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

Abstract

Selfsimilar 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 yet identified. It is important to quantify the physics underlying the irregular fractal fluctuations for predictability studies. A general systems theory for fractals visualizes the emergence of successively larger scale fluctuations to result from the space-time integration of enclosed smaller scale fluctuations. The model predictions are as follows. The probability distribution and the power spectrum for fractal fluctuations is the same inverse power law function incorporating the golden mean. 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. Since the power (variance i.e. square of eddy amplitude) spectrum also represents the probability densities as in the case of quantum systems such as the electron or photon, fractal fluctuations exhibit quantumlike chaos. 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 are analysed to show that data sets and 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.