## 3 Results
### The Seasonal Dynamics of Climate, Vegetation Indices, and GPP at the Two Sugarcane Tower Sites
The differences in the GPP-based SOSGPP, EOS, GPP, and GSLGPP between these two sites are largely determined by the air temperature and management practice (e.g., harvest time) (Figure 2)  
Estimation of the Site-Specific Optimum Air Tmeperature (T\({}_{opt}\)) for GPP at the Two sugarcane Sites  
We assessed the biophysical performance of the vegetation indices at the sugarcane sites in terms of the GPP dynamics. Figure 4 shows the correlation between the GPPEC and vegetation indices (NDVI and EVI) during the sugarcane growing seasons at the two sites. The GPPEC has slightly stronger linear relationships with EVI (R\({}^{2}\) = 0.68 at the Brazil site and R\({}^{2}\) = 0.79 at the USA site) than with the NDVI (R\({}^{2}\) = 0.52 at the Brazil site and R\({}^{2}\) = 0.76 at the USA site) (Figure 4). The slightly lower R  
Figure 2: The seasonal variation in the daily mean air temperature (°C), rainfall, and photosynthetically active radiation (PAR) at the two sugarcane EC tower sites (8-day interval). (**a**) Brazil site, 2005–2007; (**b**) Louisiana site, USA, 2017.  
increased as the daily daytime mean air temperature or daily mean air temperature increased and reached its plateau at 28 \({}^{\circ}\)C (Figure 5b,d). We further investigated the effect of air temperature (daily daytime mean air temperature, daily mean air temperature) on the vegetation indices (NDVI and EVI) (Figure 6). The NDVI and EVI rose with the daily daytime mean air temperature and reached their plateau at 25 \({}^{\circ}\)C at the Brazil location and 25 \({}^{\circ}\)C for the USA location (Figure 6a,b). The NDVI and EVI were positively correlated with the daily mean air temperature and reached their plateau at 25 \({}^{\circ}\)C at the Brazil site and 28\({}^{\circ}\)C at the USA site (Figure 6c,d). For simulations of the VPM model (see Section 3.3), the optimum air temperature (T\({}_{\text{opt}}\)) at the Brazil site is set at 25 \({}^{\circ}\)C (both GPP-based and EVI-based) and the optimum air temperature (T\({}_{\text{opt}}\)) at the USA site is set 28 \({}^{\circ}\) C (GPP-based) or 25 \({}^{\circ}\)C (EVI-based), respectively, as part of a model sensitivity test. Seasonal Dynamics of GPP as Simulated by the VPM Model with the Climate Data from the EC Flux Tower Sites (GPP\({}_{\text{VPM-Site}}\))  
The seasonal dynamics of the GPP\({}_{\text{EC}}\) and GPP\({}_{\text{VPM-Site}}\) at the two sites agreed reasonably well with each other (Figure 7). At the Brazil site, the GPP\({}_{\text{VPM-Site}}\) increased rapidly in May 2005, maximized in December 2005, and fell below 1 g C m\({}^{-2}\)day\({}^{-1}\) by May 2006 after the harvesting of the sugarcane (Figure 7a). The GPP\({}_{\text{VPM-Site}}\) remained very small from May to October in 2006, and then rose in October and decreased by May in 2007 (Figure 7a). At the USA site, the GPP\({}_{\text{VPM-Site}}\) increased from April, reached maximum its value at August, and dropped by late December. The maximum daily GPP\({}_{\text{VPM-Site}}\) was slightly lower than the GPP\({}_{\text{EC}}\) for July-August (Figure 7b). There are strong linear relationships between the GPP\({}_{\text{EC}}\) and GPP\({}_{\text{VPM-Site}}\) in the sugarcane growing seasons at the two sites (Figure 7c,d). The linear regression models between the GPP\({}_{\text{EC}}\) and GPP\({}_{\text{VPM-Site}}\) indicate discrepancy at the Brazil site (2%) and the USA site (25\({}^{\circ}\)C, -9%; 28\({}^{\circ}\)C, -11%). The seasonal sum of GPP\({}_{\text{VPM-Site}}\) during the growing season defined by the GPP\({}_{\text{EC}}\) at the Brazil site during 2005/2006 and 2006/2007 was 3968 and 2868 g C m\({}^{-2}\) yr\({}^{-1}\), approximately 1.67% lower than the sum of the GPP\({}_{\text{EC}}\) in 2005/2006 (4035 g C m\({}^{-2}\) yr\({}^{-1}\)) and 0.95% higher than the sum of the GPP\({}_{\text{EC}}\) in 2006/2007 (2841 g C m\({}^{-2}\) yr\({}^{-1}\)) (Table 1).