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Geophysical Monograph Series



  • complexity
  • extremes
  • heavy tails
  • bursts
  • long-range dependence
  • fractals

Index Terms

  • 4440 Nonlinear Geophysics: Fractals and multifractals
  • 4475 Nonlinear Geophysics: Scaling: spatial and temporal
  • 3265 Mathematical Geophysics: Stochastic processes
  • 0560 Computational Geophysics: Numerical solutions



On Self-Similar and Multifractal Models for the Scaling of Extreme Bursty Fluctuations in Space Plasmas

N. W. Watkins

B. Hnat

Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, UK

S. C. Chapman

Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, UK

A direct inspiration for the investigation of scaling behavior and extreme fluctuations in space plasmas has come from inherently multiscale physical theories such as self-organized criticality and turbulence. An additional benefit, with “space weather” implications, is an ability to assess the likelihood of an extreme fluctuation of a given size. If it is present, however, scaling behavior may not be captured by a single self-similarity exponent H but might instead require a multifractal spectrum of scaling exponents. We believe that it is, nonetheless, useful to assess how well simple monofractal models can capture the “stylized facts” of the scaling behavior of auroral indices and solar wind quantities and here illustrate it by studying the use of linear fractional stable motion (LFSM) as a model for solar wind and ionospheric time series, an example that can be taken as a prototype for other possible models. By postulating such a description, we can heuristically explore how the previously experimentally measured scaling exponents for quantities like superposed epoch averaged activity, or the probability distribution of the differenced time series, depend on the model's parameters. We can then also derive predicted scaling exponents for the exponents of more complicated measurements that have also been made, such as size and duration of bursts above a threshold or the survival probability of a burst. Comparison of these predictions with data is then used to assess the usefulness of LFSM as a toy model for space physics time series.

Citation: Watkins, N. W., B. Hnat, and S. C. Chapman (2012), On self-similar and multifractal models for the scaling of extreme bursty fluctuations in space plasmas, in Extreme Events and Natural Hazards: The Complexity Perspective, Geophys. Monogr. Ser., vol. 196, edited by A. S. Sharma et al. 299–313, AGU, Washington, D. C., doi:10.1029/2011GM001084.


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