## 3 Results
### Independent Effects of Atmospheric Drought on GPP
#### 3.4.2 Regulation of GPP by VPD Threshold Effects and Cumulative Drought Stress  
Building on the spatial heterogeneity analysis from ridge regression, we further revealed the systemic stress mechanisms of atmospheric drought on grassland productivity through dynamic fitting between VPD and ridge regression coefficients (\(a_{i}\)). Linear regression between the ridge regression coefficients (\(a_{i}\) for VPD) and VPD values revealed a significant negative correlation (\(y=-0.179\)x + 0.109, R\({}^{2}\) = 0.9575, Figure 8b), confirming that increasing atmospheric drought imposes systemic stress on grassland growth. Threshold analysis based on the linear regression model further indicated a critical VPD value of 0.61 kPa, defined as the x-intercept (i.e., where y = 0) of the fitted line beyond which ecosystem responses fundamentally shifted: within the low VPD range (\(\leq\)0.61 kPa), GPP was promoted, whereas exceeding this threshold resulted in GPP suppression. The linear regression approach was empirically justified by its strong explanatory power (R\({}^{2}\) = 0.9575) between ridge coefficients and VPD, and its direct quantification of the systemic stress response aligned with our objective to identify the tipping point (y = 0) where VPD transitions from promoting to suppressing GPP.  
The spatial distribution of the multi-year (2000-2020) average VPD revealed pronounced spatial heterogeneity across the study area (Figure 8a). The hatched regions in Figure 8a, representing major VPD contribution zones (from Figure 7a), are characterized by persistent atmospheric drought conditions. Notably, VPD values in these key areas exhibited a continuous upward trend, with increases in some locations already reaching the 0.61 kPa critical threshold. The sustained rise in VPD within high-contribution zones may progressively constrain the ecological resilience of grasslands. Analysis of the interannual variations in the main VPD contribution zones (Figure 8c) showed that the regional average VPD rose significantly from 0.66 kPa in 2000 to 0.74 kPa in 2008, representing an increase of 12.1%. Although the rate of increase in VPD slowed in the past decade (2010-2020), the ongoing upward trend remained significant, with short-term peaks frequently occurring within the fluctuation range (e.g., reaching 0.71 kPa in 2017). This phenomenon suggests that even with a deceleration in growth rate, the long-term cumulative effects of VPD may weaken the physiological resilience of grasslands through progressive stress. The regional average VPD (0.74 kPa) already exceeded the critical threshold of 0.61 kPa. Furthermore, the expanded fluctuation amplitude of VPD over the past decade (\(\pm\)0.05 kPa) led to an  
Figure 7: Analysis of ridge regression relative contribution rates. (**a**) Dominant factor spatial differences: the relative contribution rates of ridge regression were compared among the four meteorological factors, selecting the highest value for display. (**b**) Hierarchical contribution rates of factors: bar chart showing the proportion of calculation results for each meteorological factor.  
increased frequency of extreme drought events, necessitating caution regarding its potential disruption of ecosystem functions.