## 1 Introduction  
One of the fundamental components of the ecosystems on Earth is water. The spatial differentiation of water resources is a key factor determining the regional characteristics of vegetation and influencing the differentiation of total primary productivity [1; 2; 3]. The two fundamental functions of ecosystems are material cycling and energy conversion. Vegetation plays a pivotal role in the composition of ecosystems, influencing the carbon and water cycles and exerting a profound influence on a multitude of processes, including soil, water, and air [4; 5]. Among these, photosynthesis, transpiration, and respiration in plants represent the fundamental physiological and ecological processes. Not only does photosynthesis provide plants with a substantial quantity of oxygen, but it also serves as the primary energy source for transpiration. Concurrently, in plants, respiration and transpiration provide sufficient carbon dioxide and water for photosynthesis [6], the primary process through which vegetation absorbs the former and converts it into organic matter. Simultaneously, through transpiration, water is transferred from plants to the atmosphere, serving as a critical component of the water cycle and reflecting the water consumption of vegetation. Vegetation WUE is defined as the amount of carbon dioxide fixed by an ecosystem per unit mass of water consumed [7] and serves as a key link between the carbon and water cycles. Additionally, it reflects the physiological functions and adaptation of plants [8; 9]. At the ecosystem scale, water use efficiency (WUE) is defined by the ratio of gross primary productivity (GPP) or net primary productivity (NPP) to evapotranspiration (ET) [10; 11; 12] and reflects the efficiency of ecosystems in the processes of water consumption and carbon fixation. In most previous studies, researchers used flux towers, photosynthesizers, and other types of equipment to obtain the net photosynthetic and transpiration rates of plants and then estimated their WUE. However, the applicability of this method on a large scale has been limited. Advances in remote sensing and geographic information technology have made the large-scale, time-sensitive, and continuous monitoring of WUE dynamics a focus of research in China and elsewhere. This efficient and convenient method has been rapidly and widely recognized and applied to ecosystem and regional-scale studies [13; 14; 15]. This indicator not only reflects the response of terrestrial ecosystems to global climate change but is also a key parameter for assessing carbohydrate coupling relationships in ecosystems [16]. Therefore, studying the spatial and temporal variations in regional vegetation WUE and its relationship with climatic environmental factors is important for understanding the interactions between the regional carbon and water cycles under climate change conditions and contributes to the promotion of regional ecological construction and sustainable development. Some scholars have investigated WUE across various global regions from multiple perspectives. It has been shown that global WUE has been increasing over the past three decades (1982-2008). However, there are significant differences between regions, which may be due to the combination of the direction and magnitude of changes in net primary productivity (NPP) and evapotranspiration (ET) [17]. In different natural environment regions, research results show diversity. For instance, researchers examined the spatial and temporal characteristics of WUE in the Karst region of southwestern China by utilizing the MODIS remote sensing dataset [18], and the findings showed that this indicator varied among different vegetation types. In another study, the response of seasonal WUE to temperature and precipitation in the Loess Plateau in China was examined [19], and the results indicated that the WUE of different vegetation types exhibited seasonal differences and varied in response to temperature and precipitation.