## Article

GEOPHYSICAL MONOGRAPH SERIES, VOL. 196, PP. 299-313, 2012

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

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

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.,
*Extreme Events and Natural Hazards: The Complexity Perspective*, Geophys. Monogr. Ser., vol. 196, edited by

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