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| Titel |
How well does a minimal monofractal model capture the scaling of extreme bursty fluctuations in space plasmas ? |
| VerfasserIn |
Nicholas Watkins, Dan Credgington, Sam Rosenberg, Bogdan Hnat, Sandra Chapman, Nicola Longden, Mervyn Freeman |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250055331
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| Zusammenfassung |
| Direct inspiration for the investigation of scaling behaviour in space plasmas has come from
inherently multiscale physical theories such as self-organised criticality and turbulence. Work
in complexity science is now contributing to a better physical understanding of the ways by
which the interactions between components of such systems cause driven or random
perturbations to be nonlinearly amplified and spread out over a wide range of spatiotemporal
scales. These mechanisms thus lead both to non-Gaussian fluctuations and to long-ranged
temporal memory (referred to by the late Benoit Mandelbrot as the “Noah” and “Joseph”
effects, respectively). An additional benefit of scaling analysis, with “space weather"
implications, is an ability to assess the likelihood of an extreme fluctuation of a
given size. If present, however, scaling behaviour may not be captured by a single
self-similarity exponent H, but might instead require a multifractal spectrum of scaling
exponents.
We have elsewhere argued that it is nonetheless useful to try capture the “stylised facts"
of the scaling behaviour of auroral indices and solar wind quantities by simple,
purely phenomenological, monofractal models. To make this idea more concrete we
here illustrate it by studying the use of linear fractional stable motion (LFSM) as a
model for solar wind and ionospheric time series. Our example could be taken as a
prototype for other possible models. LFSM has only three parameters: the Levy
stability exponent α; the self-similarity exponent H; and a persistence exponent d
which depends additively on the other two. By postulating an LFSM description
we can semi-numerically 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 parameters.
We can then also derive predicted scaling exponents for the exponents of more
complicated measurements which 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 can then used to assess the usefulness of LFSM as a toy
model of extreme bursts in space physics time series. The relation to recent work by
Moloney and Davidsen, and Rypdal and Rypdal [both JGR, 2010] will be touched
on. |
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