## 3 Results
### Response of NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\) to Climate Data
Figure 3: The spatial patterns of the partial correlation coefficients between NDVI\({}_{\text{max}}\) and VPD, and between GFP\({}_{\text{max}}\) and VPD, respectively, after excluding the effects of SM, temperature, precipitation, and radiation (**a**,**c**). The spatial patterns of the partial correlation coefficients between NDVI\({}_{\text{max}}\) and SM, and between GFP\({}_{\text{max}}\) and SM, respectively, after excluding the effects of VPD, temperature, precipitation, and radiation (**b**,**d**). The bar charts represent the respective frequency distributions, and the numbers indicate the proportions of the significant pixels. The spatial patterns of the climate factors correspond to the maximum absolute value of the partial correlation coefficient between NDVI\({}_{\text{max}}\) and GFP\({}_{\text{max}}\) (**e**,**f**), with the bar charts representing the proportion of the pixels for each climate factor. In this study, we performed a statistical analysis to examine the correlation between vegetation peak values (NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\)) and climate factors, SM, VPD, temperature, precipitation, and radiation, focusing on four distinct vegetation types: shrub (10.56%),  
Figure 4: The intensities of the sensitivity of each meteorological factor derived from the ridge regression. The spatial distribution of the sensitivities of NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\) to VPD (**a**,**c**) and the spatial distribution of the sensitivities of NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\) to SM (**b**,**d**). The colored areas in subfigures (**a–d**) represent the regions with significant partial correlation coefficients. The spatial patterns of the climate factors correspond to the maximum absolute value of the sensitivity between NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\) (**e**,**f**), with the bar charts representing the proportion of pixels for each climate factor. alpine meadows (25.57%), alpine steppe (27.94%), and alpine sparse vegetation (11.69%). The research findings indicated that among these four vegetation types, more than 57% of the pixels exhibited a positive correlation between NDVI\({}_{\text{max}}\) and SM, with 21% of them showing a noteworthy positive correlation. On the other hand, NDVI\({}_{\text{max}}\) and VPD typically exhibited a negative correlation, accounting for more than 54% of the pixels (see Figure 5a). The patterns of the correlation between GPP\({}_{\text{max}}\) and SM, as well as between GPP\({}_{\text{max}}\) and VPD, closely resembled those observed for NDVI\({}_{\text{max}}\) (Figure 5b). Importantly, there were variations in the correlations between the vegetation peak values and SM and VPD among the vegetation types. In particular, regarding the alpine meadows, close to 60% of the pixels showed a positive correlation between NDVI\({}_{\text{max}}\) and SM, while close to 55% of the pixels exhibited a negative correlation between NDVI\({}_{\text{max}}\) and VPD. This trend held true for GPP\({}_{\text{max}}\), with slight differences in the pixel distribution, but it was more pronounced in the alpine meadows than in the other vegetation types. We observed that NDVI\({}_{\text{max}}\) and GPP\({}_{\text{max}}\) exhibited certain relationships with hydrothermal conditions in terms of their responses to SM and VPD. In areas where the precipitation exceeded 200 mm, NDVI\({}_{\text{max}}\) and VPD exhibited a generally significant negative correlation, particularly in the precipitation ranges of 400-500 mm and 800-900 mm, where the negative correlation coefficients were higher. A positive correlation between NDVI\({}_{\text{max}}\) and VPD was only observed in a small portion of areas where the temperature was below 0 \({}^{\circ}\)C and precipitation was less than 200 mm (Figure 6a). Conversely, NDVI\({}_{\text{max}}\) generally showed a positive correlation with SM, with negative correlations appearing only in regions with high temperatures and precipitation (Figure 6b).