## 3 Results and Discussion
### Comparing SIF and LUE Model Derived Bioclimatic Controls  
A generalized additive model (GAM) [55] was fit to the \(\text{SIF}_{\text{P}}\) data using each climate variable from the global record. The GAM adds smoothed non-parametric functions to the parametric part of a generalized linear model [55], allowing for greater flexibility and improved fit compared to generalized linear model [56]. A similar additive model approach was used to define the global relationship between each climate variable and the dimensionless (0-1) LUE model environmental  
Figure 5: The Red-Green-Blue (RGB) map showing the global pattern of relative influence of the three bioclimatic control variables on ecosystem productivity derived from partial correlations between \(\text{SIF}_{\text{P}}\) and VPD, SM, and Tmin monthly climatology records. Gray and white areas denote open water, barren land, and permanent ice, and snow areas are excluded from the study domain. response metric defined from the SMAP-L4C product [15]. The LUE model response functions for Tmin, VPD, and SM are prescribed for up to eight different plant functional types using a global land cover classification and general biome properties lookup table calibrated from sparse tower observations. The additive model results capture the smoothed response curves determined from the individual monthly \(\text{SIF}_{\text{P}}\) and model LUE response characteristics from every 0.5 degree grid cell within the global domain as defined from the MERRA2 climate record. The resulting \(\text{SIF}_{\text{P}}\) and LUE model global climate response relationships are presented in Figure 6. The \(\text{SIF}_{\text{P}}\) results indicate that productivity is directly proportional to VPD up to a level of approximately 1000 Pa, but with a rapid productivity decline at higher VPD levels until approximately 4000 Pa; a slight positive \(\text{SIF}_{\text{P}}\) response to more extreme VPD levels represents a small number of arid grid cells and may reflect greater SIF uncertainty in these sparsely vegetation areas. \(\text{SIF}_{\text{P}}\) is directly proportional to SM until the soil water content reaches approximately 70% of saturation, followed by a small productivity decline with higher moisture levels. The apparent \(\text{SIF}_{\text{P}}\) decline under wet soil conditions generally occurs in northern latitude boreal and tundra wetland complexes and may reflect greater soil nutrient limitations to plant growth under characteristically colder and wetter soil conditions in these areas [57]. The global \(\text{SIF}_{\text{P}}\) record shows a strong positive relationship with Tmin, consistent with stronger cold temperature constraints to productivity at lower temperatures. The slope of the \(\text{SIF}_{\text{P}}\) and Tmin relationship is also shallower below approximately 0.0 \({}^{\circ}\)C, indicating slowed biological processes and reduced vegetation activity under freezing temperatures. Overall, the resulting global response curves also indicate that VPD, SM, and Tmin respectively explain 42.7, 20.2, and 41.3 percent of \(\text{SIF}_{\text{P}}\) variability (\(p<0.001\)), respectively. The L4C results are generally consistent with the \(\text{SIF}_{\text{P}}\) response characteristics (Figure 6b), confirming global model parameterizations defined from sparse tower observations. However, there were also notable differences between the \(\text{SIF}_{\text{P}}\) and L4C derived curves. Unlike \(\text{SIF}_{\text{P}}\), the L4C results  
Figure 6: Global \(\text{SIF}_{\text{P}}\) and LUE model defined relationships with VPD, SM, and Tmin monthly climatology records; (**a**) Smoothed best-fit environmental response curves derived using a generalized additive model showing the relationship between \(\text{SIF}_{\text{P}}\) (\(y\) axis, normalized between 20 th and 90 th percentiles) and each climate variable (\(x\) axis) defined from all 0.5 degree global grid cells.