Empirical Modeling of Planetary Magnetospheres in Response to Solar Wind Dynamics Using EOF Analysis and Multivariate Linear Regression

Part of the Astrophysics and Space Science Library book series (ASSL, volume 448)


A popular approach for empirical modeling is through representing a phenomenon as a linear combination of a set of predefined basis functions, such as polynomial and harmonic functions. In comparison with predefined basis functions, the empirical orthogonal basis functions (EOFs) are constructed from the dataset according to the variance distribution, and typically summarize the data into representative features. This chapter reviews comparatively three applications of EOF analysis associated with multivariate linear regression in empirical modeling, namely in the models of the Earth’s ionospheric F 2 -layer peak, the field-aligned currents at Earth, and the induced magnetic field near Venus (He et al. Geophys. Res. Lett., 38(14): L14101, 2011; He et al. Geophys. Res. Lett., 39, 2012; He et al. 2017; He et al. J. Geophys. Res., 121(4), 3362–3380, 2016). We illustrate the physical meaning represented by the most important EOFs, detail the model constructions and methodology, and highlight the revealed main scientific results.



The authors acknowledge the online services provided by NASA’s Planetary Data System (MESSENGER data), ESA’s Planetary Science Archive (VEX data), GFZ Potsdam (CHAMP data), NGDC (POMME-6.2 coefficients), John Hopkins University APL (AACGM coefficients), and NASA OMNI (IMF/SW and other geophysical parameters). The corresponding codes are available on Source Forge or File change of MATLAB Central. This work was supported by the Deutsche Forschungsgemeinschaft through grants DFG HE6915/1-1 and VO 855/3-1.


  1. Alken, P., Maus, S.: Spatio-temporal characterization of the equatorial electrojet from CHAMP, Ørsted, and SAC-C satellite magnetic measurements. J. Geophys. Res. 112(A9), A09305 (2007). Scholar
  2. Boyle, C.B., Reiff, P.H., Hairston, M.R.: Empirical polar cap potentials. J. Geophys. Res. 102(A1), 111–125 (1997)ADSCrossRefGoogle Scholar
  3. Chao, J.K., Wu, D.J., Lin, C.H., Yang, Y.H., Wang, X.Y., Kessel, M., Chen, S.H., Lepping, R.P.: Models for the size and shape of the earth's magnetopause and bow shock. COSPAR Colloq. Ser. 12, 127–135., L. Ling-Hsiao (Eds.), Pergamon (2002). Scholar
  4. Dubinin, E., Fraenz, M., Woch, J., Zhang, T.L., Wei, Y., Fedorov, A., Barabash, S., Lundin, R.: Toroidal and poloidal magnetic fields at Venus. Venus express observations. Planet. Space Sci. 87, 19–29 (2013). Scholar
  5. He, M., Liu, L., Wan, W., Wei, Y.: Strong evidence for couplings between the ionospheric wave-4 structure and atmospheric tides. Geophys. Res. Lett. 38(14), L14101 (2011). Scholar
  6. He, M., Vogt, J., Luhr, H., Sorbalo, E., Blagau, A., Le, G., Lu, G.: A high-resolution model of field-aligned currents through empirical orthogonal functions analysis (MFACE). Geophys. Res. Lett., 39 (2012).doi:
  7. He, M., Vogt, J., Luhr, H., Sorbalo, E.: Local time resolved dynamics of field-aligned currents and their response to solar wind variability. J. Geophys. Res. 119(7), 5305–5315 (2014). Scholar
  8. He, M., Vogt, J., Zhang, T., Rong, Z.: EMVIM: an empirical model for the magnetic field configuration near venus. J. Geophys. Res. 121(4), 3362–3380 (2016). Scholar
  9. He, M., J. Vogt, D. Heyner, and J. Zhong (2017), Vogt, J., Heyner. D., Zhong. J.: Solar wind controls on Mercury's magnetospheric cusp, J. Geophys. Res. Space Physics, 122, 6150–6164 (2017).  https://doi:10.1002/2016JA023687CrossRefADSGoogle Scholar
  10. Iijima, T., Potemra, T.A.: Field-aligned currents in the dayside cusp observed by triad. J. Geophys. Res. 81(34), 5971–5979 (1976). Scholar
  11. Iijima, T., Potemra, T.A.: Large-scale characteristics of field-aligned currents associated with substorms. J. Geophys. Res. 83(A2), 599–615 (1978). Scholar
  12. Martinecz, C., et al.: Location of the bow shock and ion composition boundaries at Venus—initial determinations from venus express ASPERA-4. Planet. Space Sci. 56(6), 780–784 (2008). Scholar
  13. Masters, A., Achilleos, N., Dougherty, M.K., Slavin, J.A., Hospodarsky, G.B., Arridge, C.S., Coates, A.J.: An empirical model of Saturn's bow shock: cassini observations of shock location and shape. J. Geophys. Res. 113(A10), A10210 (2008a). Scholar
  14. Masters, A., Achilleos, N., Dougherty, M.K., Slavin, J.A., Hospodarsky, G.B., Arridge, C.S., Coates, A.J.: An empirical model of Saturn's bow shock: cassini observations of shock location and shape. J. Geophys. Res. 113(A10), (2008b).
  15. Maus, S., Rother, M., Stolle, C., Mai, W., Choi, S., Lühr, H., Cooke, D., Roth, C.: Third generation of the Potsdam Magnetic Model of the Earth (POMME). Geochem. Geophys. Geosyst. 7(7), Q07008 (2006)ADSCrossRefGoogle Scholar
  16. Olsen, N.: A new tool for determining ionospheric currents from magnetic satellite data. Geophys. Res. Lett. 23(24), 3635–3638 (1996). Scholar
  17. Papitashvili, V. O., F. Christiansen, and T. Neubert (2002), V.O., Christiansen, F., Neubert, T.: A new model of field-aligned currents derived from high-precision satellite magnetic field data. Geophys. Res. Lett., 29(14), 1683 (2002).  https://doi.10.1029/2001gl014207CrossRefGoogle Scholar
  18. Shue, J.H., et al.: Magnetopause location under extreme solar wind conditions. J. Geophys. Res. 103(A8), 17691–17700 (1998). Scholar
  19. Tsyganenko, N.A.: Data-based modelling of the Earth's dynamic magnetosphere: a review. Ann. Geophys. 31(10), 1745–1772 (2013a). Scholar
  20. Tsyganenko, N.A.: Empirical magnetic field models for the space weather program. Space Weather. 273–280 (2013b). American Geophysical Union
  21. Tsyganenko, N. A., Andreeva, V.A., Gordeev, E. I.: Internally and externally induced deformations of the magnetospheric equatorial current as inferred from spacecraft data. Ann. Geophys., 33(1) (2015).doi: Scholar
  22. Zhong, J., et al.: Mercury's three-dimensional asymmetric magnetopause. J. Geophys. Res. 120(9), 7658–7671 (2015). Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Physics and Earth SciencesJacobs University BremenBremenGermany
  2. 2.Department of Radar SoundingsLeibniz-Institute of Atmospheric Physics at the Rostock UniversityKühlungsbornGermany

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