## 3 Results  
### Spatial Pattern of Seasonal Cycle Amplitude of XCO\({}_{2}\) and NDVI  
XCO\({}_{2}\) SCA is an effective indicator of the strength of seasonal variation of XCO\({}_{2}\), which is related to the increase and drawdown of CO\({}_{2}\) in the atmosphere [13]. The spatial variation of SCA has been shown by [PERSON] et al. [14] using ground measurements from sparse TCCON stations. Further work by [PERSON] et al. [15] using satellite retrievals has shown the global variation of SCA in 10\({}^{\circ}\) by 10\({}^{\circ}\) grids based on a traditional binning method, which, however, does not consider the detailed variation information within each grid. Based on our global land mapping data, Figure 3 shows the global  
Figure 2: Example of fitting GM-XCO\({}_{2}\) using Equation (1) in the top panel, in which (\(k_{0}\), \(k_{1}\), \(a_{1}\), \(a_{2}\), \(b_{1}\), \(b_{2}\)) = (386.058, 0.0163, \(-\)0.555, 1.116, \(-\)3.731, \(-\)1.311). In the bottom panel, the seasonal GM-XCO\({}_{2}\) (dXCO\({}_{2}\)) is calculated by removing the yearly increases from the temporal variation of GM-XCO\({}_{2}\). The fitting residual is the difference between GM-XCO\({}_{2}\) and the fitting. Monthly-averaged seasonal GM-XCO\({}_{2}\) is the monthly mean of dXCO\({}_{2}\), which is used in Section 3.2.  
land distribution of XCO\({}_{2}\) SCA derived from seasonal cycle of GM-XCO\({}_{2}\) from June 2009 to May 2014 using Equation (1). This is, to our knowledge, the first reported global map of CO\({}_{2}\) SCA at fine scale derived from real measurements. The goodness-of-fit evaluated by coefficient of determination (R\({}^{2}\)) between mapping and fitting XCO\({}_{2}\), as described in Section 2.2, is shown in Figure S1. We can see that R\({}^{2}\) for all fittings is larger than 0.9, indicating that the fittings well capture the seasonal cycle of GM-XCO\({}_{2}\). This global map of XCO\({}_{2}\) SCA clearly shows the latitude gradient decrease from north to south that is consistent with previous studies using ground measurements and binned satellite observations [15; 35; 57]. In the southern hemisphere (SH), the XCO\({}_{2}\) SCA are mostly lower than 4.0 ppm except some areas in Southern Africa, where the amplitude is above 4.0 ppm. It can be seen from this SCA map, moreover, that the range border of greater than 8 ppm extended over the high latitudes mostly with boreal forest in the NH. Moreover, the tropical and subtropical areas in India and Central Africa show abnormal SCA values larger than 8 ppm, which have not been seen previously and can be detected from our mapping dataset with fine spatial details. To investigate how biosphere activities drive the spatial pattern of XCO\({}_{2}\), we correlated the XCO\({}_{2}\) SCA, as shown in Figure 3, with NDVI SCA, an indicator of the strength of vegetation photosynthesis and its resulting carbon uptake. Corresponding to Figure 3, Figure 4 presents the NDVI SCA overlapped with amplitude contour lines of GM-XCO\({}_{2}\) shown in Figure 3, which is derived in the same way as XCO\({}_{2}\) SCA for the same period. Comparing Figure 3 with Figure 4, it can be seen that the overall spatial distribution of XCO\({}_{2}\) SCA shows a very similar pattern as that of NDVI, with a high correlation coefficient of 0.69 for global land and 0.74 for the NH land. Both the SCAs of XCO\({}_{2}\) and NDVI generally decrease with latitude from north to south. Especially, the amplitude of XCO\({}_{2}\) has the largest value ranging from 8.0 ppm up to 12 ppm over high latitude in the NH, corresponding well to the highest amplitude of NDVI in these areas, which is likely caused by the strong CO\({}_{2}\) uptake during the growing season by boreal forest (Figure 1) [13; 58]. The SCA of XCO\({}_{2}\) changes mostly from 4.0 ppm to 8.0 ppm over the mid-latitude area in the NH.