## 4 Results
### Application to a Typical Flood Event  
On 17 July 2020, the Qingjiang River Basin experienced a significant torrential rain event, leading to a rapid rise in river levels. On 18 July, the flow rate at the Shuibuya station in the Qingjiang Basin reached a peak of 6767 m\({}^{3}\)/s, marking an extreme flood event. Figure 9 presents the EFFs for this flood event simulated by the four \"EPF + HM\" schemes on 1 lead day. Figure 9a,b shows the raw EPF simulation results and the post-processed EPF results using the GPP method, respectively. The schemes (A)-(D) generated ensemble member counts of 50, 70, 100, and 140, respectively. The figures display the ensemble mean and the 90% confidence interval to evaluate the EFFs' performance in capturing the flood event.  
From Figure 9a, it is evident that the EFFs generated using the raw EPF exhibit biases and under-dispersion. The ensemble mean and 90% confidence interval in scheme (A)  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Schemes**} & \multicolumn{3}{c}{**Raw**} & \multicolumn{3}{c}{**GPP**} \\ \cline{2-7}  & _ARIL_ & _PCI_ & _PUCI_ & _ARIL_ & _PCI_ & _PUCI_ \\ \hline (A) CMWF + XAJ & 1.304 & 0.331 & 0.330 & 2.615 & 0.764 & 0.331 \\ (B) GE + XAJ & 1.877 & 0.360 & 0.245 & 2.935 & 0.825 & 0.315 \\ (C) ECMWF + MHM & 1.765 & 0.450 & 0.312 & 2.671 & 0.816 & 0.343 \\ (D) GE + MHM & 2.317 & 0.470 & 0.246 & 2.980 & 0.863 & 0.323 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The Average Relative Interval Length (_ARIL_), the percentage of observations enclosed by the confidence interval (_PCI_), and the percentage of observations enclosed by the Unit Confidence Interval (_PUCI_) values for the 90% confidence interval of discharge for different schemes.  
Figure 9: Hydrograph of ensemble forecasts for a flooding event driven by RAW (**left**) and GPP post-processed (**right**) precipitation forecasts at 1 lead day.  
underestimate the observed flood peak. Compared to scheme (A), scheme (B) shows no improvement in the ensemble mean and 90% confidence interval, while scheme (C) performs slightly better in capturing the observed peak event, indicating that GE does not necessarily enhance the accuracy of the EFFs. Schemes (C) and (D), compared to schemes (A) and (B), have a wider range of forecast ensembles, suggesting that incorporating hydrological uncertainty can improve the quality of the EFFs. Thus, including multiple hydrological models (MHM) results in a broader range of ensemble forecasts and reduces bias compared to using only single hydrological models (SHMs).  
From Figure 9b, the flood forecasts conducted with the GPP-corrected EPF show improvements in the range of the forecast ensemble. The ensemble mean in scheme (A) is still underestimated, but the forecast range can better cover the observed flood. The performance of scheme (B) is similar to that of scheme (A), indicating that when using a single hydrological model, GE does not demonstrate an improvement over a single EPF. Schemes (C) and (D) outperform other schemes in terms of the ensemble mean, providing higher estimates for the flood peak. These results suggest that while post-processing of the EPF has been applied, using GE does not effectively enhance the performance of the EFFs, whereas using MHM better captures the flood event.