## 3 Results
### Response of SIF to Compound Droughts  
The SVPDI and SSMI were found to be negatively correlated, especially in the 1-month SVPDI and 1-month SSMI for July and August (Supplementary Materials, Figure S3). This suggests a strong coupling between the SVPDI and SSMI in warmer seasons and a higher probability of simultaneous occurrence. We extracted valid grids with time period means greater than 0.01 mW\(\cdot\)m\({}^{-2}\cdot\)nm\({}^{-1}\cdot\)sr\({}^{-1}\) for SIF to calculate the SIF anomaly percentages corresponding to different drought thresholds. We divided the monthly SVPDI and SSMI into 8\(\times\)8 bins at 0.5 index value intervals, then assessed the SIF anomalies at different thresholds of compound droughts. As shown in Figure 11, low SSMI and low SVPDI combination events during the GS correspond to low SIF values. This may be due to the low SVPDI caused by low temperatures, thus limiting the growth of vegetation in the TRHR during the GS [6; 40]. High SVPDIs corresponding to high temperatures in the GS favor the growth of vegetation (i.e., promote photosynthesis) and thus correspond to positive SIF anomalies. The hottest month (July) was analyzed instead of the GS to find that a further increase in the SVPDI under relatively dry conditions corresponded to a decrease in SIF due to the closure of vegetative stomata, which prevents vegetative photosynthesis [6; 41]. Figure 10: Anomalies of air mean temperature and precipitation, (**a**) annual and (**b**) GS, across TRHR grasslands during 2001–2020. Red dotted lines and blue dotted lines indicate temperature and precipitation trends, respectively. Therefore, low SSMI and high SVPDI values corresponded to negative anomalies of SIF in July in the TRHR. The constraints imposed by elevated SVPDIs and diminished SSMIs in July on vegetation photosynthesis prompted a meticulous exploration of SIF anomalies within the TRHR. In scrutinizing the effects of atmospheric, soil, and compound droughts, we found that SIF exhibited negative anomalies in the central and eastern parts of the TRHR under atmospheric stress, which is particularly evident in the CSIF dataset (Figure 12a-c). In the western part of the region, atmospheric droughts did not cause a decrease in SIF, which was particularly evident in the RTSIF dataset. This phenomenon stems from the heightened SVPDI values attributed to warming temperatures, effectively alleviating temperature constraints within alpine ecosystems. This climatic shift facilitated vegetation growth by mitigating the temperature-induced restrictions, hence accentuating vegetative photosynthesis, as indicated by the elevated SIF levels. Warming also forces snow and ice to melt, which bolsters the SM available for vegetation to absorb. The area with declining SIF caused by soil drought was substantially larger than that caused by atmospheric drought (Figure 12d-f), which suggests that the mountain ecosystem is more constrained by SM  
Figure 11: Mean SIF anomalies for each index bin of SVPDI and SSMI across TRHR grasslands during 2001–2020. Rows represent changes in SIFs (CSIF, GOSIF, and RTSIF); columns represent changes in study periods (GS and July). than by atmospheric water demand during the hottest months. The areas with declining SIF caused by compound drought in the central and western parts of the TRHR occupy an intermediary position between the SIF reduction triggered by SIF caused by atmospheric drought and that caused by soil drought. Compound droughts in the eastern parts of the TRHR resulted in a significantly greater decrease in SIF than singular drought events. The eastern parts of the TRHR are characterized by a relatively low elevation and favorable thermal and hydrological conditions, which are beneficial for vegetative regrowth. Vegetation photosynthesis in the eastern parts of the TRHR was significantly weaker under compound droughts than under individual drought events due to land-atmosphere coupling in those areas (Figure 12g-i).