## 4 Discussion
Droughts generally affect vegetation through cumulative and lagged effects. Different vegetation types respond to a drought at different speeds. The response of grassland ecosystems to short-term droughts, for example, is more pronounced than that of other land types [51]. Regarding grasslands, the cumulative and lagged effects of droughts are mainly confined to shorter timescales (1-3 months), where the cumulative effect is stronger than the lagged effect [11]. Accordingly, we focused on the effects of the 1-month SVPDI and SSMI and their compound events on grassland ecosystems in the TRHR. The responses ofgrasslands to drought also differ within different types of climates. For example, grasslands in arid regions have a strong tolerance to droughts [11]. In the future, we may explore the impacts of different combinations of cumulative and lagged effects of atmospheric and soil droughts on vegetation growth. The compound drought definition utilized in this study was determined mainly from a temporally compounding perspective at a given grid. There are other events observable from a temporally compounding perspective; for example, sequential occurrences of different types of drought (i.e., the drought propagation perspective) [52]. These include atmospheric droughts in a given month and soil droughts in the following month. The sequential concurrence of different types of droughts can be as damaging to the photosynthetic capacity of vegetation as the concurrent different types of drought events. The effects of different temporally compounding events on SIF may be explored in our next study. Overall, SIF increased with precipitation (Supplementary Materials, Figure S5), temperature (Supplementary Materials, Figure S6), and SM (Supplementary Materials, Figure S7) in the TRHR, especially in July. [PERSON], et al. [53] pointed out that precipitation regimes mainly drive GPP variations across in the Tibetan Plateau, an influence that becomes more pronounced as climate change causes temperatures to warm. In mountain grassland regions, increased temperatures favor an earlier vegetation growth period and an increase in vegetation photosynthesis [54]. An increase in SM can enhance the maximum photosynthetic capacity of mountain ecosystems, thereby promoting vegetation growth [55]. Overall, the SIF showed a decreasing trend with an increasing VPD in the TRHR (Supplementary Materials, Figure S8). A high VPD can also limit vegetative photosynthesis due to high temperatures, and this negative effect of the VPD on the productivity of grassland ecosystems may be further enhanced in a warming world [9]. We analyzed the characteristics of SIF responses to different combinations of SVPDI and SSMI during the GS and July in the TRHR, respectively. In general, SIF trended upward with rising SM levels in July. This observation underscores the dominant role of SM in driving vegetation growth within the region, a finding that aligns with prior research [8; 55]. Strong land-atmosphere interactions fortified the negative VPD-SM coupling in the TRHR during July, thus increasing the probability of compound droughts. Compound droughts can significantly reduce carbon uptake in terrestrial systems compared with individual drought events, which would be especially problematic in the eastern parts of the TRHR (i.e., the Yellow River source region), where vegetation naturally flourishes. As the severity of compound droughts intensifies, the influence of reduced vegetation photosynthesis will become more pronounced in the Yellow River source region. A typical compound drought occurred in the Yellow River source region in July of 2017, driven by a precipitation deficit, high temperature, high VPD, and low SM (Supplementary Materials, Figure S9). This compound drought event resulted in a decrease of about 10% in the SIF throughout the region but was particularly pronounced in the south, which experienced a decrease of up to 20%. This substantial decline seriously threatened the carbon balance of the region's ecosystem.