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The Probability Distribution of the Maximum Amount of Daily Precipitation During 20 Days in Summer of the Huaihe Basins
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摘要: 利用淮河流域158个站点1980—2007年夏季降水量资料，选取淮河上游、淮河中上游、淮河中下游、洪泽湖以下和沂沭河5个子流域，采用Γ分布函数分析了淮河流域首雨日 (前1日无雨) 和连续雨日 (前1日有雨) 的夏季多年降水的概率分布特点。通过对代表站息县、阜阳、商丘、淮安、连云港Γ分布概率密度与样本频率的对比分析和K-S检验表明：Γ分布函数能较好拟合分条件的淮河流域夏季雨日的概率分布，用该分布函数递推得到的1 d, 10 d, 20 d内最大日降水量概率分布比较规则合理。淮河流域5个子流域中淮河上游、淮河中下游、沂沭河流域在10 d，20 d内最大日降水量不低于10 mm，25 mm，50 mm的可能性更大。Abstract: 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.
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图 1 研究流域区以及和流域内有关站点分布
Fig. 1 The illustration of the test catchments and the locations of relevant stations
图 2 淮河流域子流域代表站首雨日和连续雨日的Γ分布概率密度函数与样本频率
(a) 息县, (b) 阜阳, (c) 商丘, (d) 淮安, (e) 连云港
Fig. 2 Gamma distribution density function and sample frequencies function of the daily precipitation following a dry or a wet preceding day at representative stations of Xixian (a), Fuyang (b), Shangqiu (c), Huaian (d) and Lianyungang (e), respectively
图 3 代表站1 d, 10 d, 20 d内最大日降水量的概率密度曲线
(a) 息县, (b) 阜阳, (c) 商丘, (d) 淮安, (e) 连云港
Fig. 3 Probability density functions of the maximum daily precipitation within 1, 10, 20 days derived from Gamma distributions of representative stations of Xixian (a), Fuyang (b), Shangqiu (c), Huaian (d) and Lianyungang (e), respectively
图 4 淮河流域10 d，20 d内最大日降水量不低于10 mm，25 mm，50 mm概率分布
Fig. 4 Probability distribution of the maximum daily precipitation no less than 10 mm, 25 mm, 50 mm within 10 and 20 days of the Huaihe Basins
表 1 淮河流域代表站雨日形状参数αi和尺度参数βi的样本估计
Table 1 Sample estimates of shape parameter αi and scale parameter βi of representative stations in the Huaihe Basins
子流域 代表站 首雨日 连续雨日 样本数 α0 β0 样本数 α1 β1 淮河上游 息县 408 0.427 29.42 516 0.411 42.19 淮河中上游 阜阳 420 0.351 34.69 571 0.335 49.73 淮河中下游 商丘 417 0.356 35.07 424 0.406 34.12 洪泽湖以下 淮安 435 0.312 43.21 566 0.404 41.16 沂沭河流域 连云港 439 0.516 30.50 484 0.368 45.57 
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