## 3 Results
### Relationships between Air Temperature and GPP and Enhanced Vegetation Index (EVI)
The \(\mathrm{ET_{EC}}\)/P ratio was consistently ~72.5% in Brazil during the study period, while the \(\mathrm{T_{VTM}}\):\(\mathrm{ET_{EC}}\) ratio for 2016 (complete calendar year) ranged between 64% and 75%, compared to the range of 78% to 95% for 2017 (only including data until August) (Tables 4 and 5). The USA site displayed stronger and clearer seasonal dynamics. It had peaks during the summer months, showing \(\mathrm{ET_{EC}}\) values ranging between 3 and 5 mm/day and \(\mathrm{T_{VTM,EC}}\) values between 2 and 3 mm/day (2018 and 2019), with higher rates in 2020 ranging between \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Site**} & **VI-Based** & **GPP\({}_{\mathrm{EC}}\)** & **GPP\({}_{\mathrm{VPM-LS-S2}}\)** & **GPP\({}_{\mathrm{VPM-MOD}}\)** \\  & **Growing season** & **(g C m\({}^{-2}\) yr\({}^{-1}\))** & **(g C m\({}^{-2}\) yr\({}^{-1}\))** & **(g C m\({}^{-2}\) yr\({}^{-1}\))** \\ \hline \multirow{2}{*}{Brazil} & 12/15/2015–10/23/2016 & 2263 & 2630 & 2312 \\  & 12/10/2016–08/26/2017 & 1642 & 1794 & 1952 \\ \hline \multirow{2}{*}{USA} & 05/22/2018–10/29/2018 & 599 & 700 & 1287 \\  & 05/25/2019–11/17/2019 & 1896 & 2256 & 1592 \\ \cline{1-1}  & 05/10/2020–11/06/2020 & 2696 & 2536 & 1280 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 9: \(\mathrm{ET_{EC}}\) estimate time series from the EC flux sites (black line) and the \(\mathrm{T_{VTM,EC}}\) (red line) for (**a**) the FAYS Brazil site and (**b**) Chachoula, USA. 3 mm/day and 4 mm/day. The year 2020 was the driest year, with an annual total P of 1438 mm, and 2019 was the wettest with a value of 1721 mm. This site displayed the strongest Pearson correlation coefficients and R\({}^{2}\) values of either site. For this site, the strongest relationship was between ET\({}_{\text{EC}}\) and T\({}_{\text{VTM\_LS-S2}}\) (\(p\) = 0.78, R\({}^{2}\) = 0.61), while the relationship between ET\({}_{\text{EC}}\) and T\({}_{\text{VTM\_MOD}}\) remained moderate (\(p\) = 0.72, R\({}^{2}\) = 0.52) (Table 3). Tables 4 and 5 display the results of the T\({}_{\text{VTM}}\) estimates derived using the GPP\({}_{\text{EC}}\) (T\({}_{\text{VTM-EC}}\)), GPP\({}_{\text{VTM-LS2}}\) (T\({}_{\text{VTM-LS2}}\)), and GPP\({}_{\text{VPM-MOD09}}\) (T\({}_{\text{VTM-MOD09}}\)). The ET\({}_{\text{EC}}\):P ratios had a similar magnitude over the years (45% to 51%), the T\({}_{\text{VTM-ET}}\) rates varied widely, with a 41% average for 2018, 79% average for 2019, and abnormally high average of 91% for 2020. MODIS images at daily and 8-day temporal resolutions can effectively track the seasonal variation and interannual dynamics of vegetation canopies [29; 107; 108; 109; 110]. In comparison, as Landsat and Sentinel-2 (HSR images) acquire images at multi-day intervals (for example, Landsat has a 16-day revisit cycle and Sentinel-2 has a 10-day revisit cycle), one sensor often cannot provide enough good-quality observations to track temporal changes in the vegetation canopy. A few studies have combined Landsat images and Sentinel-2 images to construct VI time series and then used them to track the seasonal dynamics of the vegetation canopy [111; 112; 113; 76]. In comparison to the MODIS time-series data, our results also showed that a combination of Landsat and Sentinel-2A/B images increased the number of good-quality observations, providing sufficient data to track the seasonal dynamics and interannual variation of the sugarcane canopy at the Brazil (tropical climate) and USA (subtropical climate) sites. Furthermore, our results indicated that despite the limitations of HSR data in tropical climates, the combined time series of the Landsat and Sentinel-2A/B images provided a better representation of the vegetation carbon uptake, with a linear relationship (R\({}^{2}\) = 0.74) stronger than the linear relationship between EVI\({}_{\text{MODIS}}\) and the EC site vegetation carbon uptake data (R\({}^{2}\) = 0.67).