Scaling laws from geomagnetic time series

Vörös, Z.; Kovács, Péter; Juhász, Á.; Körmendi, A.; Green, A. W.

doi:10.1029/98gl01910

Cited by 17 publications

(14 citation statements)

References 11 publications

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“…For example, bursty transport events have been reported in the magnetotail [ Angelopoulos et al , 1992] and their auroral signatures suggest self‐similar statistics [ Lui et al , 2000; Uritsky et al , 2001, 2002b, 2003; Kozelov et al , 2004]. The fluctuations in the ground based measurements of the magnetic field are non‐Gaussian and also exhibit scaling [ Consolini et al , 1996; Kovács et al , 2001; Vörös et al , 1998]. In the context of time series analysis, geomagnetic indices are of particular interest as they provide a global measure of magnetospheric output and are evenly sampled over a long time interval.…”

Section: Introductionmentioning

confidence: 99%

Scaling and a Fokker‐Planck model for fluctuations in geomagnetic indices and comparison with solar wind ε as seen by Wind and ACE

2005

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[1] The evolution of magnetospheric indices on temporal scales shorter than that of substorms is characterized by bursty, intermittent events that may arise from turbulence intrinsic to the magnetosphere or that may reflect solar wind-magnetosphere coupling. This leads to a generic problem of distinguishing between the features of the system and those of the driver. We quantify scaling properties of short-term (up to few hours) fluctuations in the geomagnetic indices AL and AU during solar minimum and maximum, along with the parameter that is a measure of the solar wind driver. We find that self-similar statistics provide a good approximation for the observed scaling properties of fluctuations in the geomagnetic indices, regardless of the solar activity level, and in the parameter at solar maximum. This self-similarity persists for fluctuations on timescales at least up to about 1-2 hours. The scaling exponent of AU index fluctuations show dependence on the solar cycle, and the trend follows that found in the scaling of fluctuations in . The values of their corresponding scaling exponents, however, are always distinct. Fluctuations in the AL index are insensitive to the solar cycle, as well as being distinct from those in the parameter. This approximate self-similar scaling leads to a Fokker-Planck model which, we show, captures the probability density function of fluctuations and provides a stochastic dynamical equation (

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Section: Introductionmentioning

confidence: 99%

Scaling and a Fokker‐Planck model for fluctuations in geomagnetic indices and comparison with solar wind ε as seen by Wind and ACE

2005

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“…Alternatively, Consolini and De Michelis [1998] used the Castaing distribution -the empirical model derived in Castaing et al [1990] and based on a turbulent energy cascadeto obtain a two parameter functional form for the Probability Density Functions (PDF) of the AE fluctuations on various temporal scales. Turbulent descriptions of magnetospheric measures also model observed statistical intermittency, i.e., the presence of large deviations from the average value on different scales [Consolini et al, 1996;Vörös et al, 1998]. An increased probability of finding such large deviations is manifested in the departure of the PDF from Gaussian toward a leptokurtic distribution [Sornette, 2000].…”

Section: Introductionmentioning

confidence: 99%

“…Geomagnetic indices are of particular interest in this context as they provide a global measure of magnetospheric output and are evenly sampled over a long time interval. There is a wealth of literature on the magnetosphere as an input-output system (see for example, [Klimas et al, 1996;Sitnov et al, 2000;Tsurutani et al, 1990;Vassiliadis et al, 2000;Vörös et al, 1998]. Recent work has focussed on comparing some aspects of the scaling properties of input parameters such as [Perreault and Akasofu, 1978] and the AE index [Davis and Sugiura, 1966] to establish whether, to the lowest order, they are directly related [Freeman et al, 2000;Uritsky et al, 2001].…”

Section: Introductionmentioning

confidence: 99%

Scaling of solar wind ϵ and the AU, AL and AE indices as seen by WIND

Hnat

Chapman

Rowlands

et al. 2002

Geophysical Research Letters

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[1] We apply the finite size scaling technique to quantify the statistical properties of fluctuations in AU, AL and AE indices and in the parameter that represents energy input from the solar wind into the magnetosphere. We find that the exponents needed to rescale the probability density functions (PDF) of the fluctuations are the same to within experimental error for all four quantities. This selfsimilarity persists for time scales up to $4 hours for AU, AL and and up to $2 hours for AE. Fluctuations on shorter time scales than these are found to have similar long-tailed (leptokurtic) PDF, consistent with an underlying turbulent process. These quantitative and modelindependent results place important constraints on models for the coupled solar wind-magnetosphere system.

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“…There is a considerable literature concerning scaling in auroral region magnetometers and in geomagnetic indices (such as Tsurutani et al, 1990;Takalo et al, 1993;Consolini et al, 1996;Vörös et al, 1998;Uritsky and Pudovkin, 1998;Watkins et al, 2001;Kovács et al, 2001). This is motivated in part…”

Section: Introductionmentioning

confidence: 99%

Scaling collapse and structure functions: identifying self-affinity in finite length time series

Chapman

Hnat

Rowlands

et al. 2005

Nonlin. Processes Geophys.

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Abstract. Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) attempting a scaling collapse of the Probability Density Functions which should then be well described by the solution of the corresponding Fokker-Planck equation and ii) using structure functions to determine the scaling properties of the higher order moments. We consider a method of conditioning that recovers the underlying self affine scaling in a finite length time series, and illustrate it using a Lévy flight.

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Scaling laws from geomagnetic time series

Cited by 17 publications

References 11 publications

Scaling and a Fokker‐Planck model for fluctuations in geomagnetic indices and comparison with solar wind ε as seen by Wind and ACE

Scaling and a Fokker‐Planck model for fluctuations in geomagnetic indices and comparison with solar wind ε as seen by Wind and ACE

Scaling of solar wind ϵ and the AU, AL and AE indices as seen by WIND

Scaling collapse and structure functions: identifying self-affinity in finite length time series

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