Ensemble precipitation forecasts (EPFs) can help to extend lead times and provide reliable probabilistic forecasts, which have been widely applied for streamflow predictions by driving hydrological models. Nonetheless, inherent biases and under-dispersion in EPFs require post-processing for accurate application. It is imperative to explore the skillful lead time of post-processed EPFs for summer streamflow predictions, particularly in mountainous regions. In this study, four popular EPFs, i.e., the CMA, ECMWF, JMA, and NCEP, were post-processed by two state of art methods, i.e., the Bayesian model averaging (BMA) and generator-based post-processing (GPP) methods. These refined forecasts were subsequently integrated with the Xin’anjiang (XAJ) model for summer streamflow prediction. The performances of precipitation forecasts and streamflow predictions were comprehensively evaluated before and after post-processing. The results reveal that raw EPFs frequently deviate from ensemble mean forecasts, particularly underestimating torrential rain. There are also clear underestimations of uncertainty in their probabilistic forecasts. Among the four EPFs, the ECMWF outperforms its peers, delivering skillful precipitation forecasts for 1–7 lead days and streamflow predictions for 1–4 lead days. The effectiveness of post-processing methods varies, yet both GPP and BMA address the under-dispersion of EPFs effectively. The GPP method, recommended as the superior method, can effectively improve both deterministic and probabilistic forecasting accuracy. Moreover, the ECMWF post-processed by GPP extends the effective lead time to seven days and reduces the underestimation of peak flows. The findings of this study underscore the potential benefits of adeptly post-processed EPFs, providing a reference for streamflow prediction over mountain river basins.

Exploring the characteristics of uneven temporal and spatial distribution of precipitation in mountain watersheds can provide a reference for regional agricultural development and resource utilization, and contribute to the protection of the ecological environment. Based on the daily precipitation observation data of 40 meteorological stations in the Wujiang River Basin from 1963 to 2021, the temporal- and spatial-variation characteristics of the precipitation concentration degree (PCD) and precipitation concentration period (PCP) were analyzed using the Randall S analysis method, Mann–Kendall test method, Pettitt method, wavelet analysis and empirical orthogonal function (EOF). The results showed that the fluctuation range of PCD in Wujiang River Basin from 1963 to 2021 was 0.34–0.59, with a multi-year average of 0.47, which was obviously higher than the national average level and is showing a trend of slowly increasing. The fluctuation range of PCP was between 17.1 and 21.5 days, with a multi-year average of 19.0. The annual precipitation was mostly concentrated around the middle of July and showed a slowly decreasing trend. The abrupt change in PCD and PCP occurred around 1983 and 2001, respectively. There is an obvious Hearst phenomenon in PCP. In the future, the trend of precipitation concentration in the middle period will remain in advance, and the degree of precipitation concentration will continue to increase. The maximum precipitation in the flood season will continue to be delayed. The spatial pattern of the first mode of PCD and PCP in the Wujiang River basin was consistent and showed an opposite pattern between the upper reaches and the middle-lower reaches of the basin, which reflects the influence of the topography of the basin on the spatial distribution of precipitation. The distribution of precipitation is affected by topography. The elevation change in the basin was complex, and the leeward slope varied a lot. Therefore, it has a significant impact on precipitation. Areas with less precipitation are at higher elevations and on mountain leeward slopes, with a lack of moist air flow. The area with more precipitation was the summer monsoon mountain windward slope, and the topography blocks the increase in precipitation. The elevation of the central region is relatively uniform and the terrain is flat. Therefore, the distribution of precipitation is more uniform.

Aiming at the rainstorm days (≥50 mm/d) in the middle and lower reaches of the Yangtze River during 2010–2020, the obliquely rotated principal component in T-mode (PCT) method is used to classify the daily mean 850 hPa geopotential height, including Type 1 (vortex/shear line), Type 2 (frontal surface), Type 3 (warm shear line), Type 4 (warm inverse trough line), Type 5 (typhoon-westerly trough), and Type 6 (easterly wave). We studied the weather system configurations of different synoptic circulation patterns, their long-term trends, and their impacts on diurnal variations of heavy precipitation and drew the following conclusions: Type 1, Type 2, or Type 3 shows balanced double-peak frequencies of the start time of heavy precipitation during 06:00–08:00 BT and around 17:00 BT, respectively. For Type 1, dynamical lifting and thermal lifting play balanced roles, while for Type 2 and Type 3, dynamical lifting plays a key role. The number of rainstorm stations for Type 1 shows a slight increasing trend, while that for Type 2 or Type 3 shows a significant increasing trend. Type 4, Type 5, or Type 6 show a significant single peak frequency of the start time during 15:00–16:00. Type 5 and Type 6 are mainly affected by dynamical lifting along with favorable cape values, which can trigger rainstorms. The number of rainstorm stations for Type 4 or Type 6 shows a decreasing trend (that for Type 4 is more significant), while that for Type 5 shows a slightly increasing trend.

In order to improve the calculation accuracy of the rainfall probability distribution in related applications, this study aimed to select a theoretical function from applicable functions for three classes of the class-conditional probability density function (CCPD) of hourly rainfall series. The three applicable functions are generalized gamma distribution (GΓD), generalized normal distribution (GND), and Weibull distribution. For the reason that it is hard to distinguish the advantages and disadvantages of the three functions by the probability plot and error analysis of fitted values, optimization criteria are proposed, which are the Bayesian information criterion (BIC) and the estimated accuracy of both the annual average rainfall (AAR) and the annual average continuous rainfall (AACR). The results show that by using three applicable functions in 15 regions, the relative fitting deviations for CCPD1 were less than 2.3% and less than 3.3% for ln(CCPD1). The goodness-of-fit values were all above 0.98 for CCPD1 and greater than 0.94 for ln(CCPD1). The fitting effect of the Weibull distribution was relatively poor from the perspective of the probability plot and error analysis of the fitted values, while the three applicable functions could be used to fit CCPD. GΓD had the highest fitting accuracy for the three classes of CCPDs, but there is concern about overfitting due to its broad spectrum. GND, with fewer parameters, had comparable performance to GΓD, and when fitting CCPD1 using GND, the mean relative fitting deviation was 0.6%, the coefficient of determination was 0.999, and for ln(CCPD1), they were 1.45% and 0.989. At the same time, GND performed well in estimating the AARs, with an 8.6% relative error and a 0.92 correlation coefficient in the fifteen regions, indicating that GND can well reflect the spatial variation characteristics of the AAR. Moreover, the function form of GND is simple. GND follows the parsimonious principle, and it is suitable for the whole domain. Therefore, GND is recommended as the theoretical density function based on the optimization criteria. The genetic algorithm was adopted to obtain the approximate solution of the parameters through optimization, which can simplify the derivation and calculation steps. The multiplicative and additive fitting errors were both used in the objective functions, which gave comprehensive consideration to both ends of the fitting curve.