## Results
### Relationships between Vegetation Indices and Tower GPP
On average, the relationship was relatively strong for EBF (average R\({}^{2}\) = 0.42-0.72), COSH (average R\({}^{2}\) = 0.28-0.81), and WSA (average R\({}^{2}\) = 0.48-0.68), moderate for ENF (average R\({}^{2}\) = 0.16-0.34), GRA (average R\({}^{2}\) = 0.29-0.41), WET (average R\({}^{2}\) = 0.12-0.34), and CRO (average R\({}^{2}\) = 0.09-0.54), and relatively weak for DBF (average R\({}^{2}\) = 0.09-0.50) and MF (average R\({}^{2}\) = 0.02-0.32). For each biome, the R\({}^{2}\) value varied with VI, particularly for ENF, DBF, and COSH. We then examined the relationships between VIs and tower GPP across all sites for each biome (Figure 4; Table 1). For each site, annual tower GPP and annual mean VIs were separately averaged across all years. Overall, at the site level, tower GPP exhibited moderate to strong relationships with all or most VIs at the annual scale for all biomes except savannas. For savannas, tower GPP was weakly correlated with VIs, particularly NDVI, EVI, and NDVI\({}_{\rm IBRDF}\). The R\({}^{2}\) for the relationship between each VI and GPP varied with biome. There was no universally robust vegetation index that had strong correlation with tower GPP across all ten biomes. Notably, for all biomes except mixed forests, savannas, and croplands, the performance of NDVI, EVI2, EVI\({}_{\rm IBRDF}\), EVI\({}_{\rm 2 BRDF}\), and NIR\({}_{\rm V}\) in approximating GPP was comparable to MODIS GPP; for mixed forests, savannas, and croplands,  
Figure 2: The boxplots of the R\({}^{2}\) values for the relationships between MODIS-derived VIs and tower GPP at the monthly scale across all sites within each biome. The letters on the x axis stand for: A - NDVI, B - EVI, C - EVI2, D - NDVI\({}_{\rm IBRDF}\), E - EVI\({}_{\rm IBRDF}\), F - EVI\({}_{\rm 2 BRDF}\), G - NIR\({}_{\rm V}\), H - NIR\({}_{\rm V,BRDF}\), and I - MODIS GPP. The biome types are as follows: evergreen needleleaf forest (ENF); evergreen broadleaf forest (EBF); deciduous needleleaf forest (DNF); mixed forest (MF); closed and open shrublands (COSH); woody savannas (WSA); savannas (SAV); grasslands (GRA); wetlands (WET); croplands (CRO). these VIs was more strongly correlated with tower GPP than was MODIS GPP. In addition, at the annual scale, the BRDF-corrected VIs generally had similar performance in approximating GPP as VIs that were not adjusted with BRDF. For example, the traditional NDVI generally performed as well as NDVI\({}_{\text{BRDF}}\) in estimating GPP. For each biome, the annual VIs and tower GPP averaged across all years were further averaged across all the sites within the biome, and we then examined the relationships between VIs and tower GPP at the biome level (Figure 5). All VIs were strongly correlated with tower GPP across the biomes with R\({}^{2}\) ranging from 0.73 to 0.86. The biome averaged EVI had slightly weaker relationship with tower GPP (R\({}^{2}\) = 0.73, p < 0.0001) than did other VIs likely due to the low value of EVI in shrublands. Across the ten biomes, EVI\({}_{\text{BRDF}}\) (R\({}^{2}\) = 0.86, p < 0.0001) was more strongly correlated with tower GPP than was EVI (R\({}^{2}\) = 0.73, p < 0.0001), while NDVI\({}_{\text{BRDF}}\) and EVI\({}_{\text{BRDF}}\) had comparable performance in estimating GPP to NDVI and EVI, respectively. All the VIs except EVI were more strongly correlated with averaged tower GPP across the ten biomes than MODIS GPP. Figure 3: The bar graphs of the R\({}^{2}\) values for the relationships between the annual averaged VIs and tower GPP for all the sites with at least six years of flux data for each biome. The letters on the x axis stand for the R\({}^{2}\) values; the letters on the y axis stand for the sites. The asterisks - * and ** stand for the significance level p < 0.1 and p < 0.05, respectively. The biome types are as follows: evergreen needleaf forest (ENF); evergreen broadleaf forest (EBF); deciduous needleaf forest (DNF); mixed forest (MF); closed and open shrublands (COSH); woody savannas (WSA); savannas (SAV); grasslands (GRA); wetlands (WET); croplands (CRO).