## 3 Results
### Relationships between Air Temperature and GPP and Enhanced Vegetation Index (EVI)  
Given the importance of the optimal temperature in multiple biophysical processes and the limited availability of these data, we assessed the relationships between the \(\mathrm{GPP_{EC}}\) and air temperature (T\({}_{\mathrm{DT}}\), T\({}_{\mathrm{DA}}\)) during the growing seasons (Figure 6), as this is one of the most reliable methods to estimate T\({}_{\mathrm{opt}}\). For the site in Brazil, \(\mathrm{tGP_{EC}}\) increased as the T\({}_{\mathrm{DT}}\) and T\({}_{\mathrm{DA}}\) rose and reached its plateau at -25 \({}^{\circ}\)C and 23 \({}^{\circ}\)C, respectively (Figure 6a,c). In the USA plantation, the \(\mathrm{GPP_{EC}}\) increased when the T\({}_{\mathrm{DT}}\) and T\({}_{\mathrm{DA}}\) rose and found its plateau at 28 \({}^{\circ}\)C and 26 \({}^{\circ}\)C, respectively (Figure 6b,d). Figure 5: **(Left panel): The relationship between the estimated gross primary production (\(\mathrm{GPP_{EC}}\)) and enhanced vegetation index derived from moderate-spatial-resolution images (MSR, MODIS) and high-spatial-resolution images (HSR, Landsat and Sentinel-2) within the growing season. (Right panel): 3 m 4-band planet Scope and 5 m RapidEye Ortho tile surface reflectance true-color images of vegetation cover in the Chacahoula, USA study area. The red circle represents the area used to obtain the time-series of HSR data. **  
We also studied the relationships between the vegetation index (EVI\({}_{\text{LS-S2}}\), EVI\({}_{\text{MODIS}}\)) and air temperature (T\({}_{\text{DT}}\) and T\({}_{\text{DA}}\)) (Figure 7) as a potential method to calculate T\({}_{\text{opt}}\). At the Brazil site, both EVI\({}_{\text{LS-S2}}\) and EVI\({}_{\text{MOD}}\) had weak but similar relationships with air temperature (T\({}_{\text{DT}}\) and T\({}_{\text{DA}}\)) (Figure 7a,b). For the T\({}_{\text{DT}}\), the EVI rose and peaked at 20 \({}^{\circ}\)C with a greater density of high values at 26 \({}^{\circ}\)C; the EVI reached its plateau at a T\({}_{\text{DA}}\) of 23 \({}^{\circ}\)C. The results at the USA location (Figure 7c,d) displayed high EVI values at 28 \({}^{\circ}\)C T\({}_{\text{DT}}\) and 25 \({}^{\circ}\)C T\({}_{\text{DA}}\). The results were consistent for both sites and similar for HSR EVI\({}_{\text{LS-S2}}\) and MSR EVI\({}_{\text{MOD}}\). EVI\({}_{\text{LS-S2}}\) reached a plateau at slightly warmer temperatures at both sites, but remained overall close to the EVI\({}_{\text{MOD}}\) (\(\sim\)0.15 \({}^{\circ}\)C). Following these results, the optimum air temperature (Topt) for modeling purposes was established as 25 \({}^{\circ}\)C (GPP-based) or 26 \({}^{\circ}\)C (EVI-based) for Brazil and 28 \({}^{\circ}\)C (GPP-based and EVI-based) for the USA. Figure 6: Relationships between estimated gross primary production (GPP_EC), mean daily temperature, and mean daily daytime temperature within the sugarcane growing seasons. (**a,c**) FAYS Brazil site, 2015–2017. (**b,d**) Chacahoula, USA site (2018–2020). Figure 7: Relationship between enhanced vegetation index derived from MODIS (EVI 500 m) and Landsat/Sentinel-2 (EVI 10 m) with mean daily air temperature and mean daily daytime temperature during the growing seasons. (**a,b**) FAYS Brazil site, 2015–2017. (**c,d**) Chacahoula, USA site (2018–2020). Comparison between GPP from VPM Simulations (\(GPP_{\text{VPM}}\)) and GPP Estimates from the Eddy Flux Sites (\(GPP_{\text{EC}}\))  
At the Brazil site, the seasonal dynamics of the \(GPP_{\text{EC}}\) and \(GPP_{\text{VPM}}\) agreed reasonably well (Figure 8a). The Pearson correlation coefficients and R\({}^{2}\) values indicated that there was a stronger relationship between the \(GPP_{\text{EC}}\) and \(GPP_{\text{VPM,LS-S2}}\) (r = 0.86, R\({}^{2}\) = 0.74) than between the \(GPP_{\text{EC}}\) and \(GPP_{\text{VPM-MOD}}\) (r = 0.78, R\({}^{2}\) = 0.62) (Figure 8c, Table 1). The seasonal sums of the \(GPP_{\text{EC}}\) and \(GPP_{\text{VPM}}\) within the sugarcane growing season differed noticeably (Table 2).