## 2 Study Area, Methods, and Data Sources
### Data Sources  
To assess the reduced carbon uptake (RCU hereafter), the data sources included a soil map, digital elevation model (DEM), and vegetation cover, which were used to segment S-T-V patches, and climate dataset and annual NPP from MODIS (Moderate Resolution Imaging Spectroradiometer) 17A3 (MOD17A3), which were used to compute RCU along with the segmented S-T-V patches. The climatic variables were acquired from China's climate data-sharing platform ([[http://cdc.cma.gov.cn](http://cdc.cma.gov.cn)]([http://cdc.cma.gov.cn](http://cdc.cma.gov.cn))). Both the climate dataset and MODIS NPP were at an annual step in the time window during 2001-2018. RCU was assessed for each year during the time window. The explanatory variables grazing and population  
Figure 1: Study area. Some administrative units (counties) in the west mainly covered by desert or sandy areas or having very small vegetated area were excluded in the study. (**a**) Study area (Inner Mongolia) with administrative boundaries at the county level, and (**b**) Averaged NPP during 2001–2018.  
were compiled from yearbooks, and the road network was extracted from Open Street Map (OSM) [26]. All resultant raster layers were resampled to 1 km \(\times\) 1 km if they were not at that resolution.  
Vegetation cover types were extracted from the vegetation Atlas of China, which includes 55 vegetation types ([[http://www.nsii.org.cn/chinavegetaion](http://www.nsii.org.cn/chinavegetaion)]([http://www.nsii.org.cn/chinavegetaion](http://www.nsii.org.cn/chinavegetaion))). The non-vegetated area was excluded from further analysis. The soil map came from the Harmonized World Soil Database (ver. 1.2), which is the most up-to-date world soil map that incorporates data of 48,148 soil profile descriptions related to various soils associated with each mapping unit at a spatial resolution of \(\approx\)1 km at the equator [27]. Topography was prepared from DEM SRTM30 ([[http://earthexplorer.usgs.gov](http://earthexplorer.usgs.gov)]([http://earthexplorer.usgs.gov](http://earthexplorer.usgs.gov))), which was resampled to the resolution at 1 km \(\times\) 1 km and then reclassified to three groups, namely \(<\)500 m, 500-1500 m, and \(>\)1500m. The three layers were overlaid to segment the study area into S-T-V patches. RCU was assessed for each year during 2001-2018 based on the MOD17A3 time series and the climatic variables, and it was temporally averaged in the end.  
The data sources for the explanatory variables, including grazing intensity and population, were compiled for 84 county-level administrative units (with the exclusion of those in sandy areas or having a very small vegetated area) from the yearbook of IMAR for each year during 2001-2018. This county-level yearbook covering the whole study area is the most consistent data available. The grassland has multiple grazing animals, for example, sheep, horse, buffalo, camel, and donkey. To uniformly measure grazing intensity, the impact from all other animals was converted into sheep units. Specifically, one horse is equivalent to 6 sheep and thus was multiplied by 6 to transform into the sheep unit. Similarly, cattle, camels, and donkeys were multiplied by 5, 7, and 3, respectively. The converted numbers were summed up to make a total value of sheep units, which was then divided by the vegetated area of each administrative unit to be grazing intensity. Similarly, population density was computed to be the total population divided by the area of administrative unit. Both the processed grazing intensity and population density were temporally averaged to represent an overall impact from each of them during the study period. Road network density, in the form of total road length in a square kilometer, was prepared using a line density algorithm with road network input from Open Street Map (OSM) [28].