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

  • Maosheng He
  • Joachim Vogt
Part of the Astrophysics and Space Science Library book series (ASSL, volume 448)

Abstract

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.

Notes

Acknowledgments

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.

References

  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).  https://doi.org/10.1029/2007ja012524ADSCrossRefGoogle 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).  https://doi.org/10.1016/S0964-2749(02)80212-8CrossRefGoogle 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).  https://doi.org/10.1016/j.pss.2012.12.003ADSCrossRefGoogle 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).  https://doi.org/10.1029/2011GL047855ADSCrossRefGoogle 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:  https://doi.org/10.1029/2012gl053168
  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).  https://doi.org/10.1002/2014JA019776CrossRefGoogle 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).  https://doi.org/10.1002/2015JA022049CrossRefGoogle 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).  https://doi.org/10.1029/JA081i034p05971ADSCrossRefGoogle 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).  https://doi.org/10.1029/JA083iA02p00599ADSCrossRefGoogle 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).  https://doi.org/10.1016/j.pss.2007.07.007ADSCrossRefGoogle 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).  https://doi.org/10.1029/2008ja013276ADSCrossRefGoogle 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).  https://doi.org/10.1029/2008ja013276
  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).  https://doi.org/10.1029/96gl02896ADSCrossRefGoogle 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).  https://doi.org/10.1029/98JA01103ADSCrossRefGoogle Scholar
  19. Tsyganenko, N.A.: Data-based modelling of the Earth's dynamic magnetosphere: a review. Ann. Geophys. 31(10), 1745–1772 (2013a).  https://doi.org/10.5194/angeo-31-1745-2013ADSCrossRefGoogle Scholar
  20. Tsyganenko, N.A.: Empirical magnetic field models for the space weather program. Space Weather. 273–280 (2013b).  https://doi.org/10.1029/GM125p0273. 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: https://doi.org/10.5194/angeo-33-1-2015CrossRefADSGoogle Scholar
  22. Zhong, J., et al.: Mercury's three-dimensional asymmetric magnetopause. J. Geophys. Res. 120(9), 7658–7671 (2015).  https://doi.org/10.1002/2015JA021425CrossRefGoogle Scholar

Copyright information

© 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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