Earth, Planets and Space

, Volume 55, Issue 7, pp 405–418 | Cite as

A modulation model for the solar and lunar daily geomagnetic variations

  • Frans De Meyer
Open Access


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.

Key words

Solar and lunar daily magnetic variations Chapman-Miller method modulation model 


  1. 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.CrossRefGoogle Scholar
  2. Broyden, H., Quasi-Newton methods and their application to function minimisation, Math. Comp., 21, 97–105, 1967.CrossRefGoogle Scholar
  3. 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
  4. Chapman, S. and S. R. C. Malin, Atmospheric tides, thermal and gravitational: nomenclature, notation and new results, Journ. Atmos. Sci., 27, 707–710, 1970.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.CrossRefGoogle Scholar
  7. Coulson, C. A., Waves, 159 pp., Oliver and Boyd, Edinburgh, 1955.Google Scholar
  8. De Meyer, F., Modulation of the solar daily geomagnetic variation, J. Atmosph. Terr. Phys., 48, 115–130, 1986.CrossRefGoogle Scholar
  9. De Meyer, F., Modulation of the solar magnetic cycle, Sol. Phys., 181, 201–219, 1998.CrossRefGoogle Scholar
  10. 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.CrossRefGoogle Scholar
  11. 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.CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. 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.CrossRefGoogle Scholar
  14. Marquardt, D. W., An algorithm for least squares estimation of nonlinear parameters, Journ. Soc. Industr. Appl. Math., 11, 431–441, 1963.CrossRefGoogle Scholar
  15. 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
  16. 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.CrossRefGoogle Scholar
  17. Tarantola, A. and B. Valette, Generalized nonlinear inverse problems solved using the least squares criterion, Rev. Geophys. & Space Physics, 20, 219–232, 1982.CrossRefGoogle Scholar
  18. 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.CrossRefGoogle Scholar

Copyright information

© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences. 2003

Authors and Affiliations

  1. 1.Royal Meteorological InstituteBrusselsBelgium

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