## 4 Results and Analysis
### Performance Investigation of Traditional Models
#### 4.1.2 Results of Standard AI Models Combined with Pre-Processing Techniques  
Given the limited prediction accuracy of the standard AI models, in this section, two preprocessing techniques with different characteristics and proven applications, EMD and EEMD, were combined with the standard AI models. First, each decomposition method was used to decompose the monthly runoff series of the validation set and to obtain the respective components. Second, the BP model and the Elman model were used to predict each component of each pre-processing decomposition, and the predicted components were summed to obtain the monthly runoff series. Finally, all the above prediction effects were compared and analyzed, and the best pre-processing-technique-based model was selected. Four coupled models based on the pre-processing techniques and standard AI models were constructed: EMD-BP, EMD-Elman, EEMD-BP, and EEMD-Elman. The predictions of these four coupled models were compared with the standard BP and Elman models to evaluate the models' performance and to determine the runoff prediction model with the best prediction results. Additionally, the original data and IMF component data were divided using the same training and validation sets. The division ratio was set to 8.2. The prediction results of the above four coupled models are shown in Figures 7-9, and the index performance results of different coupled models are shown in Table 3.  
Figure 7: Forecasted and observed monthly streamflow during the validation period by the BP model, based on EMD and EEMD pre-processing techniques. (**a**) Prediction results of EMD–BP model. (**b**) Prediction results of EEMD–BP model. (**c**) Prediction results of EMD–BP model, and EEMD–BP model. Figure 8: Forecasted and observed monthly streamflow during the validation period by Elman model, based on EMD and EEMD pre-processing techniques. (**a**) Prediction results of EMD–Elman model. (**b**) Prediction results of EEMD–Elman model. (**c**) Prediction results of EMD–Elman model, and EEMD–Elman model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **NSE** & **MAPE (\%)** & **RMSE (mm)** & **PPTS (10)** \\ \hline BP & 0.49 & 84.35 & 45.46 & 4.69 \\ EMD–BP & 0.71 & 160.74 & 34.32 & 2.39 \\ EEMD–BP & 0.70 & 117.01 & 36.08 & 2.51 \\ Elman & 0.43 & 108.36 & 50.00 & 4.37 \\ EMD–Elman & 0.72 & 138.53 & 42.76 & 2.40 \\ EEMD–Elman & 0.65 & 166.75 & 38.99 & 2.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation of double-coupled models’ monthly runoff predictions during the validation period. Figure 9: Forecasted and observed monthly streamflow during validation period by all four double-coupled models. As seen in Figure 7 and Table 3, for the BP model, the coupling the model with pre-processing techniques showed better prediction results than the standard BP model alone. In terms of the NSE evaluation index, the NSE values of the EMD-BP and EEMD-BP models were 0.71 and 0.70, respectively. Compared with the BP model alone, the EMD-BP coupled model improved by 0.22, and the EEMD-BP coupled model improved by 0.21. The coupled prediction accuracies both reached Grade B, indicating a better model-fitting effect. In terms of the MAPE evaluation index, the two coupled models did not show a significant performance improvement compared with the BP model alone. In terms of the RMSE evaluation index, both coupled models improved compared with the unmodified model. The RMSE value of EMD-BP model was reduced by 25% compared to the BP model alone, while the RMSE value of the EEMD-BP model was reduced by about 21%. In terms of the PPTS evaluation index, the PPTS values of the EMD-BP and EEMD-BP models were 2.39 and 2.51, respectively. Compared with the unmodified BP model, the EMD-BP coupled model reduced its score by 2.30, and the EEMD-BP model reduced its score by 2.18.