The Probability Distribution of the Maximum Amount of Daily Precipitation During 20 Days in Summer of the Huaihe Basins

The daily precipitation records of 158 meteorological rain gauges over the Huaihe Basins make it possible to analyze the probability distribution, using gamma distribution of precipitation during the summer of 1980—2007 by distinguishing rainy days following a dry or wet preceding day over the years. Five precipitation rain gauge stations, namely Xixian, Fuyang, Shangqiu, Huaian, Lianyungang stations, are investigated as representative stations of five catchments, namely the upper stream of the Huaihe River, the part stream between Wangjiaba Dam and Bengbu Station of the Huaihe River, the part stream between Bengbu Station and Hongze Lake of Huaihe River, the Huaihe River downstream below Hongze Lake and the Yishu River watershed, to analyze their probability distribution respectively. Through the Kolmogorov-Smirnov (K-S) test and the comparison between the gamma distribution probability density function of the five representative stations and the sample frequency of the daily precipitation records, it is proved that gamma distribution function can be an adequate fitting to the probability distribution of the precipitation in summer of the rainy days following a dry or wet preceding day. The probability density function of gamma distribution, to a certain extent, overcomes the influence that the random oscillation of the samples caused to the estimation of daily precipitation probability distribution.The probability distribution of maximum daily precipitation in 1 to 20 days derived from gamma distribution function is reasonable. The curve of precipitation probability density of 1 day is monotonically decreasing which takes on the trend of reverse "J". The peak of probability distribution of the maximum daily precipitation in 10 days or 20 days tilts toward the side of large precipitation with the days increased.From the Huaihe Basin's probability distribution of the maximum daily precipitation more than 10 mm, 25 mm, 50 mm in 10 or 20 days, it indicates that the probability of the upper stream of the Huaihe River, the Huaihe River downstream below Hongze Lake, and the Yishu River watershed are evidently higher than the rest regions of the five catchments, which means that the maximum daily precipitation of these areas is more likely to be over 10 mm, 25 mm, 50 mm in 10 or 20 days.The high values of the probability of the maximum daily precipitation over 50 mm in 10 days locates in the eastern part of Yishu River watershed and the upper stream of the Huaihe River, while the high values of the probability of the maximum daily precipitation over 50 mm in 20 days locates in the junction of the downstream of the Huaihe River and eastern of the Hongze Lake, indicating large precipitation are more likely to occur in these areas. This approach can provide practical applications such as decision supports for the management of hydro-meteorological forecasting, agricultural, and water resources management.