## 4 Conclusions  
The inter-relationship between soil moisture (SM), vegetation activity, and atmospheric CO\({}_{2}\) concentration was analyzed using MODerate resolution imaging spectroradiometer (MODIS), an optical multispectral sensor. The SM was also estimated using MODIS. The calculated SMMODIS was compared with the SMfluor observed in a flux tower of the study area. As a result, both points showed high correlation (SMC: 0.75, CMC: 0.66). A relatively large bias was obtained in SMC due to the influence of heterogeneous land surface albedo in mixed forest areas. In the case of atmospheric CO\({}_{2}\) flux, MODIS gross primary productivity (GPP) product was used to leverage the flux's relationship with respiration in the calculation. Similarly, the calculated results were compared with the CO\({}_{2}\) flux results of SMC and CMC to confirm their applicability. The flux values proved the relatively high applicability of the SMC result, which is due to the effect of leaf area index (LAI). This implies SMC in a dense forest area has a high value of LAI.  
Lastly, the relationship between each variable was identified by comparing SM, VI, and CO\({}_{2}\) under the extreme drought periods of 2014 and 2015 in South Korea. As a result, the highest correlation was obtained when there was a time lag of one month between SM and vegetation and half month between vegetation and CO\({}_{2}\). This tendency was similar in both SMC and CMC. As such, these three variables have been proved to affect each other with time lag, and it was confirmed that the lag is longer than the normal season during the drought period. In the long term, however, changes in atmospheric CO\({}_{2}\) concentration may affect carbon reservoirs in the land and the subsurface. In the future, relationship studies between SM, VI, and CO\({}_{2}\) on the land and the subsurface during thoughts should be followed by considering sources and depletions in carbon fluxes.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**(a) SMC**} & \multicolumn{8}{c}{**Lag Time (Month)**} \\ \cline{2-10}  & **-2.0** & **-1.5** & **-1.0** & **-0.5** & **0** & **0.5** & **1.0** & **1.5** & **2.0** \\ \hline SM \(-\) NDVI & \(-\)0.12 & 0.04 & 0.11 & 0.21 & 0.61 & **0.78 \({}^{\star}\)** & **0.81 \({}^{\star}\)** & 0.52 & 0.24 \\ SM \(-\)CO\({}_{2}\) & \(-\)0.21 & \(-\)0.03 & 0.22 & 0.45 & 0.64 & 0.67 & **0.86 \({}^{\star}\)** & **0.88 \({}^{\star}\)** & 0.31 \\ NDVI \(-\)CO\({}_{2}\) & \(-\)0.02 & 0.12 & 0.34 & 0.55 & **0.78 \({}^{\star}\)** & **0.82 \({}^{\star}\)** & 0.62 & 0.53 & 0.21 \\ \hline \multirow{2}{*}{**(b) CMC**} & \multicolumn{8}{c}{**Lag Time (Month)**} \\ \cline{2-10}  & **-2.0** & **-1.5** & **-1.0** & **-0.5** & **0** & **0.5** & **1.0** & **1.5** & **2.0** \\ \hline SM \(-\) NDVI & \(-\)0.43 & \(-\)0.15 & \(-\)0.05 & 0.45 & 0.65 & **0.72 \({}^{\star}\)** & **0.77 \({}^{\star}\)** & 0.57 & 0.06 \\ SM \(-\)CO\({}_{  
**Author Contributions:** Conceptualization, C.S. and D.-H.K.; methodology, C.S., J.E.Y. and Y.S.; software, D.-H.K. and K.J.L.; validation, C.S., Y.S. and Y.J.; formal analysis, C.S.; investigation, C.S. and K.J.L.; resources, D.-H.K. and J.E.Y.; data curation, C.S., K.J.L., J.E.Y., Y.S. and Y.J.; writing--original draft preparation, C.S.; writing--review and editing, D.-H.K., K.J.L., J.E.Y. and Y.J.; visualization, Y.S.; supervision, D.-H.K.; project administration, K.J.L. and J.Y.; funding acquisition, K.J.L. and J.E.Y. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This subject is supported by Korea Ministry of Environment as \"The SS (Surface Soil conservation and management) projects; 2019002820002\".  
**Acknowledgments:** The authors send special thanks to the Korean Institute of Hydrological Survey (KIHS) for their data collection efforts.  
**Conflicts of Interest:** The authors declare no conflict of interest.