## 2 Materials and Methods
### Dataset  
In this study, we collected a variety of sources of vegetation and climate data to drive the model (Table 1). To ensure data consistency and facilitate subsequent analysis, all data were unified to the Albers equal area conic projection with WGS 84 as the datum, and by using the neighbor assignment method and bilinear interpolation method, the spatial resolution of vegetation and meteorological data was further resampled to 500 m, respectively [41]. The Climate Change Initiative-Land Cover (CCI-LC) dataset was obtained from the European Space Agency ([[https://www.esa-landcover-cci.org](https://www.esa-landcover-cci.org)]([https://www.esa-landcover-cci.org](https://www.esa-landcover-cci.org)) (accessed on 22 September 2022)). We accessed data for each year from 2001 to 2018 and classified the land cover types as cropland, forestland, grassland, urban areas, and bare areas according to the IPCC classes considered for change detection. As we mainly considered the carbon source/sink of vegetation, we did not consider water bodies or land permanently covered by snow and ice; thus, these were excluded from this study. Ultimately, the total area of the five remaining land cover types in the study area is approximately 2.06 million km\({}^{2}\). The MOD13Q1 vegetation index products (NDVI and EVI) were obtained from the National Aeronautics and Space Administration ([[https://ladsweb.modaps.eosdis.nasa.gov/search](https://ladsweb.modaps.eosdis.nasa.gov/search)]([https://ladsweb.modaps.eosdis.nasa.gov/search](https://ladsweb.modaps.eosdis.nasa.gov/search)) (accessed on 6 March 2022)). When we acquired this data. It was first pretreated by format conversion, mosaic, and projection, revised by its quality control layer, eliminating outliers and masks, and eventually synthesized to a monthly scale by applying the maximum synthesis method. For resampling these vegetation data, we chose the nearest neighbor assignment method that is suitable for discrete data, which will not change the pixel values and has a maximum spatial error of half the pixel size. The monthly average temperature and precipitation dataset for China was obtained from the National Earth System Science Data Center, National Science and Technology Infrastructure of China ([[http://www.geodata.cn](http://www.geodata.cn)]([http://www.geodata.cn](http://www.geodata.cn)) (accessed on 4 March 2021)) [41]. The surface solar radiation dataset was obtained from the National Tibetan Plateau Data Center ([[https://data.tpdc.ac.cn](https://data.tpdc.ac.cn)]([https://data.tpdc.ac.cn](https://data.tpdc.ac.cn)) (accessed on 8 March 2022)) [42]. The monthly scale potential evapotranspiration (PET) and evapotranspiration (ET) data were obtained from the University of California Climatology Laboratory ([[https://www.climatologylab.org/terraclimate.html](https://www.climatologylab.org/terraclimate.html)]([https://www.climatologylab.org/terraclimate.html](https://www.climatologylab.org/terraclimate.html)) (accessed on 29 April 2022)) [43]. These data were all pretreated by format conversion, projection, and mask. In addition, considering that meteorological data are continuous, we chose the bilinear interpolation method to resample these data to 500 m, as this method uses the weighted distance average of the four most adjacent pixels as the target pixel value, and the