Magnetic storms constitute the most remarkable large-scale phenomena of nonlinear magnetospheric dynamics. Studying the dynamical organization of macroscopic variability in terms of geomagnetic activity index data by means of complexity measures provides a promising approach for identifying the underlying processes and associated time scales. Here, we apply a suite of characteristics from recurrence quantification analysis (RQA) and recurrence network analysis (RNA) in order to unveil some key nonlinear features of the hourly Disturbance storm-time (Dst) index during periods with magnetic storms and such of normal variability. Our results demonstrate that recurrence-based measures can serve as excellent tracers for changes in the dynamical complexity along non-stationary records of geomagnetic activity. In particular, trapping time (characterizing the typical length of “laminar phases” in the observed dynamics) and recurrence network transitivity (associated with the number of the system’s effective dynamical degrees of freedom) allow for a very good discrimination between magnetic storm and quiescence phases. In general, some RQA and RNA characteristics distinguish between storm and non-storm times equally well or even better than other previously considered nonlinear characteristics like Hurst exponent or symbolic dynamics based entropy concepts. Our results point to future potentials of recurrence characteristics for unveiling temporal changes in the dynamical complexity of the magnetosphere.
References
1.
P.
Song
, H. J.
Singer
, and G. L.
Siscoe
, Space Weather
, AGU Geophysical Monograph Series Vol. 125 (American Geophysical Union
, Washington
, 2011
).2.
H. J.
Singer
, P. T.
Loto’Aniu
, J. C.
Green
, J. V.
Rodriguez
, B. J.
Anderson
, J. J.
Love
, V.
Angelopoulos
, D. N.
Baker
, M. G.
Connors
, W. F.
Denig
, E. F.
Donovan
, O.
Lecontel
, T. G.
Onsager
, T.
Nagatsuma
, A.
Runov
, and E. L.
Spanswick
, “Multipoint observations of the large substorm associated with the galaxy 15 anomaly
,” in American Geophysical Union, Fall Meeting 2010
(American Geophysical Union, WA
, 2010
), pp. SM22B–05.3.
D. H.
Boteler
, R. J.
Pirjola
, and H.
Nevanlinna
, “The effects of geomagnetic disturbances on electrical systems at the Earth’s surface
,” Adv. Space Res.
22
(1
), 17
–27
(1998
). 4.
L.
Bolduc
, “GIC observations and studies in the Hydro-Québec power system
,” J. Atmos. Solar-Terrestrial Phys.
64
(16
), 1793
–1802
(2002
). 5.
M.
Wik
, R.
Pirjola
, H.
Lundstedt
, A.
Viljanen
, P.
Wintoft
, and A.
Pulkkinen
, “Space weather events in July 1982 and October 2003 and the effects of geomagnetically induced currents on Swedish technical systems
,” Ann. Geophys.
27
(4
), 1775
–1787
(2009
). 6.
V.
Bothmer
and A.
Zhukov
, The Sun as the Prime Source of Space Weather
(Springer Berlin Heidelberg
, Berlin, Heidelberg
, 2007
), pp. 31
–102
.7.
I. G.
Richardson
and H. V.
Cane
, “Solar wind drivers of geomagnetic storms over more than four solar cycles
,” AIP. Conf. Proc.
1539
(1
), 422
–425
(2013
). 8.
D. N.
Baker
, A. J.
Klimas
, and D.
Vassiliadis
, Nonlinear Dynamics in the Earth’s Magnetosphere
(Springer New York
, New York, NY
, 2007
), pp. 53
–67
.9.
D. N.
Baker
, Introduction to Space Weather
(Springer
, Berlin, Heidelberg
, 2005
), pp. 3
–20
.10.
I. A.
Daglis
, G.
Balasis
, N.
Ganushkina
, F.-A.
Metallinou
, M.
Palmroth
, R.
Pirjola
, and I.
Tsagouri
, “Investigating dynamic coupling in geospace through the combined use of modeling, simulations and data analysis
,” Acta Geophys.
57
(1
), 141
–157
(2009
). 11.
G.
Consolini
, P.
De Michelis
, and R.
Tozzi
, “On the Earth’s magnetospheric dynamics: Nonequilibrium evolution and the fluctuation theorem
,” J. Geophys. Res. Space Phys.
113
(A8
), A08222
(2008
). 12.
N. W.
Watkins
, M. P.
Freeman
, S. C.
Chapman
, and R. O.
Dendy
, “Testing the SOC hypothesis for the magnetosphere
,” J. Atmos. Solar-Terrestrial Phys.
63
(13
), 1435
–1445
(2001
). 13.
D. V.
Vassiliadis
, A. S.
Sharma
, T. E.
Eastman
, and K.
Papadopoulos
, “Low-dimensional chaos in magnetospheric activity from AE time series
,” Geophys. Res. Lett.
17
(11
), 1841
–1844
(1990
). 14.
J.
Takalo
, J.
Timonen
, and H.
Koskinen
, “Properties of AE data and bicolored noise
,” J. Geophys. Res. Space Phys.
99
(A7
), 13239
–13249
(1994
). 15.
H. L.
Wei
, S. A.
Billings
, and M.
Balikhin
, “Analysis of the geomagnetic activity of the Dst index and self-affine fractals using wavelet transforms
,” Nonlinear Process. Geophys.
11
(3
), 303
–312
(2004
). 16.
X.
Shao
, M. I.
Sitnov
, S. A.
Sharma
, K.
Papadopoulos
, C. C.
Goodrich
, P. N.
Guzdar
, G. M.
Milikh
, M. J.
Wiltberger
, and J. G.
Lyon
, “Phase transition-like behavior of magnetospheric substorms: Global MHD simulation results
,” J. Geophys. Res. Space Phys.
108
(A1
), 1037
(2003
). 17.
A. S.
Sharma
, “Global and multiscale features of the magnetosphere: data-derived and global MHD modeling
,” in Proceedings of the ILWS Workshop 2006, Goa, India, February 19–24, 2006
, edited by N.
Gopalswamy
and A.
Bhattacharyya
(2006
), p. 340
.18.
M. I.
Sitnov
, A. S.
Sharma
, K.
Papadopoulos
, and D.
Vassiliadis
, “Modeling substorm dynamics of the magnetosphere: From self-organization and self-organized criticality to nonequilibrium phase transitions
,” Phys. Rev. E
65
, 016116
(2001
). 19.
G.
Balasis
, I. A.
Daglis
, P.
Kapiris
, M.
Mandea
, D.
Vassiliadis
, and K.
Eftaxias
, “From pre-storm activity to magnetic storms: A transition described in terms of fractal dynamics
,” Ann. Geophys.
24
(12
), 3557
–3567
(2006
). 20.
A. T.
Monk
and A. H.
Compton
, “Recurrence phenomena in cosmic-ray intensity
,” Rev. Mod. Phys.
11
, 173
–179
(1939
). 21.
N.
Marwan
, M. C.
Romano
, M.
Thiel
, and J.
Kurths
, “Recurrence plots for the analysis of complex systems
,” Phys. Rep.
438
(5
), 237
–329
(2007
). 22.
Recurrence Quantification Analysis: Theory and Best Practices
, edited by C. L.
Webber
, Jr. and N.
Marwan
(Springer International Publishing
, Cham
, 2015
).23.
G.
Robinson
and M.
Thiel
, “Recurrences determine the dynamics
,” Chaos
19
(2
), 023104
(2009
). 24.
R. V.
Donner
, M.
Small
, J. F.
Donges
, N.
Marwan
, Y.
Zou
, R.
Xiang
, and J.
Kurths
, “Recurrence-based time series analysis by means of complex network methods
,” Int. J. Bifurcat. Chaos
21
(4
), 1019
–1046
(2011
). 25.
G.
Balasis
, I. A.
Daglis
, C.
Papadimitriou
, M.
Kalimeri
, A.
Anastasiadis
, and K.
Eftaxias
, “Dynamical complexity in time series using non-extensive Tsallis entropy
,” Geophys. Res. Lett.
35
(14
), L14102
(2008
). 26.
G.
Balasis
, I. A.
Daglis
, C.
Papadimitriou
, M.
Kalimeri
, A.
Anastasiadis
, and K.
Eftaxias
, “Investigating dynamical complexity in the magnetosphere using various entropy measures
,” J. Geophys. Res. Space Phys.
114
(A9
), A00D06
(2009
). 27.
J. A.
Bastos
and J.
Caiado
, “Recurrence quantification analysis of global stock markets
,” Physica A
390
(7
), 1315
–1325
(2011
). 28.
J. P.
Zbilut
, N.
Thomasson
, and C. L.
Webber
, “Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals
,” Med. Eng. Phys.
24
(1
), 53
–60
(2002
). 29.
S.
Schinkel
, N.
Marwan
, and J.
Kurths
, “Brain signal analysis based on recurrences
,” J. Physiol.
103
(6
), 315
–323
(2009
). 30.
J. F.
Donges
, R. V.
Donner
, K.
Rehfeld
, N.
Marwan
, M. H.
Trauth
, and J.
Kurths
, “Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis
,” Nonlinear Process. Geophys.
18
(5
), 545
–562
(2011
). 31.
J. F.
Donges
, R. V.
Donner
, M. H.
Trauth
, N.
Marwan
, H. J.
Schellnhuber
, and J.
Kurths
, “Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution
,” Proc. Natl. Acad. Sci. U.S.A.
108
, 20422
–20427
(2011
). 32.
R. V.
Donner
, G.
Balasis
, V.
Stolbova
, M.
Georgiou
, M.
Wiedermann
, and J.
Kurths
, “Recurrence based quantification of dynamical complexity in the Earth’s magnetosphere at geospace storm timescales
,” e-print arXiv:1801.09412, 2018
.33.
G.
Balasis
, I. A.
Daglis
, C.
Papadimitriou
, A.
Anastasiadis
, I.
Sandberg
, and K.
Eftaxias
, “Quantifying dynamical complexity of magnetic storms and solar flares via nonextensive tsallis entropy
,” Entropy
13
(10
), 1865
–1881
(2011
). 34.
R. V.
Donner
and G.
Balasis
, “Correlation-based characterisation of time-varying dynamical complexity in the earth’s magnetosphere
,” Nonlinear Process. Geophys.
20
(6
), 965
–975
(2013
). 35.
N. H.
Packard
, J. P.
Crutchfield
, J. D.
Farmer
, and R. S.
Shaw
, “Geometry from a time series
,” Phys. Rev. Lett.
45
, 712
–716
(1980
). 36.
F.
Takens
, Detecting Strange Attractors in Turbulence
(Springer
, New York
, 1981
), pp. 366
–381
.37.
J.-P.
Eckmann
, S.
Oliffson Kamphorst
, and D.
Ruelle
, “Recurrence plots of dynamical systems
,” Europhys. Lett.
4
(9
), 973
(1987
). 38.
Since the Dst data are given as integer values, we add some small Gaussian white noise with a standard deviation of 0.01 before computing the distances to avoid problems by properly fixing the recurrence rate. It has been checked that different realizations or somewhat different standard deviations of the noise do not affect the results presented in this paper.
39.
K. H.
Krämer
, R. V.
Donner
, J.
Heitzig
, and N.
Marwan
, Dimension-scalable recurrence threshold estimation
, e-print arXiv:1802.01605, 2018
.40.
N.
Marwan
, J. F.
Donges
, Y.
Zou
, R. V.
Donner
, and J.
Kurths
, “Complex network approach for recurrence analysis of time series
,” Phys. Lett. A
373
(46
), 4246
–4254
(2009
). 41.
R. V.
Donner
, Y.
Zou
, J. F.
Donges
, N.
Marwan
, and J.
Kurths
, “Recurrence networks—A novel paradigm for nonlinear time series analysis
,” New J. Phys.
12
(3
), 033025
(2010
). 42.
J. P.
Zbilut
and C. L.
Webber
, Jr., “Embeddings and delays as derived from quantification of recurrence plots
,” Phys. Lett. A
171
(3–4
), 199
–203
(1992
). 43.
C. L.
Webber
and J. P.
Zbilut
, “Dynamical assessment of physiological systems and states using recurrence plot strategies
,” J. Appl. Physiol.
76
(2
), 965
–973
(1994
). 44.
N.
Marwan
, N.
Wessel
, U.
Meyerfeldt
, A.
Schirdewan
, and J.
Kurths
, “Recurrence plot based measures of complexity and its application to heart rate variability data
,” Phys. Rev. E
66
(2
), 026702
(2002
). 45.
S.
Schinkel
, N.
Marwan
, O.
Dimigen
, and J.
Kurths
, “Confidence bounds of recurrence-based complexity measures
,” Phys. Lett. A
373
(26
), 2245
–2250
(2009
). 46.
Y.
Zou
, R. V.
Donner
, J. F.
Donges
, N.
Marwan
, and J.
Kurths
, “Identifying shrimps in continuous dynamical systems using recurrence-based methods
,” Chaos
20
(4
), 043130
(2010
). 47.
J. F.
Donges
, R. V.
Donner
, N.
Marwan
, S. F. M.
Breitenbach
, K.
Rehfeld
, and J.
Kurths
, “Non-linear regime shifts in holocene asian monsoon variability: Potential impacts on cultural change and migratory patterns
,” Clim. Past
11
(5
), 709
–741
(2015
). 48.
Note that we have omitted here the -dependence of for brevity.
49.
J. R.
Johnson
and S.
Wing
, “A solar cycle dependence of nonlinearity in magnetospheric activity
,” J. Geophys. Res. Space Phys.
110
(A4
), A04211
(2005
). 50.
R. V.
Donner
, J.
Heitzig
, J. F.
Donges
, Y.
Zou
, N.
Marwan
, and J.
Kurths
, “The geometry of chaotic dynamics—A complex network perspective
,” Eur. Phys. J. B
84
(4
), 653
–672
(2011
). 51.
R. J.
Barlow
, Statistics—A Guide to the Use of Statistical Methods in the Physical Sciences
(Wiley
, Chichester
, 1989
).52.
F.
Wilcoxon
, “Individual comparisons by ranking methods
,” Biom. Bull.
1
(6
), 80
–83
(1945
). 53.
T.
Fawcett
, “An introduction to ROC analysis
,” Pattern Recognit. Lett.
27
(8
), 861
–874
(2006
). 54.
G.
Balasis
, I. A.
Daglis
, A.
Anastasiadis
, and K.
Eftaxias
, Detection of Dynamical Complexity Changes in Dst Time Series Using Entropy Concepts and Rescaled Range Analysis
(Springer Netherlands
, Dordrecht
, 2011
), pp. 211
–220
.55.
G.
Balasis
, R. V.
Donner
, S. M.
Potirakis
, J.
Runge
, C.
Papadimitriou
, I. A.
Daglis
, K.
Eftaxias
, and J.
Kurths
, “Statistical mechanics and information-theoretic perspectives on complexity in the earth system
,” Entropy
15
(11
), 4844
–4888
(2013
). 56.
S. M.
Pincus
, “Approximate entropy as a measure of system complexity
,” Proc. Natl. Acad. Sci.
88
(6
), 2297
–2301
(1991
). 57.
J. S.
Richman
and J. R.
Moorman
, “Physiological time-series analysis using approximate entropy and sample entropy
,” Am. J. Physiol. Heart Circ. Physiol.
278
(6
), H2039
–H2049
(2000
). 58.
W.
Chen
, Z.
Wang
, H.
Xie
, and W.
Yu
, “Characterization of surface EMG signal based on fuzzy entropy
,” IEEE Trans. Neural. Syst. Rehabil. Eng.
15
(2
), 266
–272
(2007
). 59.
G.
Balasis
, I. A.
Daglis
, A.
Anastasiadis
, C.
Papadimitriou
, M.
Mandea
, and K.
Eftaxias
, “Universality in solar flare, magnetic storm and earthquake dynamics using Tsallis statistical mechanics
,” Physica A
390
(2
), 341
–346
(2011
). 60.
A.
Witt
and B. D.
Malamud
, “Quantification of long-range persistence in geophysical time series: Conventional and benchmark-based improvement techniques
,” Surv. Geophys.
34
(5
), 541
–651
(2013
). 61.
E. J.
Ngamga
, D. V.
Senthilkumar
, A.
Prasad
, P.
Parmananda
, N.
Marwan
, and J.
Kurths
, “Distinguishing dynamics using recurrence-time statistics
,” Phys. Rev. E
85
, 026217
(2012
). 62.
J. F.
Donges
, J.
Heitzig
, B.
Beronov
, M.
Wiedermann
, J.
Runge
, Q. Y.
Feng
, L.
Tupikina
, V.
Stolbova
, R. V.
Donner
, N.
Marwan
, H. A.
Dijkstra
, and J.
Kurths
, “Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
,” Chaos
25
(11
), 113101
(2015
). © 2018 Author(s).
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