## 3 Results
### Response of NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\) to Climate Data  
After controlling for the effects of SM, temperature, precipitation, and radiation, a negative correlation between NDVI\({}_{\text{max}}\) and VPD was noted in the TP. Notably, approximately 11.51% of the significant negative correlations were mostly in the northeast and southwest areas, while a significant positive correlation of 8.38% was observed (Figure 3a). This suggested an overall detrimental effect of higher VPD on NDVI\({}_{\text{max}}\). Conversely, upon eliminating the impacts of VPD, temperature, precipitation, and radiation, roughly 57.46% of the pixels exhibited a positive relationship with SM, with 12.61% indicating a significant positive correlation (\(p<0.05\), Figure 3b). These regions were primarily scattered across the eastern, central, and southwestern areas of the TP. Instances of significant negative correlations were less prevalent (6.59%) and were mostly observed in some central and western regions. This implied that higher SM was conducive to vegetation growth in the central TP. Compared with NDVI\({}_{\text{max}}\), GPP\({}_{\text{max}}\) displayed similar responses to VPD and SM. After the influence of SM, temperature, precipitation, and radiation was mitigated, GPP\({}_{\text{max}}\) exhibited a negative correlation with VPD. Among the significant correlations (18.29%), negative associations accounted for 61.55% (Figure 3c). These notable negative correlations were mainly observed in the central and northeastern portions of the TP, indicating an overall adverse effect of higher VPD on GPP\({}_{\text{max}}\). Conversely, after the effects of VPD, temperature, precipitation, and radiation were eliminated, GPP\({}_{\text{max}}\) exhibited a positive correlation with SM. Approximately 19.21% of the pixels within the research region demonstrated a significantly biased correlation (Figure 3d), among which 12.65% displayed a notable positive correlation, and were mostly in the central and eastern regions. The remaining pixels exhibited a notable negative correlation (6.57%). This finding underscores the favorable impact of elevated SM on GPP\({}_{\text{max}}\). As can be seen from Figure 3, temperature, precipitation, and radiation played important roles in both NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\), which is consistent with other research results. Furthermore, from the distributions in the figures and the bar charts, it is evident that among the meteorological factors most strongly correlated with NDVI\({}_{\text{max}}\), SM accounted for 16.83% and VPD accounted for 16.85% (Figure 3e). For the meteorological factors most strongly correlated with GPP\({}_{\text{max}}\), SM accounted for 12.38% and VPD accounted for 13.49% (Figure 3f). It can be seen that the correlation between SM and VPD on peak vegetation growth was as important as precipitation and radiation. Figure 4 shows the ridge regression coefficients for the regions with significant partial correlation coefficients, which represent the intensity of the sensitivity. It can be seen that the spatial distribution of the sensitivities of SM and VPD to NDVI\({}_{\text{max}}\) was similar to the spatial distribution of the partial correlation, and the distribution of GPP\({}_{\text{max}}\) also showed a similar trend (Figure 4a-d). Furthermore, when comparing the sensitivities of the various meteorological factors to vegetation growth peaks, SM accounted for 15.76% of the most sensitive factors for NDVI\({}_{\text{max}}\), while precipitation accounted for 17.55% (see Figure 4e). For GPP\({}_{\text{max}}\), SM represented 15.55%, and precipitation accounted for 11.12% (see Figure 4f). This indicates that the sensitivities of SM and precipitation to vegetation growth peaks are consistent, further supporting the results of the strongest correlation.