## 2 Materials and Methods
### Data Sources and Processing of MODIS Products  
#### 2.2.1 Data Sources and Descriptions  
The boundary of the study area comes from the extraction and cutting of the boundaries of 71 cities through which the Yellow River flows, and this operation was completed in ArcGIS 10.4. The study area was 3,207,084 km\({}^{2}\). The vegetation classification data in this study were obtained from the CNLUCC in 2018 ([[http://www.resdc.cn/DOI](http://www.resdc.cn/DOI)]([http://www.resdc.cn/DOI](http://www.resdc.cn/DOI)), accessed on 15 May 2021). With reference to the existing vegetation classification system, the vegetation distribution map of China, and the needs of the Biome-BGC model, we divided the vegetation types into nine categories, namely, deciduous broadleaf forest, evergreen broadleaf forest, evergreen needleleaf forest, deciduous broadleaf shrubland, warm temperate tussock, temperate steppe, temperate meadow, alpine meadow, and alpine steppe ([[http://westdc.westgis.ac.cn](http://westdc.westgis.ac.cn)]([http://westdc.westgis.ac.cn](http://westdc.westgis.ac.cn)), accessed on 15 May 2021) [33]. The 2018 NDVI, topographic data (DEM, slope), and residential area distribution data used to construct the coospatial network in this study were obtained from the Resource and Environmental Science and 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 16 May 2021). MNDWI data were extracted from MODIS images with few clouds in summer 2018 ([[https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)]([https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)), accessed on 17 May 2021). Data on road network, water network, and railroad network were obtained through Overpass API ([[http://www.overpass-api.de/](http://www.overpass-api.de/)]([http://www.overpass-api.de/](http://www.overpass-api.de/)), accessed on 20 May 2021). Ecological sources comprise multiple ecological services that maintain ecosystem stability. Ecological sources are usually high-quality and representative landscape patches that are characterized by continuity and integrity [34]. When selecting ecological sources, fragmented and discontinuous patches are usually avoided. Combining the large area of the YRB (3,207,084 km\({}^{2}\)) in this study and avoiding fragmentation of the selected ecological sources, we chose 1 km as the resolution for each type of raster data.  
The site geographic data required to drive the Biome-BGC model, including elevation, slope, and aspect, were extracted from the DEM data ([[https://www.resdc.cn/](https://www.resdc.cn/)]([https://www.resdc.cn/](https://www.resdc.cn/)), accessed on 16 May 2021). The soil data required to drive the Biome-BGC model came from the spatial distribution data of soil texture in China ([[http://resdc.cn/](http://resdc.cn/)]([http://resdc.cn/](http://resdc.cn/)), accessed on 16 May 2021). The CO\({}_{2}\) concentration data came from the annual average observation value of the Mauna Loa Observatory in the United States ([[https://www.co2.earth/](https://www.co2.earth/)]([https://www.co2.earth/](https://www.co2.earth/)), accessed on 18 May 2021). The daily meteorological data required by the Biome-BGC model needs to be simulated by inputting the original data of the meteorological observatory into the MTCLIM4.3 model ([[http://data.cma.cn](http://data.cma.cn)]([http://data.cma.cn](http://data.cma.cn)); [[http://www.ntsg.umt.edu/project/mt-clim.php](http://www.ntsg.umt.edu/project/mt-clim.php)]([http://www.ntsg.umt.edu/project/mt-clim.php](http://www.ntsg.umt.edu/project/mt-clim.php)), accessed on 21 May 2021). The vegetation cops physiological parameters required by the Biome-BGC model were all obtained by collecting reports in the literature.