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

Abstract: 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 distribution in China's meteorological departments, was not the first choice. In fact, the average total deviations calculated by Gamma distribution was about 10% at all the five different time scales;when it comes to the other three distributions, i.e., normal distribution, generalized Pareto distribution and log-logistic distribution, the average total deviation all exceeded the results obtained by the Gamma distribution. The proposed procedures are of great flexibility for analyses involving contrasting standardized index among different distributions of both precipitation and other hydrologic variables, such as streamflow, soil moisture and so on.

Key words: meteorological drought, droughts index, the standardized precipitation index(SPI), distribution functions, Kolmogorov-Smirnov(K-S)test, Huai River Basin