## 1 Introduction  
Global climate change is significantly affecting land-based ecosystem productivity and water use distribution patterns. Climate warming may promote plant growth in heat-limited high-latitude and high-altitude regions. However, in many water-limited regions, temperature increases may lead to increased drought, the deceleration of plant growth and increased ecosystem disturbance, resulting in reduced terrestrial carbon uptake capacity [1, 2]. To evaluate ecosystems' vulnerability to climate change, scientists employ indicators such as ecosystem water use efficiency (eWUE), which is a crucial aspect of research related to carbon-water cycle coupling [3]. The quantification of the temporal and spatial changes in the water use efficiency of ecosystems in response to climate change is highly significant in light of the increasing visibility of environmental problems caused by global change, and it provides a basis for humans to exercise control over scarce water resources to obtain the greatest yield and economic benefits [4]. The first studies regarding water use efficiency were mainly experimental observations, and most of them took measurements directly in the field [5]. Later, with the development of observation technology, eddy correlation technology was gradually applied to the simulation of water-carbon cycles and to determine the productivity and water use efficiency of different types of ecosystems [6; 7; 8]. In regional ecosystems, to estimate water usage efficiency, extensive use has been made of remote sensing technology due to its robust capacity to acquire surface information and high temporal resolution [9; 10], and breakthroughs have been made in the study of water use efficiency at the ecosystem level [11]. In recent years, researchers from both China and elsewhere have used ecosystem process models to assess the efficacy of water usage at various spatial and temporal scales in China's terrestrial ecosystems. Research regarding the former has suggested that drought has different effects on water use efficiency in different regions [12]. Research regarding the latter has revealed the zonal law of WUE with increasing latitude [13]. In addition, variations in eWUE are directly tied to the conditions of the climate, such as temperature [14], precipitation [15], solar radiation [16] and saturated water vapor pressure difference [17]. However, the effects of these factors on eWUE are significantly different in different regions and among different vegetation types. Studies have found that eWUE has a positive correlation with temperature in areas with high latitudes [18], but it has a negative correlation in relatively diffuse South America, Southeast Asia and other regions [19]. An increase in precipitation can reduce the eWUE in forests in eastern China [20]. However, it can promote eWUE in the temperate grasslands of Inner Mongolia [21]. It can be seen that the response of eWUE to global change is very complex; therefore, it is necessary to strengthen our understanding of the spatiotemporal patterns of eWUE in different regions and its relationship with climate factors. As the global water resource crisis worsens, water usage efficiency, a comprehensive physiological and ecological gauge of plant growth appropriateness, has become a hot topic in arid and semi-arid zone research [22]. Inner Mongolia is distinguished by its extreme climate, water and geographical diversity. Even though it serves as a vital ecological security barrier in China's northern regions, the region's ecosystem is highly vulnerable and delicate. The scarcity of water is a major contributor to environmental degradation and a barrier to economic growth in developing regions. Most of Inner Mongolia is becoming warmer and more humid because of global climate change [23].