Determining the most accurate program for the Mann-Kendall method in detecting climate mutation

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 self-included 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.