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 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 for fractals visualising the emergence of successively larger scale fluctuations resulting from the space-time integration of enclosed smaller scale fluctuations is proposed. The theoretical model predictions are: (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 quantumlike 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.Key words Fractals and statistical normal distribution, power law distributions, longrange correlations and fat tail distributions, golden mean and fractal fluctuations followed by decrease on all scales (space-time), for example in atmospheric flows, cycles of increase and decrease in meteorological parameters such as wind, temperature, etc. occur from the turbulence scale of millimeters-seconds to climate scales of thousands of kilometers-years. The power spectra of fractal fluctuations exhibit inverse power law of the form f - where f is the frequency and  is a constant. Inverse power law for power spectra indicate long-range space-time correlations or scale invariance for the scale range for which  is a constant, i.e., the amplitudes of the eddy fluctuations in this scale range are a function of the scale factor  alone. In general the value of  is different for different scale ranges indicating multifractal structure for the fluctuations. The long-range space-time correlations exhibited by dynamical systems are identified as self-organized criticality [2][3] . The physics of selforganized ...

Improving Global Forecast System of extreme precipitation events with regional statistical model: Application of quantile‐based probabilistic forecasts

“…However, the current NWP ensemble forecasts are found to be typically biased and often underestimate precipitation with huge forecast ensemble uncertainty, primarily resulting from model structure and approximations of subgridscale processes [Goddard et al, 2001;Maraun et al, 2010]. Furthermore, NWP models are not very efficient in predicting heavy rainfall events [Březková et al, 2010;Hong and Lee, 2009;Khaladkar et al, 2007;Selvam, 2011]. To overcome this limitation, the mesoscale atmospheric models are used on a finer spatial resolution of 0.5-1 km incorporating land surface processes; they are effective in predicting extreme heavy rainfall events [Dodla and Ratna, 2010;Chang and Chiang, 2009].…”

Universal Spectrum for Atmospheric Suspended Particulates: Comparison with Observations: Data Set II

“…Identifiable large eddies can exist in the atmosphere only for scale ratios more than 10 since, for smaller scale ratios the fractional volume dilution rate k becomes more than half. Thus atmospheric eddies of various scales, i.e., convective, meso-, synoptic and planetary scale eddies are generated by successive decadic scale range eddy mixing process starting from the basic turbulence scale (Selvam et al 1984a, b;1992;Joshi 1995 Selvam andFadnavis 1998;Joshi and Selvam 1999;Selvam 1990Selvam , 1993Selvam , 2005Selvam , 2007Selvam , 2009Selvam , 2011.…”

“…It would be nice if there were some general rule to the effect that, in any given complex system, the steady state which produces entropy at the maximum rate would at the same time be the steady state of maximum order and minimum entropy (Paltridge, 2009). Selvam (2011) has shown that the eddy continuum energy distribution P (Eq. 15) is the same as the Boltzmann distribution for molecular energies.…”