## 1 Introduction  
Ecosystem water use efficiency (WUE), which is typically defined as the quantity of dry matter fixed per unit mass of water absorbed by terrestrial ecosystems, is a measure of ecosystem carbon-water interactions [1], calculated as the ratio of gross primary production (GPP) to evapotranspiration (ET) [2]. WUE not only reflects the vegetation carbon and water cycle mechanism and its coupling relationship, but also a thorough physiological and ecological index to assess if plant growth is suitable [3]. The characteristics of WUE depend mainly on the strength of the coupling of the GPP and ET components, which are important variables linking the carbon cycle and hydrological cycle of vegetated ecosystems [4]. The research on the long time series of WUE can help to explore the impact of climate change behind the ecosystem changes at a macro level and reveal the mechanism of global changes on the interaction relationship between water and carbon cycles. The Yellow River Basin, a typical arid and semiarid region, contains the middle and upper sections of the Loess Plateau, the world's largest loess accumulation area [5]. Due to the long-term unreasonable use of land by human beings, the original carbon and water balance has been destroyed, which, together with the loose soil of the Loess Plateau, makes the ecosystem in a long-term unstable state, with strong storm washing and severe soil erosion, making it a typical ecologically vulnerable region in China [6]. Since the beginning of the \"Grain for Green\" project (GGP) in 1999, many national policies have been introduced to restrict land degradation on the Loess Plateau, and, since 2000, the Loess Plateau has been in the ecological restoration stage. The ecological environment of the Loess Plateau has been greatly improved by the large-scale implementation of the GGP to forests and grasses and building green water and green mountains [7]. As a typical area of aridity and semi-aridity, the Loess Plateau has precipitation as the main source of water, often due to insufficient precipitation resulting in low groundwater reserves in the area, and the growth of large vegetation needs to absorb and use a large amount of water, thus leading to excessive water consumption, carbon and water imbalance, and some vegetation degradation [8]. Therefore, it is important to investigate the effects of vegetation cover and precipitation temperature on vegetation WUE to promote the future-oriented ecological restoration management system and modernization of governance capacity in Loess Plateau. In recent years, many scholars have conducted numerous studies on plant WUE using remote sensing methods. For example, [PERSON] et al. [9] found that WUE increases mainly at high latitudes and decreases at middle and low latitudes under the context of current climate change. [PERSON] et al. [10] calculated WUE using MODIS data and showed that the latitudinal distribution of WUE increases from subtropical to middle and high latitudes and then decreases with increasing latitude. [PERSON] et al. [11] used eddy correlation techniques and stable isotopes to measure the WUE of forest ecosystems at different scales in the Mediterranean region. [PERSON] et al. [12] analyzed the mechanism of WUE on precipitation temperature and drought in the Hai River basin in China using MODIS data. [PERSON] et al. [13] studied the mechanism of soil water content underlying the efficiency of vegetation water utilization in China. Since the national implementation of ecological restoration projects such as the return of cultivated land to forest and grass in 1999, large-scale ecological restoration has significantly changed the regional ecohydrological processes. Research has been conducted on vegetation types and climate change in the Loess Plateau. [PERSON] et al. [14] studied the Loess Plateau's vegetation growth over a lengthy timeseries from 1982 to 2014 using AVHRR and MODIS NDVI data. In order to accurately assess the ecological effects of reforestation, [PERSON] et al.