## 3 Results  
### Temporal Relationship between \(\mathrm{GPP_{VI}}\) and \(\mathrm{GPP_{EC}}\)  
Cloud cover affected the number of effective images of the sites, determining whether the gaps in the VI needed to be filled or not. The percentage of cloud-free pixels in the Sentinel-2 tiles of grassland sites was mostly less than 50%. In particular, at YNC, more than 70% of the data had \(P_{clar}\) values greater than 30%. However, the EBF sites contained much more cloud cover than did the GRA sites. At the TUM site, 10% of the data had less than 70% cloud cover (Figure 2). During the 16-day standard interval, the number of effective images was less than two at the grassland sites before the launch of Sentinel-2A (Figure 3). After the launch of Sentinel-2B, the networking system of Sentinel-2A and Sentinel-2B increased the number of effective images to four during the 16-day interval. The number of effective images at CUM also significantly increased (average from one image per month to two or more per month). During the end of winter to the early summer, the number of effective images after Sentinel-2B launched was two times more than when the images were obtained by Sentinel-2A alone. However, during the end of summer and early autumn at the TUM and WOM sites, there were almost no cloud-free images due to the rainy season in southeast Australia. Thus, although the networking Sentinel-2 system has a five-day revisit cycle, it cannot get low-cloud-cover images during continuously rainy days at the sites with humid summers. The general relationships between red-edge- and non-red-edge-related VIs derived from Sentinel-2 with \(\mathrm{GPP_{EC}}\) in the main footprint region of the flux towers at the EBF sites are shown in Table 3. These results show how much of the temporal variation in \(\mathrm{GPP_{EC}}\) can be captured by \(\mathrm{GPP_{VI}}\). Both red-edge VIs and non-red-edge VIs corresponded closely to \(\mathrm{GPP_{EC}}\) during the study period at the WOM and TUM sites. The WOM site showed the highest correlation between \(\mathrm{GPP_{VI}}\) and \(\mathrm{GPP_{EC}}\) across all VIs. The non-red-edge VIs, such as EVI and NIRv, explained more than 90% of the temporal variance in GPP, with an average rRMSE of approximately 11%. The red-edge-based \(\mathrm{GPP_{VI}}\), including \(\mathrm{CIr}\), \(\mathrm{CIg}\), \(\mathrm{MTCI}\), \(\mathrm{NDRE1}\), and \(\mathrm{NDRE2}\), showed \(R^{2}\) values of 0.87, 0.90, 0.83, 0.89, and 0.89 with \(\mathrm{GPP_{EC}}\), respectively. The TUM site also showed similar results, while the highest correlation between \(\mathrm{GPP_{VI}}\) and \(\mathrm{GPP_{EC}}\) in the red-edge VIs was found for \(\mathrm{MTCI}\) (\(R^{2}\) = 0.75, rRMSE = 0.18). The other red-edge VIs showed \(R^{2}\) values of 0.73, 0.70, 0.53, and 0.09 for \(\mathrm{NDRE1}\), \(\mathrm{NDRE2}\), \(\mathrm{CIr}\), and \(\mathrm{CIg}\) with \(\mathrm{GPP_{EC}}\), respectively. The non-red-edge-related VIs showed high relevance with \(\mathrm{GPP_{EC}}\) (average \(R^{2}\) = 0.73, rRMSE = 0.19). The CUM site showed a different result between the red-edge and non-red-edge VIs with \(\mathrm{GPP_{EC}}\). The \(\mathrm{GPP_{CIr}}\) and \(\mathrm{GPP_{Clg}}\) corresponded well with \(\mathrm{GPP_{EC}}\), with an average \(R^{2}\) of 0.56. However, other red-edge-related VIs (\(\mathrm{NDRE1}\), \(\mathrm{NDRE2}\), \(\mathrm{MTCI}\)) showed low correlation with \(\mathrm{GPP_{EC}}\). The non-red-edge VIs, including EVI, NDVI, and NIRv, showed \(R^{2}\) values of 0.38, 0.43, and 0.38 with \(\mathrm{GPP_{EC}}\), respectively. Table 4 shows the temporal relationship between different \(\mathrm{GPP_{VI}}\) and \(\mathrm{GPP_{EC}}\) at the grassland sites. At RIG, the red-edge VI-related \(\mathrm{GPP_{CIr}}\) and \(\mathrm{GPP_{Clg}}\) had \(R^{2}\) values of 0.87 and 0.84 with \(\mathrm{GPP_{EC}}\), respectively, whereas the non-red-edge VI-related \(\mathrm{GPP_{NIRv}}\) and \(\mathrm{GPP_{EVI}}\) also showed high \(R^{2}\) values of 0.86 and 0.77 with \(\mathrm{GPP_{EC}}\), respectively.