## 4 Discussion
Although EVI2 contains the same information as NDVI, the additional weight on the red reflectance in the denominator allows EVI2 to be less sensitive to soil darkening [23], which explained why the EVI2 had the best performance in estimating GPP at the monthly scale among the traditional vegetation indices. Our results showed that NDVI\({}_{\text{BBDF}}\), EVI\({}_{\text{BBDF}}\), EVI\({}_{\text{BBDF}}\), and NIR\({}_{\text{V}}\) had stronger relationships with tower GPP than did NDVI, EVI, EVI2, and NIR\({}_{\text{V, BBDF}}\), respectively, at the month timescale, indicating that the correction of surface reflectance based on BRDF can improve the correlation between VIs and GPP. This finding is consistent with the results of a recent study [2] showing that NDVI\({}_{\text{BBDF}}\), EVI\({}_{\text{BBDF}}\), and had stronger relationships with tower GPP than did NDVI and EVI at the daily timescale. Changing illumination and viewing geometry (i.e., Solar Zenith Angle, View Zenith Angle, and Relative Azimuth Angle) can change satellite-measured surface reflectance [28] and the resulting VIs [46]. For example, changes in the sun-sensor geometry could alter EVI across the range of view zenith angles used for most land remote sensing [47]. Another previous study showed that NDVI was highly sensitive to solar zenith angle at intermediate LAI values (0.25-2.00) [48]. It should be noted that for MCD43A4 product, the solar zenith angle is at the local noon, meaning that the solar zenith angle is different at different sites. Moreover, BRDF effects are typically higher in the red wavelength than in the NIR wavelength [46]. Since NDVI captures the difference in reflectance between the NIR and red bands, the BRDF correction could likely alter the behavior of NDVI. Unlike NDVI, with the additional weight on the red band in the denominator, EVI and EVI2 with BRDF correction had varying behaviors because of low BRDF effects in the NIR wavelength and higher BRDF effects in the red wavelength [46]. As a result, the BRDF-corrected VIs performed better in estimating GPP than the traditional VIs without BRDF correction. The different performance of the EVI\({}_{\text{BBDF}}\) and EVI\({}_{\text{BBDF}}\) resulted from the different formula of the EVI and EVI2. By contrast, the BRDF-corrected VIs had no apparent advantage over the traditional VIs at the annual scale. This is likely because the BRDF effect depends on the sun-object-sensor geometry that changes with season, while the annually averaged sun-object-sensor geometry and BRDF effect do not exhibit interannual variations. Therefore, the correction of BRDF could improve the correlation between BRDF-corrected VIs and tower GPP at the monthly scale but not at the annual scale. Our results showed that VIs exhibited moderate to strong relationships with tower GPP for EBF, COSH, and WSA and weaker relationships for other biomes at the annual scale. The R\({}^{2}\) values for the relationship between the VIs and GPP differed among sites. We examined how the R\({}^{2}\) values varied with vegetation cover and water stress. For each site, the Vegetation Continuous Fields (VCF) product [49] derived from MODIS was used to extract the percent vegetation cover (the sum of percent tree cover and percent non-tree cover), and VPD from tower data was used a measure of water stress. The strength of the relationship between VIs and GPP (R\({}^{2}\) value) exhibited weak relationships with percent vegetation cover (Table S2) and moderately strong relationships with VPD (Table S3). This indicates that the relationship between VIs and GPP at the annual scale was more dependent on water stress than on vegetation coverage. The performance of the VIs in capturing the interannual variability of tower GPP was generally similar to that of the MODIS GPP product. There is no vegetation index that had strong correlation with tower GPP across all biomes at the annual scale. The correlation between the VIs and tower GPP at the annual scale was generally not as strong as that at the monthly scale for several reasons.