## 3 Results and Discussion
### Analysis of Relationship SM-VI-CO\({}_{2}\) under Drought Condition
#### 3.2.3 Relationship between SM, Vegetation and CO\({}_{2}\) during Drought Periods  
The results mentioned above confirm the close correlation between SM, VI, and CO\({}_{2}\) during the drought period. Since there was a time lag between the correlations of these factors, a lag correlation was performed (Figure 8 and Table 6). For homogeneous comparison of the factors, the standardized factors SM and NDVI were applied. The range of the CO\({}_{2}\) flux was also standardized from \(-1\) to \(1\) through standardized normalization.  
Figure 7: Temporal variations of SSMI and VCI during drought periods at (**a**) SMC and (**b**) CMC site.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**(a) SMC**} & \multicolumn{3}{c}{**Soil Moisture**} & \multirow{2}{*}{**Sum**} & \multirow{2}{*}{**Drought Accuracy**} \\ \cline{3-3} \cline{5-6}  & & **Drought** & & **No Drought** & & **Accuracy** \\ \hline \multicolumn{6}{c}{Moderate drought (\((\text{SM}_{\text{flatrower\_median}})=23.14\text{ m}^{3}\text{ m}^{-3}\))} \\ \hline \multirow{3}{*}{SSMI} & Drought & 8 & 3 & 11 \\  & No drought & 3 & 10 & 13 \\  & Sum & 11 & 13 & 24 \\ \hline \multirow{3}{*}{VCI} & Drought & 7 & 4 & 11 \\  & No drought & 5 & 8 & 13 \\  & Sum & 12 & 12 & 24 \\ \hline \multicolumn{6}{c}{Severe drought (\((\text{SM}_{\text{flatrower\_lower\_quantile}})=8.34\text{ m}^{3}\text{ m}^{-3}\))} \\ \hline \multirow{3}{*}{SSMI} & Drought & 6 & 6 & 12 \\  & No drought & 4 & 8 & 12 \\  & Sum & 10 & 14 & 24 \\ \hline \multirow{3}{*}{VCI} & Drought & 7 & 5 & 12 \\  & No drought & 3 & 9 & 12 \\  & Sum & 10 & 14 & 24 \\ \hline \multicolumn{6}{c}{**Soil Moisture**} & \multirow{3}{*}{**Sum**} & \multirow{3}{*}{**Drought Accuracy**} \\ \cline{3-3} \cline{5-6}  & & **Drought No Drought** & & **No Drought** \\ \hline \multicolumn{6}{c}{Moderate drought (\((\text{SM}_{\text{flatrower\_median}})=25.37\text{ m}^{3}\text{ m}^{-3}\))} \\ \hline \multirow{3}{*}{SSMI} & Drought & 7 & 2 & 9 \\  & No drought & 3 & 12 & 15 \\  & Sum & 10 & 14 & 24 \\ \hline \multirow{3}{*}{VCI} & Drought & 6 & 3 & 9 \\  & No drought & 6 & 9 & 15 \\  & Sum & 12 & 12 & 24 \\ \hline \multicolumn{6}{c}{Severe drought (\((\text{SM}_{\text{flatrower\_lower\_norm}})=9.28\text{ m}^{3}\text{ m}^{-3}\))} \\ \hline \multirow{3}{*}{SSMI} & Drought & 5 & 3 & 8 \\  & No drought & 8 & 8 & 16 \\  & Sum & 13 & 11 & 24 \\ \hline \multirow{3}{*}{VCI} & Drought & 6 & 4 & 10 \\  & No drought & 8 & 6 & 14 \\  & Sum & 14 & 10 & 24 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Error analysis for the study area.  
Figure 8: Lag correlation plot of SM, NDVI, and CO\({}_{2}\) flux at at **a)** SMC and **b)** CMC site.  
Figure 8 shows the result obtained from the lag correlation. Based on SM, the result showed the highest correlation for both NDVI and CO\({}_{2}\) after the time lag. In the case of NDVI, the highest correlation was found at a lag time of half to one month, and CO\({}_{2}\) showed the highest correlation at a lag time of one and a half month. When compared with the results of CO\({}_{2}\) correlation based on NDVI, the highest correlation was obtained at half month. Taken together, the two results reveal that the variation of SM started first followed by the variation in VI and CO\({}_{2}\) flux after a certain period of time.  
[PERSON] et al. (2014) studied the temporal lag of precipitation, soil moisture, evapotranspiration, and vegetation index. In their paper, the lag between SM and NDVI was approximately 16 days. However, such a result is generalized as extreme weather conditions are not considered. Therefore, the results presented in this study differ from the previous ones because they were obtained as the agricultural drought condition progressed. In extreme climatic conditions such as drought, a time lag of approximately one month between SM and VI, and half month between vegetation activity and photosynthesis had occurred.