## 1 Introduction
As a result, the overlap between the FLUXNET2015 dataset and MODIS data products is up to 15 years (2000-2014), which makes it feasible to examine the VI-GPP relationship at the annual scale. Moreover, in most previous studies, satellite-derived VIs were calculated from surface reflectance that was not corrected with the bidirectional reflectance distribution function (BRDF). For a given ground object, the surface reflectance measured by satellites varies with changing illumination and viewing geometry (i.e., solar zenith angle, view zenith angle, and relative azimuth angle), leading to varying values in the resulting VIs [28]. The BRDF mathematically describes the surface reflectance as a function of sun-object-sensor geometry and can be used to standardize reflectance observations with varying sun-view geometries to a common standard geometry [29]. A large number of previous studies based on VIs (e.g., [8; 27]) made use of the AVHRR NDVI record, while this NDVI dataset is derived from surface reflectance that was not corrected with BRDF. The MODIS-derived VIs used in many studies [7; 30; 31] were also based on surface reflectance (e.g., the MOD09 and MYD09 products) that was not corrected with BRDF. Some previous studies reported that VIs based on BRDF-corrected reflectance exhibited better performances than the traditional VIs (i.e., VIs based on surface reflectance not corrected with BRDF) [1; 2]. For example, the BRDF-corrected NDVI and EVI had slightly stronger correlation with tower GPP than the traditional VIs. Recently, a new index based on BRDF-corrected reflectance, the near-infrared reflectance of vegetation (NIRv), was proposed [32]. NIRV is the product of the BRDF-corrected NIR reflectance and BRDF-corrected NDVI. NIRV represents the proportion of reflectance attributable to the vegetation from a physical perspective and has been shown to be better related to GPP than NDVI or NIR alone [32]. To our knowledge, no study has compared traditional VIs (i.e., VIs based on surface-reflectance that is not corrected with BRDF) against BRDF-corrected VIs for estimating GPP for a large number of sites across a wide variety of biomes at both seasonal and annual scales. The MODIS ASCII Subsets for BRDF-corrected surface reflectance products (e.g., MCD43A4) were not available until very recently. Prior the release of the Collection 6 MODIS ASCII Subsets in 2017, the MCD43A4 subsets for each EC site had to be extracted from entire MODIS tiles by the users, while extracting MODIS subsets for a large number of sites globally for multiple years is computationally intensive and time consuming. The recent release of the MCD43A4 subsets makes it feasible to extract BRDF-corrected surface reflectance and then to calculate BRDF-corrected VIs for a large number of sites in a timely fashion. The recent concurrent availability of FLUXNET and MODIS data for a large number of sites over a 15-year period (2000-2014) and the recent availability of the MODIS ASCII subsets for BRDF-corrected surface reflectance products provide an unprecedented opportunity to examine the relationships between satellite-derived VIs (both traditional and BRDF-corrected VIs) and tower GPP across a wide variety of biomes at various timescales. Here we examined the relationships between VIs and tower GPP for a total of 121 EC sites across the globe and assessed how the VI-GPP relationship varied among various VIs and a wide variety of biomes and at both monthly and annual timescales. We used three widely-used VIs: NDVI, EVI, and EVI2 along the new index - NIRV, and used surface reflectance products both with and without BRDF correction to calculate these VIs. Besides these six VIs, the new VI based on BRDF-corrected reflectance - NIRV was also used. To evaluate the usefulness of the VIs for estimating GPP, we also assessed the relationship between the MODIS GPP product and flux tower GPP for these sites. We then investigated the correlations of VIs with temperature and water stresses to reveal how VIs respond to temperature and water availability.