# Evidence of Carbon Uptake Associated with Vegetation Greening Trends in Eastern China
## 2 Data and Methods
### Trends in Regional XCO\({}_{2}\) Summer Drawdown
#### 2.2.2 Merging and Gap-Filling XCO\({}_{2}\) Data Products (Integration and Mapping)  
In order to construct a long-term XCO\({}_{2}\) dataset, BESD-XCO\({}_{2}\) from January 2003 to May 2009, ACOS-XCO\({}_{2}\) from June 2009 to August 2014, and OCO-XCO\({}_{2}\) from Sep 2014 to March 2016 were used for XCO\({}_{2}\) integration and mapping. XCO\({}_{2}\) integration and mapping is the extension of the spatio-temporal geostatistical mapping method applied to multiple satellite observations. Corrections were made to account for differences in vertical measurement sensitivity, differences in satellite overpass times and fields of view, and observation gaps. Steps included: (1) Applying an averaging kernel correction based on vertical profiles from CarbonTracker, (2) normalizing overpass times and unifying spatio-temporal scales of multi-satellite XCO\({}_{2}\) data, and (3) global land mapping of XCO\({}_{2}\) based on spatio-temporal geostatistics. In the first step, we corrected for differences in altitude sensitivity of the sensors and normalized the measurements using averaging kernels and a-priori vertical profiles of CO\({}_{2}\) from CarbonTracker (CT-XCO\({}_{2}\)) selected as the common proxy for adjustment (Equation (2)) [43; 62]. \[XCO_{2 adj,t}=XCO_{2 ret,t}+h^{T}(I-A)(X_{M,t}-X_{a,t}) \tag{2}\]  
where \(XCO_{2 adj,t}\) is the adjusted XCO\({}_{2}\) value at observation time \(t\), \(XCO_{2 ret,t}\) corresponds to retrieved XCO\({}_{2}\) of BESD, ACOS, or OCO-2, \(h\) and \(A\) are the pressure weighting functions and column-averaging kernels from the retrieval algorithm, respectively, \(I\) is an identity matrix, \(X_{M,t}\) is the common priori CO\({}_{2}\) profile from CT, and \(X_{a,t}\) is a priori CO\({}_{2}\) profile from satellite retrievals. Considering the diurnal variability in XCO\({}_{2}\) and differences in satellite overpass times, step 2 unified XCO\({}_{2}\) from multiple satellites to a common observing local time and spatial resolution. We introduced a scale factor derived from the diurnal variation of XCO\({}_{2}\) using CT-XCO\({}_{2}\) to normalize the overpass time of XCO\({}_{2}\) retrievals from these three satellites to a reference time (Equation (3)). \[XCO_{2 nor,t}=\frac{XCO_{2 CT,t}}{XCO_{2 CT,t}}\star XCO_{2 adj,t} \tag{3}\]  
where \(XCO_{2 nor,t}\) is the normalized satellite-observed XCO\({}_{2}\) at the reference time (\(rt\): 13:00, local time); \(XCO_{2 adj,t}\) is the adjusted satellite XCO\({}_{2}\) derived from Equation (2) at satellite overpass time \(t\); \(XCO_{2 CT,t}\) and \(XCO_{2 CT,t}\) are the XCO\({}_{2}\) from CT model at the reference time \(rt\) and satellite overpass time \(t\), respectively. Additionally, we unified the different field of views (\(30\times 60\) km, diameter of 10.5 km and \(2.25\times 1.5\) km, respectively) and repeat cycles (36 days, 3 days, and 16 days, respectively) of SCIAMACHY, GOSAT, and OCO-2 before using a gap-filling method. In this study, we used a uniform spatio-temporal scale of \(30\times 30\) km as a space unit and 8-day as a time unit to average \(XCO_{2 nor,t}\) of BESD-XCO\({}_{2}\), ACOS-XCO\({}_{2}\), and OCO-XCO\({}_{2}\) respectively. This uniform spatio-temporal scale was introduced to aggregate different XCO\({}_{2}\) data products in order to maintain as much as possible the spatial (regional and national) and temporal (monthly and seasonally) variation of XCO\({}_{2}\) observed by these three satellites. The integrated XCO\({}_{2}\) dataset in \(30\times 30\) km and 8 days was generated from 2003 to 2016, hereafter referred to as integrated-XCO\({}_{2}\). The data quantity and trends of integrated-XCO\({}_{2}\) from 2003 to 2016 is shown in Figure S2. In step 3, we applied a gap-filling interpolation method to the integrated XCO\({}_{2}\) to produce continuous global XCO\({}_{2}\) maps in time and space. The spatio-temporal geostatistical mapping method, GM-XCO\({}_{2}\), applied in GOSAT observations has been previously used in global carbon research studies [28; 31; 63; 64].