## Appendix C Comparison of Results Using Different Radiation Input Datasets  
Estimates of the global monthly SW flux at the surface under all-sky conditions are provided in the Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) dataset at a \(1^{\circ}\times 1^{\circ}\) spatial resolution. The CERES temporal sampling is enhanced with the use of geostationary data. We used the Edition 2.8 CERES EBAF data.  
We also used daily-averaged surface all-sky incoming shortwave flux (SWGDN), as well as clear-sky shortwave flux (SWGDNCLR) from the NASA Global Modeling and Assimilation Office (GMAO) Modern-Era Retrospective analysis for Research and Applications 2 (MERRA-2) data assimilation reanalysis system [99]. These are two-dimensional fields from the radiation diagnostics. In addition, we computed daily TOA SW flux (SW\({}_{\rm TOA}\)) as being proportional to the cosine of the solar zenith angle (SZA) integrated over a day.  
To compare results with different radiation input datasets, we used monthly averaged GPP estimates provided in the FLUXNET 2015 dataset to train models of the form of Equation (2), where NDVI and NIR\({}_{V}\) computed from the MCD43D reflectances were used as simple proxies for FAPAR\({}_{\rm chl}\). Here, we assume that \(S\) (or LUE) is a constant. The NIR\({}_{V}\) is defined here as NIR\({}_{V}\) = (NDVI\(-\)0.08)\(\times\rho_{2}\) and is also evaluated without multiplication by radiation as in [PERSON] et al. [23].  
We first compare results using two different radiation input datasets: (1) surface short-wave flux from CERES (SW\({}_{\rm CERES}\)) in all-sky conditions and (2) SW\({}_{\rm TOA}\). Note that corresponding PAR values are simply proportional to these quantities; the latter is an approximation of PAR\({}_{\rm pot}\), defined as clear-sky PAR at the top-of-canopy, to be used in Equation (3). The main difference between SW\({}_{\rm TOA}\) and incident SW (or PAR) at top of canopy is the effect of the clouds.  
Table 14 shows that improved results are achieved using SW\({}_{\rm TOA}\) as compared with all-sky SW\({}_{\rm CERES}\) for both NDVI- and NIR\({}_{V}\)-based GPP estimates. These improvements are statistically significant. Similar improvements are obtained on daily results using MERRA-2 clear-sky SW (SWGDNCLR) as compared with all-sky estimates (SWGDN). We also compared the use of SWGDNCLR to SW\({}_{\rm TOA}\); note that SWGDNCLR accounts for clear-sky atmospheric scattering and absorption (but not clouds), while SW\({}_{\rm TOA}\) does not. Results using SW\({}_{\rm TOA}\) or SWGDNCLR were similar. Finally, we note that the use of NDVI\({}^{\prime}\) has a lower bias as compared with NDVI.  
Figure A4: Similar to Figure A2 (same data sample, eight-day at 0.00833\({}^{\circ}\) resolution at 64 sites), but with data corresponding to Figure 6. Units of GPP are g C m\({}^{-2}\) d\({}^{-1}\).  
Figure A7: Similar to Figure A2, but with eight-day anomalies corresponding to Figure 9 at 0.0833\({}^{\circ}\) resolution. Data are from 64 individual sites. Units of GPP are g C m\({}^{-2}\) d\({}^{-1}\).  
Figure A11. Similar to Figure A2 but with eight-day data at 0.00833\({}^{\circ}\) resolution corresponding to Figures 14 and 15. Units of GPP are g C m\({}^{-2}\) d\({}^{-1}\).