{2}=1-\frac{\sum\Bigl{\{}\left[\log(chla_{meas})-\log(chla_{mod})\right]^{2} \Bigr{\}}}{\sum\Bigl{\{}\left[\log(chla_{meas})-\overline{\log(chla_{meas})} \right]^{2}\Bigr{\}}} \tag{11}\]  
where the \(\sum\) signs above denote summation over \(i=1,\ldots,n\). Generally, lower absolute values for the root-mean-squared logarithmic error (RMSLE), root-mean-squared error (RMSE), and mean absolute error (MAE) indicate better model performance, while highervalues for R\({}^{2}\) imply better goodness of fit. Bias values near one indicate little bias, while values above and below one indicate average under- and over-prediction, respectively. Mean absolute percentage error (MAPE) and median absolute percentage error (MDAPE) measure the percentage error, with 0% implying perfect prediction. Similarly, the metrics \(\epsilon\) and \(\beta\) report relative errors, with 100% indicating an accurate median prediction while values above (below) 100% indicate model overestimation (underestimation). Using these metrics together enabled a comprehensive model performance assessment. Note that, for some of the metrics, a base-10 logarithmic transformation was used to enhance data normality and reliability [51]. The overview of data and methodology and key steps is summarized in Figure 3.