## 4 Discussion
To estimate GPP at the global scale, we prefer the VI which has linear relation with chlorophyll content and Pmax_capacity2000. If we use the VI which has exponential relation with chlorophyll content and Pmax_capacity2000, it may cause big error in high chlorophyll content or Pmax_capacity2000 region. In big VI region, and with exponential form VI, small error of VI makes big error of chlorophyll content and Pmax_capacity2000. Therefore, we selected VIs that had linear correlations with Pmax_capacity2000. The Clgreen showed a strong linear correlation (R\({}^{2}>0.67\)) with Pmax_capacity2000 for each of the plant functional types and did not have saturation problems in various plant-canopy structures. Linear correlations between remote sensing-obtained VI values and GPP from local flux measurements were found in North American vegetation [83], evergreen needle leaf forests [84], deciduous broadleaf forests [85], and Amazon rainforests [86]. However, these studies did not use GPP in low-stress conditions and the linear regressions showed some scattered data [51]. In Figure 10, linear correlations were observed at every site except US-Dk1 and TH-SKR. US-Dk1 has a spatial resolution problem with MOD09. US-Dk1 covers approximately 480 \(\times\) 305 m, which is less than the MOD09 1-km spatial resolution [87]. Furthermore, the Clgreen range of 3.5-6.5 is relatively high for grassland, suggesting contamination by light reflected from surrounding evergreen and deciduous forests. Similarly, linear correlations were not found at TH-SKR, where Clgreen and large photosynthetic capacity changed less year-round. These results indicate that when canopy greenness is stable, other meteorological factors will play limiting roles for GPP [42]. The maximum and minimum of Pmax_capacity2000 at TH-SKR in 2003 were 1.37 and 0.94 mg\(\cdot\)CO\({}_{2}\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\), respectively. These results are consistent with those of [PERSON] _et al._[88], who reported that maximum and minimum values of the saturation point of photosynthesis (GPPmax) at TH-SKR in 2003 were 1.54 and 0.82 mg\(\cdot\)CO\({}_{2}\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\), respectively. Tropical forests have the least seasonality in terms of carbon absorption, emission, and greenness [89]. JP-FJY is generally classified as a needleleaf evergreen forest, but seasonal changes in leaves occur. Our results agree with those of [PERSON] _et al._[90], who found that the seasonal change in LAI at JP-FJY ranged from 3 to 5. Needle-fall and expansion mainly occurred in November and May, respectively. The LAI increased rapidly in early May, reached a maximum in midsummer, and then decreased from September to November. Moreover, for further global GPP estimation, we may use the same empirical linear equation for evergreen forest sites JP-FJY and TH-SKR (Pmax_capacity2000 = 0.001 \(\times\) CIgreen + 0.006; R2 = 0.44, P<0.01). Pmax_capacity2000 can be converted to the maximum incident LUE (GPP/PAR) as shown in Figure 10. Observed CI represents different growth states and is related to seasonal changes of incident LUE in a similar manner as for wheat [38]. This method has good potential for estimating seasonal changes of maximum incident LUE from CIgreen. Our Pmax_capacity2000 estimation concept is more similar to the greenness and radiation (GR) model [37, 39, 42] than to the LUE model. However, the framework for the estimation of GPPcapacity differs from those of both the GR and LUE models. The GR and LUE models assume a linear relationship between GPP and incident PAR or PAR during an integral time such as 1 day or 1 month. Our GPP capacity estimation framework introduced a non-linear relationship between photosynthesis velocity and PAR. Pmax_capacity was the parameter of the photosynthesis response curve (Equation (1)) and was estimated from CIgreen. Using this parameter, the photosynthesis response curve was determined. Using the response curve and PAR data, the velocity of GPPcapacity was estimated.