## Data and Methods
### Data Analysis  
Linear regression analysis and the coefficient of determination (\(R^{2}\)) metric were used to quantify relationships between tower GPP and GOME2 SIF monthly climatology records (\(n=12\)) at each tower location. Regression analysis and the Spearman correlation metric (\(r\)-value) were used to quantify the sign and strength of the relationships between SIF\({}_{\text{P}}\) and collocated Tmin, VPD, and SM records from MERRA2; here, regression analysis was used to evaluate relationships between SIF\({}_{\text{P}}\) and each climate variable while accounting for the influence of other covariates on the regression relationship.  
Figure 1: Location of carbon flux tower sites used for comparison with GOME-2 SIF and MERRA2 data records. Background land cover map represents IGBP land cover types from the MODIS MCD12 QI [36] land cover product. Dashed lines denote selected sub-regions used for evaluating spatially aggregated relationships between PAR-adjusted SIF (SIF\({}_{\text{P}}\)) and underlying moisture and temperature control factors influencing productivity.  
A climate aridity index (AI), defined as the ratio of annual precipitation to potential evapotranspiration (P/PET) [42], was used to characterize general climate aridity over the global domain. The AI follows United Nations Environmental Program (UNEP) defined aridity categories [36], including hyperarid (AI! 0.03), arid (0.03! AI! 0.20), semi-arid (0.20! AI! 0.5), sub-humid (0.50! AI!0.65), and humid (AI? 0.65) categories. Partial correlations were determined between \(\mathrm{SIF_{P}}\) and each climate variable for each tower site. The tower site results were then analyzed in two-dimensional climate space defined by the global AI and mean annual temperature distributions. The resulting relationships were assessed using a 95% (\(p<0.05\)) significance threshold.  
An analysis was conducted to identify the pattern of influence and relative impact of each climate variable in explaining spatial and seasonal variations in vegetation growth. Partial correlations were analyzed between \(\mathrm{SIF_{P}}\) and the monthly climate variables for each global grid cell. The monthly \(\mathrm{SIF_{P}}\) and climate variables were also spatially aggregated and analyzed for selected global sub-regions, including northern arctic, southern USA, southern Africa, African Sahel, eastern Amazonia, and central Australia (Figure 1).  
A generalized additive model [43] was used to define the smoothed curvilinear relationships between \(\mathrm{SIF_{P}}\) and each climate variable from the global record. The resulting productivity response to each climate variable indicated from the \(\mathrm{SIF_{P}}\) record was then compared with prescribed parameterizations of these response characteristics defined in the SMAP-LAC model product [15]. The SMAP-LAC global product is produced operationally using a satellite data driven LUE model to estimate daily GPP using MODIS vegetation and SMAP derived soil moisture observations as primary model drivers. The L4C model incorporates daily SM, VPD, and Tmin to define environmental reductions in LUE from prescribed optimal rates due to low soil moisture levels, excessive atmosphere moisture deficits, and cold temperatures. The LUE reduction is defined as the product of dimensionless environmental constraint factors ranging from 1 (no constraint) to 0 (fully constrained). Daily surface meteorological inputs to the L4C model are derived using a similar GEOS-5 land model as MERRA2, while the L4C response functions are calibrated from historical tower site observations representing major global biomass and plant functional types. All analyses were conducted in the R programing environment [44].