As presented in Sect. 2.3, the gamma function was used to fit observed precipitation data first with a view to provide smooth changes and long-time projection. Table 3 shows the mean values of α and β of the gamma curves in the four seasons. Related research shows that when the shape parameter α was ≤1, the gamma distribution has a asymmetric J-shaped probability density function (Loucks et al., 2005), which indicates that events with small amounts of rainfall account for a substantial, large proportion, while events with large amounts of rainfall account for a very small proportion (Rodrigo, 2010). This case is common for the four seasons in Table 3, especially in summer and autumn when α is ≤0.1, indicating that these two seasons are characterized with occasional and sudden extreme heavy precipitation in all stations. The β parameter characterizes the scale of the gamma distribution. When β increases, the distribution curve squeezes leftward and upward, indicating high intensity of precipitation (Rodrigo, 2010). β has a greater temporal variability. β is the biggest in summer, followed by that in spring, autumn and winter. The highest values of β in spring are from Nd and Ln. These two stations are located in the mountainous upstream areas where northerly cold air meets with warm air from the ocean in spring, often resulting in frontal and cyclone precipitation. The highest values of β in summer appear in Nc, Zs and Yof, which are located in the alluvial plains where the precipitation is often caused by typhoons heading west and southwest in summer (Yin et al., 2007). The highest values of β in autumn are in Sc, Yof, Nd and Ln, indicating that fronts, typhoons and other air activities are frequent in autumn, and the main precipitation occurs in the hilly area of the upper Ganjiang River.

Temporal trends of the shape parameter α and the scale parameter β were further analyzed using the Mann–Kendall test. Table 4 summarizes the results, which indicated that precipitation would occur more occasionally but with higher intensity in spring, winter and autumn. The two parameters in most stations are experiencing more intensive changes in spring. α in spring shows a significant downward trend in Yf, Yc, Jgs, Sc, Nc, Zs and Nd with the absolute value of Z bigger than 2.32, while β exhibits an upward trend in Yf, Lh, Zs, Nd and Ln. The trend of α is tested downward in Jgs, Yof and Ln in autumn, while the trend of β is upward in Ja, Zs and Yof. β in Ja, Jgs, Sc, Gx, Yof and Nd shows an upward trend in winter. No obvious trends are detected in summer. Studies have showed that decreasing the shape parameter α will reduce the threshold for the extreme precipitation threshold, which in turn increases the risk of storm flooding (Rodrigo, 2010). The downtrend α along with upward-trend scale parameter β in Yf, Zs and Nd means that the intensity and occasional probability of concentrated precipitation events in these stations will increase in the future, which will thereby increase the risk of storm floods in spring. Similar cases were also found in Yof in autumn and Jgs in winter, which indicated that extreme precipitation would become more intensive with a warmer and warmer climate. The particular case is the station of Jgs, with α decreasing in all the seasons except summer. Jgs is located in the mountain at an elevation of 843 m. We may infer this mountainous station will present increasingly obvious maritime precipitation characteristics in the future.

As defined in Sect. 2.2, the 99 % percentile of the 12 h precipitation data and their gamma distribution estimates were first calculated as extreme precipitation thresholds. Table 5 shows the mean values for each station. The estimated threshold values show higher variability from winters to summers in Table 5. The maximum threshold values occur in summer, followed by spring, autumn and winter. The study area is mainly controlled by monsoons and typhoons in summer, which result in the most concentrated heavy precipitation (Shan et al., 2001). In spring, the ridge of the subtropical high system moved to the south of 20∘ N latitude. The warm and humid air from the south along the subtropical high ridge intersects with cold air from the north, forming fronts and cyclone activities, which bring a wide range of cloudy and rainy weather. Autumn and winter are often affected by the winter monsoon, which is characterized with cold air and low precipitation (Zhang and Song, 2018).

What stands out in Table 5 is that the estimated gamma values are 0.3 %–0.8 % lower than those observed on average, with the smallest in spring (0.3 %) and the largest in autumn (0.8 %). This result is similar to that of Rodrigo (2010). A slightly lower threshold for extreme precipitation will increase the estimated risk, which allows risk managers to improve risk management before storm floods occur. Therefore, the lower values from the gamma function would help reduce risks. The 99th percentile estimates are maintained as the threshold values to obtain the risk analysis.

The estimated thresholds of 12 h to 120 h precipitation events (1 to 10 runs of 12 h events) were also calculated and plotted. The Kolmogorov–Smirnov (KS) test was used to test the goodness of the fits at the 95 % confidence level. KS values range from 0.06 to 0.12, which shows that gamma distribution had a good agreement with the selected thresholds from the observations. Forty-eight fits (4 seasons × 12 stations) were calculated eventually, and Fig. 4 shows an example in Gx. Its horizontal axis represents scenarios or probability, while the vertical axis represents thresholds of extreme precipitation events in millimeters (mm). The lowest curve is fitted from run 1 observed precipitation. Curves from the run 2 to the run 10 are higher and higher. Figure 4 shows that there are bigger intervals between curves in summer and winter, indicating that runs of precipitation events in summer and winter have a greater impact on the extreme event thresholds. Compared with runs 5 to 10, the intervals are even bigger between runs 1 and 4, indicating that the precipitation threshold changes greatly when the events happen within 48 h. The curve slopes in all the four pictures are steep when the probability is less than 0.5 (1/2), which shows precipitation thresholds increase quickly. The slopes gradually decline when the probability is less than 0.2 (1/5). It shows the precipitation threshold increases slowly as the probability decreases. Fits in other stations show similar trends.

With the help of these gamma fits, thresholds under any given probability can be estimated. The hollow orange points in Fig. 4 show estimates when the return period is set to be one in 2 years (its probability is 0.5), one in 5 years (0.2), one in 10 years (0.1), one in 20 years (0.05) and one in 50 years (0.02), respectively, which is used for risk analysis later in the following section.

The estimated thresholds in Sect. 3.3.1 could help to analyze extreme precipitation events and their risks. In order to identify what kinds of extreme events would cause floods, we selected Gx, a meteorological station, and Hanlinqiao, a hydrological observation station, to do a comparative analysis, due to the available hydrological data. Figure 5 shows their location. Gx (25.87∘ N, 115∘ E), located at the lower reach of the Gongshui River (a branch of the Ganjiang River in its upper reach), is a national meteorological observatory. It is one of the four basic national stations in the upper reach of the Ganjiang River. The records in Gx began in 1951, and they are relatively complete with good data consistency. Hanlinqiao is a regional representative hydrological station at 115∘12′ E and 26∘03′ N. It was established in February 1953 and is located in the village of Laoheshi, Jibu, Ganxian, downstream of the Pingjiang River, whose catchment area is 2689 km2. It is 17 km away from the entrance to the Gongshui River. The two stations are close, and the representative area covers almost the same region.

The extreme events supposed to be with risk-causing floods in Gx are selected according to the following standards, and Table 6 shows the number of selected events:

events above thresholds estimated by the gamma curves of runs 1–10 in Sect. 3.3.1;

The flood events in Hanlinqiao are selected according to the standards below, and Table 7 shows the result:

events above the threshold, which is the 99 % percentile of the daily flow records, and

Analysis from Tables 6 and 7 shows that the predicted extreme precipitation events have similar trends as the flood records. Both have more events in spring than in summer, followed by autumn and winter. Table 6 shows the predicted events of all the runs in spring account for more than 40 % under scenarios of probability at 0.5, 0.2 and 0.1 and about 30 % under scenarios of probability at 0.05 and 0.02. Events in summer account for more than 30 % under all scenarios. Those in autumn and winter only account for 20 % or so from 2009 to 2014. Records in Hanlinqiao find 12 flood events in the 6 years. Seven events were in spring and five in summer. No events are found in autumn and winter. The precipitation records at Gx were selected with the flood occurrence date. There are nine precipitation events found on the same day when the floods happened, with the highest precipitation of 72.2 mm in 12 h and 118.1 mm in 24 h. There was no precipitation recorded with the same date of the rest of the three floods, but precipitation was found on the previous day, with the highest precipitation of 73.3 mm in 12 h before the date and 83 mm in 24 h before the date. Two floods were found with a run 6 precipitation event in the early stage, four floods with a run 4 precipitation event, two floods with a run 3 precipitation event, one flood with a run 2 precipitation event and three floods with a run 1 precipitation event. Compared with the flood records, thresholds in Scenario 1 (probability at 0.5) are a little lower, which will overestimate the number of extreme precipitation events. Scenarios 3, 4 and 5 (probabilities at 0.1, 0.05 and 0.02) have high thresholds, which will underestimate the number of the flood events. The predicted extreme precipitation events from Scenario 2 (probability at 0.2) are very close to the recorded flood events.

Of all the runs under Scenario 2, the predicted events from runs more than seven are lower than the recorded floods. It is a complex process from precipitation to floods, involving several disaster-generating environments such as land covers, topography, soil, temperature, shape of the catchment area, etc. It is reasonable that the predicted extreme precipitation events are bigger than or equal to flood events in the risk assessment. Therefore, runs 1, 2, 3, 4, 5 and 6 are more suitable for predicting extreme events. According to the flood events at Hanlinqiao station, the predicted events from run 1 (one 12 h precipitation) under Scenario 1 are almost double the flood records. Events from runs 2, 3, 4, 5 and 6 are all more or very close to the flood records. The analysis suggests that events predicted using the gamma distribution based on 12–72 h of precipitation data are highly beneficial for flood estimates. However, events predicted using data beyond 72 h may result in underestimation of the risk of flooding. There are some cases where little precipitation (less than the given threshold) was observed at the beginning, which was not considered to cause floods. However, a new record of precipitation that was just above the threshold in the following periods eventually led to flooding because of rainfall accumulated in the previous period. If time intervals between precipitation are too long, this flood event will be missed because of the high threshold. Run 1 (12 h precipitation) will be the best time interval for predicting extreme events in disaster management, which will avoid such missed cases.

The paper further analyzed the spatial distribution of extreme precipitation risk in the study area. The method is listed below according to the analysis above:

The observed precipitation was 12 h precipitation from the 12 meteorological stations. The 99th percentile was selected as thresholds in each season.

Maps of extreme precipitation risk in spring, summer, autumn and winter with the methods above are followed in Fig. 6 to show spatial distribution of extreme precipitation risk. Figure 6 shows that the high-risk centers of extreme precipitation are distributed on the east side of the Luoxiao Mountains in spring, moving south to the upper reaches of the Ganjiang River, which is the north side of the Nanling Ranges in summer. Two new high-risk centers are found in the middle reaches of the Ganjiang River, near the west side of Wuyi Mountain in autumn, and tend to move eastward and northward in winter. The low-risk areas are distributed in the Jitai Basin, which is in the middle reaches of the Ganjiang River and the upper Ganzhou Basin in spring, moving north to the lower reaches to Poyanghu Lake in summer, then moving slightly to the south in autumn. During winter, a new low-risk center develops in the northwest region and gradually moves towards the northwest, approaching the Luoxiao Mountain range in the west. In general, extreme precipitation has a high risk of flooding in the upper reaches of the Ganjiang River, the Jitai Basin in the middle reaches and the northern plains. Risk tends to increase with elevation in the northern river–lake plain area and the Jitai Basin in the midstream area, while risk in the southern hilly area is the opposite and shows signs of decreasing as elevation rises. This risk result is similar to the conclusions of Yin et al. (2018).

The main weather systems that cause extreme precipitation in the study area include low- and medium-level shear lines, low-level jets, typhoons with low pressure, etc. (Shan et al., 2001). Monsoons in spring and summer from the tropical ocean cyclones run southwest in the study area, are uplifted with micro-topography, and result in high-risk centers in the west and south mountain regions. The winter monsoons in autumn and winter from deep inland move south-eastward and form frontal precipitation when they encounter stranded warm air currents, causing high-risk centers in the eastern and southern parts of the study area.

Precipitation events, especially occasional extreme precipitation events, are highly variable in time (Beck et al., 2015), and intermittency is a core characteristic (Trenberth et al., 2017). This paper investigated the timescales of precipitation with 12 h data and found run 3 precipitation events contributed the most precipitation but with lower frequency. The study area was mainly characterized with short-duration precipitation events, and events greater than 10 runs occurred very rarely. Hence, short-duration precipitation events would be a key hazard factor for extreme precipitation forecasting and flood and disaster risk management analysis. Section 3.2 further analyzes the trend of short-duration precipitation and finds that it will occur less frequently but with higher intensity in future. Other associated studies have yielded similar results. Cheng et al. (2014) investigated the precipitation intensity–duration–frequency (IDF) in a changing climate and found that climate-induced changes on heavy rainfall events are non-uniform. Shorter precipitation events have changed more in the past decades, while longer events have not changed substantially (Cheng and Aghakouchak, 2014). Hosseinzadehtalaei et al. (2020) found the frequency of sub-daily extreme precipitation events of 50- and 100-year return periods will be tripled under the high-end RCP8.5 (Representative Concentration Pathway) scenario in the future, which will increase the risk of flooding. Similar cases are also found in China. Ren et al. (2016) analyzed the data from 2300 stations across China. Their research shows that the frequency of trace precipitation (precipitation with a daily rainfall of less than 0.1 mm) has shown a more significant downward trend than the frequency of light rain events in the eastern monsoon region. The frequency of light precipitation in the eastern monsoon region has shown a very obvious downward trend (Ren et al., 2016). The Ganjiang River basin is located in the south of the east Asian monsoon region. Changes in short-duration precipitation events caused by climate warming will cause a higher risk of flooding, which is certainly the key indicator for further study on climate change, floods and other extreme weather disasters.

In fact, most precipitation events bring us necessary beneficial freshwater resources. Only a few events, especially extreme precipitation events, cause disasters and losses. However, which extreme events will result in flooding is not very clear. Researchers should consider how extreme precipitation is defined and carefully choose the data for their analysis of extreme precipitation (Pendergrass, 2018). We compared the extreme precipitation events from runs 1–10 of 12 h data with the flood records at the hydrological observation station and found that the number of events from runs 1, 2, 3 and 4 were close to the number of flood records. The number of diagnosed extreme events decreases as precipitation runs of 12 h increase; i.e., precipitation of more than 5 runs would underestimate the risk. A similar case has also been found in Merino et al. (2018), who selected 29 floods between 2000 and 2014 in Spain and compared them with the extreme precipitation events calculated with hourly and daily precipitation data in order to find their capability to identify flood events. The result shows that no extreme precipitation events are identified in eight of the flood events using definitions based on daily precipitation, but events based on sub-daily data permit much more accurate identification of events posing hydrologic risks (Merino et al., 2018). Obviously, it would be better to use short-duration data, for example, sub-daily precipitation, in extreme event analysis to avoid underestimation of potentially dramatic consequences they caused, such as flooding. In practice, daily precipitation series are commonly used to analyze extreme precipitation events with sufficient quantities and few homogeneity problems. The reason might be that high time resolution precipitation data are not provided or recorded in most regions. Therefore, remotely sensed data from satellites or rain radar would be used to replace sub-daily precipitation in follow-up research (Müller and Kaspar, 2014).