Multifractal characterization of global temperature anomalies

Abstract

The global monthly temperature anomaly time series for the period 1850–2012 has been investigated in terms of multifractal detrended fluctuation analysis (MF-DFA). Various multifractal observables, such as the generalized Hurst exponent, the multifractal exponent, and the singularity spectrum, are extracted and are fitted to a generalized binomial multifractal model consists of only two free parameters. The results of this analysis give a clear indication of the presence of long-term memory in the global temperature anomaly time series which causes multifractal pattern in the data. We investigate the possible other source(s) of multifractality in the series by random shuffling as well as by surrogating the original series and find that the probability density function also contributes to the observed multifractal pattern along with the long-memory effect. Surprisingly, the temperature anomaly time series are well described by the two-parameter multifractal binomial model.

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Notes

  1. 1.

    Autocorrelations between two x i values separated by n steps (lags) in the same series are defined by \(C(n)=\left < x_{i} x_{i+n}\right > \).

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Acknowledgments

I thank the anonymous reviewer for his/her careful reading of the manuscript and valuable comments and suggestions which help to improve the quality of the paper.

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Correspondence to Provash Mali.

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Mali, P. Multifractal characterization of global temperature anomalies. Theor Appl Climatol 121, 641–648 (2015). https://doi.org/10.1007/s00704-014-1268-y

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Keywords

  • Temperature Anomaly
  • Detrended Fluctuation Analysis
  • Multifractal Analysis
  • Singularity Spectrum
  • Fluctuation Function