## 3 Results
### Relationships between Air Temperature and GPP and Enhanced Vegetation Index (EVI)
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Metric**} & \multicolumn{2}{c}{**Brazil**} & \multicolumn{2}{c}{**USA**} \\ \cline{2-5}  & \(GPP_{\text{EC}}\) **vs.** & \(GPP_{\text{EC}}\) **vs.** & \(GPP_{\text{EC}}\) **vs.** & \(GPP_{\text{EC}}\) **vs.** \\  & \(GPP_{\text{VPM-MOD}}\) & \(GPP_{\text{VPM,LS-S2}}\) & \(GPP_{\text{VPM-MOD}}\) & \(GPP_{\text{VPM,LS-S2}}\) \\ \hline
**R\({}^{2}\)** & 0.62 & 0.74 & 0.63 & 0.82 \\ \hline
**CC** & 0.78 & 0.86 & 0.79 & 0.90 \\ \hline
**MAE** & 2.96 & 2.03 & 2.21 & 1.83 \\ \hline
**NRMSE** & 0.23 & 0.17 & 0.16 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A comparison of statistical metrics from the correlation analyses between \(GPP_{\text{EC}}\) (g C m\({}^{-2}\) day\({}^{-1}\)) and \(GPP_{\text{VPM}}\) (g C m\({}^{-2}\) day\({}^{-1}\)) for the Brazil and USA sites. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Site**} & **GPP-Based** & \(GPP_{\text{EC}}\) & \(GPP_{\text{VPM-1S-S2}}\) & \(GPP_{\text{VPM-MOD}}\) \\  & **Growing Season** & **(g C m\({}^{-2}\) yr\({}^{-1}\))** & **(g C m\({}^{-2}\) yr\({}^{-1}\))** & **(g C m\({}^{-2}\) yr\({}^{-1}\))** \\ \hline \multirow{2}{*}{Brazil} & 11/05/2015–10/31/2016 & 2428 & 2688 & 2464 \\  & 11/16/2016–08/26/2017 & 1722 & 1817 & 1974 \\ \hline \multirow{2}{*}{USA} & 05/09/2018–09/22/2018 & 608 & 766 & 1102 \\  & 04/01/2019–11/11/2019 & 2304 & 2704 & 1728 \\ \cline{1-1}  & 04/09/2020–12/02/2020 & 2976 & 2688 & 1432 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Seasonal sums of \(GPP_{\text{EC}}\) and \(GPP_{\text{VPM}}\) during the growing the season defined by the GPP-based method and VI-based method at the Brazil and USA sites. Figure 8: GPP estimate time series from the EC flux sites (black line) and the VPM (HSR GPP in blue and MSR GPP in red). **(a)** FAYS Brazil site GPP time series estimates (2015–2017). **(b)** Chacahoula, USA site GPP time series estimates (2018–2020). Relationship between \(GPP_{\text{EC}}\) and the VPM (HSR GPP in blue and MSR GPP in red) **(c)** FAYS Brazil. **(d)** Chacahoula, USA site. At the USA site, the seasonal dynamics of the \(\mathrm{GPP_{EC}}\) and \(\mathrm{GPP_{VPM}}\) agreed reasonably well (Figure 8b). The \(\mathrm{GPP_{VPM,LS-S2}}\) values had a stronger relationship with the \(\mathrm{GPP_{EC}}\) (CC = 0.90, R\({}^{2}\) = 0.82) than the \(\mathrm{GPP_{VPM-MOD}}\) values did with the \(\mathrm{GPP_{EC}}\) (CC = 0.79, R\({}^{2}\) = 0.63) (Figure 8d, Table 1). The seasonal sums of the \(\mathrm{GPP_{EC}}\) and \(\mathrm{GPP_{VPM}}\) throughout the growing season also differed noticeably (Table 2). Seasonal Dynamics of ET as Measured at the Tower Site (ET\({}_{\mathrm{EC}}\)) and Transpiration as Estimated by VTM Simulations (T\({}_{\mathrm{VTM}}\))  
At the Brazil site, the seasonal dynamics of the \(\mathrm{ET_{EC}}\) and \(\mathrm{T_{VTM,EC}}\) agreed reasonably well (Figure 9a). The peak \(\mathrm{ET_{EC}}\) values ranged between 4 and 5 mm/day during December to February, while the peak \(\mathrm{T_{VTM,EC}}\) values varied between 2 and 3 mm/day for the same peak periods. The Pearson correlation coefficients and R\({}^{2}\) values indicated that there was a moderate relationship between the \(\mathrm{ET_{EC}}\) and \(\mathrm{T_{VTM,EC}}\) (\(p\) = 0.68, R\({}^{2}\) = 0.47) at the Brazil site (Table 3). The Brazil site had the worst performance of the two sites, as the VTM estimates had weak to moderate relationships with the \(\mathrm{ET_{EC}}\) and \(\mathrm{T_{VTM}}\), whereas these relationships at the site in the USA were moderate to strong. The \(\mathrm{T_{VTM-LS}}\) in Brazil (\(p\) = 0.45, R\({}^{2}\) = 0.21) had a stronger linear relationship than the \(\mathrm{T_{VTM-MOD}}\), which had the weakest correlation across the study (\(p\) = 0.09, R\({}^{2}\) = 0.009).