On the connection between the multifractality and the predictability from the auroral index time series (original) (raw)
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Rank ordering multifractal analysis of the auroral electrojet index
Nonlinear Processes in Geophysics, 2011
In the second half of the 90s interest grew on the complex features of the magnetospheric dynamics in response to solar wind changes. An important series of papers were published on the occurrence of chaos, turbulence and complexity. Among them, particularly interesting was the study of the bursty and fractal/multifractal character of the high latitude energy release during geomagnetic storms, which was evidenced by analyzing the features of the Auroral Electrojet (AE) indices. Recently, the multifractal features of the small time-scale increments of AE-indices have been criticized in favor of a more simple fractal behavior. This is particularly true for the scaling features of the probability density functions (PDFs) of the AE index increments. Here, after a brief review of the nature of the fractal/multifractal features of the magnetospheric response to solar wind changes, we investigate the multifractal nature of the scaling features of the AE index increments PDFs using the Rank Ordering Multifractal Analysis (ROMA) technique. The ROMA results clearly demonstrate the existence of a hierarchy of scaling indices, depending on the increment amplitude, for the data collapsing of PDFs relative to increments at different time scales. Our results confirm the previous results by and the more recent results by Rypdal and .
Multifractal characteristics of magnetospheric dynamics and their relationship with sunspot cycle
Advances in Space Research
Multifractal analysis deals with a process whose power-law scaling behavior is a nonlinear function of statistical moments having a spectrum of scaling exponents. In contrast, monofractal process has a scaling behavior which is a linear function of moments with a single scaling exponent. In this study, multifractal analysis of complex magnetosphere using boxcounting approach has been considered for a better understanding of intermittent and persistent features, focusing on the auroral electrojet index (AE), SYM-H and Dst indices. For the analysis, 1-min AE, SYM-H and Dst indices are taken during the interval 1985-2007. We compare the sunspot cycle dependence of self-similarity and multifractality of magnetospheric proxies such as AE, SYM-H and Dst indices, using both monofractal and multifractal paradigms. The results indicate that monofractal features of AE, SYM-H and Dst indices are solar activity dependent. But, while analyzing the multifractal features, multifractal spectrum of AE index is less dependent on solar activity when compared with that of SYM-H and Dst indices. This implies that, other than solar wind forcing, certain complex phenomena of internal origin also modify the dynamics of geomagnetic fluctuations in the high-latitude auroral region.
Characteristic time scale of auroral electrojet data
Geophysical Research Letters, 1994
The structure run, on of the AE time series shows that the AE time series is self-affine such that the scaling exponent changes at the time scale of approximately 113 (ñ9) minutes. Autocorrelation fimction is shown to have scaling properties similar to those of the structure function. From this result it can be deduced that the time scale at which the scaling properties of the AE data change should equal the typical autocorrelation time of these data. We find the typical autocorrelation time of the AE data is 118 (+9) minutes. The characteristic time scale of the AE data appears as a spectral break in their power spectrum at a period of about twice the autocorrelation time.
Multifractal detrended fluctuation analysis of sunspot time series
Journal of Statistical Mechanics-theory and Experiment, 2006
We use multifractal detrended fluctuation analysis (MF-DFA), to See query 1 study sunspot number fluctuations. The result of the MF-DFA shows that there are three crossover timescales in the fluctuation function. We discuss how the existence of the crossover timescales is related to a sinusoidal trend. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The Hurst exponent of the time series without the sinusoidal trend is 0.12pm0.010.12\pm 0.010.12pm0.01. Also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to long range correlations.
The earth’s ionosphere is well recognized as a dynamical system and non-linearly coupled with the magnetosphere above and natural atmosphere below. The shape and time variability of the ionosphere indeed shows chaos, pattern formation, random behaviour and self-organization. The present paper studies the propriety of Multifractal Detrended Fluctuation Analysis (MF-DFA) technique for the ionospheric scintillation index time series. MF-DFA is used to identify the scaling behaviour of the ionospheric scintillation time-series data of two different nature. The obtained results show the robustness and the relevancy of the MF-DFA technique for the ionospheric scintillation index time series. The comparison of the MF-DFA results of original data to those of shuffled and surrogate series shows that the multifractal nature of considered time-series is almost due to long-range correlations. Subsequently, the Hurst exponents derived from two parallel methods namely Rescaled range analysis (R/S) and Auto Correlation Function (ACF) are also suggesting the presence of long range correlation. The presented results in this work may be of assistance for future modeling and simulation studies.
Characteristic time scale auroral electrojet data
Geophysical Research Letters, 1994
The structure run, on of the AE time series shows that the AE time series is self-affine such that the scaling exponent changes at the time scale of approximately 113 (ñ9) minutes. Autocorrelation fimction is shown to have scaling properties similar to those of the structure function. From this result it can be deduced that the time scale at which the scaling properties of the AE data change should equal the typical autocorrelation time of these data. We find the typical autocorrelation time of the AE data is 118 (+9) minutes. The characteristic time scale of the AE data appears as a spectral break in their power spectrum at a period of about twice the autocorrelation time.
Signal Processing Approach To Study Multifractality And Singularity Of Solar Wind Speed Time Series
2017
This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1<sup>st </sup>January, 1997 to 28<sup>th</sup> October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.
Nonlinear Processes in Geophysics, 2010
The predictability of the monthly North Atlantic Oscillation, NAO, index is analysed from the point of view of different fractal concepts and dynamic system theory such as lacunarity, rescaled analysis (Hurst exponent) and reconstruction theorem (embedding and correlation dimensions, Kolmogorov entropy and Lyapunov exponents). The main results point out evident signs of randomness and the necessity of stochastic models to represent time evolution of the NAO index. The results also show that the monthly NAO index behaves as a white-noise Gaussian process. The high minimum number of nonlinear equations needed to describe the physical process governing the NAO index fluctuations is evidence of its complexity. A notable predictive instability is indicated by the positive Lyapunov exponents. Besides corroborating the complex time behaviour of the NAO index, present results suggest that random Cantor sets would be an interesting tool to model lacunarity and time evolution of the NAO index.
Physical Science International Journal, 2017
Wavelet based Multifractal analysis techniques provides a sophisticated statistical characterization of many complex dynamical phenomena related with Sun and its environment. In this work multifractal property of the Sunspot number time series, has been analyzed during Solar cycle 23 and ascending phase of Solar cycle 24 using Wavelet transform and wavelet based multifractal approach. Present analysis has been performed using the software FRACLAB, developed at INRIA and available online at http://www-rocq.inria.fr. It was found that the singularities spectrum for sunspot time series was well Gaussian in shape suggesting the multifractal characteristics of time series. Thus we conclude that the multifractal based approach provide the local and adaptive description of dynamical processes related with Sun and its climate and can be applied effectively in the study of solar activity.