## 1 Introduction
Previous studies have shown that the temporal trend in WUE was influenced by a combination of factors [23; 24; 25; 26],  
Figure 1: Example of WUE changes for a cropland pixel (38\({}^{\circ}\)11\({}^{\prime}\)N, 102\({}^{\circ}\)38\({}^{\prime}\)E) during 2002–2021. such as climate factors, LAI, soil moisture, vegetation cover, and phenology, but factors influencing the temporal variation in WUE may differ from those influencing spatial variation [17]. The research to date has tended to focus on the influence of different factors on WUE temporal variation rather than on spatial variation. Therefore, it is challenging to detect the effects of various factors and their interactions on the spatial variation of WUE. Geodetector, a spatial analysis method, could detect the linear and non-linear relationships between the dependent variable and its explanatory variables and could quantitatively capture the impact of different factors on spatial heterogeneity [27]. A major advantage of the Geodetector method is that it overcomes the limitations of traditional statistical methods that cannot handle category variables. Hence, this method may be a valid tool to differentiate the drivers of WUE spatial variation in arid lands of Northwest China. In recent years, the development of cloud computing has substantially improved the processing capability of RS big data. For example, Google Earth Engine (GEE) can provide planetary-scale geospatial analysis based on its advanced cloud computing and storage capability [28] and has been widely used in land cover mapping [29], crop yield estimation [30], global water monitoring [31], etc. GEE offers a platform for investigating the spatio-temporal variation of WUE over a long period at the local, regional, or even global scale. To understand the impacts of various factors and their interactions on the spatial variation of WUE in the arid land of Northwest China, we selected the Qilian Mountains (QM) and Hexi Corridor (HC) as the study areas, a typical arid land environment with mountains, oases, and deserts. The QM and HC regions are located in the middle of Northwest China with complex topography. The vegetation status of the QM and HC is critical to the ecological security in Northwest China. Recently, studies on vegetation RS monitoring in this region have mainly focused on vegetation phenology [32], vegetation index [33; 34], vegetation cover [35; 36], biomass [37; 38], and GPP [39; 40]. WUE was rarely concerned. In recent years, the vegetation status in this region has experienced obvious changes in response to climate change, and a thorough investigation of changes in its WUE of vegetation is needed. As discussed above, this study aims to (1) investigate the spatio-temporal variations of WUE in QM and HC from 2002 to 2021, based on the GEE platform, using MODIS products and the STL decomposition method, and (2) quantify the influence of potential factors (climate, topography, and ecological factors) and their interactions on the spatial heterogeneity of WUE, based on the Geodetector method. The study results will help to protect the ecological environment, and further understand the underlying mechanisms of WUE changes in the arid land of Northwest China.