# Investigation of the EWT-PSO-SVM Model for Runoff Forecasting in the Karst Area
## 4 Results and Discussion
### Performance Analysis
#### 4.5.2 Forecasting Results with Different Input Models  
Furthermore, verifying the stability of the developed model, the model forecasting results under different data structures were compared. The original sequential structure runoff data were reconstructed into monthly structure runoff data, and the new data structure models were named SVM (M), PSO-SVM (M), and EWT-PSO-SVM (M). The 12 subseries of the monthly structural runoff data were substituted into the SVM (M), PSO-SVM (M), and EWT-PSO-SVM (M) models for prediction, and the forecasting and evaluation results of the models are shown in Figures 10-12 and Tables 3 and 4.  
Figure 10 shows the forecasted runoff depth of the models using the monthly structure. It demonstrates that the forecasting results of the EWT-PSO-SVM (M) model are closer to the measured results and better simulate the monthly runoff, which indicates that the EWT-PSO-SVM (M) model outperforms the PSO-SVM (M) model and the SVM (M) model.  
Figure 11 shows the scatter plot of the model forecasting results under the monthly structure. Figure 11 demonstrates that the linear correlation coefficient of the EWT-PSO-SVM (M) model (0.73) is the highest, while the linear correlation coefficient of the PSO-SVM (M) model (0.58) and the SVM (M) model (0.62) are close. EWT-PSO-SVM (M) exhibits the highest performance in all three models.  
In addition, Figure 12 displays the Taylor diagram of the model forecasting results under the monthly structure. Figure 12 presents that the point of the EWT-PSO-SVM (M) model is closest to the observation point, which indicates that the EWT-PSO-SVM (M) model has the highest forecasting accuracy compared with the SVM (M) model and the PSO-SVM (M) model. Meanwhile, the Taylor diagram demonstrates similar conclusions to Figures 10 and 11 Therefore, the three pictures indicate that the developed model has good stability.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & _NSE_ & _MAPE_ & _RMSE_ & _MAE_ & \(R\) & \(\mathbf{M_{R}}\) \\ \hline SVM (M) & 3 & 3 & 3 & 3 & 3 & 0 \\ PSO–SVM (M) & 2 & 2 & 2 & 2 & 2 & 0.33 \\ EWT–PSO–SVM (M) & 1 & 1 & 1 & 1 & 1 & 0.67 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ranking of evaluation indexes and overall evaluation scores of the three models.  
Figure 12: Taylor Diagram under the monthly structure.  
Table 3 shows the forecasting performance of the three new data structure models under different evaluation indexes. It shows that EWT-PSO-SVM (M) demonstrates the optimal results in all evaluation indexes. Compared with the PSO-SVM (M) model, the _MAPE_, _RMSE_, and _MAE_ values of the EWT-PSO-SVM (M) model are reduced by 22.77%, 26.02%, and 26.75%, respectively, and the _NSE_ and \(R\) values are improved by 37.31% and 15.59%. Compared with the SVM (M) model, the _MAPE_, _RMSE_, and _MAE_ values of the EWT-PSO-SVM (M) model are reduced by 25.28%, 28.66%, and 30.25%, respectively, and the _NSE_ and \(R\) values are improved by 18.45% and 46.41%.  
Table 4 further evaluates the monthly structure models using the composite rating index method. The M\({}_{\text{R}}\) of the EWT-PSO-SVM (M) model reaches 0.67 and the model comprehensive performance is optimal.  
In conclusion, the hybrid EWT-PSO-SVM model consistently outperforms the other two models across different data structures. This suggests the high stability of the hybrid EWT-PSO-SVM model developed in this study for runoff forecasting in Chengbi River Karst Basin.