## 2 Overview of Study Area, Data, and Methods
### Data Sources and Processing  
1. Carbon sink data: The carbon sink data were calculated based on the carbon content of vegetation NPP corresponding to vegetation dry matter. The NPP data in this study were derived from the MODIS satellite-based MOD17A3 HGF product released by the National Aeronautics and Space Administration (NASA). The spatial resolution of the data is 500 meters, and the time resolution is annual. MRT software and ArcGIS 10.7 software were used to pre-process the data for splicing, cropping, and projection, and the raster calculator function was used to eliminate the NPP data outliers. Finally, the annual NPP sequence data of China from 2001 to 2019 were obtained, and the unit is gC/m\({}^{2}\). After calculating these data, according to the green vegetation photosynthesis chemical formula (6 CO\({}_{2}\) + 6H\({}_{2}\)O\(\rightarrow\)C\({}_{6}\)H\({}_{12}\)O\({}_{6}\) + 6O\({}_{2}\)), for every 1 kg of dry matter produced by vegetation, 1.63 kg of CO\({}_{2}\) can be fixed, and the carbon content in the dry matter accounts for approximately 45% of the total NPP. Therefore, the calculation formula for the fixed CO\({}_{2}\) of vegetation is as follows: W\({}_{\text{CO2}}\) = NPP/0.45 \(\times\) 1.63, and the unit of W\({}_{\text{CO2}}\) is g/m\({}^{2}\). Based on this, the carbon sink data for China's forests were calculated in grid form. Then, according to the base map of the 40 key SOFRs, ArcGIS 10.7 was used to extract the carbon sink of each forest region from 2001 to 2019, which was processed according to the unit area to obtain the carbon sink data used in the model. 2. FMI and socioeconomic data: 1. Data on the FMI, total output value, number of employees, and total wages of each forest region were all sourced from the 2001-2019 China Forestry and Grassland Statistical Yearbook, which is compiled and obtained each year. 2. The administrative boundary data of Heilongjiang Province came from the basic geographic database ([[http://www.webmap.cn](http://www.webmap.cn)]([http://www.webmap.cn](http://www.webmap.cn)), accessed on 16 July 2021); the vector maps of the 40 key SOFRs were based on the forest base map and drawn according to ArcGIS geographic registration. 3. Natural data: 1. The basic precipitation data in each forest region came from multiyear station data on the website of the China Meteorological Administration ([[http://data.cma.cn/](http://data.cma.cn/)]([http://data.cma.cn/](http://data.cma.cn/)), accessed on 20 August 2021). We selected a total of 40 sites in and near the SOFRs, and we used the ArcGIS 10.7 interpolation analysis function to perform spatial interpolation processing; additionally, kriging was used to interpolate based on the covariance function and to extract the area mean, and the pixel size after processing was 100 m. 2. The average temperature data for each forest region in July came from the Loess Plateau Science Data Center, National Earth System Science Data Sharing Infrastructure, National Science and Technology Infrastructure of China ([[http://loess.geodata.cn](http://loess.geodata.cn)]([http://loess.geodata.cn](http://loess.geodata.cn)), accessed on 25 August 2021). This dataset is based on the global 0.5\({}^{\circ}\) climate dataset released by the CRU ([[https://crudata.uea.ac.uk/cru/data/hrg/](https://crudata.uea.ac.uk/cru/data/hrg/)]([https://crudata.uea.ac.uk/cru/data/hrg/](https://crudata.uea.ac.uk/cru/data/hrg/)), accessed on 13 July 2021) and the high-resolution climate dataset released by WorldClim ([[http://www.worldclim.org/](http://www.worldclim.org/)]([http://www.worldclim.org/](http://www.worldclim.org/)), accessed on 6 August 2021). The data were generated by downscaling in China through the Delta space downscaling scheme and had a spatial resolution of approximately 1 km [42]. Then, ArcGIS 10.7 software was used to define the geographic coordinates of the NC data format, project them, and finally extract the annual average temperature in July in the study area. 3.