基于Γ函数的暖季小时降水概率分布

Study on Probability Distribution of Warm Season Hourly Rainfall with Γ Distribution

我国暖季小时降水的气候概率分布特征分析是开展短时强降水概率预报的重要基础工作。本文使用1991—2009年5月1日至9月30日的小时降水资料,采用最大似然估计方法,对用于描述518个观测站点降水分布的Γ函数的形状参数α和尺度参数β进行了估算,对极端α和β分布情况下大于0.1 mm的暖季小时降水的概率密度分布状况及其累积概率密度分布函数进行了分析,并给出了多个站点基于Γ函数的超过给定阈值的降水累积概率的分布。结果表明:α和β之间的相关性高达0.975,其分布与我国的地势分布有很大的关系。Γ分布可以很好地描述小时降水的分布状况,模拟得到的结果具有更好的连续性,揭示了实况降水中不能观测到的极端降水发生的可能性;华南沿海和海南西北部为最容易出现短时强降水的区域,在有降水的情况下,其小时雨量超过10、20和30 mm的累积概率分别达到了8.0%、2.0%和0.7%,另一个常出现极端降水的区域为鲁苏皖交界处,这是强对流预报中值得注意的区域;95%累积概率密度对应的小时降水阈值分布显示,自西北向东南,极端小时降水的阈值不断增大;α与站点海拔高度之间具有很好的指数相关性,其相关系数达到了0.709,表明地形对我国暖季小时降水量的分布具有重要的影响。

Climatology and probability distribution of hourly rainfall are very important for the operational probabilistic short-duration heavy rainfall forecasts.By adopting the maximum likelihood estimation,the shape parameterαand scale parameterβof 5 1 8 stations are obtained with observed warm season (May 1 to September 30)hourly rainfall data from 1991 to 2009,and Γdistribution function of every station is uniquely determined.The fittedΓdistribution and the distribution of relative frequency of observed hourly rainfall are well matched.For stations with maximum and minimumαandβ,the probability distribution and the accumulative probability of hourly rainfall exceeds 0 .1 mm are analyzed,and the probability distri-bution exceeds given thresholds are studied.The results show that the correlation coefficient ofαandβgets up to 0.975,and highly dependent on the altitudes.Extreme rainfall probability that could not be re-vealed by observation data is well displayed byΓdistribution.Distributions of observed hourly rainfall are well depicted,and better continuity obtained.The coastal region of South China has the largest probability to have stronger hourly precipitation and the accumulated probabilities of hourly rainfall exceed 10.0 mm, 20.0 mm and 30.0 mm are 8.0%,2.0%and 0.7%,respectively.Another remarkably high probability ar-ea is the intersectional region of Shandong,Jiangsu and Anhui,which is noticeable during the severe con-vective forecast.The 95%CDF hourly threshold increases from 5.0 mm at the Northwest to 20.0 mm at the Southeast of China with the maximum hourly rainfall threshold located at the south of Guangxi.Bothαandβare highly affected by terrain,the relation betweenαand altitude can be well fitted by an exponential function with the correlation coefficient getting up to 0.709,which indicates the decisive effect of terrain on hourly rainfall distribution.