## 1 Introduction  
Alpine grasslands, covering 67% of the Qinghai-Tibet Plateau, are crucial to terrestrial ecosystems, influencing ecological dynamics and carbon cycling through processes like photosynthesis, respiration, and transpiration [1, 2, 3, 4]. Net primary productivity (NPP) reflects carbon fixation by plants, minus autotrophic respiration, and serves as a key indicator of ecosystem productivity and health [5, 6, 7]. Water-use efficiency (WUE) is the ratio of carbon fixed by vegetation to water consumed, represented as NPP/ET, and reflects the ability of plants to fix carbon under specific water consumption conditions [8; 9]. Studying the WUE of alpine grasslands not only helps us to understand the changes in vegetation carbon-water coupling in these ecosystems but also allows for an exploration of how alpine grassland ecosystems respond to climate change and water stress. This research provides a reliable basis for the management of alpine grassland ecosystems. The impact of WUE on vegetation growth is primarily reflected in the ecological and physiological processes of vegetation. With changes in precipitation, temperature, and other climatic factors, along with the increase in the atmospheric CO\({}_{2}\) concentration, the ecological and physiological processes of vegetation are affected, primarily including transpiration, respiration, and photosynthesis. This enhances the carbon absorption rate of vegetation, thereby influencing its carbon-fixation capacity during growth and development [10; 11; 12; 13; 14; 15; 16]. Warming accelerates vegetation greening, which in turn increases spring ET, resulting in a greater depletion of soil moisture and intensifying summer drought. Consequently, vegetation growth becomes constrained by drought stress and, due to water shortage, droughs can directly inhibit plant growth or even lead to plant mortality [17; 18]. During the growth and development of vegetation, stomatal conductance regulates photosynthesis and transpiration. As stomatal conductance increases, both the assimilation rate of CO\({}_{2}\) and water loss through transpiration rise simultaneously [19; 20]. However, since the diffusion resistance of CO\({}_{2}\) is only 0.64-times that of water vapor, an increase in stomatal conductance leads to relatively higher water loss, thereby reducing vegetation WUE. In addition to stomatal transpiration, vegetation also loses water through cuticular transpiration. Notably, C\({}_{4}\) plants lose about 100 molecules of water per molecule of fixed CO\({}_{2}\), whereas C\({}_{3}\) plants are less efficient, losing approximately 600 molecules of water per CO\({}_{2}\) fixed [21; 22]. In alpine ecosystems, there is controversy regarding the response of WUE to environmental factors such as temperature, precipitation, and radiation. Under the context of climate change, precipitation and temperature are the primary climatic factors influencing variations in WUE. An increase in precipitation not only enhances soil moisture, which in turn promotes soil water evaporation, but also higher air humidity helps to maintain a higher stomatal conductance, making photosynthesis more efficient in vegetation [23; 24]. For instance, a study by [PERSON] et al. [25]. suggested that the WUE in grasslands of Inner Mongolia, China, increases with precipitation. However, the response of WUE to precipitation differs under varying climatic conditions. Studies have shown that under arid conditions, WUE initially increases and then decreases [26]. Temperature influences vegetation growth and physiological activities by regulating the activity of enzymes within the plants. A rise in temperature increases stomatal conductance (gs) of vegetation [27]; when the increase in photosynthetic rate (Pn) is relatively higher than the rise in gs, WUE correspondingly increases. However, when the temperature exceeds a specific threshold, transpiration becomes stronger than photosynthesis, leading to a decrease in WUE [28].