## 2 Methods
### Selection of Vegetation Indices (VIs)  
At leaf and canopy scales, we resampled spectral reflectance for the following spectral bands of GCM-C/SGLI: blue (\(\rho_{\text{blue}}\); 438-448 nm), green (\(\rho_{\text{green}}\); 520-540 nm), red (\(\rho_{\text{red}}\); 663.5-683.5 nm), and NIR (\(\rho_{\text{NIR}}\); 858.5-878.5 nm), as summarized in Table 1. At the satellite scale, we used data from the MODIS sensor on board the TERRA satellite (MOD09A1.005; 8-day land-surface reflectance). The wavelengths of TERRA/MODIS are summarized in Table 1. We used MODIS sensor data in this study because MODIS is the most similar sensor to SGLI in that both have a short repeat cycle (2-4 days), wide swath (\(>\)2,000 km), high radiance resolution, moderate spatial resolution (1 km/250 m), and spectrally similar bands. Figure 1: Canopy light-response curve. Low-stress global gross primary production (GPP capacity) (mg\(\cdot\)CO\({}_{2}\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)) is the low-stress GPP, Pmax_capacity (mg\(\cdot\)CO\({}_{2}\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)) is the maximum GPP capacity under light saturation, and \(\alpha_{\text{slope}}\) is photosynthetic quantum efficiency representing the initial slope of the light-response curve. [PERSON] _et al._[50] suggested that chlorophyll concentration can be derived using reflectance at 550 nm (\(\rho_{\rm green}\)) and 675 nm (\(\rho_{\rm red}\)). For low chlorophyll concentrations, the reflectance sensitivity is higher at the maximum absorption located around 675 nm (\(\rho_{\rm red}\)). At medium to high concentrations, reflectance sensitivity is higher at 550 nm (\(\rho_{\rm green}\)). Thus, we selected several VIs that may relate to chlorophyll content. Moreover, it better to select the VI which has the best linear relationship with chlorophyll content to estimate GPP at the global scale. Because the uncertainty involved in aggregating remote sensing data from smaller to larger spatial scales (up-scaling) is related both to non-linearity in the response function and to heterogeneity within a site. When the response is non-linear, conventional averaging of reflected radiation gives a biased estimate of photosynthesis [49]. Spectral reflectance data were used to calculate VIs as illustrated in the following Equations (2) to (8):  
(1) The **NDVI**[55] is the most widely used index for many vegetation applications. However, the NDVI has a saturation problem with very dense vegetation. \[\rm{NDVI}=\frac{\rho_{\rm{NIR}}~{}-\rho_{\rm{red}}}{\rho_{\rm{NIR}}~{}+~{} \rho_{\rm{red}}} \tag{2}\]  
(2) The **enhanced VI (EVI)**[56] is an improved VI that accounts for the effects of residual atmospheric contamination and soil background. The EVI reduces the saturation problem in various canopies. \[\rm{EVI}=\frac{2.5(\rho_{\rm{NIR}}~{}-~{}\rho_{\rm{red}})}{(\rho_{\rm{NIR}}~ {}+~{}6\rho_{\rm{red}}-7.5\rho_{\rm{blue}}+1)} \tag{3}\]  
(3) The **modified NDVI (mNDVI)**[57] was developed to eliminate the effects of surface reflectance by incorporating the blue band. This VI is more strongly correlated with total chlorophyll and eliminates the effect of surface reflectance. \[\rm{mNDVI}=\frac{\rho_{\rm{NIR}}~{}-~{}\rho_{\rm{red}}}{\rho_{\rm{NIR}}~{}+~ {}\rho_{\rm{red}}-2\rho_{\rm{blue}}} \tag{4}\]  
(4) The **green and red ratio VI (GRVI)**[58] was proposed as an index to monitor the photosynthetically active biomass of plant canopies. The GRVI is calculated from the visible green and red reflectance. \[\rm{GRVI}=\frac{\rho_{\rm{green}}~{}-~{}\rho_{\rm{red}}}{\rho_{\rm{green}}~ {}+~{}\rho_{\rm{red}}} \tag{5}\]  
(5) The **simple ratio index (SR)**[59] is probably the first index and is the most commonly used to derive LAI for a forest canopy.