## 4 Results
### Application in Streamflow Prediction  
In this section, the application of EPFs in streamflow prediction and the efficacy of BMA and GPP methods were evaluated. Firstly, the XAJ model was calibrated with observed streamflow using observed precipitation, temperature, and evaporation from the summers of 2014-2016 as inputs. This model was then validated for the summer of 2017. Subsequently, individual precipitation ensemble members of both raw and post-processed EPFs were applied to drive the calibrated XAJ model, generating streamflow ensembles. These were then used to derive the ensemble mean of streamflow prediction. Figure 8 presents the time series of the simulated and observed streamflow during both calibration and validation periods. The NSE values are 0.91 and 0.89 for the calibration and validation periods, respectively, and the RE values are 9.3% and \(-2.6\%\) for the calibration and validation periods, respectively. The XAJ shows a good applicability in terms of NSE and RE compared with earlier studies [27; 30]. It also can be seen that both the peak and low flows are well captured by the simulated discharge. The results demonstrate that the XAJ model is accurately calibrated and thus can be used for streamflow prediction. Figure 6: CRPSS for the raw and post-processed ensemble forecasts by the (**a**) CMA, (**b**) ECMWF, (**c**) JMA, and (**d**) NCEP at 1—7 lead days. The mean value of CRPSS for all seven lead days is also presented. Figure 8: Time series of simulated discharge based on XAJ model during calibration (2014–2016 summer) and validation (2017 summer) periods, compared with observed streamflow. Figure 7: TS of the raw and post-processed CMA, ECMWF, JMA, and NCEP data at 1—7 lead days for precipitation in four categories, i.e., (**a**) light rain, (**b**) moderate rain, (**c**) heavy rain, and (**d**) torrential rain. Lines 1–3 represent the raw, BMA, and GPP data, respectively. Figures 9 and 10, respectively, present the NSE and RE for the ensemble means of streamflow simulated by the raw and post-processed (a) CMA, (b) ECMWF, (c) JMA, and (d) NCEP data for all seven lead days. The mean values of the NSE and absolute RE are also presented. The mean values of the NSE for the raw CMA, ECMWF, JMA, and NCEP data are, respectively, \(-0.26\), \(0.36\), \(0.35\), and \(0.30\) for all seven lead days. According to previous studies [42; 43], NSE = 0 is regularly used as a benchmark to distinguish \"good\" and \"bad\" models. Based on this provided benchmark, the CMA is unsuitable for predicting streamflow. In addition, [PERSON] and [PERSON] [42] pointed out that reported NSE values can be properly interpreted while providing appropriate reference values. In this study, a skillful performance is set to be above 0.4, which is larger than that of the best model, i.e., the ECMWF. By using the GPP method, the mean values of NSE are overall improved for the four EPFs, among which the CMA shows the largest improvement, with an increase of 0.36. The mean values of the NSE for GPP-CMA, GPP-ECMWF, GPP-JMA, and GPP-NCEP are, respectively, 0.1, 0.5, 0.37, and 0.43 for all seven lead days. The NSE values of GPP-ECMWF are all above 0.4, and those of GPP-CMA are all below 0.4 for all seven lead days. The NSE values of GPP-ECMWF are above 0.4 at the first four lead days, and those of GPP-JMA are above 0.4 only at one lead day. The RE values of the raw CMA, ECMWF, JMA, and NCEP data, respectively, range from \(-58\)\(\sim\)\(-15\)%, \(-7.88\)\(-20\)%, \(3.4\)\(-44\)%, and \(5.89\)-\(27\)% over 1\(\sim\)\(7\)-lead days. The CMA shows a general underestimation of streamflow, while the other three show general overestimations of streamflow. The mean value of absolute RE, respectively, decreases by \(17\)%, and \(16\)% for GPP-CMA and GPP-JMA. The decreases in absolute RE for GPP-ECMWF and GPP-NCEP are not significant. Using the BMA method, the NSE values generally decrease and the RE values generally increase for the four EPFs. This indicates that EPF post-processed by BMA leads to a worse skill in streamflow prediction.