## 1 Introduction  
The conflict between the gain in carbon (through photosynthesis) and loss of water (through transpiration) in plants or terrestrial ecosystems is referred to as water use efficiency (WUE), which is an important component of ecosystem function [1, 2, 3]. By quantifying spatiotemporal changes in WUE and identifying its drivers, ecosystem responses to changing environments can be revealed, which has important implications for management of ecosystems [4, 5]. WUE is defined as the ratio of Gross Primary Productivity (GPP) and evapotranspiration (ET), and there are several ways to estimate GPP and ET. For example, the eddy covariance technique is used for field measurements, evaluation based on a data mining model or process model, and estimation through remote sensing products [6]. Given that observed data are very sparse and limit the data mining model's function, remote sensing data are currently one of the most commonly used methods for estimating GPP and ET at the regional scale [7]. Many studies have confirmed the applicability of remote sensing data in GPP and ET estimation [5, 8, 9, 10, 11]. Changes in WUE are the combined result of changes in GPP and ET and the drivers that affect them. The photosynthetic utilization rate of vegetation can be improved by increasing the photosynthetic rate of vegetation. When the CO\({}_{2}\) absorption rate of leaf stomata reaches saturation, transpiration may be reduced by the reduction in leaf stomata [12]. Sunlight, rainfall, and temperature are important climatic factors that affect the photosynthetic rate of vegetation [8; 13]; CO\({}_{2}\) is an important participant in vegetation photosynthesis, and elevated atmospheric CO\({}_{2}\) concentration (Ca) will have a fertilizing effect on plant growth [4]. An increase in vapor pressure deficit may cause reductions in stomatal conductance and photosynthetic rates in vegetation [14; 15]. The leaf area index (LAI) can be used as an important indicator of vegetation growth. Increasing LAI leads to increasing ET by affecting canopy transpiration and interception, decreasing the proportion of solar radiation reaching the surface of the soil and decreasing evaporation of bare soil, thereby reducing ET [16]. In addition, plants extract water from the soil, and vegetation growth can be affected by the availability of soil moisture [17; 18]. The mechanisms regulating changes in WUE are driven by the highly complex interplay between climatic environmental changes and vegetation growth. In theory, environmental variables impacting GPP or ET can also impact WUE. Potential controlling factors for WUE include air temperature, precipitation, LAI, shortwave radiation, vapor pressure deficit, soil content of water, and atmospheric CO\({}_{2}\) content [7; 19; 20; 21; 22]. Scholars have investigated the driving factors underlying WUE. [PERSON] et al. (2016) explored the spatial relationship between global WUE and climate variables through regression analysis [23]. [PERSON] et al. (2021) further analyzed the global annual WUE response to the drought index using Spearman correlation analysis [24]. [PERSON] et al. (2022) used a random forest algorithm to analyze the control of various biometeorological drivers in WUE for various forest type groups in India [25]. [PERSON] et al. (2021) and [PERSON] et al. (2022) identified the driving factors of various WUE changes in China through a sensitivity analysis, and argued that vegetation growth and elevated atmospheric CO\({}_{2}\) emissions are the main factors underlying WUE changes in China [26; 27; 28]. Most studies employing partial correlation analysis or simple correlation have found that the spatial distributions of climate variables show strong correlations with those of WUE [26]. However, the actual contribution of each driver to WUE dynamics remains unknown. The variation trend of WUE cannot be determined solely by the correlation strength between the driving factor and WUE; rather, the trends in drivers, including trends in quantity and direction, must be considered.