Skip to main content
SpringerLink
Log in

Evaluating Solar Quiet Variation of the Horizontal Geomagnetic Field using Nonlinear Time Series Analysis Techniques

  • Published:
Geomagnetism and Aeronomy Aims and scope Submit manuscript

Abstract—

In this present paper, the nonlinear time series techniques were used to analyse solar quiet variation in the horizontal component of the geomagnetic field (SqH) data collected from the INTERMAGNET during the year 2012. The complexity of the nonlinear dynamics based on estimated time delay (τ) and embedding dimension (m) are expressed by Lyapunov exponents (LE). The positive values of the Lyapunov exponent for the Addis Abba (AAE), Eskdalemuir (ESK), Hartebeesthoek (HBK), Hermanus (HER), Mbour (MBO), Sodankyla (SOD) and Tamanrasset (TAM) time series are 0.0027, 0.0118, 0.0082, 0.0042, 0.0027, 0.016 and 0.0036 respectively for the year 2012. We observed positive values of Lyapunov exponent which are more significant at high latitudes (ESK and SOD) and mid latitudes (TAM, HBK and HER) which are located outside the electrojet region. The low latitudes (AAE and MBO) have low values of Lyapunov exponent which are located within electrojet region. The internal dynamics and inherent irregularities of ionosphere may be responsible for the occurrence of chaos during the Sq (H) variation, which show evidence of nonlinear properties. The external factors such as counter electrojet (CEJ) and equatorial electrojet (EEJ) might be responsible for inherent dynamics.This may possibly be the reason for the higher and lower values of Lyapunov exponents during SqH.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.

Similar content being viewed by others

REFERENCES

  1. Abarbanel, H.D.I. and Lali, U., Nonlinear dynamics of the Great Salt Lake: system identification and perdition, Clim. Dyn., 1996, vol. 12, pp. 287–297.

    Article  Google Scholar 

  2. Bhattacharyya, A., Chaotic behavior of ionosphere turbulence from scintillation measurements, J. Geophys. Res., 1990, vol. 17, pp. 733–738.

    Google Scholar 

  3. Bolaji, O.S., Adeniyi, J.O., Adimula, I.A., Radicella, S.M., and Doherty, P.H., Total electron content and magnetic field intensity over Ilorin, Nigeria, J. Atmos. Sol.-Terr. Phys., 2013, vol. 98, pp. 1–11.

    Article  Google Scholar 

  4. Butcher, E.C. and Brown, G.M., The variability of Sq(H) on normal quiet days, Geophys. J. R. Astron. Soc., 1981, vol. 64, no. 2, pp. 527–537.

    Article  Google Scholar 

  5. Campbell, W.H., The regular geomagnetic-field variations during quiet solar conditions, in Geomagnetism, Jacobs, J., Ed., San Diego, Calif.: Academic Press, 1989, vol. 3, pp. 386–460.

    Google Scholar 

  6. Casdagli, M., Nonlinear prediction of chaotic time series, Phys. D (Amsterdam, Neth.), 1989, vol. 35, no. 3, pp. 335–356.

  7. Chapman, S. and Bartels, J., Geomagnetism, Oxford: Clarendon Press, 1940, vol. 1.

    Google Scholar 

  8. Cheng, C.-C., Russell, C.T., Reeves, G.D., Connors, M., and Moldwin, M.B., On the relationship between double-onset substorm, pseudobreakup, and IMF variation: The 4 September 1999 event, J. Geophys. Res., 2005, vol. 110, A07201. https://doi.org/10.1029/2004JA010778

    Article  Google Scholar 

  9. Falayi, E.O., Oyebanjo, O.A., Omotosho, T.V., and Okusanya, A.A., Storm-time variation of the horizontal and vertical components of the geomagnetic fields and rate of induction at different latitudes, Adv. Space Res., 2016, vol. 58, pp. 1208–1218.

    Article  Google Scholar 

  10. Falayi, E.O., Ogundile, O.O., Adepitan, J.O., and Okusanya, A.A., Solar quiet variation of the horizontal and vertical components of geomagnetic field using wavelet analysis, Can. J. Phys., 2018, vol. 97, no. 4, pp. 450–460. https://doi.org/10.1139/cjp-2018-0034

    Article  Google Scholar 

  11. Forbush, S.E. and Casaverde, M., Equatorial Electrojet in Peru, Washington, DC: Carnegie Institution of Washington, 1961.

    Google Scholar 

  12. Fraser, A.M. and Swinney, H.L., Independent coordinates for storage attractors from mutual information, Phys. Rev. A, 1986, vol. 33, pp. 1134–1141.

    Article  Google Scholar 

  13. George, B., Renuka, G., Satheesh Kumar, K., Anil Kumar, C.P., and Venugopal, C., Nonlinear time series analysis of the fluctuations of the geomagnetic horizontal field, Ann. Geophys., 2002, vol. 20, pp. 175–183. http://www.ann-geophys.net/20/175/2001.

    Article  Google Scholar 

  14. Geoscience Australia, 2019. http://www.ga.gov.au/oracle/ geomag/iqd_form.jsp.

  15. Hnat, B., Chapman, S.C., and Rowlands, G., Scaling and a Fokker–Planck model for fluctuations in the geomagnetic indices and comparison with solar wind as seen by Wind and ACE, J. Geophys. Res., 2005, vol. 110, A08206. https://doi.org/10.1029/2004JA010824

    Article  Google Scholar 

  16. INTERMAGNET, International real-time magnetic observatory network, 2019. http://www.intermagnet.org.

  17. Kennel, M.B., Brown, R., and Abarbanel, H.D.I., Determining minimum embedding dimension using a geometrical construction, Phys. Rev. A, 1992, vol. 45, pp. 3403–3441.

    Article  Google Scholar 

  18. Klimas, A., Vassiliadis, D., Baker, D., et al., The organized nonlinear dynamics of the magnetosphere, J. Geophys. Res., 1996, vol. 101, pp. 13 089–13 113.

    Article  Google Scholar 

  19. Mayaud, P.N., Analyse morphologique de la variabilité jour-a-jour de la variation journalière régulière SR du champ magnetique terrestre. II. Le système de courants Cp (régions polaires et subpolaires), Ann. Geophys., 1965, vol. 21, pp. 514–544.

    Google Scholar 

  20. Ogunsua, B.O., Laoye, J.A., Fuwape, I.A., and Rabiu, A.B., The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days, Nonlinear Processes Geophys., 2014, vol. 21, pp. 127–142. https://doi.org/10.5194/npg-21-127

    Article  Google Scholar 

  21. Okeke, F.N., Onwumechili, C.A., and Rabiu, B.A., Day-to-day variability of geomagnetic hourly amplitudes at low latitudes, Geophys. J. Int., 1998, vol. 134, pp. 484–500.

    Article  Google Scholar 

  22. Onwumechili, C.A. and Ezema, P.O., On the course of the geomagnetic daily variation in low latitudes, J. Atmos. Sol.-Terr. Phys., 1977, vol. 39, pp. 1079–1086.

    Article  Google Scholar 

  23. Palumbo, A., Lunar and solar daily variations of the geomagnetic field at Italian stations. J. Atmos. Sol.-Terr. Phys., 1981, vol. 43, no. 7, pp. 633–642.

    Article  Google Scholar 

  24. Pavlos, G.P., Athanasiu, M.A., Kugiumtzis, D., Hantzigeorgiu, N., Rigas, A.G., and Sarris, E.T., Nonlinear analysis of magnetospheric data, Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data, Nonlinear Processes Geophys., 1999, vol. 6, pp. 51–65.

    Article  Google Scholar 

  25. Pulkkinen, A., Klimas, A., Vassiliadis, A., and Uritsky, V., Role of stochastic fluctuations in the magnetosphere–ionosphere system: A stochastic model for the AE index variations, J. Geophys. Res., 2006, vol. 111, A10218. https://doi.org/10.1029/2006JA011661

    Article  Google Scholar 

  26. Rabiu, A.B., Ogunsua, B.O., Fuwape, I.A., and Laoye, J.A., The transient variation in the complexes of the low-latitude ionosphere within the equatorial ionization anomaly region of Nigeria, Nonlinear Processes Geophys., 2015, vol. 22, pp. 527–543. https://doi.org/10.5194/npg-22-527-2015

    Article  Google Scholar 

  27. Remya, R.and Unnikrishnan, K., Chaotic behaviour of interplanetary magnetic field under various geomagnetic conditions, J. Atmos. Sol.-Terr. Phys., 2010, vol. 72, pp. 662–675.

    Article  Google Scholar 

  28. Tsurutani, B.T., Sugiura, M., Iyemori, T., Goldstein, B.E., Gonzalez, W.D., Akasofu, S.I., and Smith, E.J., The nonlinear response of AE to the IMF Bs driver: A spectral break at 5 hours, Geophys. Res. Lett., 1990, vol. 17, pp. 279–282.

    Article  Google Scholar 

  29. Unnikrishnan, K., Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series, Ann. Geophys., 2008, vol. 26, pp. 941–953. https://doi.org/10.5194/angeo-26-941-2008

    Article  Google Scholar 

  30. Unnikrishnan, K., A comparative study on chaoticity of equatorial/low latitude ionosphere over Indian subcontinent during geomagnetically quiet and disturbed periods, Nonlinear Processes Geophys., 2010, vol. 17, pp. 765–776. https://doi.org/10.5194/npg-17-765-2010

    Article  Google Scholar 

  31. Unnikrishnan, K., Saito, A., and Fukao, S., Differences in magnetic storm and quiet ionospheric deterministic chaotic behavior: GPS TEC analyses, J. Geophys. Res., 2006a, vol. 111, A06304. https://doi.org/10.1029/2005JA011311

    Article  Google Scholar 

  32. Unnikrishnan, K., Saito, A., and Fukao, S., Differences in day and night time ionosphere determine chaotic behavior: GPS TEC analyses, J. Geophys. Res., 2006b, vol. 111, A07310. https://doi.org/10.1029/2005JA011313

    Article  Google Scholar 

  33. Wernik, A.W. and Yeh, K.C., Chaotic behavior of ionospheric scintillation medelling and observations, Radio Sci., 1994, vol. 29, pp. 135–139.

    Article  Google Scholar 

  34. Wolf, A., Swift, J.B., Swinney, H.L., Swinney, J., and Vastano, A., Determining Lyapunov exponents from a time series, Phys. D(Amsterdam,Neth.), 1985, vol. 16, pp. 285–317. https://doi.org/10.1016/0167-2789(85)90011-9

    Book  Google Scholar 

  35. Yamazaki, Y., Yumoto, K., Cardinal, M.G., Fraser, B.J., Hattori, P., Kakinami, Y., Liu, J.Y., Lynn, J.W., Marshall, R., McNamara, D., Nagatsuma, T., Nikiforov, V.M., Otadoy, R.E., Ruhimat, M., Shevtsov, B.M., Abe, S., Uozumi, T., and Yoshikawa, A., An empirical model of the quiet daily geomagnetic field variation, J. Geophys. Res., 2011, vol. 116, A10312. https://doi.org/10.1029/2011ja016487

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

The results presented in this research paper depend on data obtained at magnetic observatories. The authors express sincere thanks to the national institutes and International Real Time Magnetic Observatory Network (INTERMAGNET, www.intermagnet.org) for promoting high standards of magnetic observatory practice.

Author information

Authors and Affiliations

  1. Department of Physics, Tai Solarin University of Education, Ijagun, Ijebu ode, Nigeria

    E. O. Falayi & J. O. Adepitan

  2. Department of Physics, Adeniran Ogunsanya College of Education, Ijanikin, Lagos State, Nigeria

    A. S. Ajose

  3. Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria

    T. O. Roy-Layinde

  4. Federal College of Forestry, P.M.B. 5087, Ibadan, Oyo State, Nigeria

    A. T. Adewole

Authors
  1. E. O. Falayi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Ajose
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. O. Roy-Layinde
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. T. Adewole
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. O. Adepitan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to E. O. Falayi, A. S. Ajose, T. O. Roy-Layinde, A. T. Adewole or J. O. Adepitan.

Ethics declarations

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Falayi, E.O., Ajose, A.S., Roy-Layinde, T.O. et al. Evaluating Solar Quiet Variation of the Horizontal Geomagnetic Field using Nonlinear Time Series Analysis Techniques. Geomagn. Aeron. 60, 661–671 (2020). https://doi.org/10.1134/S0016793220050060

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0016793220050060

Keywords:

Search

Navigation