## 3 Results
### Correlation between XCO\({}_{2}\) and Biosphere Parameters  
In this section, correlation analyses are conducted, respectively, between seasonal variations of GM-XCO\({}_{2}\) data and several biophysical parameters associated with biosphere activities, including NDVI, EVI, LAI and GPP, to explore the underlying biosphere-atmospheric coupling process that drives the XCO\({}_{2}\) seasonality. Figure 5 shows the global distribution of the Pearson Correlation Coefficients (PCCs) with a significant level (\(p\)-value \(<\) 0.01) between monthly-averaged dXCO\({}_{2}\) and NDVI, EVI, LAI, and GPP, respectively, from June 2009 to May 2014 in each grid. Due to the lack of available data, the tropical forests in Amazon and Southeast Asia and the Tibetan Plateau are not considered here. All of the PCCs between seasonal cycles of XCO\({}_{2}\) and seasonal variations of NDVI, EVI, LAI, and GPP, shown in Figure 5, present similar spatial patterns and are mostly negatively correlated, except for the bare land areas (shown in Figure 1). Especially, the seasonal cycle of XCO\({}_{2}\) show stronger and significant negative correlations with the biosphere parameters over Northeast Asia around 45\({}^{\circ}\)N than those over the other areas. Among the indices of NDVI, EVI, LAI, and GPP, XCO\({}_{2}\) shows stronger negative correlation with NDVI and EVI than those with LAI and GPP globally. In the NH high-latitude region, the correlation coefficients are \(-\)0.69, \(-\)0.68, \(-\)0.66, and \(-\)0.59 for NDVI, EVI, LAI, and GPP, respectively. They are \(-\)0.74, \(-\)0.69, \(-\)0.64, and \(-\)0.67 in the NH low-latitude region. It is known that LAI and GPP are the vegetation parameters derived from semi-empirical biophysical models, which likely induce more uncertainty than NDVI and EVI that are directly retrieved from MODIS-observed radiance. Moreover, it can be seen that the PCCs between XCO\({}_{2}\) and LAI are slightly weaker than those from other indices in the low latitudes, which is likely because LAI is an indicator of vegetation biophysical structure rather than biochemical activities [59; 60]. The PCCs from EVI, moreover, are slightly higher than that from NDVI over Northeast China. This difference may be related to the saturation effect of NDVI in high biomass regions, while EVI data does not become saturated as easily as NDVI by using the non-saturated NIR band for high biomass regions [61]. We selected six regions of interest with a PCC higher than 0.5 distributed across multiple latitudes as shown in Figure 6 to investigate the correlation of seasonal variations of XCO\({}_{2}\) and NDVI from June 2009 to May 2014. These six regions of interest are shown in Figure 1, including FnC: forest in Northern Canada covered by 63% of forest, FeR: forest in Eastern Russia covered by 86% of forest, CwR: crop in Western Russia covered by 70% of cropland, CnC: crop in Northern China covered by 58% of cropland with mixed 18% grassland and shrub-land, GcA: grass in Central Africa covered by 36% of grassland mixed with 30% of forest, and CnI: crop in Northern India covered by 89% of cropland. Figure 4: Spatial distribution of NDVI SCA, which is calculated for each grid by fitting Equation (1) to the 5-year NDVI data and obtaining the annual-mean differences between peaks and troughs after subtracting the linear trend. The two overlapped contour lines are the XCO\({}_{2}\) SCA from GM-XCO\({}_{2}\), with 8.0 ppm in solid black line and 4.0 ppm in dotted black line as shown in Figure 3.  
Figure 5: Pearson Correlation Coefficients (PCCs) between monthly mean of detrended GM-XCO\({}_{2}\) (dXCO2) and parameters for biosphere activities, including **(a)** NDVI, **(b)** EVI, **(c)** LAI, and **(d)** GPP from MODIS data products in each grid from June 2009 to May 2014. Only grids with significant levels of correlation (\(p\)-value < 0.01) are shown. In calculation of the correlation coefficient, all data are averaged by month.