# Evidence of Carbon Uptake Associated with Vegetation Greening Trends in Eastern China
## 2 Data and Methods
### Trends in Regional XCO\({}_{2}\) Summer Drawdown
#### 2.2.4 XCO\({}_{2}\) Detrending Methods  
To quantify local biosphere-driven changes in XCO\({}_{2}\) over time, we need to remove the background XCO\({}_{2}\) increase due to sustained fossil fuel emissions and influence from ocean exchange and fire, as well as remote biospheric influence from the study region [69; 70]. The precise influence of all non-local non-biospheric processes cannot be directly measured, so we tested four different approaches for defining the background trend to isolate the local biospheric influence in the GM-XCO\({}_{2}\) record. For a first approximation, we adopted the global mean yearly increase from NOAA ([[https://www.esrl.noaa.gov/gmd/ccgg/trends/gr.html](https://www.esrl.noaa.gov/gmd/ccgg/trends/gr.html)]([https://www.esrl.noaa.gov/gmd/ccgg/trends/gr.html](https://www.esrl.noaa.gov/gmd/ccgg/trends/gr.html))) to build a global background XCO\({}_{2}\) increase and applied that uniformly to all grid cells in the study region. The three other detrending methods were based on curve-fitting long-term trends, calculated and applied on a grid cell-by-cell basis. For one, we used the long-term trend XCO\({}_{2}\) increase from the gridded GM-XCO\({}_{2}\) observations themselves. In another, we used the fitted XCO\({}_{2}\) gridded results from CT-XCO\({}_{2}\). Finally, we fitted the global background and nested GEOS-Chem simulated XCO\({}_{2}\) to clarify the remote influences from the local influences.  
The curve-fitting equation applied to each of the three XCO\({}_{2}\) records used a combination of a step-wise linear function and annual periodic function as shown in Equation (4).  
\[f(t)=k_{0}+k_{1}t+\sum\
olimits_{m=1}^{4}(a_{i}\cos(2\pi mt)+b_{i}\sin(2\pi mt )) \tag{4}\]  
Here, \(f(t)\) is XCO\({}_{2}\) in time \(t\), \(k_{0}\) and \(k_{1}t\) are treated as the background and cumulated increase of XCO\({}_{2}\) in each year, and \(\sum\
olimits_{i=1}^{4}(a_{i}\cos(2\pi mt)+b_{i}\sin(2\pi mt))\) is used for characterizing the XCO\({}_{2}\) seasonal cycle. An example of GM-XCO\({}_{2}\) and CT-XCO\({}_{2}\) fitting of 13 years in one grid cell (Lat: 38.5\({}^{\circ}\)N; Lon: 115.5\({}^{\circ}\)E) over EC is shown in Figure 3. Because fitting trends for individual years leads to discontinuities due to the start and end values, we used the mean value of three fitting results using 3 different time windows, starting from 1 December of previous year, 1 January, or 1 February of that year. Example curve fits are shown in Figure 3, but different patterns may be observed at other grid cells. The background XCO\({}_{2}\) increase (\(y\)) in year \(i\) and day \(j\) are extracted from the non-seasonal portion of Equation (4) and can be interpolated to daily values using Equation (5).  
\[y_{i,j}=k_{i0}+k_{11}\mathsf{sj}/n \tag{5}\]  
where \(k_{i0}\) and \(k_{i1}\) are the fitted XCO\({}_{2}\) background (\(k_{0}\)) and increase ratio (\(k_{1}\)) in year \(i\) (from Equation (4) fit), \(n\) is the total units in one year ('365' used for daily data and '46' used for data with time resolution of 8 days), and \(j\) is the current time step (day or number of 8-day interval). The yearly fitting performed well in global/site CO\({}_{2}\) yearly increase with differences of \(-0.04\pm 0.27\) ppm for NOAA global mean, \(-0.03\pm 0.13\) ppm for global mean of CT-XCO\({}_{2}\), and \(-0.06\pm 0.19\) ppm for Mauna Loa shown in Figure S7 and Table S1.