## 3 Results
### The Independent Effects of RSM and PRE on GPP  
Utilizing the standardized anomalies of RSM and PRE, we partitioned the anomaly data, ranging from \(-2\) to \(2\), into eight discrete intervals of \(0.5\) units each. From these, four intervals exhibiting greater variability--specifically, \([-2,\,-1.5)\), \([-1.5,\,-1)\), \([1,\,1.5)\), and \([1.5,\,2]\)--were selected for detailed analysis. Within the \(SA_{PRE}\) intervals, characterized by the absence of coupling between RSM and PRE, the standardized anomaly of \(SA_{GPP}\) demonstrated an increasing trend concomitant with the rising standardized anomaly of \(SA_{RSM}\). Notably,  
Figure 4: **(a)** shows the spatial distribution of partial correlation coefficients between RSM and GPP. (**b**) displays the spatial distribution of partial correlation coefficients between PRE and GPP. (**c**) presents the spatial distribution of partial correlation coefficients between RSM and PRE. (**d**) The violin plots depict the correlation coefficients between RSM and GPP, PRE and GPP, and RSM and PRE. The red dots indicate the median, the boxes represent the interquartile range, and the thin lines extend to the 5 th and 95 th percentiles. in lower \(SA_{PRE}\) intervals, the rate of \(SA_{GPP}\) increase decelerated as \(SA_{RSM}\) rose, whereas in higher \(SA_{PRE}\) intervals, the rate of \(SA_{GPP}\) increase accelerated with increasing \(SA_{RSM}\) (Figure 6a). Examining the \(SA_{RSM}\) intervals, when \(SA_{PRE}\) values were positive, \(SA_{GPP}\) exhibited an upward trajectory with increasing \(SA_{PRE}\); however, in intervals of elevated \(SA_{RSM}\), this growth rate either diminished or plateaued. Conversely, when \(SA_{PRE}\) values were negative, \(SA_{GPP}\) displayed pronounced variability without a discernible trend as \(SA_{PRE}\) increased (Figure 6b). Collectively, these findings indicate that within the study region, in the absence of RSM-PRE coupling, elevated levels of either RSM or PRE independently contributed to enhancements in gross primary productivity. This suggests that the observed increases in \(SA_{GPP}\) are not solely attributable to the interaction between RSM and PRE. To assess the impacts of RSM and PRE on GPP within the study area, we independently quantified \(SA_{RSM}\) and \(SA_{PRE}\). As illustrated in Figure 6c, the mean \(SA_{GPP}\) was \(-0.2775\) when both \(SA_{RSM}\) and \(SA_{PRE}\) were below zero; \(-0.0246\) when \(SA_{RSM}\) was negative and \(SA_{PRE}\) positive; \(-0.0036\) when \(SA_{RSM}\) was positive and \(SA_{PRE}\) negative; and \(0.2749\) when both \(SA_{RSM}\) and \(SA_{PRE}\) exceeded zero. To further elucidate the predominant influences of RSM and PRE, we constrained the ranges of \(SA_{RSM}\) and \(SA_{PRE}\) as depicted in Figure 4d. Specifically, when \(SA_{RSM}\) was less than \(-1\) and \(SA_{PRE}\) greater than \(1\), the mean \(SA_{GPP}\) was \(-0.0876\), whereas when \(SA_{RSM}\) exceeded \(1\) and \(SA_{PRE}\) was below \(-1\), the mean \(SA_{GPP}\) reached \(0.2492\). These findings indicate that elevated levels of both RSM and PRE contribute to increases in GPP within the study area; however, \(SA_{RSM}\) exhibited a more pronounced positive effect on GPP compared to \(SA_{PRE}\). To validate these results, analogous analyses  
Figure 5: Absolute contributions of RSM, PRE, and RUM to GPP calculated via ridge regression; (**a**) spatial distribution of RSM’s absolute contribution to GPP; (**b**) spatial distribution of PRE’s absolute contribution to GPP; (**c**) spatial distribution of RUM’s absolute contribution to GPP; (**d**) pixel-level statistics of absolute contributions from RSM, PRE, and RUM to GPP across different land cover types. were conducted utilizing the MODIS GPP dataset, yielding consistent outcomes indicating that both high RSM and PRE enhance GPP.