## 3 Results
### Global Pattern of Phase Delay Effect of XCO\({}_{2}\) to NDVI  
While almost impossible for surface measurements, the GM-XCO\({}_{2}\) and NDVI data in this study allow us to investigate the global distribution of phase delay effect in terms of lags of months. The results are shown in Figure 7a, which is the averaged phase lag for five years of GM-XCO\({}_{2}\) and NDVI data. This map of phase delay effect, to our knowledge, is the first such map derived from a completely data-driven approach using satellite observations. Generally, the phase delay in southern hemisphere is either zero or one, probably due to the much smaller change of CO\({}_{2}\) mass in the column that needs time to be well mixed in column. In the NH mid- and high-latitude regions, interestingly, the pattern of the phase delay is similar to the seasonal \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Sites** & **Location** & **Coincident** & **Averaged** & **Averaged Absolute** & **Standard** & **GM-XCO\({}_{2}\)** & **TCCON** & **SCA** \\  & **(Latitude Longitude)** & **Data Pairs** & **Bases (ppm)** & **Bias (ppm)** & **Deviation (ppm)** & **SCA (ppm)** & **SCA (ppm)** & **Difference (ppm)** \\ \hline Bailyback & (332, 23.02) & 231 & 0.33 & 1.10 & 2.03 & 7.38 & 8.38 & \(-\)1.00 \\ Bremen & (331, 8.85) & 119 & \(-\)0.35 & 1.23 & 2.67 & 6.67 & 7.35 & \(-\)0.68 \\ Karlsruhe & (491, 8.44) & 103 & \(-\)0.57 & 1.33 & 2.59 & 6.12 & 7.50 & \(-\)1.38 \\ Orleans & (4797, 211) & 259 & 0.21 & 1.11 & 1.94 & 5.87 & 7.62 & \(-\)1.75 \\ Garinch & (474, 118, 102) & 322 & \(-\)0.49 & 1.21 & 2.09 & 5.99 & 6.99 & \(-\)1.00 \\ Park Falls & (454, 90.27) & 453 & \(-\)0.24 & 1.02 & 1.62 & 9.25 & 9.2 & 0.05 \\ Lamont & (66.6) & (74.97) & 513 & 0.25 & 0.95 & 1.40 & 5.18 & 5.8 & \(-\)0.62 \\ Turkaba & (06.6) & (140.12) & 246 & \(-\)1.72 & 1.94 & 2.70 & 7.38 & 6.38 & 1.00 \\ JPl/Caltech & (04.2) & \(-\)118.19 & 195 & 0.10 & 1.29 & 2.45 & 5.32 & 6.07 & \(-\)0.75 \\ Sagie & (032, 130.29) & 208 & 1.08 & 1.37 & 1.39 & 6.94 & 6.65 & 0.29 \\ Darwin & (12-143, 130.89) & 413 & \(-\)0.36 & 1.02 & 1.37 & 2.27 & 1.12 & 1.15 \\ Wollongong & (\(-\)34.41, 150.88) & 412 & \(-\)0.36 & 0.68 & 0.65 & 1.34 & 1.41 & \(-\)0.07 \\ Overall & & 3564 & \(-\)0.18 & 1.19 & 1.91 & 1.91 & & \(-\)0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics of comparison between GM-XCO\({}_{2}\) and TCCON data (smoothed by applying the ACOS-GOSAT averaging kernel), and their SCAs for the following 12 sites. Bias is calculated using GM-XCO\({}_{2}\) minus TCCON XCO\({}_{2}\) for each coincident data pair and averaged for each site. Figure 7: **(a)** The global distribution of phase delay effect, in terms of lags of months, between seasonal variations of XCO\({}_{2}\) and NDVI, and (**b**) the correlation between XCO\({}_{2}\) and NDVI if the phase delay effect is excluded. Only grids with month lags of no more than three are shown. cycle pattern derived from GM-XCO\({}_{2}\) shown in Figure 3 and from NDVI shown in Figure 4. The larger amplitudes, such as North America and North Eurasia boreal forest regions, correspond to a smaller time delay, suggesting that the strength of vertical mixing is much stronger in these areas, even though the biosphere-atmosphere exchange in these areas is also large. As shown in [64] by [PERSON] et al., the strength of vertical mixing in boreal and arctic regions is not as strong as that in the tropics, which may lead to stronger phase delay effect in high latitude regions. Moreover, XCO\({}_{2}\) has a large footprint, which is supposed to have contributions from different oceanic and land regions. However, satellite observations of XCO\({}_{2}\), such as from ACOS-GOSAT, are more sensitive to CO\({}_{2}\) variations within the boundary layer [65], which allows us to explore the biosphere-atmosphere interactions by correlating seasonal cycles of satellite-observed XCO\({}_{2}\) and surface biosphere parameters. Figure 7b shows the PCC between seasonal variation of XCO\({}_{2}\) and NDVI if the phase delay effect is excluded.