## 3 Results  
### Interdependency Analysis and Model Calibration  
The interdependency analysis between the in situ GPP and VIs showed that greenness-sensitive VIs derived the highest coefficients of determination. The CLr resulted in the highest correlation with GPP, with a coefficient of determination R\({}^{2}\) = 0.90 and statistical significance \(p\) < 0.05. The NDVI showed the lowest correlation among the greenness-related VIs with R\({}^{2}\) = 0.57. Water-sensitive vegetation indices did not show a high correlation with the GPP measurements. Among those, the NDII had the highest R\({}^{2}\) of 0.39 and a significance level of \(p\) < 0.05. Table 5 summarizes the results of the interdependency analysis, obtained using only SRS VIs.  
By including the EV in the model formulation, we observed an increase in the correlation with in situ GPP. In total 784 models (VI \(\times\) EV) were analyzed and the coefficient of determination was acquired for all the models. In general, the VIs showed a higher correlation when combined with rainfall-related variables in contrast with temperature or vapor pressure deficit data. The first fifty VIs and environmental variables combinations with higher correlation are displayed in Table 10. The product between the CLr and the rainfall data calculated with a rolling average of 90 days and delay of five months (RAIN_90_150)yielded the strongest correlation with an R\({}^{2}\) of 0.93. We, therefore, selected the CLr and the RAIN_90_150 for the model formulation (Equation (12)):  
\[\mathrm{GPP}=\mathrm{m}(\mathrm{CLr}\times\mathrm{RAIN\_90\_150})+\mathrm{b} \tag{12}\]  
where m and b represent the slope and intercept parameters of the linear model, estimated by means of the OLS method. The summary of the calibration process, including the parameter values and their corresponding significance levels, is displayed in Table 6.  
From the calibration process, an offset parameter b = 0.3308 and a scale parameter m = 3.3743 were derived. The final linear model for GPP prediction was, therefore, formulated as follows:  
\[\mathrm{GPP}_{\mathrm{model}}=3.3743(\mathrm{CLr}\times\mathrm{RAIN\_90\_150} )+0.3308 \tag{13}\]  
The scatter plot between the observed GPP values and the estimated ones is shown in Figure 6 together with the 95% confidence interval. It can be seen that the model performances were accurate with most of the points within the prediction interval.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Coef** & **Std Err** & **t** & **P \textgreater{} \text{\{t}}\textbackslash{}** & **0.025** & **0.975** \\ \hline Intercept & 0.331 & 0.061 & 5.420 & 0 & 0.210 & 0.451 \\ CLr \(\times\mathrm{RAIN\_90\_150}\) & 3.374 & 0.065 & 52.017 & 0 & 3.246 & 3.502 \\ \hline \end{tabular}
\end{table}
Table 6: Summary of model fit using the linear least-squared method from Statsmodels python tool. The table shows the coefficients of the linear model and their statistical significance.  
Figure 6: Scatter plot and corresponding regression line and 95% confidence interval for the relationship between the GPP calculated as the product between the Red-edge index (CLr) and the rainfall data calculated with a rolling average of 90 days and delay of five months (RAIN_90_150) and the ground measurements of GPP.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Vegetation Index** & **R\({}^{2}\)** \\ \hline CLr & 0.904 \\ \hline MNDVI & 0.899 \\ \hline EVI2 & 0.853 \\ \hline EVI & 0.853 \\ \hline NDVI & 0.576 \\ \hline NDIII & 0.358 \\ \hline LSWI & 0.329 \\ \hline MNDWI & 0.189 \\ \hline \end{tabular}
\end{table}
Table 5: Coefficient of determination between different VIs and in situ GPP.