# Evidence of Carbon Uptake Associated with Vegetation Greening Trends in Eastern China
## 2 Data and Methods
### Trends in Regional XCO\({}_{2}\) Summer Drawdown
#### 2.2.5 Quantifying XCO\({}_{2}\) Trends  
Global detrended GM-XCO\({}_{2}\) maps derived from integrated and gap-filled satellite observations with temporal and spatial resolution of 8 days and \(1\times 1\) degree were examined for growing period (GP) drawdown trends from 2003 to 2015. The GP was defined for each grid cell using the EVI analysis presented in Section 2.1.2 and the mean GP value of the detrended GM-XCO\({}_{2}\) was calculated for each grid cell and for each year. Least-squares linear fitting and the Mann-Kendal test were used to calculate XCO\({}_{2}\) trends and significance for each grid cell.  
Estimating Surface CO\({}_{2}\) Fluxes from XCO\({}_{2}\) Variability Based on Correlations in Inversion Models  
XCO\({}_{2}\) variability is closely related to surface CO\({}_{2}\) fluxes, however quantifying that relationship is challenging due to uncertainties in atmospheric transport and remote versus local CO\({}_{2}\) contributions. To estimate the magnitude of the surface flux responsible for observed trends in XCO\({}_{2}\), we derived a relationship between surface CO\({}_{2}\) fluxes and atmospheric XCO\({}_{2}\) from model simulations including CarbonTracker and MACC-III across different time and spatial scales: Daily and 16 days and global and grid cells in EC regions (shown in Figure 1). The total area of selected grid cells in EC shown in Figure S8 is \(4.47\times 10^{12}\) m\({}^{2}\). As the regions become smaller, we expected more noise in the correlations due to transport of CO\({}_{2}\) in/out of the region. We also examined the relationship over different time intervals. Daily XCO\({}_{2}\) changes were calculated from the difference between two consecutive days and compared to the daily mean CO\({}_{2}\) flux. The daily XCO\({}_{2}\) and CO\({}_{2}\) flux changes from 1 January 2003 to 31 December 2016 in each grid cell were calculated using CT and MACC. XCO\({}_{2}\) changes of several days were defined as the sum of daily changes and CO\({}_{2}\) flux changes were defined as total CO\({}_{2}\) fluxes of these days. Correlation analysis and least-squares fitting were calculated for the flux-XCO\({}_{2}\) relationships (defined as transform ratios) at these different time and space scales. For this analysis of EC, we chose the 16-day correlation over EC to estimate CO\({}_{2}\) flux anomalies from XCO\({}_{2}\) changes.  
Figure 3: Example of GM-XCO\({}_{2}\) trend “correction” methods aimed at removing remote and local non-biospheric CO\({}_{2}\) flux influence from an individual grid cell (Lat: 38.5”N; Lon: 115.5”E). (**a**) GM-XCO\({}_{2}\) (red points) and different XCO\({}_{2}\) background characterizations: National Oceanic and Atmospheric Administration (NOAA) surface CO\({}_{2}\) increase (grey line) is calculated from the NOAA mean global CO\({}_{2}\) growth rate (+372 ppm), CT-XCO\({}_{2}\) (black line), Back-GEOS-XCO\({}_{2}\) (green line), Nested-GEOS-XCO\({}_{2}\) (blue dashed line) and GM-XCO\({}_{2}\) increase (red line) are the fitted results using corresponding XCO\({}_{2}\) and Equation (4). (**b**) Corrected GM-XCO\({}_{2}\) time series after removing the background characterizations from panel a. Same color key as above.