Investigating dynamical complexity in the magnetosphere using various entropy measures

[1] The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather applications.

[1]  Cheng-Chin Wu,et al.  Complexity induced anisotropic bimodal intermittent turbulence in space plasmas , 2003 .

[2]  I. Priogine Time, chaos and the laws of nature , 1996 .

[3]  C. Mira,et al.  Chaotic Dynamics: From the One-Dimensional Endomorphism to the Two-Dimensional Diffeomorphism , 1987 .

[4]  Georgios Balasis,et al.  Dynamical complexity in Dst time series using non‐extensive Tsallis entropy , 2008 .

[5]  S. M. Watson,et al.  Multifractal modeling of magnetic storms via symbolic dynamics analysis , 2005 .

[6]  Georgios Balasis,et al.  Investigating dynamic coupling in geospace through the combined use of modeling, simulations and data analysis , 2009 .

[7]  A. Sharma,et al.  Modeling substorm dynamics of the magnetosphere: from self-organization and self-organized criticality to nonequilibrium phase transitions. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  R. Steuer,et al.  Entropy and optimal partition for data analysis , 2001 .

[9]  G. Consolini,et al.  On the Earth’s magnetospheric dynamics: Nonequilibrium evolution and the fluctuation theorem , 2008 .

[10]  G. Consolini,et al.  Fractal time statistics of AE-index burst waiting times: evidence of metastability , 2002 .

[11]  Daniel N. Baker,et al.  Technological impacts of space storms: Outstanding issues , 2001 .

[12]  Konstantinos Karamanos Entropy analysis of substitutive sequences revisited , 2001 .

[13]  A L Goldberger,et al.  Physiological time-series analysis: what does regularity quantify? , 1994, The American journal of physiology.

[14]  Pierre Gaspard,et al.  Toward a probabilistic approach to complex systems , 1994 .

[15]  M. Liemohn,et al.  Lognormal form of the ring current energy content , 2003 .

[16]  Mark R. Titchener A measure of information , 2000, Proceedings DCC 2000. Data Compression Conference.

[17]  Catherine Nicolis,et al.  Chaotic dynamics, Markov partitions, and Zipf's law , 1989 .

[18]  M. Akay,et al.  Wavelets for biomedical signal processing , 1997, Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 'Magnificent Milestones and Emerging Opportunities in Medical Engineering' (Cat. No.97CH36136).

[19]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[20]  Janet U. Kozyra,et al.  Outstanding issues of ring current dynamics , 2002 .

[21]  H. Eugene Stanley,et al.  Scaling properties and entropy of long-range correlated time series , 2007 .

[22]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[23]  I. Daglis,et al.  Particle acceleration in the frame of the storm-substorm relation , 2004, IEEE Transactions on Plasma Science.

[24]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[25]  Z. Voros,et al.  Intermittent turbulence, noisy fluctuations, and wavy structures in the Venusian magnetosheath and wake , 2008, Journal of Geophysical Research.

[26]  S. Maus,et al.  Wavelet Analysis of CHAMP Flux Gate Magnetometer Data , 2005 .

[27]  S. Pincus,et al.  Randomness and degrees of irregularity. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Georgios Balasis,et al.  From pre-storm activity to magnetic storms: A transition described in terms of fractal dynamics , 2006 .

[29]  W. J. Cunningham,et al.  Introduction to Nonlinear Analysis , 1959 .

[30]  Annette Witt,et al.  Analysis of solar spike events by means of symbolic dynamics methods , 1993 .

[31]  Simon Wing,et al.  A solar cycle dependence of nonlinearity in magnetospheric activity , 2004 .

[32]  Georgios Balasis,et al.  The SGR 1806-20 magnetar signature on the Earth's magnetic field , 2006 .

[33]  Werner Ebeling,et al.  Word frequency and entropy of symbolic sequences: a dynamical perspective , 1992 .

[34]  H E Stanley,et al.  Scale-independent measures and pathologic cardiac dynamics. , 1998, Physical review letters.

[35]  Konstantinos Karamanos,et al.  Symbolic Dynamics and Entropy Analysis of Feigenbaum Limit Sets , 1999 .

[36]  D. Vassiliadis,et al.  Intense space storms: Critical issues and open disputes , 2003 .

[37]  L. Burlaga,et al.  Tsallis distributions of magnetic field strength variations in the heliosphere: 5 to 90 AU , 2007 .

[38]  Werner Ebeling,et al.  PARTITION-BASED ENTROPIES OF DETERMINISTIC AND STOCHASTIC MAPS , 2001 .

[39]  Constantino Tsallis,et al.  Special issue overview Nonextensive statistical mechanics: new trends, new perspectives , 2005 .

[40]  C. Tsallis Generalized entropy-based criterion for consistent testing , 1998 .

[41]  K. Mursula,et al.  Explaining and correcting the excessive semiannual variation in the Dst index , 2005 .

[42]  V. Uritsky,et al.  Geomagnetic substorms as perturbed self-organized critical dynamics of the magnetosphere , 2001 .

[43]  V. Uritsky,et al.  Analysis and prediction of high-latitude geomagnetic disturbances based on a self-organized criticality framework , 2006 .

[44]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[45]  Giuseppe Consolini,et al.  Complexity, Forced and/or Self-Organized Criticality, and Topological Phase Transitions in Space Plasmas , 2003 .

[46]  Wolfgang Baumjohann,et al.  Dissipation scales in the Earth's plasma sheet estimated from Cluster measurements , 2005 .

[47]  M. Titchener Deterministic computation of complexity, information and entropy , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[48]  M. Mandea,et al.  Can electromagnetic disturbances related to the recent great earthquakes be detected by satellite magnetometers , 2007 .

[49]  Vadim M. Uritsky,et al.  Low frequency 1/f-like fluctuations of the AE-index as a possible manifestation of self-organized criticality in the magnetosphere , 1998 .

[50]  Tom Chang,et al.  Self-organized criticality, multi-fractal spectra, sporadic localized reconnections and intermittent turbulence in the magnetotail , 1999 .

[51]  Benoit B. Mandelbrot,et al.  Fractals and Chaos , 2004 .

[52]  G. McDarby,et al.  Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.