## 5 Discussion and Conclusions  
EPFs play a pivotal role in extending forecast lead times and minimizing the uncertainties associated with precipitation predictions. When harnessed correctly, EPFs enhance both the reliability and accuracy of streamflow predictions by driving hydrological models. Nonetheless, given their inherent bias and under-dispersion, effective post-processing is imperative for corrections. In this study, four popular EPFs, i.e., the CMA, ECMWF, JMA, and NCEP, were post-processed by two state-of-the-art methods, i.e., the BMA and GPP methods, before their application to summer streamflow predictions using the XAJ model for a mountainous river basin. For a comprehensive evaluation, the deterministic metric MAE and the probabilistic CRPSS and TS metrics were utilized for precipitation forecast assessment. Streamflow prediction performance was analyzed using the NSE and RE metrics. Both precipitation forecasts and streamflow predictions were assessed before and after post-processing. Additionally, skillful forecast lead times of summer streamflow prediction restored by post-processing methods were also investigated. In general, compared with the observed precipitation amount, the ensemble mean forecasts by the CMA, ECMWF, JMA, and NCEP exhibit biases, notably underestimating torrential rain. [PERSON], [PERSON] [44] identified a consistent underestimation of heavy precipitation across China, with particular emphasis on the western and southern regions. This systematic underestimation can be attributed to factors such as resolution and the related convection parameterization. Furthermore, forecasts distinctly demonstrate under-dispersive tendencies, suggesting a marked underestimation of uncertainty in probabilistic precipitation forecasts. Of the EPFs assessed, the ECMWF and JMA outperform the NCEP and CMA in terms of precipitation ensemble mean forecasts, showing lower MAE values. The ECMWF performed better in precipitation ensemble forecasts with higher CRPSS  
Figure 11: Hydrograph of ensemble streamflow driving using raw and post-processed ECMWF data at one lead day during the summer of 2017 compared with observed hydrograph. values and performed better in both light rain and torrential rain forecasts with higher TS values. The superior performance of the ECMWF has been ascertained by plenty of studies [11; 21; 45]. In addition, the ECMWF's prowess extends to streamflow predictions, which shows skill over 1\(\sim\)4 lead days, with NSE values above 0.4 and absolute RE values below 20%. Despite this, there is underestimation of the observed peak discharge, underscoring the indispensability of post-processing EPFs to improve the application of precipitation forecasts to streamflow predictions. The effectiveness of precipitation correction varies depending on the post-processing methods selected. In this study, both the GPP and BMA methods effectively countered the under-dispersion of EPFs and improved their deterministic performances as measured by the MAE. Specifically, the GPP method also showcased an improvement in probabilistic accuracy in terms of CRPSS, aligning with the findings of [PERSON], [PERSON] [27]. Regarding the TS, only minimal enhancements for the CMA at light rain rates were achieved using the GPP method. Post-processing torrential rain proves challenging due to its dual discrete-continuous nature and the notably non-normal distribution of its errors [12]. The advantage of GPP can be propagated to the performance of streamflow forecasts. After post-processing with the GPP method, the ECMWF ensemble mean can add additional lead times up to the seventh lead day, as indicated by its well behaved NSE and RE metrics. The underestimations of two peak flows at one lead day are reduced by about 4.64% and 2.74%, respectively. Conversely, while the BMA method's contributions to precipitation forecast accuracy were marginal, this translated into limited advancements in streamflow prediction accuracy.