Skip to main content
Earth, Planets and Space
Download PDF
  • Article
  • Published:

A modulation model for the solar and lunar daily geomagnetic variations

Earth, Planets and Space volume 55, pages 405–418 (2003)Cite this article

Abstract

The traditional Chapman-Miller analysis for the solar, S, and lunar, L, geomagnetic variations is generalized by incorporating a time description of the seasonal changes of the harmonic coefficients. The modulation model consists of the sum of harmonic oscillators with basic carriers having the fundamental frequencies of the solar and lunar daily components, which are being amplitude and phase modulated by the annual variation and its harmonics. The solar cycle effect is a priori taken into account by using the daily sunspot numbers as an auxiliary input and including the Wolf ratios in the amplitude and phase terms. For the station Dourbes (Belgium), solar and lunar harmonics show a marked increase in amplitude from winter to summer, but the seasonal changes of L significantly exceed that of S. The phase shift from winter to summer in L is about three times that of S. The Wolf ratios of the Fourier amplitudes are of the same order of magnitude for both the S and L variations. Removal of the relatively important ocean dynamo contribution does not have an appreciable consequence for the determination of the seasonal changes and the sunspot cycle influence.

References

  • Black, D. I., Lunar and solar magnetic observations at Abinger: Their detection and estimation by spectral analysis via Fourier transforms, Phil. Trans. R. Soc., 268 A, 233–263, 1970.

    Article  Google Scholar 

  • Broyden, H., Quasi-Newton methods and their application to function minimisation, Math. Comp., 21, 97–105, 1967.

    Article  Google Scholar 

  • Campbell, W. H., The regular geomagnetic-field variations during quiet solar conditions, in Geomagnetism, vol. 3, edited by J. A. Jacobs, 76 pp., Academic Press, New York, 1987.

    Google Scholar 

  • Chapman, S. and S. R. C. Malin, Atmospheric tides, thermal and gravitational: nomenclature, notation and new results, Journ. Atmos. Sci., 27, 707–710, 1970.

    Article  Google Scholar 

  • Chapman, S. and J. C. P. Miller, The statistical determination of lunar daily variations in geomagnetic and meteorological elements, Mon. Notices Roy. Astron. Soc., Geophys. Suppl., 4, 649–669, 1940.

    Article  Google Scholar 

  • Chapman, S., J. C. Gupta, and S. R. C. Malin, The sunspot cycle influence on the solar and lunar daily geomagnetic variations, Proc. R. Soc. London, A 324, 1–15, 1971.

    Article  Google Scholar 

  • Coulson, C. A., Waves, 159 pp., Oliver and Boyd, Edinburgh, 1955.

    Google Scholar 

  • De Meyer, F., Modulation of the solar daily geomagnetic variation, J. Atmosph. Terr. Phys., 48, 115–130, 1986.

    Article  Google Scholar 

  • De Meyer, F., Modulation of the solar magnetic cycle, Sol. Phys., 181, 201–219, 1998.

    Article  Google Scholar 

  • Green, P. and S. R. C. Malin, Lunar and solar daily variations of the geomagnetic field at Waterhoo, West Australia, J. Atmosph. Terr. Phys., 33, 305–318, 1971.

    Article  Google Scholar 

  • Malin, S. R. C., Separation of lunar daily geomagnetic variations into parts of ionospheric and oceanic origin, Geophys. J. R. astr. Soc., 21, 447–455, 1970.

    Article  Google Scholar 

  • Malin, S. R. C. and S. Chapman, The determination of lunar daily geophysical variations by the Chapman-Miller method, Geophys. J. R. astr. Soc., 19, 15–35, 1970.

    Article  Google Scholar 

  • Malin, S. R. C., A. Cecere, and A. Palumbo, The sunspot cycle influence on lunar and solar daily geomagnetic variations, Geophys. J. R. astr. Soc., 41, 115–126, 1975.

    Article  Google Scholar 

  • Marquardt, D. W., An algorithm for least squares estimation of nonlinear parameters, Journ. Soc. Industr. Appl. Math., 11, 431–441, 1963.

    Article  Google Scholar 

  • Matsushita, S., Solar quiet and lunar daily variation fields, in Physics of Geomagnetic Phenomena, edited by S. Matsushita and W. H. Campbell, pp. 302–424, Academic Press, New York, 1967.

    Google Scholar 

  • Matsushita, S. and H. Maeda, On the geomagnetic solar quiet daily variation field during the I. G. Y., J. Geophys. Res., 70, 2535–2558, 1965.

    Article  Google Scholar 

  • Tarantola, A. and B. Valette, Generalized nonlinear inverse problems solved using the least squares criterion, Rev. Geophys. & Space Physics, 20, 219–232, 1982.

    Article  Google Scholar 

  • Winch, D. E. and R. A. Cunningham, Lunar magnetic tides at Watheroo: seasonal, elliptic, evectional, variational and nodal components, J. Geomag. Geoelectr., 24, 381–414, 1972.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Royal Meteorological Institute, Ringlaan 3, B-1180, Brussels, Belgium

    Frans De Meyer

Authors
  1. Frans De Meyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frans De Meyer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

De Meyer, F. A modulation model for the solar and lunar daily geomagnetic variations. Earth Planet Sp 55, 405–418 (2003). https://doi.org/10.1186/BF03351774

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03351774

Key words