# Investigation of the EWT-PSO-SVM Model for Runoff Forecasting in the Karst Area
## 4 Results and Discussion
### Performance Analysis  
#### 4.5.1 Forecasting Results  
This study evaluates the effectiveness of the EWT-PSO-SVM hybrid model in comparison to the SVM, GA-SVM, PSO-SVM, and EMD-PSO-SVM models. The runoff forecasting results of the five models are presented in Figure 6. It shows that the SVM model has a relatively poor forecasting effect, and there is a large error between the measured and forecasted values in large runoff events. The forecasting results of PSO-SVM are slightly improved compared with the GA-SVM and single SVM models. The high consistency between the forecasted and original runoff series trends indicates that the model using series decomposition has higher forecasting accuracy. The EWT-PSO-SVM model optimizes the forecasting results in large runoff events significantly, and the results are also fitted close to the actual measured values predicted in small runoff events. Plotting the absolute error of the model can better show the forecasting effect of the model under different events. Considering that the absolute error (AE) in the model prediction results is not intuitively presented in Figure 6, the AE values of the five models obtained by calculating the difference between the measured values and the predicted values are plotted in Figure 7. In Figure 7, the lower the height of the column chart representing AE, the better the model's predictive performance. Analysis of Figure 7 shows that when the runoff process line has extreme values, the column height of the EWT-PSO-SVM model is significantly lower than those of the other models. In addition, the maximum positive AE value of the EWT-PSO-SVM model is 106.11 mm, which is reduced by 43.12% and 34.27% compared with the SVM and EMD-PSO-SVM models, respectively. The minimum negative AE value is \(-\)69.56 mm, which increases by 24.78% and 22.27%, respectively. This indicates that under high-flow conditions, the hybrid model developed in this study can achieve better predictive performance. Figure 6: Monthly runoff forecasting results. To see the fitting effect of each model and the main evaluation indexes more intuitively, the Taylor diagram and scatter fitting plot were also further adopted to performance comparison. The scatter plot is drawn with the measured values as horizontal coordinates and the predicted values as vertical coordinates, and the correlation between the predicted and measured results of the model is visualized by linear fitting of the scatter points of each model. Figure 8 is the scatter plot of forecasting by each model. The blue line \(y=x\) represents the ideal fit measured values. Comparing the linear trend of each model with the line \(y=x\). The closer the linear trend of the model is to \(y=x\), the better the fitting results of the model. Figure 8 presents that the linear fitting of EMT-PSO-SVM model is the closest  
Figure 7: The AE of five models. to y = x, while the linear fitting of SVM model exhibits the largest deviation from y = x, and the linear trend of GA-SVM, PSO-SVM, and SVM model is similar. Among the five models, the linear correlation coefficient of the EWT-PSO-SVM model (0.79) is the highest, while the remaining models have the highest to lowest linear correlation coefficients as EMD-PSO-SVM (0.74), PSO-SVM (0.44), GA-SVM (0.43), and SVM (0.42), respectively. This demonstrates that the forecasting results of EWT-PSO-SVM model are the best, while the forecasting results of the PSO-SVM model exhibit a slight improvement over those of the SVM model. The Taylor diagram is drawn based on three indicators: correlation coefficient, standard deviation, and root mean square error. It can quantify the correlation between model forecasting results and measured results [38]. Figure 9 is a Taylor diagram of the five models. In the Taylor diagram, the five coordinate points represent the models, the radiation lines represent the correlation coefficients, the horizontal and vertical axes represent the standard deviations, and the dashed lines represent the root mean square errors.