## 3 Results and Discussion
### Regional Scale Analysis of Bioclimatic Factors  
We analyzed partial correlations between spatially averaged monthly \(\mathrm{SIF_{P}}\) and climate records within six sub-regions (Figure 1) representing a range of global climate and land cover diversity. The partial correlation results for the six sub-regions are presented in Figure 4. The AI was used to show the proportional area of each region characterized by different climate aridity categories [52]. The direction and strength of the correlations between \(\mathrm{SIF_{P}}\) and the different climate variables for each sub-region varied in accordance with regional differences in vegetation and climate conditions, consistent with the tower site results. The \(\mathrm{SIF_{P}}\).SM relationship is congruent with climate aridity and showed direct correspondence in dry biomes, inverse relationships in humid biomes, and intermediate (+/ -) correlations in areas with a seasonal dry climate. In Arctic tundra, characterized by an extended winter cold season, \(\mathrm{SIF_{P}}\) follows Tmin and VPD seasonal cycles, but it is inversely correlated with SM. In central Australia, which has a relatively warm and arid climate, \(\mathrm{SIF_{P}}\) follows the seasonal cycle in SM and shows inverse and relatively weak correlations with VPD and Tmin, despite having similar IGBP land cover conditions as tundra. In the southern US, which has a predominantly semi-arid climate, \(\mathrm{SIF_{P}}\) is significantly correlated with multiple climate variables, but is directly proportional to soil moisture during the growing season. In the semi-arid African Sahel, soil moisture has a dominant influence on \(\mathrm{SIF_{P}}\) and is the most significant variable controlling productivity. \(\mathrm{SIF_{P}}\) has a positive but relatively weak correlation with Tmin and a negative correlation with VPD, which is of secondary importance after  
Figure 3: Partial correlations between \(\mathrm{SIF_{P}}\) and moisture and temperature variables affecting productivity (VPD, SM, Tmin) for selected global carbon flux tower sites. The Spearman correlation coefficients for each tower site are superimposed on global climate space defined by mean annual temperature and climate aridity (AI). The AI and annual temperature distributions of all grid cells within the global domain are also plotted, where darker and lighter shading denotes respective higher and lower cell densities. The boxplots show the spatial variability in tower site \(\mathrm{SIF_{P}}\) correlations for VPD (\(\mathrm{SIF_{P}}\).VPD), SM (\(\mathrm{SIF_{P}}\).SM), and Tmin (\(\mathrm{SIF_{P}}\).Tmin) by land cover class. Only tower sites with statistically significant correlations (\(p<0.05\)) were used in the analysis (2, 6, and 3 sites did not show statistically significant correlation with VPD, SM, and Tmin, respectively).  
soil moisture in influencing productivity in the Sahel. In southern Africa, which is also predominantly semi-arid, productivity is still strongly and directly proportional to soil moisture, while the other climate variables have a significant but weaker influence on productivity. In eastern Amazonia, \(\text{SIF}_{\text{P}}\) shows enhanced productivity from July to October, consistent with increasing photosynthetic activity during the dry season [53; 54]; in this humid tropical region, \(\text{SIF}_{\text{P}}\) is directly proportional to VPD and negatively correlated with SM and Tmin.  
Figure 4: Monthly variability in \(\text{SIF}_{\text{P}}\) and associated climate variables for VPD, SM, and Tmin for the selected global sub-regions. The dominant IGBP land cover categories within each sub-region are also shown. Annotations show the partial correlation matrix between \(\text{SIF}_{\text{P}}\) and the different climate variables. The AI annotations show the relative proportion of different climate aridity categories in each sub-region.