## 2 Materials and Methods
### Methods
#### 2.3.5 Interdependence Analysis and Model Calibration  
An analysis of interdependence was performed to assess the correlation between the calculated in situ GPP and the set of all the possible combinations of VI \(\times\) EV. The squared Pearson correlation coefficient (r\({}^{2}\)) was used to identify the product (VI \(\times\) EV) with the highest correlation selected for the final model formulation. The latest followed the linear formulation suggested by [PERSON] et al. [45] and used by [PERSON] et al. [25] reported in Equation (4):  
\[\mathrm{GPP}=\mathrm{m}\times(\mathrm{VI}\times\mathrm{EV})+\mathrm{b} \tag{4}\]  
where m and b are slope and intercept parameters, respectively, of the linear regression model. The Ordinary Least Squares (OLS) method was used to compute the parameters of  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Units** & **Description** \\ \hline AT\_MAX & \({}^{\circ}\)C & Maximum temperature \\ AT\_MIN & \({}^{\circ}\)C & Minimum temperature \\ AT\_MEAN & \({}^{\circ}\)C & Daily mean temperature \\ AT\_OSC & \({}^{\circ}\)C & Daily thermal oscillation \\ AT\_MEAN\_f * & \({}^{\circ}\)C & Daily mean temperature \\ VPD\_MEAN\_f & Pa & Daily mean of vapor pressure deficit \\ RAIN & mm & Daily rainfall \\ RAIN\_7 & mm & 30-days rainfall average \\ RAIN\_15 & mm & 60-days rainfall average \\ RAIN\_30 & mm & 30-days rainfall average \\ RAIN\_60 & mm & 60-days rainfall average \\ RAIN\_90 & mm & 90-days rainfall average \\ RAIN\_7N & mm & 7-day rainfall average with N-day lag \\ RAIN\_15\_N & mm & 7-day rainfall average with N-day lag \\ RAIN\_15\_N & mm & 15-day rainfall average with N-day lag \\ RAIN\_30\_N & mm & 30-day rainfall average with N-day lag \\ RAIN\_60\_N & mm & 60-day rainfall average with N-day lag \\ RAIN\_90\_N & mm & 90-day rainfall average with N-day lag \\ RAIN\_C & mm & Daily CHIRPS rainfall \\ RAIN\_C\_7\_N & mm & 7-day CHIRPS rainfall rolling average with N-day lag \\ RAIN\_C\_15\_N & mm & 15-day CHIRPS rainfall rolling average with N-day lag \\ RAIN\_C\_30\_N & mm & 30-day CHIRPS rainfall rolling average with N-day lag \\ RAIN\_C\_60\_N & mm & 60-day CHIRPS rainfall rolling average with N-day lag \\ RAIN\_C\_90\_N & mm & 90-day CHIRPS rainfall rolling average with N-day lag \\ \hline \hline \end{tabular} *  
the regression model. The OLS method is a statistical analysis aiming at deriving the m and b parameters of a linear model by minimizing the sum of squared errors, where the errors are the differences between the observed and predicted dependent variables. The m and b linear regression parameters were calculated using the OSL method with the following expressions (Equations (5) and (6)):  
\[\mathrm{m}=\frac{\mathrm{n}\Sigma\mathrm{x}\mathrm{y}-\sum\mathrm{x}\Sigma \mathrm{y}}{\mathrm{n}\Sigma\mathrm{x}^{2}-\left(\mathrm{x}\right)^{2}} \tag{5}\]  
\[\mathrm{b}=\frac{\mathrm{n}\Sigma\mathrm{x}^{2}\mathrm{y}-\sum\mathrm{x} \Sigma\mathrm{x}\mathrm{y}}{\mathrm{n}\Sigma\mathrm{x}^{2}-\left(\mathrm{x} \right)^{2}} \tag{6}\]  
where y is the independent variable (GPP), x is the dependent variable (VI \(\times\) E), and n is the number of data pairs. The estimation of the parameters was performed with a data set consisting of 80% of the original samples of in situ GPP. The statistical significance of the linear parameters and the overall model was evaluated with a confidence level of 95% (\(p\)-value < 0.05). In the case statistical significance was achieved, the model was accepted and used in the validation process.