## 5 Conclusions  
Our study made the first comprehensive global analysis of how the traditional vegetation indices (NDVI, EVI, EVI2), BRDF-corrected vegetation indices (NDVI\({}_{\text{BRDF}}\), EVI\({}_{\text{BRDF}}\), EVI\({}_{\text{2 BRDF}}\)), and a newly proposed vegetation index - \(\mathrm{NIR_{V}}\) with and without BRDF correction (\(\mathrm{NIR_{V}}\), \(\mathrm{NIR_{V, BRDF}}\)) are related to tower GPP for a total of 121 sites encompassing ten biomes across the globe and at both monthly and annual scales. At the monthly scale, all the eight VIs were moderately or strongly correlated with tower GPP. Compared with the traditional VIs (NDVI, EVI, and EVI2), the BRDF-corrected VIs (\(\mathrm{NDVI_{BRDF}}\), EVI\({}_{\text{BRDF}}\), and EVI\({}_{\text{2 BRDF}}\)) generally had stronger correlation with tower GPP, indicating that the VIs based on BRDF-correction had an advantage over the traditional VIs. EVI\({}_{\text{BRDF}}\) and \(\mathrm{NIR_{V, BRDF}}\) had the strongest correlation with tower GPP (averaged \(\mathrm{R^{2}}\) = 0.70, \(\mathrm{p}\) \(<\) 0.0001), and their performance was comparable to the MODIS GPP product (averaged \(\mathrm{R^{2}}\) = 0.70, \(\mathrm{p}\) \(<\) 0.0001) based on a light use model. The VIs explained lower variance in tower GPP at the annual scale than at the monthly scale. BRDF-corrected VIs had no advantage over the traditional counterparts at the annual scale. The capability of the VIs in capturing the interannual variability in GPP was also similar to that of the MODIS GPP product. At the site level, VIs generally exhibited moderate to strong correlation with tower GPP at the annual scale for all biomes except savannas. Similar to the MODIS GPP product, all VIs were strong predictors of GPP at the biome level. Our results also showed that monthly VIs were also influenced by the environmental stresses (temperature stress and water stress). As with the MODIS GPP product, monthly VIs were more sensitive to temperature stress than to water stress. Our findings have implications for improving our understanding of the relationships between satellite-derived VIs and tower GPP, the influences of the BRDF effect on the VI-GPP relationship, and the variations of the VI-GPP relationship among indices, biomes, and timescales. The following are available online at [[http://www.mdpi.com/2072-4292/11/15/1823/s1](http://www.mdpi.com/2072-4292/11/15/1823/s1)]([http://www.mdpi.com/2072-4292/11/15/1823/s1](http://www.mdpi.com/2072-4292/11/15/1823/s1)). Figure S1: Flux tower GPP (\(\mathrm{GPP_{EC}}\)) and MODIS-derived VIs against latitude: (a) GPP; (b) VIs. There are no significant relationships between VIs (GPP) and latitude. Figure S2: Daily VIs, temperature, precipitation, temperature stress (\(\mathrm{f_{Topt}}\)) and water stress (\(\mathrm{f_{VPD}}\)) in croplands site (US-Ne1) in a normal period from August to September in 2003 and a drought period from June to July in 2004. Figure S3: VIs, temperature, precipitation, temperature stress (\(\mathrm{f_{Topt}}\)) and water stress (\(\mathrm{f_{VPD}}\)) at mixed forest site (BE-Vie) in a normal year (2010) and a low temperature year (2011). Figure S4: Daily VIs, temperature, precipitation, temperature stress (\(\mathrm{f_{Topt}}\)) and water stress (\(\mathrm{f_{VPD}}\)) in deciduous broadleaf forest site (DE-Hai) in a normal year (2003) and a relative low temperature year (2004). Table S1: List of 121 eddy covariance flux tower sites used in this study. IGBP refers to the International Geosphere-Biosphere Program land cover classification. ENF: evergreen needleleaf forest; EBF: evergreen broadleaf forest; DBF: deciduous broadleaf forest; MFN: mixed forest; OCSH: open and closed shrundbands; SAV: savannas; WSA: woody savannas; GRA: grassland; CRO: cropland; WET: wetland. Table S2: The correlation of \(\mathrm{R^{2}}\) of the relationships between VIs and tower-based GPP with vegetation coverage at the annual scale across all sites.