## 3 Results and Discussion
### The Use of Downscaled SIF to Estimate GPP  
[PERSON] and [PERSON] (2010) showed that SIF* agreed better with flux tower GPP as compared with MOD17 GPP (see Appendix A for a description of MOD17). Here, we further evaluate SIF* by comparing it consistently with the results of our models. We first verified that all of our models also outperformed MOD17 GPP on eight-day to monthly time scales in all statistical measures. Note that because SIF depends upon incident radiation, we did not explicitly use PAR in SIF-based models (other \begin{table}
\begin{tabular}{l c c} \hline \hline
**Input Dataset** & **Temporal Res.** & **Spatial Res.** \\ \hline MCD43D reflectances \({}^{a}\) & daily & \(0.0083^{\circ}\times 0.0083^{\circ}\) \\ GOME-2 SIF \({}^{b}\) & monthly & \(0.05^{\circ}\times 0.05^{\circ}\) \\ GOME-2 SIF \({}^{c}\) & monthly & \(0.5^{\circ}\times 0.5^{\circ}\) \\ VPM GPP \({}^{d}\) & monthly & \(0.05^{\circ}\times 0.05^{\circ}\) \\ FLUXCOM GPP \({}^{d}\) & 8 day & \(0.083^{\circ}\times 0.083^{\circ}\) \\ \(\mathrm{NIR}_{V}\times\mathrm{SW}_{\mathrm{TOA}}\)\({}^{b,e}\) & any of the above & any of the above \\ NDVI \(\times\mathrm{SW}_{\mathrm{TOA}}\)\({}^{b,e}\) & any of the above & any of the above \\ FLUXNET 2015 GPP \({}^{f}\) & daily, monthly & site footprint \\ \hline \hline \end{tabular} \({}^{a}\) Used to compute FAPAR proxies such as NDVI, \(\mathrm{NIR}_{V}\) and linear combinations of channels; \({}^{b}\) used as a GPP proxy with optional LUE parameterization; \({}^{c}\) used to identify highly productive regions optionally; \({}^{d}\) used for benchmark evaluation; \({}^{e}\) computed using MCD43D reflectance dataset; \({}^{f}\) half of sites used for training, the other half used for independent evaluation.  
\end{table} 
Table 1: Summary of input datasets used for GPP estimation and evaluation with their native spatial and temporal resolutions (Res.). than to normalize it appropriately as described above); here, we simply applied a single scaling factor to SIF* at monthly time-scales to estimate GPP globally. The assumption of a single scaling factor to relate SIF to GPP, at least encompassing many plant functional types, has been suggested [53; 74]; however, the use of a single scaling factor was not generally supported by previous studies (e.g., [46]). We examine monthly SIF* along with NDVI\({}^{\prime}\) and NIR\({}_{V}\) results in more detail in Figure 3 by comparison with tower-derived GPP for years 2007-2013 when GOME-2 SIF v25 data were available. Note that the resolution for SIF* was 0.05\({}^{\circ}\), while the MCD43D reflectances had been resampled to 0.083\({}^{\circ}\); note that the MCD43D results were degraded as compared with the \(\sim\)1 km\({}^{2}\) results in Table 14, which were much closer to the footprint of the eddy covariance technique [34]. While the positive SIF* bias was clearly seen at GPP values near zero, SIF* was shown to have a more dynamic range as compared with the NDVI\({}^{\prime}\)-based GPP estimates; NDVI\({}^{\prime}\)-based GPP estimates tended to saturate at around 10 g C m\({}^{-2}\) d\({}^{-1}\); while SIF* and NIR\({}_{V}\)-based estimates reached values close to 15 g C m\({}^{-2}\) d\({}^{-1}\). SIF* appeared somewhat noisier than the NDVI\({}^{\prime}\)- or NIR\({}_{V}\)-based GPP estimates. This was expected as the downscaled SIF was directly tied to the more coarsely-gridded GOME-2 SIF that was inherently noisy due to the very small SIF signal. Correlations were significantly different between all three models (i.e., null hypothesis rejected) with \(p\)-values \(<\) 0.0001. The apparent noise in SIF* may also have resulted from the effects of vegetation structure on the escape of SIF through the canopy [75; 76]. We attempted to account for the variations in canopy escape as suggested by [PERSON] and [PERSON] [76] using MODIS Band 2 (near infrared) reflectance for normalization. However, we did not find improvement in the global statistics.