Long term climate deviations: an alternative approach and application on the Palmer drought severity index in Hungary

Abstract

A new statistical test (Makra-test), applicable for long time series, is introduced to identify extended sub-periods, namely, “breaks”, average of which is significantly higher or lower than the mean of the entire time series. In order to apply this test, normal distribution of the time series being examined is a sufficient condition. In another case, if the number of elements increases in the time series, its distribution is near normal and the test can be applied, as well (according to the Central Limit Theorem). The method is demonstrated on monthly Palmer drought severity index (PDSI) data sets, computed for five stations of East Hungary in 1901–1999. Due to strongly recursive (auto-correlative) nature of PDSI every second month of the warm season (April, June, August and October) is analysed and treated as independent samples. Normality of the time series, which is a sufficient condition of the Makra-test, is validated by Kolmogorov–Smirnov test and χ 2-test. Analysis of the PDSI time series indicates that separate treatment of the months is important not only to ensure the normality, but also to consider the existing slight seasonal differences in standard deviation and skewness of the index in the East-Hungarian region. The Makra-test delimits one or more (maximum 4) significant sub-periods of the PDSI in every station and month (not considering the sub-intervals within the significant breaks, although most of them are also significant). Since the PDSI is based on monthly temperature and precipitation data that exhibit considerable inhomogeneities ( Szentimry, 1999), the test is applied both for the original and the homogeneous time series. Effect of the inhomogeneity on long term variations of PDSI is strong: about the half of the significant breaks in the original time series disappear or become totally different from the time series based on homogenised data. All negative (dry) breaks of each month and station, however, occurred in more recent decades of the 20th century, according to both homogeneous and original series.