Determining the most accurate program for the Mann-Kendall method in detecting climate mutation
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ORIGINAL PAPER
Determining the most accurate program for the Mann-Kendall method in detecting climate mutation Jinsong Wang 1 Received: 19 March 2019 / Accepted: 15 July 2020 # Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In the detection of abrupt changes in a time sequence using the Mann-Kendall method, two programs (PRGM1 and PRGM2) were found to provide two different mutation points for the same temperature sequence. The code of PRGM1 was programmed according to the step-by-step direction of the Mann-Kendall method described in the original report, and PRGM2 is the selfincluded program therein. To determine the reason for the different calculation results between the two programs for the same method and the same time series, and thereby verify the correctness of the programs, this study performed some analyses. First, the original reference, in which the basic principle of the Mann-Kendall method was put forward and developed, was reviewed to find the original mathematical formula of the Mann-Kendall method. Then, the mutation points calculated by PRGM1, PRGM2, and additional methods of detecting climate mutation were comparatively analyzed. The results show that the self-compiled program (i.e., PRGM1) and the self-included program (i.e., PRGM2) have different definitions of their main statistics when calculating the rank of a time series. Mutation points obtained by other methods were found to be consistent with those calculated by PRGM1 but different from those calculated by PRGM2. This proves that the definition of the main statistics for the rank of a sequence in PRGM1 is correct. Certain problems still exist in the definition of the main statistics for the rank of a sequence in PRGM2.
1 Introduction An abrupt change in the climate system refers to a transition of the climate state. In other words, the climate state evolves from one mode to another, reflecting a discontinuous jump from a relatively stable state. Accurate detection of abrupt climate change is an important means to understand changes in the climate system and predict the trend of climate system evolution in the future. From the viewpoint of the stability of the dynamic structure of a climate system, climate mutation can be classified into two types: phase mutation of the climate system and mutation of the climate dynamic structure. The first type of mutation, statistically, can be defined as a sharp change from one statistical feature to another. Thus, the statistical significance of state variables is generally investigated in this type of mutation, such as the change of mean value, * Jinsong Wang [email protected]; [email protected] 1
Institute of Arid Meteorology of China Meteorological Administration, Key Laboratory of Arid Climatic Change and Disaster Reduction, China Meteorological Administration, Key Laboratory of Arid Climatic Change and Reducing Disaster of Gansu Province, No. 2070 Donggang East Rd, Lanzhou 730020, China
variance, and frequency. Traditional statistical methods for phase mutation detection i
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