## Results  
### Relationships between Vegetation Indices and Tower GPP  
We examined the relationship between each VI and tower GPP at the monthly scale and calculated the coefficient of determination (R\({}^{2}\)) for each of the 121 flux sites. For each VI, the R\({}^{2}\) values were averaged over the 121 sites. On average, NDVI, EVI, EVI2, NIR\({}_{\text{V}}\), NDVI\({}_{\text{IRPDF}}\), EVI\({}_{\text{IRPDF}}\), EVI\({}_{\text{2 BRDF}}\), and NIR\({}_{\text{V, BRDF}}\) explained 55%, 48%, 66%, 67%, 56%, 62%, 70%, and 70% of the variance in GPP, respectively. Compared with the traditional VIs (NDVI, EVI, EVI2, and NIR\({}_{\text{V}}\)), the BRDF-corrected VIs (NDVIBRDF, EVI\({}_{\text{IRPDF}}\), EVI\({}_{\text{2 BRDF}}\), and NIR\({}_{\text{V, BRDF}}\)) generally exhibited stronger correlation with tower GPP, indicating that BRDF-corrected VIs had higher performance in estimating GPP than their traditional counterparts at the monthly scale. EVI\({}_{\text{2 BRDF}}\) (average R\({}^{2}\) = 0.70, p \(<\) 0.0001) and NIR\({}_{\text{V, BRDF}}\) (average R\({}^{2}\) = 0.70, p \(<\) 0.0001) had the strongest correlation with tower GPP. To evaluate the usefulness of the VIs for estimating GPP, we also examined the relationship between MODIS GPP and tower GPP for each flux site. NDVI (55%), EVI (48%), and NDVI\({}_{\text{IRPDF}}\) (66%) explained lower variance in tower GPP than did MODIS GPP (70%). By contrast, EVI\({}_{\text{IRPDF}}\), EVI\({}_{\text{2 BRDF}}\), and NIR\({}_{\text{V, BRDF}}\) explained the same proportion (average R\({}^{2}\) = 0.70, p \(<\) 0.0001) of the variance in tower GPP as did MODIS GPP (Figure 2), although the MODIS GPP is driven by incident photosynthetically active radiation (PAR), the fraction of PAR absorbed by vegetation canopies (fPAR), temperature stress, and water stress. We then stratified the 121 flux sites by biome type. For each biome, the R\({}^{2}\) values for the relationship between each VI and tower GPP were averaged over all the sites within the biome. The R\({}^{2}\) values for all the ten biomes and VIs are summarized in Figure 2. The performance of each VI generally varied with biome. On average, deciduous broadleaf forests (R\({}^{2}\) = 0.65-0.86, p \(<\) 0.0001), grasslands (R\({}^{2}\) = 0.62-0.72, p \(<\) 0.0001), mixed forests (R\({}^{2}\) = 0.57-0.86, p \(<\) 0.0001), evergreen needleleaf forests (R\({}^{2}\) = 0.47-0.82, p \(<\) 0.0001) and shrublands (R\({}^{2}\) = 0.17-0.77, p \(<\) 0.0001) had the strongest correlation, followed by woody savannas (R\({}^{2}\) = 0.31-0.61, p \(<\) 0.0001), savannas (R\({}^{2}\) = 0.35-0.63, p \(<\) 0.0001),wetlands (R\({}^{2}\) = 0.49-0.68, p \(<\) 0.0001) and croplands (R\({}^{2}\) = 0.44-0.58, p \(<\) 0.0001); evergreen broadleaf forests (R\({}^{2}\) = 0.18-0.53, p \(<\) 0.0001) had moderate correlation (Table 1). To examine the relationships between VIs and tower GPP at the annual scale, we identified those sites having at least 6 years of flux data from the 121 FLUXNET sites. A total of 48 sites had at least 6 years of data. For each site, we analyzed the relationships between VIs and tower GPP at the annual scale. For each VI, the R\({}^{2}\) values were averaged over all the 48 sites. On average, NDVI, EVI, EVI2, NIR\({}_{\rm V}\), NDVI\({}_{\rm IBRDF}\), EVI\({}_{\rm IBRDF}\), EVI\({}_{\rm BBRDF}\), NIR\({}_{\rm V,BRDF}\), and MODIS GPP explained 30%, 29%, 31%, 28%, 25%, 27%, 25%, 30%, and 23% of the variance in tower GPP. This indicates that VIs generally had weaker correlation with tower GPP at the annual scale than at the monthly scale. At the annual scale, the correlation of VIs with tower GPP was comparable to or slightly stronger than MODIS GPP (23%). Compared with the traditional VIs, the BRDF-corrected VIs had no advantage at the annual scale. The relationships between VIs and GPP varied with biome at the annual scale (Figure 3).