## 1 Introduction  
As highlighted in the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR6), the global surface temperature increased by 0.99 [0.84-1.1] \({}^{\circ}\)C during the years between 2001 and 2020 compared to the period of 1850-1900, with land areas experiencing more pronounced warming than oceans [1]. The frequency, duration, and intensity of global land-based droughts are projected to increase significantly under global warming, especially during the summer months [2;3]. These increasingly frequent and severe droughts pose substantial threats to the structure and function of terrestrial ecosystems [4;5]. In broader terms, soil drought and atmospheric drought are recognized as important factors affecting plant hydraulic processes and ecosystem productivity [5;6]. The significance of these drought types lies in their impact on vegetative photosynthesis. Plant roots extract water molecules from the soil, facilitating the process of vegetative photosynthesis. Soil drought, which is usually characterized by diminished available soil moisture (SM), signifies reduced water availability. This condition marks vegetation stress, which significantly impacts productivity [7;8]. Atmospheric drought, conversely, is defined by a high vapor pressure deficit (VPD), which causes plants to reduce water loss at the leaf level, thereby curtailing photosynthesis across the ecosystem [8;9]. Both soil and atmospheric droughts can significantly limit plant photosynthesis, consequently reducing terrestrial carbon uptake and crop yields. Grassland ecosystems are vital carbon sinks due to their capacity to absorb carbon dioxide through photosynthesis [10;11]. However, the susceptibility of grassland ecosystems to drought raises concerns regarding their potential transformation from carbon sinks to carbon sources. Such shifts have the potential to reshape the structure and functions of terrestrial ecosystems [12]. Notably, mountain grassland ecosystems are particularly sensitive to SM and temperature. The combined stress of low SM and elevated temperature, often accompanied by a high VPD, can severely impact vegetation growth [9;13]. Soil drought events reduce water uptake through plant roots, while atmospheric droughts prompt the closure of plant stomata, thus affecting vegetation photosynthesis. Interestingly, atmospheric droughts, often induced by heatwaves, can coincide with soil droughts. For example, the simultaneous occurrence of atmospheric and soil droughts in southern China during the 2019 summer-autumn transition season had severe repercussions for both crops and ecosystems [14]. The scientific community and the public alike are growing increasingly aware of such compound events, given their heightened capacity to inflict damage compared to singular or isolated events [15;16]. The alignment of atmospheric and soil droughts into a compound drought exemplifies this concept. A compound drought can significantly amplify the adverse consequences inherent to individual drought events. While previous research has centered on singular atmospheric drought or soil drought events over large scales (typically at spatial resolutions around 0.5\({}^{\circ}\)) or within specific small areas [9;11;17;18;19], research on compound droughts in grassland ecosystems is still very limited [5;6], especially in the case of mountain grasslands based on high-resolution data. Vegetation is a crucial component of terrestrial ecosystems, serving as a natural linkage connecting soil, atmosphere, and water dynamics. Modern advances in remote sensing technology have facilitated the utilization of various vegetation indicators, such as the normalized difference vegetation index (NDVI) and the leaf area index (LAI), for comprehensive vegetation monitoring. These indicators are advantageous in terms of their extensive spatial coverage and provision of continuous temporal observations [9;20;21;22].