Correlation dimension and affinity of AE data and bicolored noise

Takalo, Jouni; Timonen, J.; Koskinen, H.

doi:10.1029/93gl01596

Cited by 89 publications

(79 citation statements)

References 20 publications

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“…It is reasonable to assume that the large-amplitude fluctuations are produced by internal bursts and the externally driven fluctuations contribute mostly to the small amplitude portion. Takalo et al (1993) have estimated the correlation dimension of AE index as 3.4 and reported that bicoloured noise shares many properties with AE index. It is believed that the stochastic nature of the AE index fluctuations is of internal, and not of external origin (Burlaga, 1995).…”

Section: Discussionmentioning

confidence: 99%

Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

Unnikrishnan

2008

Ann. Geophys.

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Abstract. The deterministic chaotic behaviour of magnetosphere was analyzed, using AE index time series. The significant chaotic quantifiers like, Lyapunov exponent, spatiotemporal entropy and nonlinear prediction error for AE index time series under various physical conditions were estimated and compared. During high solar activity (1991), the values of Lyapunov exponent for AE index time series representing quiet conditions (yearly mean = 0.5±0.1 min −1 ) have no significant difference from those values for corresponding storm conditions (yearly mean = 0.5±0.17 min −1 ). This implies that, for the cases considered here, geomagnetic storms may not be an additional source to increase or decrease the deterministic chaotic aspects of magnetosphere, especially during high solar activity. During solar minimum period (1994), the seasonal mean value of Lyapunov exponent for AE index time series belong to quiet periods in winter (0.7±0.11 min −1 ) is higher compared to corresponding value of storm periods in winter (0.36±0.09 min −1 ). This may be due to the fact that, stochastic part, which is D st dependent could be more prominent during storms, thereby increasing fluctuations/stochasticity and reducing determinism in AE index time series during storms. It is observed that, during low solar active period (1994), the seasonal mean value of entropy for time series representing storm periods of equinox is greater than that for quiet periods. However, significant difference is not observed between storm and quiet time values of entropy during high solar activity (1991), which is also true for nonlinear prediction error for both low and high solar activities. In the case of both high and low solar activities, the higher standard deviations of yearly mean Lyapunov exponent values for AE index time series for storm periods compared to those for quiet periods might be due to the strong interplay between stochasticity and determinism during storms.Correspondence to: K. Unnikrishnan (kaleekkal unni@yahoo.com) It is inferred that, the external driving forces, mainly due to solar wind, make the solar-magnetosphere-ionosphere coupling more complex, which generates many active degrees of freedom with various levels of coupling among them, under various physical conditions. Hence, the superposition of a large number of active degrees of freedom can modify the stability/instability conditions of magnetosphere.

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Section: Discussionmentioning

confidence: 99%

Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

Unnikrishnan

2008

Ann. Geophys.

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“…a measure of fluctuations with no characteristic scales (power law), over a wide range of scales. Examples include (a) power spectra of ground magnetic fields (Cambell, 1976;Francia et al, 1995;Consolini et al, 1998;Weatherwax et al, 2000;Abel and Freeman, 2002), and ionospheric electric fields (Kintner, 1976;Weimer et al, 1985;Bering et al, 1995;Buchert et al, 1999;Abel and Freeman, 2002;Golovchanskaya et al, 2006), (b) probability density functions (PDFs) of durations between threshold crossings of the auroral electrojet indices AU and AL (Freeman et al, 2000), (c) PDFs of durations, areas, and other quantities of auroral bright patches (Lui et al, 2000;Uritsky et al, 2002;Kozelov et al, 2004) and (d) structure functions of the auroral electrojet indices AU, AL and AE, the polar cap index PC (Takalo et al, 1993;Takalo and Timonen, 1998;Hnat et al, 2002), ground magnetic fields (Pulkkinen et al, 2006) and ionospheric convection (Parkinson, 2006;Abel et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Investigating turbulent structure of ionospheric plasma velocity using the Halley SuperDARN radar

Abel

Freeman

Chisham

et al. 2007

Nonlin. Processes Geophys.

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Abstract. We present a detailed analysis of the spatial structure of the ionospheric plasma velocity in the nightside Fregion ionosphere, poleward of the open-closed magnetic field line boundary (OCB), i.e. in regions magnetically connected to the turbulent solar wind. We make use of spatially distributed measurements of the ionospheric plasma velocity made with the Halley Super Dual Auroral Radar Network (SuperDARN) radar between 1996 and 2003. We analyze the spatial structure of the plasma velocity using structure functions and P (0) scaling (where P (0) is the value of the probability density function at 0), which provide simple methods for deriving information about the scaling, intermittency and multi-fractal nature of the fluctuations. The structure functions can also be compared to values predicted by different turbulence models. We find that the limited range of velocity that can be measured by the Halley SuperDARN radar restricts our ability to calculate structure functions. We correct for this by using conditioning (removing velocity fluctuations with magnitudes larger than 3 standard deviations from our calculations). The resultant structure functions suggest that Kraichnan-Iroshnikov versions of P and log-normal models of turbulence best describe the velocity structure seen in the ionosphere.

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“…So far, evidence to support this is based on the observation of (a) intermittent energy transport in the magnetotail -"bursty bulk flow events" [Angelopoulos et al, 1992], (b) magnetotail turbulence [Hoshino, 1994;Borovsky, 1997], (c) the apparent low dimensionality [Sharma, 1995;Klimas, 1996] of the Auroral Electrojet (AE) indices [Davis and $ugJura, 1966], and (d) scale-free properties of the AE indices including a "l/f" region in the power spectrum [Tsurutani et al, 1990], self-affinity [Takalo et al, 1993], and power law distributions of the lifetimes [Takalo, 1993;Consolini, 1999;Takalo, 1999] and energies [Consolini, 1997;Consolini, 1999] of burst events. Burst lifetime probability densities …”

Section: Introductionmentioning

confidence: 99%

Evidence for a solar wind origin of the power law burst lifetime distribution of the AE indices

Freeman

Watkins

Riley

2000

Geophysical Research Letters

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Abstract.In this paper we examine the claim that the power law distribution of burst lifetimes in the AE index is evidence that the magnetosphere is a Self-Organized Critical (SOC) system. To do this we compare the burst lifetime distributions of the AU and [AL I indices with those of the vBs and e solar wind input functions. We show for the first time that both the vBs and e burst lifetime distributions are of power law form with an exponential cut-off, consistent with the solar wind being an SOC system. Furthermore, the power law of the e burst lifetime distribution is not significantly different to that of the AU and IALI indices, indicating that this scale-free property of the AE indices could arise from the solar wind input and may not be an intrinsic property of the magnetospheric system. We discuss the implications of this result for SOC theories of the magnetosphere.

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Correlation dimension and affinity of AE data and bicolored noise

Cited by 89 publications

References 20 publications

Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

Investigating turbulent structure of ionospheric plasma velocity using the Halley SuperDARN radar

Evidence for a solar wind origin of the power law burst lifetime distribution of the AE indices

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