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2017 | Buch

Self-organized Criticality and Predictability in Atmospheric Flows

The Quantum World of Clouds and Rain

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This book presents a new concept of General Systems Theory and its application to atmospheric physics. It reveals that energy input into the atmospheric eddy continuum, whether natural or manmade, results in enhancement of fluctuations of all scales, manifested immediately in the intensification of high-frequency fluctuations such as the Quasi-Biennial Oscillation and the El-Nino–Southern Oscillation cycles. Atmospheric flows exhibit self-organised criticality, i.e. long-range correlations in space and time manifested as fractal geometry to the spatial pattern concomitant with an inverse power law form for fluctuations of meteorological parameters such as temperature, pressure etc. Traditional meteorological theory cannot satisfactorily explain the observed self-similar space time structure of atmospheric flows. A recently developed general systems theory for fractal space-time fluctuations shows that the larger-scale fluctuation can be visualised 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 interconnected network of eddy circulations responds as a unified whole to local perturbations such as global-scale response to El-Nino events.

The general systems theory model predicts an inverse power law form incorporating the golden mean τ for the distribution of space-time fluctuation patterns and for the power (variance) spectra of the fluctuations. Since the probability distributions of amplitude and variance are the same, atmospheric flows exhibit quantumlike chaos. Long-range correlations inherent to power law distributions of fluctuations are identified as nonlocal connection or entanglement exhibited by quantum systems such as electrons or photons. The predicted distribution is close to the Gaussian distribution for small-scale fluctuations, but exhibits a fat long tail for large-scale fluctuations. Universal inverse power law for fractal fluctuations rules out unambiguously linear secular trends in climate parameters.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Nonlinear Dynamics and Chaos: Applications in Meteorology and Atmospheric Physics
Abstract
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm-sec to climate scales of thousands of kilometres/years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power-law form signifying long-range correlations identified as self-organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or ‘deterministic chaos’ in finite precision computer realizations of nonlinear mathematical models of real-world dynamical systems such as atmospheric flows. Though the self-similar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and incorporate basic physical concepts of nonlinear dynamics and chaos into classical meteorological theory for more realistic simulation and prediction of weather and climate. A historical review of nonlinear dynamics and chaos in meteorology and atmospheric physics is summarized in this chapter.
Amujuri Mary Selvam
Chapter 2. Noise or Random Fluctuations in Physical Systems: A Review
Abstract
‘Noise’ or random fluctuations characterize all physical systems in nature ranging from biology, botany, physiology, meteorology, astronomy, etc. The apparently irregular or chaotic fluctuations were considered as ‘noise’ in all fields except in astronomy, where the fluctuations from astronomical sources were referred to as signal. Noise and fluctuation has been a field of study since 1826 with the study of Brownian motion which indirectly confirmed the existence of atoms and molecules. The measured characteristics of noise contain recognizable patterns or signal and convey useful information about the system. Statistical data analysis techniques are used to extract the signal, i.e. recognizable patterns in the apparently random fluctuations of physical systems. The analysis of data sets and broad quantification in terms of probabilities belongs to the field of statistics. Early attempts resulted in identification of the following two quantitative (mathematical) distributions which approximately fit data sets from a wide range of scientific and other disciplines of study. The first is the well-known statistical normal distribution and the second is the power-law distribution associated with the recently identified ‘fractals’ or self-similar characteristic of data sets in general. Abraham de Moivre, an eighteenth-century statistician and consultant to gamblers made the first recorded discovery of the normal curve of error (or the bell curve because of its shape) in 1733. The importance of the normal curve stems primarily from the fact that the distributions of many natural phenomena are at least approximately normally distributed. This normal distribution concept underlies how we analyse experimental data over the last 200 years. Most quantitative research involves the use of statistical methods presuming independence among data points and Gaussian ‘normal’ distributions. The Gaussian distribution is reliably characterized by its stable mean and finite variance. Normal distributions place a trivial amount of probability far from the mean and hence the mean is representative of most observations. Even the largest deviations, which are exceptionally rare, are still only about a factor of two from the mean in either direction and are well characterized by quoting a simple standard deviation. However, apparently rare real-life catastrophic events such as major earth quakes, stock market crashes, heavy rainfall events, etc., occur more frequently than indicated by the normal curve, i.e. they exhibit a probability distribution with a fat tail. Fat tails indicate a power-law pattern and interdependence. The ‘tails’ of a power-law curve—the regions to either side that correspond to large fluctuations—fall off very slowly in comparison with those of the bell curve. The normal distribution is therefore an inadequate model for extreme departures from the mean. For well over a century evidence had been mounting that real-world behaviour in particular, behaviour of systems, whether natural, social, economic, or financial does not follow normal distribution characteristics. There is increased evidence for non-normality in real-world settings and in its place an alternative distribution, namely the power-law distribution is shown to be exhibited by real-world systems in all fields of science and other areas of human interest. In this chapter, the following are discussed. (i) A brief history of the two chief quantitative methods of statistical data analysis, namely the statistical normal distribution and the power-law distribution. (ii) The association of power-law distributions with complex systems, scale invariance, self-similarity, fractals, 1/f noise, long-term memory, phase transitions, critical phenomena, and self-organized criticality. (iii) Current status of power-law distributions. (iv) Power-law relations (bivariate) and power-law (probability) distributions. (v) Allometric scaling and fractals. (vi) Fractals and the golden section in plant growth. (vii) Turbulent fluid flow structure, fractals, and the golden ratio (≈1.618). (viii) Fractal space-time and the golden ratio. (ix) Power-law (probability) distributions in the meteorological parameters precipitation, temperature, quaternary ice volume fluctuations and atmospheric pollution. (x) General systems theory model for self-organized criticality (SOC) in atmospheric flows with universal quantification for power-law distribution in terms of the golden ratio.
Amujuri Mary Selvam
Chapter 3. Self-organized Criticality: A Signature of Quantum-like Chaos in Atmospheric Flows
Abstract
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power-law form for power spectra of temporal fluctuations on all space-time scales ranging from turbulence (centimetres-seconds) to climate (kilometres-years). Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. Mathematical models for simulation and prediction of atmospheric flows are nonlinear and do not possess analytical solutions. Finite precision computer realizations of nonlinear models give unrealistic solutions because of deterministic chaos, a direct consequence of round-off error growth in iterative numerical computations. Recent studies show that round-off error doubles on an average for each iteration of iterative computations. Round-off error propagates to the mainstream computation and gives unrealistic solutions in numerical weather prediction (NWP) and climate models, which incorporate thousands of iterative computations in long-term numerical integration schemes. A general systems theory model for atmospheric flows developed by the author predicts the observed self-organized criticality as intrinsic to quantumlike chaos in flow dynamics. The model provides universal quantification for self-organized criticality in terms of the golden ratio τ (≈1.618). Model predictions are in agreement with a majority of observed spectra of time series of several standard meteorological and climatological data sets representative of disparate climatic regimes. Universal spectrum for natural climate variability rules out linear trends. Man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high-frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference to possible prediction of climate change. Model concepts, if correct, rule out unambiguously, linear trends in climate. Climate change will only be manifested as increase or decrease in the natural variability. However, more stringent tests of model concepts and predictions are required before applications to such an important issue as climate change. The cell dynamical system model for atmospheric flows is a general systems theory applicable in general to all dynamical systems in other fields of science, such as, number theory, biology, physics and botany.
Amujuri Mary Selvam
Chapter 4. Universal Inverse Power-Law Distribution for Temperature and Rainfall in the UK Region
Abstract
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit self-similar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden ratio for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic monthwise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
Amujuri Mary Selvam
Chapter 5. Signatures of Universal Characteristics of Fractal Fluctuations in Global Mean Monthly Temperature Anomalies
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.
Amujuri Mary Selvam
Backmatter
Metadaten
Titel
Self-organized Criticality and Predictability in Atmospheric Flows
verfasst von
Amujuri Mary Selvam
Copyright-Jahr
2017
Electronic ISBN
978-3-319-54546-2
Print ISBN
978-3-319-54545-5
DOI
https://doi.org/10.1007/978-3-319-54546-2