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R/S analysis of the Dst index

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Abstract

The paper addresses estimation of the Hurst exponent for time series of the hourly values of the Dst index for the period from 1957 to 2011. It is found that the Hurst exponent is 0.79–0.94 for yearly intervals and 0.8–1.0 for monthly intervals. Based on R/S graphs, the Dst cycles are identified; they range from 3–4 months to 2.2 years and from 8.5 to 22 years in length. It is shown that a Dst time series can be quite satisfactorily described by an α-stable Levy process.

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References

  • Aizenberg, G.Z., Belousov, S.P., Zhurbenko, E.M., Kliger, G.A., and Kurashov A.G., Korotkovolnovye antenny (Shortwave Antennas), Moscow: Radio i svyaz’, 1985.

    Google Scholar 

  • Al’pert, Ya.L., Rasprostranenie elektromagnitnykh voln i ionosfera (Propagation of Electromagnetic Waves in the Atmosphere), Moscow: Nauka, 1972.

    Google Scholar 

  • Arnold, N.F., Robinson, T.R., Lester, M., Byrne, P.B., and Chapman, P.J., Super dual auroral radar network observations of fluctuations in the spectral distribution of near range meteor echoes in the upper mesosphere and lower thermosphere, Ann. Geophys., 2001, vol. 19, no. 4, pp. 425–434.

    Article  Google Scholar 

  • Bezrodnyi, V.G., Galushko, V.G., and Rainish, B.V., Aspect scattering of high-frequency radio waves on magnet-oriented inhomogeneities of the plane-stratified ionosphere, Radiofiz. Radioastron., 2011, vol. 16, no. 1, pp. 33–42.

    Google Scholar 

  • Blagoveshchensky, D.V. and Kornienko, V.A., Studying the ionosphere with the incoherent scatter radar during the magnetic storm of January 10, 1997, Geomagn. Aeron. (Engl. Transl.), 2007, vol. 47, no. 2, pp. 227–237.

    Article  Google Scholar 

  • Booker, H.G., A theory of scattering by nonisotropic irregularities with application to radar reflections from aurora, J. Atmos. Terr. Phys., 1956, vol. 8, nos. 4/5, pp. 204–221.

    Article  Google Scholar 

  • Chernyshev, V.P., Antenno-fidernye ustroistva radiosvyazi i radioveshchaniya (Antenna–Feeder Devices for Radio Communication and Radio Broadcasting), Moscow: Svyaz’, 1978.

    Google Scholar 

  • Davis, K., Ionospheric Radio Waves, Waltham: K. Blaisdell, 1969; Moscow: Mir, 1973.

    Google Scholar 

  • Dolukhanov, M.P., Rasprostranenie radiovoln (Radio Wave Propagation), Moscow: Svyaz’, 1972.

    Google Scholar 

  • Galushko, V.G., Bezrodnyi, V.G., Koloskov, A.V., and Zalizovskii, A.V., On the possible mechanism of “selfscattering effect” of strong high-frequency signals in the ionosphere, Radiofiz. Radioastron., 2012, vol. 17, no. 2, pp. 112–124.

    Google Scholar 

  • Gershman, B.N., Erukhimov, L.M., and Yashin Yu.A., Volnovye yavleniya v ionosfere i kosmicheskoi plazme (Wave Phenomena in the Ionosphere and Space Plasma), Moscow: Nauka, 1984.

    Google Scholar 

  • Gillies, R.G., Hussey, G.C., Sofko, G.J., and James, H.G., Relative O- and X-mode transmitted power from SuperDARN as it relates to the RRI instrument on ePOP, Ann. Geophys., 2010, vol. 28, no. 3, pp. 861–871.

    Article  Google Scholar 

  • Greenwald, R.A., Baker, K.B., Dudeney, J.R., et al., DARN/SuperDARN: A global view of the dynamics of high latitude convection, Space Sci. Rev., 1995, vol. 71, pp. 761–796.

    Article  Google Scholar 

  • Gurevich, A.V., Nonlinear effects in the ionosphere, Phys.- Usp., 2007, vol. 50, no. 11, pp. 1091–1122.

    Article  Google Scholar 

  • Izhovkina, N.I., The effect of particles and electromagnetic waves on vortex structures in the atmosphere and the ionosphere, Geomagn. Aeron. (Engl. Transl.), 2015, vol. 55, no. 3, pp. 333–343.

    Article  Google Scholar 

  • Kashcheev, S.B., Koloskov, A.V., Zalizovskii, A.V., Galushko, V.G., Pikulik, I.I., Yampol’skii, Yu.M., Kurkin, V.I., Litovkin, G.I., Orlov, A.I., and Pet’ko, P.V., Experimental studies of spectral characteristics of shortwave signals on far-field and extremely far-field trajectories, Radiofiz. Radioastron., 2009, vol. 14, no. 1, pp. 12–25. 2009.

    Google Scholar 

  • Mentzer, J.R., Scattering and Diffraction of Radio Waves, London: Pergamon, 1955; Moscow: Sovetskoe radio, 1958.

    Google Scholar 

  • Radar systems developed in Russia for activities in the Arctiv. http://vpk.name/news/126744_rls_dlya_rabotyi_v_ arktike_razrabotanyi_v_rossii.html. Rohde Schwarz EB510. https://www.rohde-schwarz.com.

  • Rytov, S.M., Kravtsov, Yu.A., and Tatarskii, V.I., Vvedenie v statisticheskuyu radiofiziku (Introduction to Statistical Radiophysics), Moscow: Nauka, 1978.

    Google Scholar 

  • Shalimov, S.L., Dynamics and electrodynamics of ionospheric inhomogeneities of the midlatitude E region (review), Geomagn. Aeron. (Engl. Transl.), 2014, no. 2, pp. 137–152.

    Article  Google Scholar 

  • Sivokon’, V.P. and Druzhin, G.I., Geomagnetic factor of Dst variations in the selective generation of ionospheric characteristic waves, Geomagn. Aeron. (Engl. Transl.), 2006, vol. 46, no. 4, pp. 492–495.

    Article  Google Scholar 

  • Sivokon’, V.P., Druzhin, G.I., Poddel’skii, I.N., et al., Hardware system for the study of rotary polarized waves in the shortwave range, Elektrosvyaz’, 2004, no. 8, pp. 9–11.

    Google Scholar 

  • Zalizovski, A.V., Kashcheyev, S.B., Yampolski, Y.M., et al., Self-scattering of a powerful HFradio wave on stimulated ionospheric turbulence, Radio Sci., 2009, vol. 44, RS3010. doi 10.1029/2008RS004111

    Article  Google Scholar 

  • Balasis, G., Daglis, I.A., Kapiris, P., Mandea, M., Vassiliadis, D., and Eftaxias, K., From pre-storm activity to magnetic storm: A transition described in terms of fractal dynamics, Ann. Geophys., 2006, vol. 24, pp. 3557–3567.

    Article  Google Scholar 

  • Balasis, G., Daglis, I.A., Papadimitriou, C., Kalimeri, M., Anastasiadis, A., and Eftaxias, K., Dynamical complexity in Dst time series using non-extensive Tsalls entropy, Geophys. Res. Lett., 2008, vol. 35, pp. 1–6, L14102. doi 10.1029/2008GL034743

    Article  Google Scholar 

  • Balasis, G., Daglis, I.A., Anastasiadis, A., and Eftaxias, K., Detection of dynamical complexity changes in Dst time series using entropy concept and rescaled range analysis, in The Dynamic Magnetosphere, 2011, pp. 211–220.

    Chapter  Google Scholar 

  • Berry, M.V. and Lewis, Z.V., On the Weierstrass–Mandelbrot fractal function, Proc. R. Soc. London, Ser. A, 1980, pp. 459–484.

    Google Scholar 

  • Cervantes-De la Torre, F., González-Trejo, J.I., Real-Ramírez, C.A., and Hoyos-Reyes, L.F., Fractal dimension algorithms and their application to time series associated with natural phenomena, in The 4th National Meeting in Chaos, Complex Systems and Time Series, 29 Nov.–2 Dec. 2011, Xalapa, Veracruz, Mexico, J. Phys.: Conf. Ser., 2013, pp. 1–10.

    Google Scholar 

  • Chernykh, Yu.V., Methods for time series analysis related with solar activity, in Trudy Sankt-Peterburgskogo instituta informatiki i avtomatizatsii RAN (Transactions of the St. Petersburg Institute of Informatics and Automation), St. Petersburg: SPIIRAN, 2003, vol. 1, no. 3, pp. 126–136.

    Google Scholar 

  • Chistyakov, V.F., Solnechnye tsikly i kolebaniya klimata (Solar Cycles and Climate Oscillations), Vladivostok: Dal’nauka, 1997.

    Google Scholar 

  • Feder, J., Fractals, New York: Plenum, 1988; Moscow: Mir, 1991.

    Book  Google Scholar 

  • Glass, L. and Mackey, M.C., From Clocks to Chaos: The Rhythms of Life, Princeton, NJ: Princeton University Press, 1988.

    Google Scholar 

  • Hurst, H., Methods of long-term storage in reservoirs, Proc. Inst. of Civilengineers, vol. 5, pp. 519–543.

  • Hurst, H., Long-term storage capacity of reservoirs, Trans. Am. Soc. Civ. Eng., 1951, vol. 116, pp. 770–808.

    Google Scholar 

  • Kiselev, B.V., Statisticheskii R/S-analiz (pokazatel’ Kharsta). Uchebno-metodicheskoe posobie (Statistical R/S-Analysis (the Hurst Index). A Study Guide), St. Petersburg: SPbGU, 2012.

    Google Scholar 

  • Kiselev, B.V., On some specificities in the interpretation of statistical R/S-analysis, Vopr. Geofiz., 2013, no. 46, pp. 159–165.

    Google Scholar 

  • Kolmogorov, A.N., The Venus swirl and other interesting curves in the Hilbert space, Dokl. Akad. Nauk SSSR, 1940, vol. 26, no. 2, pp. 115–118.

    Google Scholar 

  • Kononovich, E.V., Mironova, I.V., and Baturin, V.A., Frequency–time analysis of solar activity series, Issled. Ross., 2006, pp. 1704–1715. http://zhurnal.ape.relarn.ru/ articles/2006/182/pdf.

    Google Scholar 

  • Levin, B.R., Teoreticheskie osnovy statisticheskoi radiotekhniki (Theoretical Foundations of Statistical Radio Engineering), Moscow: Radio i svyaz’, 1989.

    Google Scholar 

  • Loève, P. Probability Theory, New York: Van Nostrand, 1954; Moscow: Izd. inostrannoi literatury, 1962.

    Google Scholar 

  • Lorenz, E.N., Deterministic nonperiodic flow, J. Atmos. Sci., 1963, vol. 20, no. 2, pp. 130–148.

    Article  Google Scholar 

  • Mandelbrot, B., The Fractal Geometry of Nature, New York: Henry Holt and Company, 1982; Moscow: Institut komp’yuternykh issledovanii, 2002.

    Google Scholar 

  • Mandelbrot, B.B., Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot), New York: Springer, 2002.

    Google Scholar 

  • Mandelbrot, B.B. and van Ness, J.W., Fractional Browian motions, Fractional noises and applications, SIAM Rev., 1968, vol. 10, no. 4, pp. 422–437.

    Article  Google Scholar 

  • Martynyuk, V.S., Temur’yants, N.A., and Vladimirskii, B.M., U prirody net plokhoi pogody: kosmicheskaya pogoda v nashei zhizni (Nature Has No Bad Weather: Space Weather in Our Life), Kiev: Naukova dumka, 2008.

    Google Scholar 

  • Peters, E.E., Fractal Market Analysis: Applying Chaos Theory to Investment and Economics, New York: Wiley, 1994; Moscow: Internet-treiding, 2004.

    Google Scholar 

  • Prabhakaran Nayar, S.R., Radhika, V.N., Revathy, K., and Ramadas, V., Wavelet analysis of solar, solar wind and geomagnetic parameters, Sol. Phys., 2002, vol. 208, no. 2, pp. 359–373.

    Article  Google Scholar 

  • Rössler, O.E., An equation for continuous chaos, Phys. Lett., 1976, vol. 57, no. 5, pp. 397–398.

    Article  Google Scholar 

  • Shiryaev, A.N., Osnovy stokhasticheskoi finansovoi matematiki (Basics of Stochastic Financial Mathematics), vol. 1, Moscow: Fazis, 1998.

  • Smorodnitsky, G. and Taqqu, M.S., Stable Non-Gaussian Processes: Stochastic Models with Infinite Variance, New York: Chapman and Hall, 1994.

    Google Scholar 

  • Uchaikin, V.V., Self-similar anomalous diffusion and Levystable laws, Phys.-Usp., 2003, vol. 46, no. 8, pp. 821–850.

    Article  Google Scholar 

  • Vernova, E.S., Pochtarev, V.I., Ptitsina, N.G., and Tyasto, M.I., Short-period variations in the rate of solar activity change as a possible geoeffective parameter, Geomagn. Aeron., 1983, vol. 23, no. 4, pp. 519–522.

    Google Scholar 

  • Vitinskii, Yu.I., Ol’, A.I., and Sazonov, B.I., Solntse i atmosfera zemli (The Sun and the Earth’s Atmosphere), Leningrad: Gidrometioizdat, 1976.

    Google Scholar 

  • Vitinskii, Yu.I., Kopetskii, M., and Kuklin, G.V., Statistika pyatnoobrazovatel’noi deyatel’nosti solntsa (Statistics of Solar Spot Generation Activity), Moscow: Nauka, 1986.

    Google Scholar 

  • Yermolaev, Y.I., Lodkina, I.G., Nikolaeva, N.S., and Yermolaev, M.Y., Occurrence rate of extreme magnetic storm, J. Geophys. Res.: Space Phys., 2013, vol. 118, pp. 4760–4765.

    Article  Google Scholar 

  • Zotov, O.D., Self-affine fractal dynamics of solar and Earth magnetospheric activities, Geomagn. Aeron. (Engl. Transl.), 2000, vol. 40, no. 4, pp. 439–443.

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg Branch, Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, St. Petersburg, 191023, Russia

    B. V. Kiselev

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  1. B. V. Kiselev
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Correspondence to B. V. Kiselev.

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Original Russian Text © B.V. Kiselev, 2017, published in Geomagnetizm i Aeronomiya, 2017, Vol. 57, No. 3, pp. 353–362.

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Kiselev, B.V. R/S analysis of the Dst index. Geomagn. Aeron. 57, 326–334 (2017). https://doi.org/10.1134/S0016793217030069

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