## 4 Results
### Post-Processing of the Ensemble Precipitation Forecasts
[PERSON] [40] points out that it is useful to choose the same bin number when forecast systems with different ensemble sizes are compared. Therefore, for each post-processed EPF, the same bin number as that of the raw data is chosen from 1000 ensemble sizes to plot the histogram. There are 14, 50, 26, and 20 bins for the CMA, ECMWF, JMA, and NCEP, respectively. It can be seen that there are a large number of observations falling into the lowest and highest rank, forming a U-shaped rank histogram for raw EPFs (top row). The under-dispersive patterns of raw EPFs indicate underestimation of forecast uncertainty. Flatter histograms are obtained after post-processing (second and bottom rows), especially for the GPP EPFs (bottom row). Specifically, the reliability metric values decrease from 0.79 to 0.20, from 0.81 to 0.28, from 0.99 to 0.28, and from 1.01 to 0.19, for the CMA, ECMWF, JMA, and NCEP, respectively. In general, the post-processing methods, especially the GPP method, can effectively improve the under-dispersion of EPFs. Figure 3: Time series of cumulative rainfall forecasts (mm) by the (**a**) CMA, (**b**) ECMWF, (**c**) JMA, and (**d**) NCEP during the summers of 2014–2018. Observations are also presented. Lines 1–4 represent 1—4 lead days, respectively. Figure 6 presents the probabilistic performance of ensemble forecasts measured in CRPSS for the raw and post-processed (a) CMA, (b) ECMWF, (c) JMA, and (d) NCEP data for all seven lead days. The mean value of CRPSS is also presented. The CRPSS values of the raw CMA, ECMWF, JMA, and NCEP data, respectively, range from 0.25-0.48, 0.30-0.65, 0.33-0.60, and 0.04-0.55 over 1-7-lead days. This shows an overall decreasing trend with the increasing lead days. The mean values of CRPSS are 0.35, 0.47, 0.42, and 0.30 for the CMA, ECMWF, JMA, and NCEP, respectively. Among them, the ECMWF shows a better probabilistic performance, with a larger CRPSS value. In term of CRPSS, the probabilistic skills of EPFs are generally improved after post-processing. Specifically, the GPP method performs better than BMA method, with improvements of, on average, 0.07, 0.03, 0.04, and 0.17 for the ECMWF, JMA and NCEP, respectively. Figure 4: Mean absolute error (MAE) for the raw and post-processed ensemble mean forecasts by the (**a**) CMA, (**b**) ECMWF, (**c**) JMA, and (**d**) NCEP at 1–7 lead days. The mean value of MAE for all seven lead days are also presented. Figure 7 presents the probabilistic performance of ensemble forecasts measured in TS for the raw and post-processed (a) CMA, (b) ECMWF, (c) JMA, (d) NCEP data across four categories. The figure shows a generally decreasing trend in TS with the increasing lead days for each rainfall category, especially for torrential rain. Generally, there is better TS performance for smaller precipitation categories. As for light rain, the ECMEF, JMA, and NCEP are comparable, showing good performances, with TS values above 0.4 for all seven lead days. The TS value of the CMA is relatively lower than those of other three. As for moderate rain and heavy rain, the four EPFs are comparable. The TS for torrential rain ranges largely among the different EPFs, and the ECMWF shows a relatively larger value. There is little improvement in TS by using both BMA (middle row) and GPP (bottom row) methods when compared to raw EPFs (top row). The improvement is relatively more effective for the CMA when forecasting light rainfall using GPP method, with increases from 0.32-0.48 to 0.33-0.53 at 1--7-lead days, while EPFs give even worse performances when forecasting torrential rain after post-processing. Figure 5: Rank histogram for the raw and post-processed ensemble forecasts by the (**a**) CMA (14 members), (**b**) ECMWF (50 members), (**c**) JMA (26 members), (**d**) NCEP (20 members) at one lead day. Lines 1–3 represent the raw, BMA, and GPP data, respectively.