## 4 Results
### Evaluation of Ensemble Flood Forecasting Performance for Four Schemes  
Figure 5 displays the \(R\) between the ensemble mean and observed runoff, generated by the four schemes, both before and after correction with the GPP method, over a forecast horizon of 1-7 days. As shown in the figure, the \(R\) values for the 1 lead day are relatively high, at approximately 0.7 before correction and about 0.8 after correction. As the forecast horizon extends, the \(R\) values gradually decrease. Scheme (C), which focuses solely on the uncertainty of the hydrological model, consistently shows relatively higher correlations both before and after correction. In contrast, schemes (B) and (D), which consider the uncertainty of the forecasting models, exhibit a rapid decline in \(R\) values after the third day of the forecast period. Overall, the \(R\) values in the right graph are higher than those in the left graph, indicating that runoff forecasts derived by the corrected EPF exhibit a higher degree of correlation with observed values. In conclusion, these results suggest that considering the uncertainty of hydrological models in runoff forecasting, coupled with effective post-processing methods, can enhance the performance of runoff forecasts. Figure 4: Calibration and validation hydrographs generated by the XAJ and GR4J hydrological models, along with observed streamflow at the Shuibuya station. Figure 5: Correlation (R) plots for flood forecasts driven by RAW and GPP post-processed precipitation forecasts for 4 forecast schemes for 1–7 lead days. Figure 6 illustrates the _RME_ between the ensemble mean and observed runoff forecasted using the four schemes, both before and after correction with the GPP method. The plots indicate a general tendency of the ensemble mean to underestimate observed values, with schemes (A) and (C) showing a relatively lower degree of underestimation, about \(-40\%\), before correction. In contrast, schemes (B) and (D) exhibit a more significant underestimation of observed runoff, with _RME_ ranging from \(-80\%\) to \(-40\%\), and this underestimation intensifies as the forecast horizon extends. After correction, the underestimation in all schemes is markedly improved, reduced to within \(-20\%\), demonstrating that effective post-processing techniques can significantly enhance the accuracy of runoff forecasts. Figure 7 presents the _CRPSS_ of the forecasted runoff ensembles obtained from the four schemes, before and after correction with the GPP method. This evaluation measures the probabilistic skills of the ensemble forecasts. Using the classifications established by [PERSON], [PERSON] [59] and [PERSON], [PERSON] [60], the flood forecasting skill levels are defined as follows: very high if _CRPSS_ is between 0.75 and 1; high if _CRPSS_ is between 0.5 and 0.75; moderate if _CRPSS_ is between 0.25 and 0.5; low if _CRPSS_ is between 0 and 0.25; no skill if _CRPSS_ equals 0; and negative skill if _CRPSS_ is less than 0. Accordingly, it is evident that before correction, schemes (A) and (C) show moderate skills for 1-7 lead days. However, schemes (B) and (D) show low skills once the forecast period exceeds 3 days. After applying the GPP correction, the _CRPSS_ for all schemes improves. All four schemes show high skills for the first two lead days and moderate skills for 3-7 lead days. What is more, scheme (A) exhibits the lowest _CRPSS_ on 1 lead day, and the others show slightly higher _CRPSS_ values. Figure 8 shows the quantile histograms of the forecasted runoff ensembles obtained from the four schemes, both before and after correction with the GPP method. The ranks of schemes (A) through (D) are 50, 70, 100, and 140, respectively. Initially, the quantile histograms of the uncorrected EPF display a U-shape, with a large concentration of forecast values at the lowest and highest ranks, indicating a large concentration of forecast values at the lowest and highest ranks. This pattern indicates under-dispersion, reflecting an underestimation of forecast uncertainty.