Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bak, P.C., Tang, C., Wiesenfeld, K.: Self-organized criticality. Phys. Rev. A 38, 364–374 (1988)
Feigenbaum, M.J.: Universal behavior in nonlinear systems. Los Alamos Sci. 1, 4–27 (1980)
Ford, K.W.: Basic Physics. Blaisdell Publishing Company, Waltham, Massachusetts, USA (1968)
Grossing, G.: Quantum systems as order out of chaos phenomena. Il Nuovo Cimento 103B, 497–510 (1989)
Jenkinson, A. F.: A powerful elementary method of spectral analysis for use with monthly, seasonal or annual meteorological time series. Meteorological Office, Branch Memorandum No. 57, London (1977)
Maddox, J.: Licence to slang Copenhagen? Nature 332, 581 (1988)
Maddox, J.: Can quantum theory be understood? Nature 361, 493 (1993)
Mandelbrot, B.B.: Les Objets Fractals: Forme. Hasard et Dimension, Flammarion, Paris (1975)
Peterson, T.C., Vose, R.S.: An overview of the global historical climatology network temperature database. Bull. Am. Meteorol. Soc. 78, 2837–2849 (1997)
Peterson, T.C., Vose, R.S., Schmoyer, R., Razuvae, V.: Global Historical Climatology Network (GHCN) quality control of monthly temperature data. Int. J. Climatol. 18, 1169–1179 (1998a)
Peterson, T.C., Karl, T.R., Jamason, P.F., Knight, R., Easterling, D.R.: The first difference method: maximizing station density for the calculation of long-term global temperature change. J. Geophys. Res. 103, 25967–25974 (1998b)
Phillips, T.: The mathematical uncertainty principle. Monthly essays on mathematical topics November 2005, American Mathematical Society (2005). http://www.ams.org/featurecolumn/archive/uncertainty.html
Rae, A.: Quantum-Physics: illusion or reality?. Cambridge University Press, New York (1988)
Riley, K.F., Hobson, M.P., Bence, S.J.: Mathematical methods for physics and engineering, 3rd edn. Cambridge University Press, USA (2006)
Ruhla, C.: The physics of chance. Oxford University Press, Oxford (1992)
Schroeder, M.: Fractals, chaos and power-laws. W. H. Freeman and Co., N.Y. (1991)
Selvam, A.M.: Deterministic chaos, fractals and quantumlike mechanics in atmospheric flows. Can. J. Phys. 68, 831–841 (1990). http://xxx.lanl.gov/html/physics/0010046
Selvam, A.M., Fadnavis, S.: Signatures of a universal spectrum for atmospheric inter-annual variability in some disparate climatic regimes. Meteorology and Atmospheric Physics 66, 87–112. http://xxx.lanl.gov/abs/chao-dyn/9805028
Selvam, A.M., Fadnavis, S.: Superstrings, cantorian-fractal spacetime and quantum-like chaos in atmospheric flows. Chaos Solitons Fractals 10, 1321–1334 (1999). http://xxx.lanl.gov/abs/chao-dyn/9806002
Selvam, A.M., Sen, D., Mody, S.M.S.: Critical fluctuations in daily incidence of acute myocardial infarction. Chaos Solitons Fractals 11, 1175–1182 (2000). http://xxx.lanl.gov/abs/chao-dyn/9810017
Selvam, A.M.: Quantum-like chaos in prime number distribution and in turbulent fluid flows. Apeiron 8, 29–64 (2001a). http://redshift.vif.com/JournalFiles/V08NO3PDF/V08N3SEL.PDF; http://xxx.lanl.gov/html/physics/0005067
Selvam, A.M.: Signatures of quantum-like chaos in spacing intervals of non-trivial Riemann zeta zeros and in turbulent fluid flows. Apeiron 8, 10–40 (2001b). http://redshift.vif.com/JournalFiles/V08NO4PDF/V08N4SEL.PDF http://xxx.lanl.gov/html/physics/0102028
Selvam, A.M.: Cantorian fractal space-time fluctuations in turbulent fluid flows and the kinetic theory of gases. Apeiron 9, 1–20 (2002a). http://redshift.vif.com/JournalFiles/V09NO2PDF/V09N2sel.PDF; http://xxx.lanl.gov/html/physics/9912035
Selvam, A.M.: Quantumlike chaos in the frequency distributions of the bases A, C, G, T in Drosophila DNA. Apeiron 9, 103–148 (2002b). http://redshift.vif.com/JournalFiles/V09NO4PDF/V09N4sel.pdf; http://arxiv.org/html/physics/0210068
Selvam, A.M.: Quantumlike chaos in the frequency distributions of the bases A, C, G, T in human chromosome 1 DNA. Apeiron 11, 134–146 (2004). http://redshift.vif.com/JournalFiles/V11NO3PDF/V11N3SEL.PDF; http://arxiv.org/html/physics/0211066
Selvam, A.M.: Chaotic climate dynamics. Luniver Press, UK (2007)
Selvam, A.M.: Rain formation in warm clouds: general systems theory. Springer Briefs in Meteorology, Springer (2015)
Spiegel, M.R.: Statistics. Schaum’s Outline Series in Mathematics, McGraw-Hill (1961)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Selvam, A.M. (2017). Signatures of Universal Characteristics of Fractal Fluctuations in Global Mean Monthly Temperature Anomalies. In: Self-organized Criticality and Predictability in Atmospheric Flows. Springer Atmospheric Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-54546-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-54546-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54545-5
Online ISBN: 978-3-319-54546-2
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)