标准化降水指数SPI分布函数的适用性研究

Applicability of Standardized Precipitation Index with Alternative Distribution Functions

摘要: 标准化降水指数(SPI)是适用于多时间尺度的一种干旱指标，常采用Gamma分布进行拟合。以鄱阳湖流域13个气象站为研究对象，选择1961~2001年的逐月降水量为实验数据，采用三种分布函数，即Gamma分布、P-III分布、正态分布拟合了1，3，6，12，24月时间尺度下的时段累积降雨，以K-S方法检验了各分布的拟合效果，以Pearson相关系数和Nash效率系数为评价指标，比较分析了不同时间尺度下各分布计算的SPI值的差异，研究表明：P-III分布是用于拟合鄱阳湖流域各时段累积降雨量的最适宜分布函数；在12和24个月的时间尺度下，三种分布计算的SPI值差异很小，平均的相关系数均超过0.99，平均的Nash效率系数均超过98%，可以互相替代。

Abstract: Standardized Precipitation Index (SPI) can be applied to multiple time-scales and Gamma distribution is suggested to compute SPI values. Based on the monthly precipitation data of 13 meteorological stations in the Poyang Lake basin from 1961 to 2001, three distribution functions (Gamma, Pearson Type Ⅲ and Normal) are adapted to fit long-term precipitation series on different time-scales of 1, 3, 6, 12 and 24 months. The Kolmogorov-Smirnov (K-S) test is used to decide which distribution function could fit cumulative precipitation series better. The SPI values of different time scales are calculated by these three distribution functions and compared by using Pearson correlation coefficient and Nash efficiency coefficient. It is concluded that the Pearson Type Ⅲ distribution is the best for fitting precipitation data series. It is also found that for SPI values with 12 or 24-month cumulative precipitation data series, there is little difference between distribution functions, in which the average Pearson correlation coefficients and Nash efficiency coefficients are over 0.99 and 98%, respectively.