By analyzing the values of whistler dispersion observed at Wakkanai (geomag. lat. 35.3°N) or Moshiri (geomag. lat. 34.0°N) during the period 1958-1982, the characteristics of the semi-annual and annual harmonic components included in their temporal variations have been revealed. By means of a pertinent statistical procedure, the most probable values of whistler dispersion of each month normalized to sunspot numbers 0, 50, 100, 150 and 200 have been derived. The results of harmonic analysis of these values made separately for each of five sunspot numbers show that the existence of the semi-annual component can be regarded as unquestionable from statistical consideration and its phase is very stable over day and night and the range of the sunspot numbers, maxima occurring around the middle of April and October. It is to be noted that, roughly at the same times as above, the semi-annual components included in the temporal variations in various geophysical phenomena take maximum values also. As regards the annual component of variation in whistler dispersion, the reality of its existence can be statistically confirmed for the cases of sunspot numbers 50, 100 and 150, but this is not always true in other cases. Maxima come about in the time interval from the beginning of July to the beginning of October, but this time interval is entirely different from the corresponding one of the non-seasonal variation in the peak electron density of the F2 layer, in disagreement with what we expect on the basis of a simple argument.

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The secular variation of the Earth's magnetic field is itself subject to temporal variations. We investigate these with the aid of the coefficients of a series of spherical harmonic models of secular variation deduced from data for the interval 1903-1982 from the worldwide network of magnetic observatories. For some studies it is convenient to approximate the time variation of the spherical harmonic coefficients with a smooth, continuous, function; for this we have used a spline fitting. The phenomena that are investigated include periodicities, discontinuities and correlation with the length of day. The numerical data we present will be of use for further investigations and for the synthesis of secular variation at any place and at any time within the interval of the data—they are not appropriate for temporal extrapolations.

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An inconvenience attending traditional use of associated Legendre functions in global modeling is that the functions are not separable with respect to the two indices (order and degree). In 1973 Merilees suggested a way to avoid the problem by showing that associated Legendre functions of order m and degree m+k can be expressed in terms of elementary functions as
P^m_m+k(θ)=sin^m(θ)∑^k_i=0a^m_kicos(iθ)
where a^m_ki, the constants to be determined, are somewhat analogous to Fourier coefficients. Merilees noted that there are several advantages to using this form, but he also raises a question of precision for degree and order greater than 25. This note calls attention to some possible gains in time savings and accuracy in geomagnetic modeling based upon this form. For this purpose, expansions of associated Legendre polynomials in terms of sines and cosines of multiple angles are displayed up to degree and order 10. Examples are also given explaining how some surface spherical harmonics can be transformed into true Fourier series for selected polar great circle paths.

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Secular variations of Gauss coefficients are analyzed with particular emphasis on drift velocities of non-dipole fields. The existence of standing fields, which is now widely known, affects the estimates of drift velocities to such an extent that even an apparent eastward drift appears even in the case of the true westward drift. In order to determine accurate drift velocities for the drifting fields, the drift velocity is also taken as an unknown variable and a non-linear inversion method is used. The inversion turns out to be effective for most of (n, m) terms.
In order to simulate drifting non-dipole fields, a coupled-disk dynamo model is used; respective disk dynamos are arranged circularly on the equatorial plane. Gauss coefficients calculated for such a model show a peculiar time-dependence due to the non-linear nature inherent in the model used. It is shown that a predominant drift direction is possible, particularly when the main field maintains a stable polarity. This result suggests that a relative motion between the source and the observer may not be a necessary condition for the westward drift of non-dipole fields.

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