## 3 Results and Discussion
### Use of SIF to delineate Highly Productive Agricultural Areas  
One vegetation type for which GPP was not well predicted by our global linear regression models is croplands with GPP \(>\)\(\sim\)15 (see Figures 3b and 4). An examination of these points shows that they are primarily from three sites in the U.S. Corn Belt (US-Ne1, US-Ne-2 and US-Ne3) that are frequently planted with maize, a C4 plant. [PERSON] et al. (2015) used various datasets to compute grid box fractions of C4 plants (natural and agricultural) for the VPM and defined different maximum efficiencies for C3 and C4 plants within their LUE formulation. The datasets used to compute C4 fractions were static (i.e., no interannual variability) and at lower spatial resolution than the VPM datasets. Here, we explore an alternative approach that uses satellite-based SIF to delineate highly productive regions. [PERSON] et al. (2015) demonstrated that SIF was more highly correlated with GPP than EVI at flux tower sites located in the U.S. Corn Belt because EVI, like NDVI, displays saturation at high values. They also showed that data-driven models, such as the predecessors of FLUXCOM-RS, did not produce the very high values of GPP derived from flux towers in this region. Global maps of SIF show very high values in summer in these same regions, while NDVI and EVI do not ([PERSON] et al., 2015). Here, we test the use of SIF observations, albeit at low spatial resolution (0.5\({}^{\circ}\)), to identify these regions of high productivity not prominent in the NDVI that may be related to large fractions of highly productive crops that are not well captured by the reflectances alone. Using collocated GPP, SIF and NDVI data, we found that the FLUXNET 2015 sites with high maximum GPP values that were not well fit using our single linear regression models displayed the following criteria of high NDVI and a large ratio of SIF to NDVI when normalized appropriately by PAR: specifically, NDVI\({}_{t}>\) 0.76 and \(\text{SIF}_{t}/(\text{NDIVI}_{t}\times\cos{(\theta)})>\) 3.0, where \(t\) is the month with the highest climatological value of NDVI and \(\theta\) is the average solar zenith angle for that month corresponding to the GOME-2 SIF observations. The climatological monthly means are computed over the years 2007-2016. Figure 5 shows a map of the areas detected with this approach. Adjusting the thresholds upwards resulted in somewhat less flagging over areas outside the U.S. Corn Belt (e.g.,  
Figure 4: Similar to Figure 3, but showing two-dimensional histograms of the eight-day averaged results for (**a**) two-band, (**b**) seven-band and (**c**) NDVI\({}^{\prime}\)-based GPP estimates at 0.00833\({}^{\circ}\) resolution, versus GPP from the FLUXNET 2015 dataset. Data are from 64 individual sites with 13,592 individual observations. Units of GPP are g C m\({}^{-2}\) d\({}^{-1}\). Eurasia) and vice versa. Additional flux tower sites in high productivity agricultural regions may help to further constrain the thresholds. To improve GPP estimates with the simple linear regression approaches, we separated the flux tower data into two different samples, one meeting the above criteria for high GPP and SIF and the other not. We then performed separate linear fits to the GPP data for these two subsets. The designated high productivity sites included in the training set were US-Ne1, US-Ne3 and DK-Fou, and the only site in the validation dataset was US-Ne2. Table 2 shows the results of the validation from this dual fit approach, henceforth referred to as NDVI\({}_{2}^{\prime}\) or 7 band\({}_{2}\). The statistics shown here are for daily data. We note significant improvement in metrics with flux tower GPP with dual fit as compared with the single fit models (null hypothesis rejected). These results demonstrate a clear capability of the satellite data to estimate GPP down to a daily time scale. Note that for the band models, the coefficients for each band in the calculation of FAPAR\({}_{\text{chl}}\) proxies in Equation (7) were estimated using all flux tower training data.