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

Scale-free Universal Spectrum for Atmospheric Aerosol Size Distribution for Davos, Mauna Loa and Izana

Atmospheric flows exhibit fractal fluctuations and inverse power law form for power spectra indicating an eddy continuum structure for the selfsimilar fluctuations. A general systems theory for fractal fluctuations developed by the author is based on the simple visualisation that large eddies form by space-time integration of enclosed turbulent eddies, a concept analogous to Kinetic Theory of Gases in Classical Statistical Physics. The ordered growth of atmospheric eddy continuum is in dynamical equilibrium and is associated with Maximum Entropy Production. The model predicts universal (scale-free) inverse power law form for fractal fluctuations expressed in terms of the golden mean. Atmospheric particulates are held in suspension in the fractal fluctuations of vertical wind velocity. The mass or radius (size) distribution for homogeneous suspended atmospheric particulates is expressed as a universal scale-independent function of the golden mean, the total number concentration and the mean volume radius. Model predicted spectrum is in agreement (within two standard deviations on either side of the mean) with total averaged radius size spectra for the AERONET (aerosol inversions) stations Davos and Mauna Loa for the year 2010 and Izana for the year 2009 daily averages. The general systems theory model for aerosol size distribution is scale free and is derived directly from atmospheric eddy dynamical concepts. At present empirical models such as the log normal distribution with arbitrary constants for the size distribution of atmospheric suspended particulates are used for quantitative estimation of earth-atmosphere radiation budget related to climate warming/cooling trends. The universal aerosol size spectrum will have applications in computations of radiation balance of earth-atmosphere system in climate models.Comment: 18 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1105.0172, arXiv:1005.1336, arXiv:0908.2321, arXiv:1002.3230, arXiv:0704.211

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

Universal spectrum for atmospheric aerosol size distribution: Comparison with PCASP-B observations of VOCALS 2008

Atmospheric flows exhibit scale-free fractal fluctuations. A general systems theory based on classical statistical physical concepts visualizes the fractal fluctuations to result from the coexistence of eddy fluctuations in an eddy continuum, the larger scale eddies being the integrated mean of enclosed smaller scale eddies. The model predicts (i) the eddy energy (variance) spectrum and corresponding eddy amplitude probability distribution are quantified by the same universal inverse power law distribution incorporating the golden mean. (ii) The steady state ordered hierarchical growth of atmospheric eddy continuum is associated with maximum entropy production. (iii) atmospheric particulate size spectrum is derived in terms of the model predicted universal inverse power law for atmospheric eddy energy spectrum. Model predictions are in agreement with observations. Universal inverse power law for power spectra of fractal fluctuations rules out linear secular trends in meteorological parameters. Global warming related climate change, if any, will be manifested as intensification of fluctuations of all scales manifested immediately in high frequency fluctuations. The universal aerosol size spectrum presented in this paper may be computed for any location with two measured parameters, namely, the mean volume radius and the total number concentration and may be incorporated in climate models for computation of radiation budget of earth-atmosphere system

Complexity signatures in the geomagnetic H-component recorded by the Tromsø magnetometer (70°N, 19°E) over the last quarter of a century

Solar disturbances, depending on the orientation of the interplanetary magnetic field, typically result in perturbations of the geomagnetic field as observed by magnetometers on the ground. Here, the geomagnetic field's horizontal component, as measured by the ground-based observatory-standard magnetometer at Tromsø (70° N, 19° E), is examined for signatures of complexity. Twenty-five year-long 10 s resolution data sets are analysed for fluctuations with timescales of less than 1 day. Quantile–quantile plots are employed first, revealing that the fluctuations are better represented by Cauchy rather than Gaussian distributions. Thereafter, both spectral density and detrended fluctuation analysis methods are used to estimate values of the generalized Hurst exponent, α. The results are then compared with independent findings. Inspection and comparison of the spectral and detrended fluctuation analyses reveal that timescales between 1 h and 1 day are characterized by fractional Brownian motion with a generalized Hurst exponent of ~1.4, whereas including timescales as short as 1 min suggests fractional Brownian motion with a generalized Hurst exponent of ~1.6

Statistical mechanics and information-theoretic perspectives on complexity in the Earth system

This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques