## 4 Discussion
### Superiority of Time Series NDVI Approach
#### 4.2.1 Exploring the Deep Mechanism of the Relationship Between SOC and NDVI Time Series
Thus, the time series characteristics of auxiliary variables should be considered to effectively reflect the relationship between environmental factors and target variables. Meanwhile, as previously mentioned, the sum of NDVI is correlated to GPP (the sum of APAR radiation, which is NDVI times incident PAR). Single-date NDVI is not correlated to SOC and production. [PERSON] et al. [93] used multitime NDVI to estimate fAPAR. Thus, the NDVI time series data in this study, which consider a vital factor (i.e., time), can closely indicate their correlation. For the effect of regression using single-data NDVI, Table 9 shows the unsatisfactory results (with all R\({}^{2}<\)0.1). This finding indicated that single-data NDVI cannot be used to predict SOC. The predictive effect of short time series was evaluated. Two short NDVI time series data, which were correlated to summer and winter crop production, respectively, were applied to model ANN and SVM. The results (Table 10) showed that the NDVI time series data of summer crop production exhibited better precision (R\({}^{2}_{\text{P}}\) of ANN 0.281, RMSE\({}_{\text{P}}\) of ANN 4.119, R\({}^{2}_{\text{P}}\) of SVM 0.343, RMSE\({}_{\text{P}}\) of SVM 3.863) than that of winter crop production (R\({}^{2}_{\text{P}}\) of ANN 0.173, RMSE\({}_{\text{P}}\) of ANN 4.980, R\({}^{2}_{\text{P}}\) of SVM 0.162, RMSE\({}_{\text{P}}\) of SVM 4.908). This finding manifested that short NDVI time series (related to crop production) can be used for SOC prediction to some extent, but the prediction accuracy of short time series was lower compared with long time series, which was particularly evident for winter crop production. This condition was because Honghu City had more summer crops that winter crops (the most yield crop were lotus root and rice, which were summer crops). Another reason was because short time series NDVIs of summer were true time series (from 2013.4 to 2013.9), whereas that of winter was not. Although the entire NDVI time series under multiple years can be used to predict SOC regarded as pseudo time series, the short time series was susceptible to be influenced considerably. At the same \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Modeling Accuracy**} & \multicolumn{2}{c}{**Prediction Accuracy**} \\ \cline{2-5}  & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** \\ \hline NDVI\({}_{\text{Jan.}}\) & 5.542 & 0.031 & 4.693 & 0.020 \\ NDVI\({}_{\text{Feb.}}\) & 5.407 & 0.077 & 4.710 & 0.032 \\ NDVI\({}_{\text{Mar.}}\) & 5.498 & 0.046 & 4.688 & 0.023 \\ NDVI\({}_{\text{Apr.}}\) & 5.441 & 0.065 & 4.793 & 0.058 \\ NDVI\({}_{\text{MAy}}\) & 5.608 & 0.007 & 4.747 & 0.004 \\ NDVI\({}_{\text{Jun.}}\) & 5.529 & 0.035 & 4.574 & 0.064 \\ NDVI\({}_{\text{Jul.}}\) & 5.536 & 0.032 & 4.625 & 0.060 \\ NDVI\({}_{\text{Aug.}}\) & 5.568 & 0.021 & 4.600 & 0.071 \\ NDVI\({}_{\text{SPpt.}}\) & 5.488 & 0.049 & 4.675 & 0.041 \\ NDVI\({}_{\text{Oct.}}\) & 5.630 & 0.001 & 4.754 & 0.001 \\ NDVI\({}_{\text{Nov.}}\) & 5.565 & 0.022 & 4.799 & 0.001 \\ NDVI\({}_{\text{Dec.}}\) & 5.583 & 0.016 & 4.692 & 0.021 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Single-data NDVI regression analysis. time, the accuracy of these short time series predictors for the SVM model was better than that of the ANN model. This condition discussed the performance of SVM and ANN methods, as suggested by [PERSON] et al. [66]. The SVM method obtained better results (R\({}^{2}\)P for summer 0.343, RMSE\({}_{\text{P}}\) for summer 3.863, R\({}^{2}\)P for winter 0.162, RMSE\({}_{\text{P}}\) for winter 4.908) for prediction using short NDVI time series data than that of ANN (R\({}^{2}\)P for summer 0.281, RMSE\({}_{\text{P}}\) for summer 4.119, R\({}^{2}\)P for winter 0.137, RMSE\({}_{\text{P}}\) for winter 4.980), and the entire NDVI time series data provided close performance of ANN (R\({}^{2}\)P 0.391, RMSE\({}_{\text{P}}\) 3.718) and SVM (R\({}^{2}\)P 0.361, RMSE\({}_{\text{P}}\) 3.753). Thus, the SVM method was selected for SOC prediction using short time series.