## 3 Results
### Relationships between Air Temperature and GPP and Enhanced Vegetation Index (EVI)
One MODIS pixel (MSR, 500 m) often contains multiple crop fields, which could be cultivated with different types of crops or the same type of crop with different management practices, and thus reflects the spectral properties of mixed-crop fields and/or crops under various management practices [114; 115; 116]. For example, within the MODIS pixel for the USA sugarcane site, there were seven sugarcane fields at different stages in the crop cycle (e.g., fallow, recently planted cane, and ratooning cane) with different management practices, which may have affected the relationship between the MODIS-based VI values and the GPPE\({}_{\text{EC}}\). The results from this study showed that the relationships between the GPPE\({}_{\text{EC}}\) and EVI at the sugarcane plantations were stronger when the EVI was calculated from the Landsat/Sentinel-2 (HSR) images than when the EVI was calculated from the MODIS (MSR) images. Other studies have found similar results, highlighting the benefits of high-spatial-resolution images and their contribution to stronger correlations between carbon flux data and vegetation indices on grasslands and croplands [117; 118; 119]. This is important for estimating crop performance and vegetation health insurance indices over farms with multiple types of crops, rotations, and management techniques [119; 120; 121]. Sugarcane yields are affected by genotype, environmental conditions, and the time of harvest [122]. Our results showed that the EVI and LSWI tracked the phenological dynamics of sugarcane plantations well, providing a detailed cultivation history for the sugarcane at both plantations [123; 77; 31]. The LSWI was able to delineate the phenological metrics (SOS, EOS) and identify the harvest dates, consistent with previous studies on sugarcane and other crop types [124; 125; 35]. As the sugarcane plants at these two sites were harvested while they were still green, the unique phenomenon of the LSWI dropping to <0 reflected the physical system change from green sugarcane fields to brown crop residue and bare soils after harvest at both sites. The harvest date, or EOS, corresponded with the time of the initial negative LSWI value. Our results showed that the harvest dates at the Brazil and USA plantations were accurately recognized by the VI-based algorithms. However, these algorithms had limitations in identifying the SOS at the USA site, which was detected 2 to 4 weeks later across the three growing seasons. These differences could potentially impact the annual total vegetation carbon uptake in the fields. Note that the seasonal changes in GPPE\({}_{\text{EC}}\) and NEE\({}_{\text{EC}}\) could also be used to track and delineate the surface phenology of croplands in terms of physiology. The GPPE\({}_{\text{EC}}\) accurately tracked the vegetation carbon fixation period using the GPPE\({}_{\text{EC}}\)\(\geq\) 1 g C/m\({}^{2}\)/day criterion. Our results showed that the temporal agreement of the land surface phenology metrics derived from the VI-based and GPPE\({}_{\text{EC}}\)-based approaches was stronger for the USA site when the VI values from Landsat/Sentinel-2 (HSR) images were used, in part because the MODIS pixel at the USA site covered several crop fields. Finally, the results agreed well with other studies, like that of [PERSON] (2022) [76], which highlighted the potential of Landsat/Sentinel-2 images in representing planting patterns over agroecosystems. Finally, this study demon strated the capabilities and limitations of the VI-based method in determining the growing season length.