## 4 Results  
### Post-Processing of the Ensemble Precipitation Forecasts  
In this section, the raw and post-processed EPFs were compared with the observed precipitation using both deterministic and probabilistic metrics collected during the summers of 2014-2018 over the upper Qingjiang River basin. Figure 2 presents the scatter plots of observations and ensemble mean forecasts by the (a) CMA, (b) ECMWF, (c) JMA, and (d) NCEP at one lead day. The gray diagonal line is indicative of an ideal performance. Among the four raw EPFs (top row), even though the ECMWF and JMA show better performances, with scatters more clustered towards the grey diagonal, they generally underestimate precipitation at torrential rain rates (>30 mm). The CMA and NCEP show worse performances, especially for torrential rain rates, and are replete with large scatters, high false alarm rates, and large biases. After post-processing (middle and bottom rows), overestimation was reduced and underestimation of torrential rain rates could still be observed. The finding of the underestimation of torrential rain aligns with earlier studies [9; 13]. The tendency to underestimate torrential rain poses challenges for hydrological forecasting, especially when predicting peak discharges and their timing, as underscored by [PERSON], [PERSON] [41]. Figure 3 presents the time series of cumulative rainfall to evaluate the systematic error and the cover rate of ensemble forecasts. The range between the maximum member and the minimum member represents the dispersion. The post-processed EPFs (blue dash line, green dash line) show obviously larger dispersions than those of raw EPFs (gray dash line) and cover the raw EPFs well, except for the BMA-ECMWF (blue dash line in Column 2). Both the raw EPFs and EPFs post-processed by GPP (green dash line) show little variations in dispersion with the increasing lead days, while the dispersion of EPFs post-processed by BMA (blue dash line) increases with the increasing lead days. The ensemble means of GPP-EPFs (green solid line) are closer to the observed cumulative rainfall (red solid line) than those of raw (gray solid line) and BMA-EPFs (blue solid line). As the lead day increases, the cumulative rainfall error shifts from an overestimation to an underestimation, consistent with the findings of [PERSON], [PERSON] [26]. Generally, in terms of cumulative rainfall forecasting, the EPFs post-processed by GPP outperform the raw EPFs and those post-processed by BMA. Figure 4 presents the performance of ensemble mean forecasts measured in MAE for the raw and post-processed (a) CMA, (b) ECMWF, (c) JMA, (d) NCEP data, at all seven lead days. The mean value of MAE is also presented. The MAE values of raw CMA, ECMWF, JMA, and NCEP data, respectively, range from 5.47-8.31, 3.40-7.41, 3.49-6.27, and 3.94-9.35 over 1-7-lead days. This also shows better MAE performances by the ECMWF and JMA, with smaller values of mean MAE for all seven lead days than those of CMA and NCEP. The results show that by using post-processing methods, there are larger decreases in the mean MAE for CMA and NCEP than that of ECMWF. These methods are not desirable for the JMA, for which the MAE is even larger after post-processing. Specifically, by using the GPP method, the mean values of MAE decrease by about 0.81, 0.16, and 0.89 for the CMA, ECMWF, and NCEP, respectively. By using the BMA method, the mean values of  
Figure 2: Scatter plots of observed and forecasted area rainfall from the (**a**) CMA, (**b**) ECMWF, (**c**) JMA, and (**d**) NCEP at one lead day during the summers of 2014–2018. Lines 1–3 represent the raw, BMA, and GPP data, respectively. MAE decrease by about 0.74, 0.02, and 0.79 for the CMA, ECMWF, and NCEP, respectively. Generally, in term of MAE, the ECMWF and JMA perform better than the CMA and NCEP. Two post-processing methods, especially GPP, can effectively decrease the MAE of the CMA and NCEP, which have poor raw performances. Figure 5 presents the rank histograms for the raw and post-processed EPFs at one lead day.