Signatures of Universal Characteristics of Fractal Fluctuations in Global Mean Monthly Temperature Anomalies

  • Amujuri Mary SelvamEmail author
Part of the Springer Atmospheric Sciences book series (SPRINGERATMO)


Self-similar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is not completely understood. It is important to quantify the physics underlying the irregular fractal fluctuations for prediction of space-time evolution of dynamical systems. A general systems theory model for fractals visualising the emergence of successively larger-scale fluctuations resulting from the space-time integration of enclosed smaller scale fluctuations predicts the following. (i) The probability distribution and the power spectrum for fractal fluctuations is the same inverse power-law function incorporating the golden mean. (ii) The predicted distribution is close to the Gaussian distribution for small-scale fluctuations but exhibits fat long tail for large-scale fluctuations with higher probability of occurrence than predicted by Gaussian distribution. (iii) Since the power spectrum (variance, i.e. square of eddy amplitude) also represents the probability densities as in the case of quantum systems such as the electron or photon, fractal fluctuations exhibit quantum-like chaos. (iv) The fine-structure constant for spectrum of fractal fluctuations is a function of the golden mean and is analogous to atomic spectra equal to about 1/137. Global gridded time series data sets of monthly mean temperatures for the period 1880—2007/2008 were analysed. The data sets and the corresponding power spectra exhibit distributions close to the model predicted inverse power-law distribution. The model predicted and observed universal spectrum for interannual variability rules out linear secular trends in global monthly mean temperatures. Global warming results in intensification of fluctuations of all scales and manifested immediately in high frequency fluctuations.


Fractals and statistical normal distribution Power-law distributions Long-range correlations and fat tail distributions Golden mean and fractal fluctuations 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Ministry of Earth Sciences, Government of IndiaRetired from IITMPuneIndia

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