## 4 Discussion
### Superiority of Time Series NDVI Approach
#### 4.2.1 Exploring the Deep Mechanism of the Relationship Between SOC and NDVI Time Series  
SOC is a major indicator of soil fertility and plays an important role in ecosystem productivity, agricultural ecosystem function, and farmland fertility [86]. Thus, the SOC content affects crop yield to a large extent. NDVI is strongly correlated to vegetation GPP [87]. GPP is derived from the calculation of photosynthetic effective radiation (PAR), namely, the famous light energy utilization equation [87; 88; 89]:  
\[\mathrm{GPP}=\mathrm{fAPAR}\times\mathrm{PAR}\times\mathrm{LUE}, \tag{7}\]  
\[\mathrm{APAR}=\mathrm{fAPAR}\times\mathrm{PAR}, \tag{8}\]  
where fAPAR is the fraction of absorbed photosynthetically active radiation, APAR is the absorbed photosynthetically active radiation, PAR is the photosynthetically active radiation, and LUE is the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dim**} & \multirow{2}{*}{**Eigenvalue**} & \multirow{2}{*}{
\begin{tabular}{c} **Condition** \\ **Index** \\ \end{tabular} } & \multicolumn{6}{c}{**Variance Proportions**} \\ \cline{3-10}  & & & **Con** & \(\mathbf{NDVI_{Feb}}\) & \(\mathbf{NDVI_{Jul}}\) & \(\mathbf{NDVI_{Sept}}\), \(\mathbf{NDVI_{Jan}}\), \(\mathbf{NDVI_{Aug}}\), \(\mathbf{NDVI_{Jun}}\), \(\mathbf{NDVI_{Apr}}\) \\ \hline
**1** & **7.52** & 1.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline
2 & 0.20 & 6.09 & 0.00 & 0.07 & 0.00 & 0.03 & 0.09 & 0.00 & 0.10 & 0.00 \\
3 & 0.08 & 9.44 & 0.00 & 0.01 & 0.00 & 0.33 & 0.04 & 0.02 & 0.38 & 0.00 \\
4 & 0.08 & 9.61 & 0.00 & 0.01 & 0.02 & 0.05 & 0.01 & 0.18 & 0.04 & 0.24 \\
5 & 0.05 & 12.92 & 0.02 & 0.56 & 0.00 & 0.02 & 0.06 & 0.05 & 0.08 & 0.43 \\
6 & 0.03 & 15.69 & 0.38 & 0.01 & 0.02 & 0.27 & 0.41 & 0.00 & 0.25 & 0.12 \\
7 & 0.03 & 16.35 & 0.30 & 0.34 & 0.00 & 0.18 & 0.36 & 0.17 & 0.06 & 0.20 \\
8 & 0.01 & 27.10 & 0.30 & 0.00 & 0.95 & 0.12 & 0.03 & 0.58 & 0.09 & 0.01 \\ \hline \hline \end{tabular} Note: Con is the constant of function, \(\mathbf{NDVI_{Feb}}\) is the NDVI (normalized difference vegetation index) data in February, and \(\mathbf{NDVI_{Jul}}\) is NDVI data in July, etc.  
\end{table} 
Table 7: Collinearity diagnosis of environmental factors in the SLR model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \(\mathbf{NDVI_{Feb}}\), & \(\mathbf{NDVI_{Jul}}\), & \(\mathbf{NDVI_{Sept}}\), & \(\mathbf{NDVI_{Jan}}\), & \(\mathbf{NDVI_{Aug}}\), & \(\mathbf{NDVI_{Jun}}\), & \(\mathbf{NDVI_{Apr}}\) \\ \hline Tolerance & 0.48 & 0.37 & 0.63 & 0.39 & 0.41 & 0.74 & 0.60 \\ \hline VIF & 2.08 & 2.71 & 1.59 & 2.57 & 2.46 & 1.35 & 1.66 \\ \hline \hline \end{tabular} Note: VIF is the variance inflation factor, \(\mathbf{NDVI_{Feb}}\) is the NDVI (normalized difference vegetation index) data in February, and \(\mathbf{NDVI_{Jul}}\) is the NDVI data in July, etc.  
\end{table} 
Table 8: VIFs for the SLR model. vegetation light energy utilization. Several studies have shown that fAPAR and LUE are strongly correlated with VI [90; 91; 92; 93]. Thus, the following formula can be derived [94]:  
\[\text{GPP}\propto\text{PAR}\times\text{VI}, \tag{9}\]  
A feedback loop occurs where production feeds carbon into the soil, and high SOC improves the soil, indicating large production. This result was supported by [PERSON] et al. [95], who considered GPP implicate the turnover of SOC to some extent. [PERSON] et al. [96] used GPP as an auxiliary to estimate surface (<10 cm depth) SOC stocks. [PERSON] et al. [90] used NDVI to estimate fAPAR. [PERSON] et al. [97] used NDVI and ratio vegetation index (RVI) to calculate fAPAR. Crop growth in cultivated lands was influenced by soil, which was reflected in remote sensing images. Thus, time series NDVI can potentially conduct soil mapping in plain areas. On this basis, NDVI can predict SOC stocks. Considering only the environmental factors at a certain time is inaccurate because of the complexity of soil formation.