## 3 Results
### Assessing the Relationships between the Predictors for Different Vegetation Types  
First, we looked into (1) how satellite-retrieved SIF itself correlates with GPP from ground-based flux tower stations. Then, as shown in Figures 5-9, we estimated correlation and root-mean-square error (RMSE) for the following cases: (2) SIF-based GPP, (3) SIF- and precipitation-based GPP, (4) SIF-, precipitation- and soil-moisture-based GPP (i.e., MLR-based GPP). For the final case (5), we explored the SIF-precipitation-soil-moisture relationship using the lead-lag correlation analysis and its application for GPP quantification  
Figure 5 demonstrates correlation between GPP measured at the FLUXNET stations with C3 crop vegetation and GPP calculated with the use of the above-mentioned five combinations of predictors, over the entire vegetation period of a year, for 2007-2012. It can be noted that satellite SIF has a moderately strong relationship with FLUXNET GPP (Figure 5a), but the approach producing GPP estimates based on varying sets of predictors tends to yield better results, as expressed by improvements in the correlation coefficient \(R\): e.g., from 0.65 when SIF connection to FLUXNET GPP is considered (Figure 5a) to 0.68 for the case when SIF-based GPP and FLUXNET GPP are used (Figure 5b). One curious feature is related to the existence of a \"jump\" in GPP quantification quality  
Figure 4: Lead–lag relationship between SIF and plant water need based on soil moisture index calculated from ESA soil moisture data. Soil moisture index is calculated as \(1-\frac{SM-SM_{min}}{SM_{max}-SM_{min}}\), where \(SM\) is soil moisture value at any given day of the growing season, \(SM_{max}\) and \(SM_{min}\) are the highest and lowest soil moisture values during the growing season, respectively. The soil moisture index and SIF values are averaged over the study period of 2007–2012. Day 0 corresponds to April 1 st, which is considered the beginning of the growing season. SIF, soil moisture and NDVI values are estimated from grids of size \(0.5\times 0.5\), \(0.25\times 0.25\) and \(1\times 1\) km, respectively, surrounding US-Ne3 FLUXNET station (41.1797 °N, -96.4396 °E). US-Ne3 station has rotated crop assignments: soybean at even years and corn at odd years [90]. when precipitation data are taken into consideration: with the introduction of precipitation into MLR calculation, correlation coefficient \(R\) demonstrates an increase of 0.11 (from 0.68 to 0.79) as compared to the case using SIF data only (compare Figure 5b and Figure 5c); further addition of soil moisture leads to a relatively small increase in \(R\) (Figure 5d). However, the most significant rise in \(R\) is noted when the MLR equation is enhanced by the introduction of lead-lag: \(R\) increases from 0.82 to 0.98 (Figure 5e). Figure 6 illustrates changes in the tightness of the correlation between FLUXNET GPP and C3 grass GPP calculated with the use of the same methods as in Figure 5. Similarly to Figure 5, calculated GPP estimates and FLUXNET GPP become more significantly correlated as the independent variables are introduced; it is also shown that, initially, the correlation between SIF and FLUXNET GPP without any ancillary data is relatively high (\(R\) = 0.77, Figure 6a) while that for the case of C3 crops was only 0.65 (Figure 5a). A similar pattern of increasing correlation and decreasing RMSE is also noted for C4 grasses (Figure 7a-e); the MLR-based equation with the inclusion of the lead-lag relationship yields the maximum correlation (\(R\) = 0.99) between estimated and FLUXNET GPP values. One can also notice that grass and crop vegetation cases exhibit a slightly different response to the addition of predictor variables: C3 non-arctic and C4 grasses GPP values demonstrate a rather monotonic increase in correlation with FLUXNET GPP, with small incremental steps, and one significant increase when lead-lag is considered (compare Figure 6a-d and Figure 6e; Figure 7a-d and Figure 7e).