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.
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References
Feng GL, Dong WJ, Gong ZQ (2006) Nonlinear theories and methods on spatial-temporal distribution of the observational data [M]. China Meteorological Press, Beijing
Feng GL, Gong ZQ, Zhi R (2008) Latest advances of climate change detecting technologies[J]. Acta Meteorol Sin 66(6):892–905
Fisher RA (1922) On the mathematical foundation of theoretical statistics [M]. Philos Trans R Soc Lond Ser A 222:309–368
Fu CB, Wang Q (1991) The abrupt change in the long-term variation of the South Asian summer monsoon and its synchronization with the rapid global warming[J]. Science China: Series D 34(6):666–686
Fu CB, Wang Q (1992) Definition and detection method of climate abrupt change[J]. Sci Atmos Sin 16(4):482–493
Gong ZQ, Feng GL, Dong WJ, Li JP (2006) The research of dynamic structure abrupt change of nonlinear time series[J]. Acta Phys Sin 55(06):3180–3187
He WP (2008) The research and application of the abrupt detecting methods in dynamical structures[D]. Lanzhou University
He WP, Deng BS, Wu Q, Zhang W, Cheng HY (2010) A new method of detecting abrupt dynamic change based on rescaled range analysis[J]. Acta Phys Sin 59(11):8264–8271
He WP, Feng GL, Wu Q, He T, Wan SQ, Chou JF (2012) A new method for abrupt dynamic change detection of correlated time series. Int J Climatol 32(10):1604–1614
He WP, Feng GL, Wu Q, Wan SQ, Chou JF (2008) A new method for abrupt change detection in dynamic structures[J]. Nonlin Process Geophys 15:601–606
Held H, Kleinen T (2004) Detection of climate system bifurcations by degenerate fingerprinting[J]. Geophys Res Lett 312(23):23207
Hou W, Feng GL, Dong WJ (2006) A technique for distinguishing dynamical species in the temperature time series of North China[J]. Acta Phys Sin 55(5):2663–2668
Kendall MG, Charles G (1975) Rank correlation methods [M]. Oxford Univ Press, New York
Li JP, Chou JF, Shi JE (1996) Detecting methods on the mean value jump of the climate [J]. J Beijing Meteorol Coll 2:16–21
Li YH, Zhang ZQ (1991) A preliminary analysis on abrupt climatic change in Shanghai and Beijing for the last 100 years [J]. Meteorol Mon 17(10):15–20
Liu QQ, He WP, Gu B (2015) Application of nonlinear dynamical methods in abrupt climate change detection [J]. Acta Phys Sin 64(17):179201
Ma ZG, Fu CB (2006) The basic facts of aridification in North China from 1951 to 2004 [J]. Sci Bull 51(20):2429–2439
Mann HB (1945) Non-parametric tests against trend [J]. Econometrica 13:245–259
Mocenni C, Facchini A, Vicino A (2010) Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties [J]. Proc Natl Acad Sci U S A 107(18):8097–8102
Pincus SM (1995) Approximate entropy (ApEn) as a complexity measure [J]. J Chaos 5:110–117
Savit R, Green M (1991) Time series and dependent variables [J]. Physica D Nonlinear Phenom 50(1):95–116
Sun DY, Zhang HB, Huang Q (2014) Application of moving cut data-rescaled variance analysis in dynamic structure mutation testing [J]. Acta Phys Sin 63(20):209203
Wang SW (1990) Variations of temperature in China for the 100-year period in comparison with global temperatures [J]. Meteorol Mon 16(2):11–15
Wei FY (2007) Climate statistical diagnosis and prediction technology [M]. China Meteorological Press, Beijing
Yamamoto RT, Iwashima T, Sanga NK (1985) Climatic change: a hypothesis in climate diagnosis [J]. J Meteorol Soc Jpn 63:1157–1160
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The author would like to acknowledge the data providers.
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The study was supported by the National Natural Science Foundation of China (grant no. 41775093) and the project from the innovation team (team no. GHSCXTD-2020-2).
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Wang, J. Determining the most accurate program for the Mann-Kendall method in detecting climate mutation. Theor Appl Climatol 142, 847–854 (2020). https://doi.org/10.1007/s00704-020-03333-x
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DOI: https://doi.org/10.1007/s00704-020-03333-x