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A new approach to the hourly mean computation problem when dealing with missing data


Geomagnetic observatory records are unavoidably affected by primary data interruptions which, in turn, may have possible effects on the accuracy of the definitive data derived from them. One of the products most widely used by the scientific community is the mean hourly values, immediately obtained from the primary minute values of the geomagnetic field. Although some precepts have already been proposed and used, a definitive criterion regarding the procedure to follow when dealing with missing data has not yet been established. This could be seen in the last IAGA meetings and workshops, where several constructive opinions were put forward in this respect. The present discussion is devoted to analyzing the effects that different amounts of missing data have upon the accuracy of the means, a necessary step before establishing a definitive rule as to how to deal with these situations. In this statistical approach, we propose a new criterion based on the relative value of the root mean square error (between actual and computed means) with respect to the natural magnetic field variations of the original hourly interval.


  • Green, P., Lunar and solar daily variations of the geomagnetic field at Toolangi, Pure Appl. Geophys., 101(1), 194–204, 1972.

    Article  Google Scholar 

  • ISO, Guide to the Expression of Uncertainty in Measurement, Geneva, Switzerland: International Organization for Standardization, 1993.

    Google Scholar 

  • Le Mouël, J., V. Kossobokov, and V. Courtillot, On long-term variations of simple geomagnetic indices and slow changes in magnetospheric currents: The emergence of anthropogenic global warming after 1990?, Earth Planet. Sci. Lett., 232(3–4), 273–286, 2005.

    Article  Google Scholar 

  • Mandea, M., 60, 59, 58, … How many minutes for a reliable hourly mean?, Proceedings of the Xth IAGA Workshop, Hermanus, 112–120, 2002.

    Google Scholar 

  • Martini, D. and K. Mursula, Correcting the geomagnetic IHV index of the Eskdalemuir observatory, Ann. Geophys., 24(12), 3411–3419, 2006.

    Article  Google Scholar 

  • Rangarajan, G. K., Some features of annual variation in the equatorial geomagnetic field, Indian J. Radio Space Phys., 11, 152–155, 1982.

    Google Scholar 

  • Schott, J. J. and H. J. Linthe, The hourly mean computation problem revisited, Proceedings of the XIIth IAGA Workshop, Belsk, 135–143, 2007.

    Google Scholar 

  • Svalgaard, L. and E. W. Cliver, Interhourly variability index of geomagnetic activity and its use in deriving the long-term variation of solar wind speed, J. Geophys. Res., 112(A10), A10111, 2007.

    Article  Google Scholar 

  • Taylor, J. R., An Introduction to Error Analysis. The study of Uncertainties in Physical Measurements, Oxford University Press, California, 1982.

    Google Scholar 

  • Torta, J. M., J. J. Curto, and P. Bencze, Behaviour of the quiet day ionospheric current system in the European region, J. Geophys. Res., 102(A2), 2483–2494, 1997.

    Article  Google Scholar 

  • Torta, J. M., L. R. Gaya-Piqué, J. J. Curto, and D. Altadill, An inspection of the long-term behaviour of the range of the daily geomagnetic field variation from comprehensive modelling, J. Sol. Atmos. Terr. Phys., doi: 101016/j.jastp.2008.06.006, 2008.

    Google Scholar 

  • Walker, J. K., V. Y. Semenov, and T. L. Hansen, Synoptic models of high latitude magnetic activity and equivalent ionospheric and induced currents, J. Atmos. Terr. Phys., 59, 1435–1452, 1997.

    Article  Google Scholar 

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Correspondence to J. J. Curto.

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Marsal, S., Curto, J.J. A new approach to the hourly mean computation problem when dealing with missing data. Earth Planet Sp 61, 945–956 (2009).

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