## 2 Materials and Methods  
### Data Collection  
To analyze the dynamics of CUE between 2001 and 2020, we used a long-term time series of GPP and NPP. The GPP and NPP datasets, derived from the MOD17A2H product available on Google Earth Engine ([[https://earthengine.google.com/](https://earthengine.google.com/)]([https://earthengine.google.com/](https://earthengine.google.com/)), accessed on 5 January 2023), provide an annual temporal resolution and a spatial resolution of 500 m over the Three Rivers Source region. Prior to analysis, the data underwent preprocessing steps, including filtering based on MODIS product documentation and quality control bits, as well as resampling and projection adjustments. The utility of this dataset spans a range of studies, facilitating the investigation of temporal and spatial patterns at regional and global scales related to crop yield estimation, productivity, and carbon cycling [30; 31]. In addition, the normalized difference vegetation index (NDVI) dataset was obtained from the MOD13A1 product, with a temporal resolution of 16 days and a spatial resolution of 500 m. This dataset serves as a continuity index to the previously established National Oceanic and Atmospheric Administration-Advanced Very High Resolution Radiometer (NOAA-AVHRR)-derived NDVI. Furthermore, the Leaf Area Index (LAI) dataset was obtained from the MOD15A2H product, which has a temporal resolution of 8 days and a spatial resolution of 500 m. Similar to the GPP data, both NDVI and LAI datasets were accessed from the Google Earth Engine platform([[https://earthengine.google.com/](https://earthengine.google.com/)]([https://earthengine.google.com/](https://earthengine.google.com/)), accessed on 5 January 2023). Climate factors, namely temperature, precipitation, and evapotranspiration, were integral to this study. Temperature and precipitation data spanning from 2001 to 2020 [32], with a resolution of 1 km, were sourced from the monthly temperature and precipitation dataset available at [[https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)]([https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)) (accessed on 7 January 2023). This dataset was meticulously crafted by downscaling the global 0.5\({}^{\circ}\) climate dataset from CRU and the high-resolution global climate dataset from WorldClim, employing the Delta space downscaling methodology. Furthermore, the dataset's credibility is bolstered by its validation against data from 496 distinct meteorological observation points, ensuring robust validation outcomes. Moreover, evapotranspiration data covering the period from 2001 to 2020, possessing a spatial resolution of 500 m, were accessed from the Google Earth Engine platform (accessed on 7 January 2023). Notably, the updated iteration of the PML-V2 [33] evapotranspiration product rectifies limitations observed in its predecessor. Specifically, this version addresses challenges associated with LAI data corrections and addresses data gaps, enhancing the dataset's overall reliability and applicability for this study. This study utilized a Digital Elevation Model (DEM) sourced from the SRTM V3 ([[https://lpdaac.usgs.gov/products/strtmgl1v003/](https://lpdaac.usgs.gov/products/strtmgl1v003/)]([https://lpdaac.usgs.gov/products/strtmgl1v003/](https://lpdaac.usgs.gov/products/strtmgl1v003/)), accessed on 5 January 2023) product, made available by NASA's Jet Propulsion Laboratory (JPL). This DEM boasts a resolution of 1 arc-second, equivalent to approximately 30 m, providing detailed topographical insights essential for the research. Additionally, the vegetation distribution data categorized vegetation into 11 distinct groups or types, encompassing classifications, such as scrubs, meadows, steppes, among others.