## 4 Results and Analysis
### Performance Investigation of Traditional Models
#### 4.1.2 Results of Standard AI Models Combined with Pre-Processing Techniques
Therefore, both the EMD and EEMD pre-processing techniques improved the BP model's prediction accuracy of the extreme values of runoff depth, and the EMD-BP model was better than the EEMD-BP model in terms of overall prediction. As shown in Figure 8 and Table 3, for the Elman model, coupling the model with pre-processing techniques showed better prediction results than the standard Elman model alone. In terms of the NSE evaluation index, the NSE values of the EMD-Elman and EEMD-Elman models were 0.72 and 0.65, respectively, showing improvements of 0.29 and 0.22 compared with the unmodified Elman model. The prediction accuracy of the EMD-Elman coupled model reached Grade B, while that of the EEMD-Elman coupled model reached Grade C; thus, the EMD-Elman coupled model had better results. In terms of the MAPE evaluation index, neither the EMD-Elman model nor the EEMD-Elman model showed any obvious changes. In terms of the RMSE evaluation index, the RMSE value of the EMD-Elman model was reduced by 14% compared with the unmodified Elman model, while the RMSE value of the EEMD-Elman model was reduced by 22%; thus, the EEMD-Elman model performed better. In terms of the PPTS evaluation index, the PPTS values of the EMD-Elman and EEMD-Elman models were 2.40 and 2.27, respectively. Compared with the unmodified Elman model, the EMD-Elman coupled model reduced by 1.97, while the EEMD-Elman coupled model reduced by 2.10. In summary, it can be seen that applying pre-processing techniques improves the accuracy of the models' predictions of extreme runoff volumes, and that EEMD outperforms EMD, indicating that the EEMD-Elman model can predict the extreme values better than other coupled models and that it is more advantageous in general. Of the two models coupled with EMD, the EMD-Elman model had better prediction results with an NSE value of 0.72 and a prediction accuracy of Grade B. By contrast, the EMD-BP model had an NSE value of 0.71 and a prediction accuracy of Grade B. Of the two models coupled with EEMD, the EEMD-BP model had better prediction results, with an NSE value of 0.70 and a prediction accuracy of Grade B; the EEMD-Elman model had an NSE value of 0.65 and a prediction accuracy of Grade C. Overall, of the two pre-processing techniques, the models coupled with EMD had better prediction results than the corresponding models coupled with EEMD, as the EMD-coupled models both had higher NSE index scores and prediction accuracies of Grade B. Taken together, the EMD-Elman model is the best model among the four models, with an NSE value of 0.72 and a prediction accuracy of Grade B. Performance Investigation of Standard AI Models Combined with Pre-Processing Techniques and Post-Processing Methods  
In the previous section, based on the prediction results of the traditional models coupled with pre-processing techniques, it was determined that the EMD-Elman model had the best predictive capacity with an NSE value of 0.72 and a prediction accuracy of Grade B. In this section, the QM-EMD-Elman model is formed using the quantile mappingmethod coupled with the selected EMD-Elman model. The prediction results are shown in Figure 10, and the evaluation of the result indicators is shown in Table 4.  
From Table 4 and Figure 10, it can be seen that the NSE value of the QM-EMD-Elman model is 0.73, which is an improvement of 0.01 compared to the EMD-Elman model, with a prediction accuracy of Grade B. Meanwhile, the MAPE value is 74.57%, which is 63.96% lower than that of the EMD-Elman model. The RMSE value is 34.60, which is 8.16 lower than that of the EMD-Elman model. The PPTS value is 2.36, which is 0.04 lower than that of the EMD-Elman model. Thus, the QM-EMD-Elman model shows a significant improvement in MAPE and RMSE metrics, with little fluctuation in NSE and PPTS metrics. As can be seen from Figure 11, the plot is a scatter fit of the two models mentioned above.