# Spatiotemporal Analysis of Evapotranspiration and Effects of Water and Heat on Water Use Efficiency
## 1 Introduction  
Terrestrial ecosystems are a major carbon sink in the global carbon cycle [1]. The issue of how the carbon and water cycles can be balanced is of great interest to the scientific community [2]. WUE is an important indicator of the coupling of carbon and water cycles in ecosystems, which closely links biological processes (photosynthesis, transpiration) and physical processes (evaporation). It is a key parameter for ecosystem response to climate change [3]. WUE controls the coupling between plant water use and carbon assimilation and has been defined in many previous studies as the ratio of GPP (gross primary productivity) to evapotranspiration [4, 5]. In some GPP simulation models, WUE is also a critical metric [6]. Recently, other studies have determined the effects of changes in vegetation, climate, land use, and atmospheric CO\({}_{2}\) on changes in WUE [7, 8, 9]. Responses of ecosystem WUE's to climate are generally primarily based on spatial or temporal gradient analysis [10]. Due to the uncertain interactions of many environmental factors on WUE, it is still yet to be tackled how to accurately predict the regional impact of climate change on carbon water resources [11]. The application of the mechanism model makes it possible for WUE to expand from the blade or regional to the global level, so as to explore the impact of single and multiple environmental factors on WUE greatly. Climate factors such as precipitation andtemperature can sensitively reflect climate change in arid and semi-arid areas [11]. Evaporation, transpiration, and precipitation, which regulate the growth of plants, are important parts of the water cycle. [PERSON] et al. (2016) defined the GPP/p and GPP/Et (transpiration) ratio as a new indicator of water efficiency and have been widely applied [12]. [PERSON] et al. discussed the ecosystem response mechanism to drought by comparing the responses of different terrestrial ecosystems around the global to drought [13]. WUE not only exhibits strong spatial heterogeneity but also has significant interannual changes. Spatially, areas with low WUE values are mainly located in Central Asia, the Sahel in Africa, the western coasts of North and South America, and areas such as Oceania, where evaporation is strong and vegetation is scarce [14]. Global WUEs have generally increased over the 30 years from 1982 to 2008, but they vary significantly from region to region, depending on the direction and magnitude of changes between the GPP and \(ET\)[14]. Among them, meteorological factors such as precipitation, temperature, and solar radiation were crucial factors driving WUE change [12]. However, due to the different geographical environments effect, the results obtained from different studies often vary significantly [15]. For example, in the water-scarce Black River basin, precipitation plays a leading role in WUE [16]. However, in the more humid alpine meadows, temperature is a more important factor [17]. There are very few studies of WUE in arid areas, especially based on newly defined indicators of water efficiency, and studies of climate responses have not been reported. Xinjiang belongs to an arid and semi-arid area with a shortage of water resources and scarce surface vegetation. It has extremely fragile ecosystems, and the impact of climate change is severe [18; 19; 20]. The process of small water circulation in inland Xinjiang is accelerating, and the rapid melting of alpine ice and snow directly changes the composition of runoff recharge, affecting the water consumption of vegetation in mountains, oases, and deserts, and the growth of vegetation and spatial distribution patterns [21]. The total amount of water resources consumed in arid areas of Xinjiang is relatively large, leading to an increasing depletion of water resources. It has become the core restriction on the development and regional stability of Xinjiang [22].