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The (un)predictable magnetosphere: the role of the internal dynamics

Published online by Cambridge University Press:  03 March 2022

Tommaso Alberti Open the ORCID record for Tommaso Alberti [Opens in a new window]
Tommaso Alberti*
Affiliation:
INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, I-00133Roma, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The magnetosphere–ionosphere dynamics comprises processes both directly related to solar wind variability and of purely internal origin. The latter represent a huge drawback for correctly forecasting the magnetosphere–ionosphere dynamics during geomagnetic storms and substorms. Here, we use wavelet analysis to further characterize the storm–substorm relationship through the use of the AL and SYM-H geomagnetic indices. We focus our analysis on one of the strongest geomagnetic storms of solar cycle 23 that occurred on 20 November 2003. Our findings suggest that, during disturbed periods, a significant amount of information comes from the interactions between geomagnetic storms and magnetospheric substorms. Thus, predicting the intensity and the duration of a geomagnetic storm requires information coming not only from the solar wind variability but also from the nonlinear variability of the magnetosphere–ionosphere system occurring on short time scales. Our results are also discussed in the framework of Space Weather, suggesting an extended use of non-traditional dynamical systems approaches (such as those based on extreme value statistics and tipping point analysis) to deal with emergent behaviours coming from different sources during geomagnetic storms and magnetospheric substorms.

Keywords

space plasma physicscomplex plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 1 , February 2022 , 905880121
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Copyright © The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Ahn, B.H., Akasofu, S.I. & Kamide, Y. 1983 The Joule heat production rate and the particle energy injection rate as a function of the geomagnetic indices AE and AL. J. Geophys. Res. (Space Phys.) 88 (A8), 6275–6288.CrossRefGoogle Scholar
Akasofu, S.-I. 2001 Predicting geomagnetic storms as a space weather project. In Space Weather (ed. P. Song, H. J. Singer & G. L. Siscoe), Geophysical Monograph Series, vol. 125, pp. 329–337. American Geophysical Union.Google Scholar
Akasofu, S.-I. 2017 Auroral substorms: search for processes causing the expansion phase in terms of the electric current approach. Space Sci. Rev. 212 (1-2), 341–381.CrossRefGoogle Scholar
Alberti, T., Consolini, G., De Michelis, P., Laurenza, M. & Marcucci, M.F. 2018 On fast and slow Earth's magnetospheric dynamics during geomagnetic storms: a stochastic Langevin approach. J. Space Weath. Space Clim. 8, A56.CrossRefGoogle Scholar
Alberti, T., Consolini, G., Lepreti, F., Laurenza, M., Vecchio, A. & Carbone, V. 2017 Timescale separation in the solar wind-magnetosphere coupling during St. Patrick's Day storms in 2013 and 2015. J. Geophys. Res. (Space Phys.) 122 (4), 4266–4283.CrossRefGoogle Scholar
Alberti, T., Lekscha, J., Consolini, G., De Michelis, P. & Donner, R.V. 2020 Disentangling nonlinear geomagnetic variability during magnetic storms and quiescence by timescale dependent recurrence properties. J. Space Weath. Space Clim. 10, 25.CrossRefGoogle Scholar
Allen, M.R. & Smith, L.A. 1996 Monte Carlo SSA: detecting irregular oscillations in the presence of colored noise. J. Clim. 9 (12), 3373–3404.2.0.CO;2>CrossRefGoogle Scholar
Anderson, P.W. 1972 More is different. Science 177 (4047), 393–396.CrossRefGoogle ScholarPubMed
Baker, D.N. 2020 Solar-terrestrial data science: prior experience and future prospects. Front. Astron. Space Sci. 7, 65.CrossRefGoogle Scholar
Balasis, G., Daglis, I.A., Mann, I.R., Papadimitriou, C., Zesta, E., Georgiou, M., Haagmans, R. & Tsinganos, K. 2015 Multi-satellite study of the excitation of Pc3 and Pc4-5 ULF waves and their penetration across the plasmapause during the 2003 Halloween superstorm. Ann. Geophys. 33 (10), 1237–1252.CrossRefGoogle Scholar
Barbosa, S.M. & Donner, R.V. 2016 Long-term changes in the seasonality of Baltic sea level. Tellus Ser. A 68, 30540.CrossRefGoogle Scholar
Borovsky, J.E. 2020 What magnetospheric and ionospheric researchers should know about the solar wind. J. Atmos. Solar Terr. Phys. 204, 105271.CrossRefGoogle Scholar
Borovsky, J.E. & Valdivia, J.A. 2018 The Earth's magnetosphere: a systems science overview and assessment. Surv. Geophys. 39 (5), 817–859.CrossRefGoogle ScholarPubMed
Callen, H.B. & Welton, T.A. 1951 Irreversibility and generalized noise. Phys. Rev. 83 (1), 34–40.CrossRefGoogle Scholar
Camporeale, E., Wing, S., Johnson, J., Jackman, C.M. & McGranaghan, R. 2018 Space weather in the machine learning era: a multidisciplinary approach. Space Weath. 16 (1), 2–4.CrossRefGoogle Scholar
Champion, K., Lusch, B., Kutz, J.N. & Brunton, S.L. 2019 Data-driven discovery of coordinates and governing equations. Proc. Natl Acad. Sci. 116 (45), 22445–22451. Available at: https://www.pnas.org/content/116/45/22445.full.pdf.CrossRefGoogle ScholarPubMed
Chang, T., Tam, S.W.Y., Wu, C.-C. & Consolini, G. 2003 Complexity, forced and/or self-organized criticality, and topological phase transitions in space plasmas. Space Sci. Rev. 107 (1), 425–445.CrossRefGoogle Scholar
Chapman, S. & Ferraro, V.C.A. 1930 A new theory of magnetic storms. Nature 126 (3169), 129–130.CrossRefGoogle Scholar
Consolini, G. 1997 Intermittency and turbulence in magnetospheric dynamics. Proc. Intl School Phys. Enrico Fermi 134, 657–659.Google Scholar
Consolini, G., Alberti, T. & De Michelis, P. 2018 On the forecast horizon of magnetospheric dynamics: a scale-to-scale approach. J. Geophys. Res. (Space Phys.) 123 (11), 9065–9077.CrossRefGoogle Scholar
Consolini, G. & Chang, T.S. 2001 Magnetic field topology and criticality in geotail dynamics: relevance to substorm phenomena. Space Sci. Rev. 95, 309–321.CrossRefGoogle Scholar
Consolini, G. & Chang, T. 2002 Complexity, magnetic field topology, criticality, and metastability in magnetotail dynamics. J. Atmos. Solar Terr. Phys. 64 (5–6), 541–549.CrossRefGoogle Scholar
Consolini, G. & De Michelis, P. 1998 Non-Gaussian distribution function of AE-index fluctuations: evidence for time intermittency. Geophys. Res. Lett. 25 (21), 4087–4090.CrossRefGoogle Scholar
Consolini, G. & De Michelis, P. 2005 Local intermittency measure analysis of AE index: the directly driven and unloading component. Geophys. Res. Lett. 32 (5), L05101.CrossRefGoogle Scholar
Consolini, G., De Michelis, P. & Tozzi, R. 2008 On the Earth's magnetospheric dynamics: nonequilibrium evolution and the fluctuation theorem. J. Geophys. Res. (Space Phys.) 113 (A8), A08222.CrossRefGoogle Scholar
Consolini, G. & Lui, A.T.Y. 2000 Symmetry breaking and nonlinear wave-wave interaction in current disruption: possible evidence for a phase transition. In Magnetospheric Current Systems (ed. S.-I. Ohtani, R. Fujii, M. Hesse & R. L. Lysak), Geophysical Monograph Series, vol. 118, p. 395. American Geophysical Union.CrossRefGoogle Scholar
Consolini, G., Marcucci, M.F. & Candidi, M. 1996 Multifractal structure of auroral electrojet index data. Phys. Rev. Lett. 76 (21), 4082–4085.CrossRefGoogle ScholarPubMed
Daglis, I.A. 1997 Terrestrial agents in the realm of space storms: missions study oxygen ions. EOS Trans. 78 (24), 245–251.CrossRefGoogle Scholar
Daglis, L.A., Livi, S., Sarris, E.T. & Wilken, B. 1994 Energy density of ionospheric and solar wind origin ions in the near-Earth magnetotail during substorms. J. Geophys. Res. (Space Phys.) 99 (A4), 5691–5704.CrossRefGoogle Scholar
Daglis, I.A., Thorne, R.M., Baumjohann, W. & Orsini, S. 1999 The terrestrial ring current: origin, formation, and decay. Rev. Geophys. 37 (4), 407–438.CrossRefGoogle Scholar
Daubechies, I. 1990 The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inf. Theory 36, 961–1005.CrossRefGoogle Scholar
Davis, T.N. & Sugiura, M. 1966 Auroral electrojet activity index AE and its universal time variations. J. Geophys. Res. 71 (3), 785–801.CrossRefGoogle Scholar
De Michelis, P., Consolini, G., Materassi, M. & Tozzi, R. 2011 An information theory approach to the storm-substorm relationship. J. Geophys. Res. (Space Phys.) 116 (A8), A08225.CrossRefGoogle Scholar
Detman, T.R. & Vassiliadis, D. 1997 Review of techniques for magnetic storm forecasting. In Magnetic Storms (ed. B. T. Tsurutani, W. D. Gonzalez, Y. Kamide & J. K. Arballo), Geophysical Monograph Series, vol. 98, pp. 253–266. American Geophysical Union.CrossRefGoogle Scholar
Ditlevsen, P.D. & Johnsen, S.J. 2010 Tipping points: early warning and wishful thinking. Geophys. Res. Lett. 37 (19), L19703.CrossRefGoogle Scholar
Dolla, L., Marqué, C., Seaton, D.B., Van Doorsselaere, T., Dominique, M., Berghmans, D., Cabanas, C., De Groof, A., Schmutz, W., Verdini, A., West, M.J., Zender, J. & Zhukov, A.N. 2012 Time delays in quasi-periodic pulsations observed during the X2.2 solar flare on 2011 February 15. Astrophys. J. Lett. 749 (1), L16. arXiv:1203.6223.CrossRefGoogle Scholar
Donner, R. & Thiel, M. 2007 Scale-resolved phase coherence analysis of hemispheric sunspot activity: a new look at the north-south asymmetry. Astron. Astrophys. 475 (3), L33–L36.CrossRefGoogle Scholar
Ekhtiari, N., Agarwal, A., Marwan, N. & Donner, R.V. 2019 Disentangling the multi-scale effects of sea-surface temperatures on global precipitation: a coupled networks approach. Chaos 29 (6), 063116.CrossRefGoogle ScholarPubMed
Epanechnikov, V.A. 1969 Non-parametric estimation of a multivariate probability density. Theory Prob. Applics. 14 (1), 153–158. arXiv: https://doi.org/10.1137/1114019.CrossRefGoogle Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–457.CrossRefGoogle Scholar
Farge, M., Guezennec, Y., Ho, C.M. & Meneveau, C. 1990 Continuous wavelet analysis of coherent structures. In Studying Turbulence Using Numerical Simulation Databases. 3: Proceedings of the 1990 Summer Program, pp. 331–348. https://ui.adsabs.harvard.edu/abs/1990stun.proc..331FGoogle Scholar
Farge, M. & Schneider, K. 2015 Wavelet transforms and their applications to MHD and plasma turbulence: a review. J. Plasma Phys. 81 (6), 435810602. arXiv:1508.05650.CrossRefGoogle Scholar
Ghil, M. & Lucarini, V. 2020 The physics of climate variability and climate change. Rev. Mod. Phys. 92 (3), 035002. arXiv:1910.00583.CrossRefGoogle Scholar
Gonzalez, W.D., Tsurutani, B.T. & Clúa de Gonzalez, A.L. 1999 Interplanetary origin of geomagnetic storms. Space Sci. Rev. 88, 529–562.CrossRefGoogle Scholar
Grechnev, V.V., Uralov, A.M., Chertok, I.M., Slemzin, V.A., Filippov, B.P., Egorov, Y.I., Fainshtein, V.G., Afanasyev, A.N., Prestage, N.P. & Temmer, M. 2014 A challenging solar eruptive event of 18 November 2003 and the causes of the 20 November geomagnetic superstorm. II. CMEs, shock waves, and drifting radio bursts. Sol. Phys. 289 (4), 1279–1312. arXiv:1308.3010.CrossRefGoogle Scholar
Grinsted, A., Moore, J.C. & Jevrejeva, S. 2004 Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process. Geophys. 11, 561–566.CrossRefGoogle Scholar
Grossmann, A., Kronland-Martinet, R. & Morlet, J. 1989 Reading and understanding continuous wavelet transforms. In Wavelets. Time-Frequency Methods and Phase Space (ed. J.-M. Combes, A. Grossmann & P. Tchamitchian), p. 2. https://ui.adsabs.harvard.edu/abs/1989wtfm.conf....2GCrossRefGoogle Scholar
Hasselmann, K. 1976 Stochastic climate models Part I. Theory. Tellus 28 (6), 473–485.CrossRefGoogle Scholar
Holschneider, M. 1995 Some directional microlocal classes defined using wavelet transforms, pp. funct–an/9510006. e-prints, arXiv:funct-an/9510006.Google Scholar
Hu, W. & Si, B.C. 2016 Technical note: multiple wavelet coherence for untangling scale-specific and localized multivariate relationships in geosciences. Hydrol. Earth Syst. Sci. 20 (8), 3183–3191.CrossRefGoogle Scholar
Hu, W. & Si, B. 2021 Technical note: improved partial wavelet coherency for understanding scale-specific and localized bivariate relationships in geosciences. Hydrol. Earth Syst. Sci. 25 (1), 321–331.CrossRefGoogle Scholar
Iyemori, T. 1990 Storm-time magnetospheric currents inferred from mid-latitude geomagnetic field variations. J. Geomagn. Geoelectr. 42 (11), 1249–1265.CrossRefGoogle Scholar
Johnson, J.R., Wing, S. & Camporeale, E. 2018 Transfer entropy and cumulant-based cost as measures of nonlinear causal relationships in space plasmas: applications to D$_{st}$. Ann. Geophys. 36 (4), 945–952.CrossRefGoogle Scholar
Joselyn, J.A. 1985 The automatic detection of geomagnetic-storm sudden commencements. Adv. Space Res. 5 (4), 193–197.CrossRefGoogle Scholar
Kamide, Y. & Kokubun, S. 1996 Two-component auroral electrojet: importance for substorm studies. J. Geophys. Res. (Space Phys.) 101 (A6), 13027–13046.CrossRefGoogle Scholar
Klimas, A.J., Vassiliadis, D., Baker, D.N. & Roberts, D.A. 1996 The organized nonlinear dynamics of the magnetosphere. J. Geophys. Res. 101 (A6), 13089–13114.CrossRefGoogle Scholar
Kunagu, P., Balasis, G., Lesur, V., Chandrasekhar, E. & Papadimitriou, C. 2013 Wavelet characterization of external magnetic sources as observed by CHAMP satellite: evidence for unmodelled signals in geomagnetic field models. Geophys. J. Intl 192 (3), 946–950.CrossRefGoogle Scholar
Lakhina, G.S. & Tsurutani, B.T. 2016 Geomagnetic storms: historical perspective to modern view. Geosci. Lett. 3, 5.CrossRefGoogle Scholar
Laurenza, M., Storini, M., Giangravè, S. & Moreno, G. 2009 Search for periodicities in the IMP 8 charged particle measurement experiment proton fluxes for the energy bands 0.50-0.96 MeV and 190-440 MeV. J. Geophys. Res. (Space Phys.) 114 (A1), A01103.CrossRefGoogle Scholar
Laurenza, M., Storini, M. & Moreno, G. 2005 Use of cosmic ray measurements to identify the sector polarities of the interplanetary magnetic field. Intl J. Mod. Phys. A 20 (29), 6708–6710.CrossRefGoogle Scholar
Lindsay, G.M., Russell, C.T. & Luhmann, J.G. 1999 Predictability of DST index based upon solar wind conditions monitored inside 1 AU. J. Geophys. Res. 104 (A5), 10335–10344.CrossRefGoogle Scholar
Lorenz, E.N. 1963 Deterministic nonperiodic flow. J Atmos. Sci. 20 (2), 130–148.2.0.CO;2>CrossRefGoogle Scholar
Lucarini, V., Faranda, D., Wouters, J. & Kuna, T. 2014 Towards a general theory of extremes for observables of chaotic dynamical systems. J. Stat. Phys. 154 (3), 723–750. arXiv:1301.0733.CrossRefGoogle ScholarPubMed
Lui, A.T.Y. 2016 Dipolarization front and current disruption. Geophys. Res. Lett. 43 (19), 10 050–10 058.CrossRefGoogle Scholar
Lyons, L.R., Blanchard, G.T., Samson, J.C., Lepping, R.P., Yamamoto, T. & Moretto, T. 1997 Coordinated observations demonstrating external substorm triggering. J. Geophys. Res. (Space Phys.) 102 (A12), 27039–27052.CrossRefGoogle Scholar
Manshour, P., Balasis, G., Consolini, G., Papadimitriou, C. & Paluš, M. 2021 Causality and information transfer between the solar wind and the Magnetosphere–Ionosphere system. Entropy 23 (4), 390.CrossRefGoogle ScholarPubMed
Maraun, D. & Kurths, J. 2004 Cross wavelet analysis: significance testing and pitfalls. Nonlinear Process. Geophys. 11 (4), 505–514.CrossRefGoogle Scholar
Maraun, D., Kurths, J. & Holschneider, M. 2007 Continuous wavelet spectral analysis of climate dynamics. In Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology (ed. L. Schimansky-Geier, B. Fiedler, J Kurths and E. Schöll), pp. 325–346. World Scientific Publishing Co. Pte. Ltd.Google Scholar
Materassi, M. & Mitchell, C.N. 2007 Wavelet analysis of GPS amplitude scintillation: a case study. Radio Sci. 42 (1), RS1004.CrossRefGoogle Scholar
Matzka, J., Stolle, C., Yamazaki, Y., Bronkalla, O. & Morschhauser, A. 2021 The geomagnetic Kp index and derived indices of geomagnetic activity. Space Weath. 19 (5), e02641.Google Scholar
McPherron, R.L. 2020 Early studies in solar wind coupling and substorms. J. Geophys. Res. (Space Phys.) 125 (5), e27615.Google Scholar
Mihanović, H., Orlić, M. & Pasarić, Z. 2009 Diurnal thermocline oscillations driven by tidal flow around an island in the Middle Adriatic. J. Mar. Syst. 78, S157–S168.CrossRefGoogle Scholar
Ng, E.K.W. & Chan, J.C.L. 2012 Geophysical applications of partial wavelet coherence and multiple wavelet coherence. J. Atmos. Ocean. Technol. 29 (12), 1845–1853.CrossRefGoogle Scholar
Nicolis, G. & Nicolis, C. 2012 Foundations of Complex Systems: Emergence, Information and Prediction, 2nd edn. World Scientific Publishing Co. Pte. Ltd.CrossRefGoogle Scholar
Pallocchia, G., Amata, E., Consolini, G., Marcucci, M.F. & Bertello, I. 2006 Geomagnetic D$_{st}$ index forecast based on IMF data only. Ann. Geophys. 24 (3), 989–999.CrossRefGoogle Scholar
Pulkkinen, A., Kuznetsova, M., Ridley, A., Raeder, J., Vapirev, A., Weimer, D., Weigel, R.S., Wiltberger, M., Millward, G., RastäTter, L., Hesse, M., Singer, H.J. & Chulaki, A. 2011 Geospace environment modeling 2008–2009 challenge: ground magnetic field perturbations. Space Weath. 9 (2), 02004.Google Scholar
Runge, J., Balasis, G., Daglis, I.A., Papadimitriou, C. & Donner, R.V. 2018 Common solar wind drivers behind magnetic storm-magnetospheric substorm dependency. Sci. Rep. 8, 16987. arXiv:1802.02477.CrossRefGoogle ScholarPubMed
Santarelli, L., De Michelis, P. & Consolini, G. 2021 Hints on the multiscale nature of geomagnetic field fluctuations during quiet and disturbed periods. J. Geophys. Res. (Space Phys.) 126 (5), e28596.Google Scholar
Siciliano, F., Consolini, G., Tozzi, R., Gentili, M., Giannattasio, F. & De Michelis, P. 2021 Forecasting SYM H index: a comparison between long short term memory and convolutional neural networks. Space Weath. 19 (2), e02589.Google Scholar
Silverman, B.W. 1986 Density Estimation for Statistics and Data Analysis. Chapman and Hall.Google Scholar
Siscoe, G.L. 2001 70 years of magnetospheric modeling. In Space Weather (ed. P. Song, H. J. Singer & G. L. Siscoe), Geophysical Monograph Series, vol. 125, pp. 211–227. American Geophysical Union.Google Scholar
Srivastava, N., Mathew, S.K., Louis, R.E. & Wiegelmann, T. 2009 Source region of the 18 November 2003 coronal mass ejection that led to the strongest magnetic storm of cycle 23. J. Geophys. Res. (Space Phys.) 114 (A3), A03107. arXiv:0812.5046.CrossRefGoogle Scholar
Stumpo, M., Consolini, G., Alberti, T. & Quattrociocchi, V. 2020 Measuring information coupling between the solar wind and the magnetosphere-ionosphere system. Entropy 22 (3), 276.CrossRefGoogle ScholarPubMed
Taricco, C., Mancuso, S., Ljungqvist, F.C., Alessio, S. & Ghil, M. 2015 Multispectral analysis of Northern Hemisphere temperature records over the last five millennia. Clim. Dyn. 45 (1-2), 83–104.CrossRefGoogle Scholar
Torrence, C. & Compo, G.P. 1998 A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79 (1), 61–78.2.0.CO;2>CrossRefGoogle Scholar
Torrence, C. & Webster, P.J. 1999 Interdecadal changes in the ENSO-monsoon system. J. Clim. 12 (8), 2679–2690.2.0.CO;2>CrossRefGoogle Scholar
Tozzi, R., De Michelis, P., Coco, I. & Giannattasio, F. 2019 A preliminary risk assessment of geomagnetically induced currents over the Italian territory. Space Weath. 17 (1), 46–58.CrossRefGoogle Scholar
Tsurutani, B.T., Gonzalez, W.D., Tang, F. & Lee, Y.T. 1992 Great magnetic storms. Geophys. Res. Lett. 19 (1), 73–76.CrossRefGoogle Scholar
Tsurutani, B.T., Sugiura, M., Iyemori, T., Goldstein, B.E., Gonzalez, W.D., Akasofu, S.I. & Smith, E.J. 1990 The nonlinear response of AE to the IMF B$_{S}$ driver: a spectral break at 5 hours. Geophys. Res. Lett. 17 (3), 279–282.CrossRefGoogle Scholar
Uritsky, V.M., Klimas, A.J., Vassiliadis, D., Chua, D. & Parks, G. 2002 Scale-free statistics of spatiotemporal auroral emissions as depicted by POLAR UVI images: dynamic magnetosphere is an avalanching system. J. Geophys. Res. (Space Phys.) 107 (A12), 1426.CrossRefGoogle Scholar
Vassiliadis, D.V., Sharma, A.S., Eastman, T.E. & Papadopoulos, K. 1990 Low-dimensional chaos in magnetospheric activity from AE time series. Geophys. Res. Lett. 17 (11), 1841–1844.CrossRefGoogle Scholar
Vecchio, A. & Carbone, V. 2009 Spatio-temporal analysis of solar activity: main periodicities and period length variations. Astron. Astrophys. 502 (3), 981–987.CrossRefGoogle Scholar
Vörös, Z., Baumjohann, W., Nakamura, R., Runov, A., Volwerk, M., Takada, T., Lucek, E.A. & Rème, H. 2007 Spatial structure of plasma flow associated turbulence in the Earth's plasma sheet. Ann. Geophys. 25 (1), 13–17.CrossRefGoogle Scholar
Wanliss, J.A. & Showalter, K.M. 2006 High-resolution global storm index: DST versus SYM-H. J. Geophys. Res. (Space Phys.) 111 (A2), A02202.CrossRefGoogle Scholar
Wanliss, J. & Uritsky, V. 2010 Understanding bursty behavior in midlatitude geomagnetic activity. J. Geophys. Res. (Space Phys.) 115 (A3), A03215.CrossRefGoogle Scholar
Weimer, D.R. 2013 An empirical model of ground-level geomagnetic perturbations. Space Weath. 11 (3), 107–120.CrossRefGoogle Scholar
Wing, S., Johnson, J.R., Jen, J., Meng, C.I., Sibeck, D.G., Bechtold, K., Freeman, J., Costello, K., Balikhin, M. & Takahashi, K. 2005 Kp forecast models. J. Geophys. Res. (Space Phys.) 110 (A4), A04203.CrossRefGoogle Scholar
Yiou, P., Sornette, D. & Ghil, M. 2000 Data-adaptive wavelets and multi-scale singular-spectrum analysis. Phys. D Nonlinear Phenom. 142 (3–4), 254–290. arXiv:chao-dyn/9810034.CrossRefGoogle Scholar
Zaourar, N., Hamoudi, M., Mandea, M., Balasis, G. & Holschneider, M. 2013 Wavelet-based multiscale analysis of geomagnetic disturbance. Earth Planet. Space 65 (12), 1525–1540.CrossRefGoogle Scholar