## 2 Materials and Methods
### Data Source
#### 2.2.2 Auxiliary Data  
The Global Land Evaporation Amsterdam Model (GLEAM) provides estimates of various terrestrial evaporation components derived from satellite data. Its intermediate outputs include potential evaporation (Ep), actual evaporation--encompassing plant transpiration, bare soil evaporation, and open-water evaporation--RUM, and surface soil moisture. RUM is calculated using a multi-layer water balance approach, while satellite-derived surface soil moisture observations are assimilated into the soil profile to mitigate random errors in forcing data [37]. Central to the GLEAM framework is the Priestley-Taylor algorithm, which integrates diverse independent remote sensing inputs such as vegetation optical depth, soil moisture, and snow water equivalent [38]. Empirical parameters within the algorithm, including the evaporation stress factor and latent heat of evaporation, are informed by multidisciplinary research findings [37]. The GLEAM RSM dataset has been widely applied and demonstrates strong correlations with ground-based observations while maintaining minimal model bias [39]. Notably, studies have demonstrated that at the pixel scale, the GLEAM RSM product more effectively captures warm-season soil moisture dynamics on the Tibetan Plateau [40]. This investigation employs monthly datasets of RSM (0-10 cm), RUM (10-100 cm), and Ep spanning 2000 to 2022, with a spatial resolution of 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\). The data were obtained in Network Common Data Form (NetCDF) format.  
The Climate Hazards Center Infrared Precipitation with Station data (CHIRPS) represents a quasi-global rainfall dataset encompassing a temporal span exceeding 30 years. By integrating satellite imagery at a spatial resolution of 0.05\({}^{\circ}\) with ground-based station measurements, CHIRPS generates gridded precipitation time series tailored for trend analysis and seasonal drought monitoring [41]. Validation studies indicate that CHIRPS precipitation data exhibit a coefficient of determination (R\({}^{2}\)) exceeding 0.91 when compared with in situ observations in arid and semi-arid areas of China, underscoring its high reliability [42]. The dataset effectively captures monthly precipitation variability and is particularly well-suited for drought assessment application [43]. Consequently, it has been extensively employed in agricultural drought monitoring and urban hydrological modeling contexts [44]. In the present study, CHIRPS summer precipitation data from 2000 to 2022 were utilized, featuring a monthly temporal resolution and a spatial resolution of 0.05\({}^{\circ}\)\(\times\) 0.05\({}^{\circ}\). The data were acquired in TIFF.  
In the arid and semi-arid areas of China, the vegetation growing season predominantly occurs during the summer months. The concurrence of elevated temperatures, relatively stable precipitation patterns, and consistent solar radiation during this period renders it particularly conducive for examining the responses of GPP to variations in precipitation and soil moisture. To enhance the robustness of the experimental analysis, separate decoupling assessments of the effects of precipitation and RSM were performed utilizing both GOSIF-derived and MODIS-derived GPP datasets. All datasets were standardized to a monthly temporal resolution and a spatial resolution of 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\), with monthly averages for the summer months (June, July, and August) spanning the years 2000 to 2022 selected for subsequent analyses.