## 2 Materials and Methods
### Data and Preprocessing  
GPP, ET and LAI data used in this study were from the GLASS products ([[http://www.glass.umd.edu/](http://www.glass.umd.edu/)]([http://www.glass.umd.edu/](http://www.glass.umd.edu/)), accessed on 12 March 2022). The latest GLASS GPP data were generated based on the revised light-use efficiency model by taking several environmental variables into account, such as CO\({}_{2}\) concentration, radiation components and atmospheric water vapor pressure [47; 48]. The results described the spatial, interannual, and seasonal variations of global GPP. These GLASS GPP data were superior to those generated by the original eddy covariance-light-use efficiency model (EC-LUE) in terms of data accuracy. The ET product with high reliability and accuracy was generated by integrating five common latent-heat-flux algorithms using the Bayesian model-averaging (BMA) method and combing AVHRR (advanced very-high-resolution radiometer), MODIS (moderate-resolution imaging spectroradiometer), and MERRA (modern-era retrospective analysis for research and applications) reanalysis data [49; 50; 51]. In order to verify the accuracy of the GLASS data for the reliability of the subsequent analyses, we assessed the GLASS data using the measured flux data over grassland at observation stations at Xilingol League ([[http://www.chern.org.cn/index.jsp](http://www.chern.org.cn/index.jsp)]([http://www.chern.org.cn/index.jsp](http://www.chern.org.cn/index.jsp)), accessed on 12 March 2022) for site-level validation at the 8-day scale (Figure S1). Data accuracy was assessed by the determination coefficient (R\({}^{2}\)) and root-mean-square errors (RMSEs). The results demonstrated that the R\({}^{2}\) between the GLASS GPP data and the flux data was 0.92 and the RMSE was 0.33 g C m\({}^{-2}\) sd\({}^{-1}\) (Figure S1a). The R\({}^{2}\) between the ET data and the flux data was 0.82 and the RMSE was 0.29 mm 8d\({}^{-1}\) (Figure S1b). The estimated R\({}^{2}\) between the estimated WUE by the ET data and the flux data was 0.87 and the RMSE was 0.25 g C m\({}^{-2}\) mm\({}^{-1}\) sd\({}^{-1}\) (Figure S1c). This indicated that the GLASS data were highly consistent with the measured data and that they were applicable to estimate WUE. Therefore, we used the GPP and ET data from 2001 to 2018 to calculate the WUE in IM. The annual mean LAI was calculated using data with a temporal resolution of 8 d and a spatial resolution of 500 m. The DEM data came from the SRTM digital elevation product of National Aeronautics and Space Administration, with a spatial resolution of 90 m ([[https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/)]([https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/)), accessed on 12 March 2022). Vegetation types were obtained from China's vegetation-type map (1:1,000,000) from the Data Center of the Chinese Academy of Sciences ([[https://www.resdc.cn/](https://www.resdc.cn/)]([https://www.resdc.cn/](https://www.resdc.cn/)), accessed on 12 March 2022). In the study area, the vegetation was divided into six types, including forest, swamp, shrub, meadow, cultivated vegetation, and desert. We only focused on the first five in this study (Figure 1b). Meteorological data came from China National Meteorological Science Data Sharing Service Platform ([[http://data.cma.cn](http://data.cma.cn)]([http://data.cma.cn](http://data.cma.cn)), accessed on 12 March 2022). A  
Figure 1: (**a**) Digital elevation model (DEM) and (**b**) vegetation types in Inner Mongolia. statistical analysis on annual mean temperature (\({}^{\circ}\)C), annual accumulated precipitation (mm), annual mean wind speed (m s\({}^{-1}\)), annual mean relative humidity (%), annual mean sunshine duration (h), and annual mean water vapor pressure (hPa) at 118 stations in IM and surrounding areas from 2001 to 2018 was carried out. The temperature data were interpolated through the thin plate spline function by using the DEM as covariable [40], and the other climate variables were interpolated using the Kriging method.