Signatures of a universal spectrum for atmospheric interannual variability in some disparate climatic regimes

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

“…Also, traditional statistical/mathematical theory predicts that the Gaussian, its Fourier transform and therefore Fourier transform associated power spectrum are the same distributions. However, the general systems theory [4][5][6][7][14][15][16][17][18][19][20] visualises the eddy growth process in successive stages of unit length-step growth with ordered two-way energy feedback between the larger and smaller scale eddies and derives a power law probability distribution P which is close to the Gaussian for small deviations and gives the observed fat, long tail for large fluctuations. Further, the model predicts the power spectrum of the eddy continuum also to follow the power law probability distribution P. Therefore the additive amplitudes of the eddies when squared (variance), represent the probability distribution similar to the subatomic dynamics of quantum systems such as the electron or photon.…”

“…The model concepts are independent of the exact details such as the chemical, physical, physiological and other properties of the dynamical system and therefore provide a general systems theory applicable to all real world and computed dynamical systems in nature [4][5][6][7][14][15][16][17][18][19][20] . The model is based on the concept that the irregular fractal fluctuations may be visualized to result from the superimposition of an eddy continuum, i.e., a hierarchy of eddy circulations generated at each level by the space-time integration of enclosed small-scale eddy fluctuations.…”

“…The physics of fractal fluctuations generic to dynamical systems in nature is not yet identified and traditional statistical, mathematical theories do not provide adequate tools for identification and quantitative description of the observed universal properties of fractal structures observed in all fields of science and other areas of human interest. A recently developed general systems theory for fractal space-time fluctuations [4][5][6][7] shows that the larger scale fluctuation can be visualized to emerge from the space-time averaging of enclosed small scale fluctuations, thereby generating a hierarchy of selfsimilar fluctuations manifested as the observed eddy continuum in power spectral analyses of fractal fluctuations. Such a concept results in inverse power law form incorporating the golden mean τ for the space-time fluctuation pattern and also for the power spectra of the fluctuations (Section 3).…”

Universal Inverse Power-Law Distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter-Annual Variability of Indian and USA Region Rainfall

“…A recently developed general systems theory for fractal space-time fluctuations (Selvam, 1990(Selvam, , 2005(Selvam, , 2007(Selvam, , 2009(Selvam, , 2010Selvam and Fadnavis, 1998) shows that the larger scale fluctuation can be visualized to emerge from the space-time averaging of enclosed small scale fluctuations, thereby generating a hierarchy of self-similar fluctuations manifested as the observed eddy continuum in power spectral analyses of fractal fluctuations. The concept that aggregate averaged eddy ensemble properties represent the eddy continuum belongs to 19 th century classical statistical physics where the study of the properties of a system is reduced to a determination of average values of the physical quantities that characterize the state of the system as a whole (Yavorsky and Detlaf, 1975) such as gases, e.g., the gaseous envelope of the earth, the atmosphere.…”

“…LogT 50 also represents the mean value for the r. m. s. eddy fluctuations and is consistent with the concept of the mean level represented by r. m. s. eddy fluctuations. Spectra of time series of meteorological parameters when plotted as cumulative percentage contribution to total variance versus normalized deviation t have been shown to follow closely the model predicted universal spectrum (Selvam and Fadnavis, 1998;Joshi and Selvam, 1999) which is identified as a signature of quantum-like chaos. The model predicted T 50 is obtained from Eq.…”