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Reply to comment by J. Meyer
l.tSb
RESI-AR( H NOTES
significance. An annual wave in general geomagnetic activity, as Mtinch claims to have ~ound. ~. beyond any reality. However, it cannot be denied, that the average vector calculated by Mtinch--though insignifica~a.... might contain a small residual of the real 12 month wave which actually exists in single activity seque~c~:'.r (Meyer, 1972; 1973). (The results of these investigations were known to Mtinch.) Because of its alternating phase (a maximum near either one of the equinoxes), this 12 month wave is strongly reduced when adng all data from one or more whole years. In addition, the remaining residual is further diminished ',vilen being averaged over many years. However, an estimate of any possible residual in the average vector, by comparing its amplitude with that of the actual 12 month wave in activity sequences, cannot be !;i~:~. since there are no amplitude scales at all in M~incti's Figs. 2 and 3. As a consequence of his faulty significance account, Mtinch's interpretation of the calculated average vector, of course, has no reality either. It seems necessary to me to call attention again to Bartels' repeated word of warning against a too schematic application of statistical laws. JOACHIM MEYEr,
Institut fiir Geophysik, Freie Unh;ersitiit Berlin, 1 Berlin 33, Germany REFERENCES
BARTELS, J. (1932). Terrestrial-magnetic activity and its relations to solar phenomena. Terr. Magn. atmos. Elect. 37, 1-52; reprinted by Carnegie Institution of Washington, 1959. BARTELS, J. (1935). Random fluctuations, persistence, and quasi-persistence in geophysical and cosmical periodicities. Terr. Magn. atmos. Elect. 40, 1-60; reprinted by Carnegie Institution of Washington, 1959. MEYER, J. (1972). A 12 month wave in geomagnetic activity. J. geophys. Res. 77, 3566-3574. MEYER. J. (1973). Zur Modulation der erdmagnetischen Aktivit~t. Geophys. Abh., Inst. Meteor. Geophys., Freie Univ. Berlin, No. 3. D. Reimer Verlag, Berlin. Mt?NC~, J. W. (1972). The annual variation of the Earth-magnetic activity according to the character figures Ci. Planet. Space Sci. 20, 225-231.
Planet. Space Sci. 1973, Vol. 21, p. 1456. Pergamon Press. Printed in Northern Ireland
REPLY
TO COMMENT
B Y J. M E Y E R
(Received 30 March 1973) I thank J. Meyer for his comments on my paper. He is certainly right in pointing out that for a 2dimensional distribution the 3 m limit signifies the 9%99 per cent probability instead of 99 per cent as stated in my paper. His comment on the significance of the average vector of the annual wave seems to be based on a misunderstanding for which I partly assume responsibility as the wording in the second paragraph of Section 3 is slightly misleading. The statistical analysis based on a model of random vectors actually demonstrated that the resulting average vector could not be interpreted as being caused by chance. Unambiguous statements in the abstract, in the introduction and the last two paragraphs of Section 3, however, leave no doubt as to the fact that a quasi-persistent behaviour of the annual wave was considered as causing the deviation from the random walk condition. Thus, the point of departure for the discussion of the results in Section 4 remains unchanged. In particular, I wish to emphasize that I have not presented an interpretation of the average vector as is being suggested by J. Meyer in his comment. J. W. M/3NCH
Max-Planck-Institut far Aeronomie, lnstitut j~r Stratosphiirenphysik, 3411 Lindau/Harz, W. Germany
RESI-AR( H NOTES
significance. An annual wave in general geomagnetic activity, as Mtinch claims to have ~ound. ~. beyond any reality. However, it cannot be denied, that the average vector calculated by Mtinch--though insignifica~a.... might contain a small residual of the real 12 month wave which actually exists in single activity seque~c~:'.r (Meyer, 1972; 1973). (The results of these investigations were known to Mtinch.) Because of its alternating phase (a maximum near either one of the equinoxes), this 12 month wave is strongly reduced when adng all data from one or more whole years. In addition, the remaining residual is further diminished ',vilen being averaged over many years. However, an estimate of any possible residual in the average vector, by comparing its amplitude with that of the actual 12 month wave in activity sequences, cannot be !;i~:~. since there are no amplitude scales at all in M~incti's Figs. 2 and 3. As a consequence of his faulty significance account, Mtinch's interpretation of the calculated average vector, of course, has no reality either. It seems necessary to me to call attention again to Bartels' repeated word of warning against a too schematic application of statistical laws. JOACHIM MEYEr,
Institut fiir Geophysik, Freie Unh;ersitiit Berlin, 1 Berlin 33, Germany REFERENCES
BARTELS, J. (1932). Terrestrial-magnetic activity and its relations to solar phenomena. Terr. Magn. atmos. Elect. 37, 1-52; reprinted by Carnegie Institution of Washington, 1959. BARTELS, J. (1935). Random fluctuations, persistence, and quasi-persistence in geophysical and cosmical periodicities. Terr. Magn. atmos. Elect. 40, 1-60; reprinted by Carnegie Institution of Washington, 1959. MEYER, J. (1972). A 12 month wave in geomagnetic activity. J. geophys. Res. 77, 3566-3574. MEYER. J. (1973). Zur Modulation der erdmagnetischen Aktivit~t. Geophys. Abh., Inst. Meteor. Geophys., Freie Univ. Berlin, No. 3. D. Reimer Verlag, Berlin. Mt?NC~, J. W. (1972). The annual variation of the Earth-magnetic activity according to the character figures Ci. Planet. Space Sci. 20, 225-231.
Planet. Space Sci. 1973, Vol. 21, p. 1456. Pergamon Press. Printed in Northern Ireland
REPLY
TO COMMENT
B Y J. M E Y E R
(Received 30 March 1973) I thank J. Meyer for his comments on my paper. He is certainly right in pointing out that for a 2dimensional distribution the 3 m limit signifies the 9%99 per cent probability instead of 99 per cent as stated in my paper. His comment on the significance of the average vector of the annual wave seems to be based on a misunderstanding for which I partly assume responsibility as the wording in the second paragraph of Section 3 is slightly misleading. The statistical analysis based on a model of random vectors actually demonstrated that the resulting average vector could not be interpreted as being caused by chance. Unambiguous statements in the abstract, in the introduction and the last two paragraphs of Section 3, however, leave no doubt as to the fact that a quasi-persistent behaviour of the annual wave was considered as causing the deviation from the random walk condition. Thus, the point of departure for the discussion of the results in Section 4 remains unchanged. In particular, I wish to emphasize that I have not presented an interpretation of the average vector as is being suggested by J. Meyer in his comment. J. W. M/3NCH
Max-Planck-Institut far Aeronomie, lnstitut j~r Stratosphiirenphysik, 3411 Lindau/Harz, W. Germany