Signatures of universal characteristics of fractal fluctuations in global mean monthly temperature anomalies

This paper proposes 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. 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.

[1]  D. Sornette,et al.  Taming Large Events: Optimal Portfolio Theory for Strongly Fluctuating Assets , 1998 .

[2]  M. Feigenbaum Universal behavior in nonlinear systems , 1983 .

[3]  Alair Townsend,et al.  The structure of turbulent shear flow /2nd edition/ , 1976 .

[4]  Richard L. Hudson,et al.  The Misbehavior of Markets: A Fractal View of Risk, Ruin, and Reward , 2004 .

[5]  D. C. Sherrington,et al.  Spontaneous formation of space-time structures and criticality , 1991 .

[6]  Charles Gide,et al.  Cours d'économie politique , 1911 .

[7]  B. M. I︠A︡vorskiĭ,et al.  Handbook of physics , 1980 .

[8]  Tang,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[9]  Deterministic chaos, fractals, and quantumlike mechanics in atmospheric flows , 1990, physics/0010046.

[10]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[11]  G. Lloyd Aspects of the interrelations of medicine, magic and philosophy in ancient Greece. , 1975, APEIRON: a journal for ancient philosophy and science.

[12]  K. Pearson “The Grammar of Science” , 1900, Nature.

[13]  Larry S. Liebovitch,et al.  Two lessons from fractals and chaos , 2000 .

[14]  K. Pearson The Grammar of Science , 1900 .

[15]  A. Townsend The Structure of Turbulent Shear Flow , 1975 .

[16]  A. M. Taylor,et al.  Handbook of Physics , 1959 .

[17]  B. McKelvey,et al.  Beyond Gaussian Averages: Redirecting Management Research Toward Extreme Events and Power Laws , 2006 .

[18]  M. Born Statistical Thermodynamics , 1944, Nature.

[19]  Clifford A. Pickover,et al.  Fractals, Chaos, and Power Laws , 1992 .

[20]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[21]  D. Sornette,et al.  Rank‐ordering statistics of extreme events: Application to the distribution of large earthquakes , 1995, cond-mat/9510035.

[22]  A. M. Selvam,et al.  Signatures of a universal spectrum for atmospheric interannual variability in some disparate climatic regimes , 1998, chao-dyn/9805028.

[23]  J. Maddox Explosion fragments by numbers , 1988, Nature.

[24]  A. Rae,et al.  Quantum physics, illusion or reality? , 1987 .

[25]  Quantum systems as «order out of chaos» phenomena , 1989 .

[26]  C. Ruhla The Physics of Chance , 1992 .

[27]  A. Selvam,et al.  Critical fluctuation in daily incidence of acute myocardial infarction , 2000 .

[28]  W. G. V. Rosser An Introduction to Statistical Physics , 1982 .

[29]  A. Selvam Quantumlike Chaos in the Frequency Distributions of Bases A, C, G, T in Human Chromosome1 DNA , 2002, physics/0211066.

[30]  Thomas C. Peterson,et al.  First difference method: Maximizing station density for the calculation of long‐term global temperature change , 1998 .

[31]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[32]  Benoit B. Mandelbrot,et al.  Les objets fractals : forme, hasard et dimension , 1989 .

[33]  R. Vose,et al.  An Overview of the Global Historical Climatology Network Temperature Database , 1997 .

[34]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.

[35]  A. Selvam,et al.  Quantum-like Chaos in Prime Number Distribution and in Turbulent Fluid Flows , 2000, physics/0005067.

[36]  E. Fama The Behavior of Stock-Market Prices , 1965 .

[37]  A. Selvam Quantumlike chaos in the frequency distributions of the bases , 2002, physics/0210068.

[38]  Kerson Huang Introduction to Statistical Physics , 2001 .

[39]  D. Haar,et al.  Statistical Physics , 1971, Nature.

[40]  B. McKelvey,et al.  Beyond Gaussian averages: redirecting international business and management research toward extreme events and power laws , 2007 .

[41]  L. Cronbach Essentials of psychological testing , 1960 .

[42]  T. C. Dorlas Statistical Mechanics: Fundamentals and Model Solutions, , 1999 .

[43]  W. Greene,et al.  计量经济分析 = Econometric analysis , 2009 .

[44]  J. V. Bradley Distribution-Free Statistical Tests , 1968 .

[45]  A. Selvam,et al.  Universal quantification for deterministic chaos in dynamical systems , 1993 .

[46]  L F Richardson,et al.  The problem of contiguity : An appendix to statistics of deadly quarrels , 1961 .

[47]  John L. Hubisz,et al.  Quantum Physics: Illusion or Reality? , 1988 .

[48]  K. F. Riley,et al.  Mathematical Methods for Physics and Engineering , 1998 .

[49]  B. Mandelbrot The Variation of Certain Speculative Prices , 1963 .

[50]  Suvarna Fadnavis,et al.  Superstrings, Cantorian-fractal Spacetime and Quantum-like Chaos in Atmospheric Flows , 1998, chao-dyn/9806002.

[51]  E. Ungureanu,et al.  Molecular Physics , 2008, Nature.

[52]  Thomas C. Peterson,et al.  Global historical climatology network (GHCN) quality control of monthly temperature data , 1998 .

[53]  A. Selvam A General Systems Theory for Chaos, Quantum Mechanics and Gravity for Dynamical Systems of all Space-Time Scales , 2005, physics/0503028.