## 1 Introduction  
The hydrological cycle refers to the continuous and dynamic circulation of water within the Earth-atmosphere system, encompassing various processes such as evaporation,condensation, and precipitation [1]. Within this cycle, evapotranspiration (ET) represents the second largest component of the terrestrial water cycle, following precipitation, and plays a crucial role in transferring water from the land surface to the atmosphere through both evaporation from soil and water bodies and transpiration from plants [2]. It is also the key link connecting the Earth's ecosystem, hydrological cycle, and biogeochemical cycle. In our special study, ET is divided into three main components: vegetation transpiration (Et), soil evaporation (Es), and canopy interception evaporation (Ei). Among these, Et is the most significant contributor to the total evapotranspiration in terrestrial ecosystems [3]. Research has demonstrated that the ET process is significantly influenced by regional climate variations and changes in terrestrial vegetation. Climate change directly impacts the ET process by altering the atmospheric water retention capacity, which in turn affects precipitation patterns, humidity levels, and the growth and distribution of vegetation, ultimately influencing the overall hydrological cycle [4]. At the same time, it may also lead to regional changes in soil moisture, thus indirectly affecting ET [5]. Vegetation is an important part of the terrestrial ecosystem and an important link between the energy circulation and material circulation between the soil circle, the hydrosphere, and the atmosphere [6]. Changes in surface vegetation play an important role in regulating water circulation, energy circulation, and global carbon balance on the land surface. On the other hand, vegetation will also have a dynamic response to the external environment through biophysical and biochemical pathways, in which vegetation can have a profound impact on the regional and even global carbon-water cycle system through photosynthesis and transpiration [7]. Vegetation can have a feedback effect on ET by intercepting precipitation, changing surface roughness, and affecting runoff patterns [8]. ET and vegetation are closely linked and interdependent through the balance mechanism of natural evolution. Large-scale vegetation restoration and greening projects have significantly changed surface characteristics while improving the health of the local ecosystem [9]. The influence of vegetation greening on ET exhibits considerable variations across different regions and time periods. For instance, in the Loess Plateau, vegetation greening and shifts contribute more to ET than climate change, whereas in certain areas of northern China, precipitation changes play a more pivotal role in impacting ET [10]. Therefore, accurately quantifying the specific effects of vegetation greening and change and climate change on ET is of irreplaceable significance for the scientific management and efficient use of regional water resources and the promotion of ecological sustainable development [11]. Accurately revealing the characteristic trend in vegetation change is the premise of understanding vegetation change. As science and technology advance, satellite remote sensing products are offering hydrological research data with unmatched spatial resolution. However, when studying the complex dynamics of the hydrological cycle and its spatial distribution characteristics, the ET data obtained by satellite sensors alone often seem to be insufficient [12], because although these data can provide a macro-perspective ET overview, it is difficult to reveal the intricate physical interaction mechanism between ET and key hydrological variables such as soil moisture, groundwater level, precipitation, and runoff, and it is more difficult to accurately predict the temporal evolution trend in ET on different spatial scales in the future [1].