## 1 Introduction
Further, to assess the terrestrial carbon balance, gross primary productivity (GPP) and net ecosystem productivity (NEP) are often used to explore the relationships between droughts and carbon fluxes [6]. For example, [PERSON], et al. [23] assessed the carbon cycle response to extreme drought conditions in China from 2000 to 2015 based on GPP and NEP datasets, concluding that the Loess Plateau and a segment of the Tibetan Plateau suffered severe losses under extreme drought conditions. Chlorophyll fluorescence, the long-wave radiation emitted during vegetation photosynthesis, is also promising as an effective remote sensing indicator. Solar-induced chlorophyll fluorescence (SIF) is a significant optical indicator of photosynthetic status and associated stress effects in terrestrial vegetation [24]. SIF has heightened responsiveness to drought compared to traditional vegetation indicators and offers the unique capability to directly capture dynamic fluctuations during vegetation photosynthesis [18;25]. SIF is mechanistically related to photosynthesis and shows a nearly linear correlation with GPP, making it a suitable surrogate indicator for GPP at the ecosystem level. [PERSON] et al. [8] disentangled the relative roles of SM and the VPD in determining the response of vegetation (SIF) to drought using a decoupling method. They found that SM played a dominant role over the VPD in determining dryness stress impacting ecosystem productivity across terrestrial vegetated regions. However, previous studies have mainly focused on single sets of SIF data at large scales (typically around 0.5\({}^{\circ}\) spatial resolution) [8; 18; 26], with few studies on the response of vegetation photosynthesis to drought based on multiple high-resolution SIF datasets. This gap is particularly pronounced in terms of the response of SIF to compound droughts in mountain grasslands. The standardized precipitation evapotranspiration index (SPEI) can effectively reflect the dynamics of dry and wet conditions across multiple timescales [27]. Recently, scholars have explored the relationship between SPEI and SIF and analyzed the feedback characteristics of vegetation photosynthesis under drought conditions [11; 28]. For example, [PERSON] et al. [25] investigated the response characteristics of different vegetation types to drought in the Yellow River basin based on SPEI and SIF data, finding that the SIF of croplands responded to drought most rapidly, followed by grasslands and forest areas. Others have used VPD and SM datasets to investigate the responses of vegetation growth to droughts directly from the perspective of atmospheric and soil dryness [5; 8; 19]. The coupling effect of a high VPD and low SM is more obvious in warmer seasons [6], which increases the probability of simultaneous atmospheric and soil drought events, which exacerbate the adverse effects of droughts on terrestrial ecosystems. There is an urgent need for quantitative analyses of multiple SIF datasets with high spatial resolution under compound drought conditions at regional scales, particularly in alpine grasslands during the warmest months. In this study, we used the Three-River Headwaters Region (TRHR) as an illustrative case, representing the mountain grasslands in the lintlerlands of the Tibetan Plateau. Our objective is to build a comprehensive understanding of the response of vegetation photosynthesis to atmospheric drought, soil drought, and compound drought based on high-resolution gridded meteorological, SM, and SIF datasets. The primary goals of this work include (1) an exploration of atmospheric drought, soil drought, and compound drought, especially as they affect the vegetation growing season (GS); (2) an investigation of the changes in vegetation photosynthesis capacity during 2001-2020; and (3) an evaluation of SIF feedback characteristics to atmospheric drought, soil drought, and compound drought in the TRHR, especially during the hottest month (July). The compound drought criteria defined in this study can be applied to most regions of the world.