## Data and Methodology
### Framework for Quantifying GPP, SIF, Precipitation and Soil Moisture Relationships  
As stated in the introduction section, precipitation and soil moisture influence both SIF and GPP. Therefore, in order to avoid the replication of soil moisture and precipitation effects due to their multicollinearity, we have turned to multiple linear regression analysis. We have used the multiple linear regression method to estimate the relative importance of fluorescence, precipitation and soil moisture for GPP quantification. Multiple linear regression is a technique widely applied in the atmospheric sciences [79; 80; 81]. Multiple regression is an extension of linear regression with two or more predictor variables. It is also known to take into account the interdependence between independent parameters by regulating the weights assigned to them. The coefficients of independent parameters can be high but negative depending on the relationships between them [81]. This is due to the fact that the parameters can have a strong correlation with GPP while being not totally independent of each other. MLR accounts for this interdependence so that the impacts from precipitation and soil moisture are not replicated in SIF and GPP. The multiple linear regression equation is as follows  
\[Y=b_{0}+b_{1}x_{1}+b_{2}x_{2}+...+b_{p}x_{p} \tag{5}\]  
where \(Y\) is the predicted or expected value of the dependent variable, \(x_{1}\) through \(x_{p}\) are \(p\) distinct independent, or predictor, variables, \(b_{0}\) is the value of \(Y\) when all of the independent variables (\(x_{1}\) through \(x_{p}\)) are equal to zero, and \(b_{1}\) through \(b_{p}\) are the estimated regression coefficients [82]. To derive the equations, we used weekly averaged values of precipitation, SIF, soil moisture, and FLUXNET GPP in order to have a larger number of datapoints to achieve better statistical significance. A predictor contributing the most to the equation is automatically chosen at first and then other predictors are added until and unless a predictor is statistically insignificant. The relationship between SIF and GPP is deemed a biome-dependent one [29; 83]. Therefore, we have calculated the equations separately for both grass and crop vegetation types using remotely sensed SIF, precipitation and soil moisture data along with station-based GPP measurements. Our goal was to derive an equation that explains the relationships between the predicting parameters (SIF, precipitation, and soil moisture) and the predictant (GPP) the best in terms of standard error analysis and explained variance. Starting from a subset of one predictor (here, SIF), we have extended our analysis using a combination of two and three different predictors (for example, SIF and precipitation) to identify a subset of independent variables that maximizes the explained variance in GPP. We used a fraction of our data to derive MLR equations and the rest to validate the proposed equations--namely, we chose a combination of six FLUXNET stations with the longest record to derive the model and the remaining stations to validate it. This approach was chosen due to the fact that not all the FLUXNET stations in this study have a record over the entire period of interest, i.e., 2007-2012; e.g., Twitchell corn (US-Tw2) station has available data for the period of 2 years only. Using the explained variance, analysis of the error values, and the coefficient of correlation between predicted GPP and actual GPP, the equations were derived from the FLUXNET stations with C3 crop, C3 non-arctic grasses and C4 grasses. While estimating GPP within each grid cell, we multiplied GPP for grass and crop by corresponding plant functional type (PFT) fractions from Community Land Model (CLM) to avoid an overestimation of predicted GPP. This is because the amount of rainfall inside a grid cell is shared by different PFTs, and the recorded SIF is a combination of SIF emitted from vegetation belonging to different plant types.