基于站点降雨量最优拟合函数的SPI指数计算  

Calculation of the standardardized precipitation Index based on the best fitted distribution functions to the precipitation series

作　　者：吴绍飞[1,2] 张翔[1,3] 王俊钗 刘建峰[1,3] 潘国艳[1,3] 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,湖北武汉430072 [2]江西省水利科学研究院,江西南昌330029 [3]水资源安全保障湖北省协同创新中心,湖北武汉430072

出　　处：《干旱区地理》2016年第3期555-564,共10页Arid Land Geography

基　　金：国家水体污染控制与治理科技重大专项(2014ZX07204-006);国家自然科学基金项目(51279143)

摘　　要：标准化降水指数（SPI）能较好地反映不同时间尺度和区域的旱涝状况,时空适应性较强,成为科学研究和实际应用最广泛的描述多时间尺度的气象干旱指标,采用不同的概率分布函数拟合降雨量系列,将会得到不同的SPI值。利用淮河流域30个气象站点1951-2013年间约60 a的逐月降雨资料,分别采用7种不同分布函数（Gamma分布、皮尔逊III型分布、正态分布、对数正态分布、广义Pareto分布、广义Logistic分布和Weibull分布）对各站点不同时间尺度（1、3、6、12和24 mon）各月份降雨系列进行拟合,以K-S方法检验了各分布函数的拟合效果,并以均方根误差（RMSE）最小为准则选取的站点各月份最优分布函数OPT作为参考,分析比较上述7种分布函数模拟的不同时间尺度下的SPI时间序列。结果表明：在各不同时间尺度上,采用皮尔逊III型分布作为计算SPI指数的分布函数误差最小,其模拟的SPI值各站点总偏差平均值均在5%以下,Weibull分布和对数正态分布计算得到的SPI时间系列结果次之,它们模拟的SPI值各站点总偏差平均值介于5%-10%之间;当前我国气象部门统一采用的Gamma分布函数,并非计算SPI指数的最佳选择,各不同时间尺度下,采用Gamma分布计算的SPI值各站点总偏差平均值均在10%左右。其他函数,如正态分布、广义Pareto分布和广义Logistic分布,其误差介于10%-30%之间,均超过采用Gamma分布计算的结果。The standardized precipitation index （SPI）, a meteorological drought for multiple time scales, is now widely used throughout the world in both research and operational modes. The SPI has a conspicuous characteristic：it can be applied to any location, wet or dry, as it is a normalized index, and is very suitable for the specification of drought and flood dynamics as it is greatly flexible at different time scales. Obviously, the length of a precipitation record has a significant impact on the SPI values;and different SPI values can also be obtained with different distribution functions employed in the fitting of the observed series of precipitation;In the meantime, the traditional SPI index cannot help identify the seasonality of the droughts process. In this paper, on eliminating the auto-correlations and by taking the seasonal variability into account, this paper adopted seven different probability distributions （Gamma, Pearson Type Ⅲ, normal, log-normal, generalized Pareto, log-logistic and Weibull） to describe each of the twelve monthly precipitation series at five different time scales （1 month, 3 months, 6 months, 12 months and 24 months） from 1951 to 2013 of all the 30 meteorological stations in Huai River Basin, separately. And then, the Kolmogorov-Smirnov （K-S） method was used to test the goodness of fit, and the root-mean-square error （RMSE） was selected to identify the most optimal （OPT） distribution for each monthly precipitation time series of each station. Afterwards, taking the SPI series modeled by the OPT functions as a reference, a comparison of the SPI time series calculated by the above seven single distributions was made with each other. Results show that Pearson Type Ⅲ distribution performed the best with the smallest total deviations （the average value was less than 5%） at all the five time scales, followed by Weibull and log-normal distributions, of which the average total deviation values were between 5% to 10%;however, Gamma function, the most widely used

关 键 词：气象干旱 干旱指标 标准化降水指数 分布函数 K-S检验 淮河 

分 类 号：P426.616[天文地球—大气科学及气象学]