Abstract. The maximum attainable accuracy in inferring the interplanetary magnetic polarity from polar cap magnetograms is about 88 %. This is achieved in practice, when high latitude polar cap stations are used during local summer-months, and the signature in the ground records is strong. An attempt by Svalgaard (1972) to use this effect to infer an index of interplanetary magnetic polarity back to 1926 has not been so successful. Furthermore, some of the properties of the index have changed with time. Prior to 1963, the inferred polarities are strongly dependent on geomagnetic activity, while after this time they are not. Thus, this index should not be used to separate solar-magnetic from solar-activity effects prior to 1963.
Recently, terrestrial polar cap magnetic variations have been shown to be sensitive indicators of the orientation of the interplanetary magnetic field (Friis-Christensen et al., 1971; 1972). This effect, in turn, has been used to infer the interplanetary magnetic polarity from 1926-1969 (Svalgaard, 1972). If this technique is indeed accurate, it is an important breakthrough, because it permits us to study some of the characteristics of the interplanetary magnetic field before the advent of in-situ observations, and to learn about the solar magnetic field before the development of solar magnetographs. However, before we attempt to use a new technique like this, we should examine its limitations. It is the purpose of this note to perform such a study. We will first find an upper limit to the accuracy of the technique which is independent of the quality of the terrestrial data. We then compare this with the accuracy reported for practical applications. Finally, we will examine the characteristics of an index derived from this technique, examining in particular the constancy of some of its properties with time and its contamination from other effects.
2. Upper Limit to Accuracy
The component of the interplanetary magnetic field causing the variations in polar cap magnetic field is the Y-component in solar magnetospheric coordinates, i.e., the direction perpendicular to the Earth's dipole axis and the solar wind velocity (Friis-Christensen et al., 1972). On the other hand, the polarity of the interplanetary field is strictly defined in solar equatorial coordinates, i.e., by the direction in the plane defined by the radius vector from the Sun and the direction normal to both the radius vector and the solar rotation axis, i.e., the Y-solar equatorial axis. The angle between these two coordinate systems, which have a common axis, the direction toward the Sun, can vary by almost 40o in the course of a year. If the interplanetary magnetic field always lay along the Parker spiral in the solar equatorial X- Y plane, the sign of the Y-component of the field in the two systems would be identical in both systems. However, the interplanetary magnetic field is quite variable in direction, and these two components can readily have opposite signs. Thus, the solar magnetospheric Y-component is an imperfect predictor of the interplanetary polarity, and any terrestrial predictor of the Y-solar magnetospheric component will necessarily be a less accurate predictor of the polarity.
To determine the upper limit to the predictive accuracy, we have taken nearly 14000 hr of interplanetary magnetic field data from the years 1966 through 1968 and compared the sign of the Y-component in solar magnetospheric coordinates with the polarity of the magnetic field in solar equatorial coordinates. We have defined polarity by the scalar product of the field and the vector (1, - 1, 0) in solar equatorial coordinates, i.e., we have used a constant 45o spiral angle.
Table I shows the correlation for 1-hr 3-hr, 6-hr, 12-hr and 24-hr averages of the field, where we required that over half the data be present in the averaging interval in creating the average. The correlation between the two quantities varies from 85 to 91% as the averaging interval varies from 1 to 24 hr. One would expect this as departures of the interplanetary field from the spiral angle should become smaller for longer averages. We note that since a station in the polar cap is most sensitive to the interplanetary field for only a few hours a day, a correlation coefficient near 88% is probably most appropriate. Of course, the use of a single station to deduce the polarity for the entire day should further degrade the correlation.
In practice, inferring the interplanetary magnetic polarity falls short of this upper limit. The most comprehensive statistics on the accuracy of the technique have been derived by Campbell and Matsushita (1973) who attempted to automate Svalgaard's visual analysis. They found that in 1965 the predicted polarity was correct 40% of the time, incorrect 26% and undetermined for 34% of the data. Restricting their analysis to summer months, May through August when the polar cap effects were the strongest, and further making determinations only on days with strong (>10o) signatures, the predictions were correct 70% of the time, incorrect 12% and undetermined 18%. Eliminating those days for which polarity was undetermined the success rate varied from 60% for all days of the year to 85% for the 'best' days. Thus, under the most favorable conditions the accuracy does approach the theoretical upper limit, and the low overall success rate (60%) is probably due simply to ambiguities arising in low signal to noise situations.
We note that Svalgaard (1973) points out that the overall agreement between identifications made at the two high latitude stations Resolute Bay and Thule agreed only 85% of the time. This is despite the fact that the peak of the most sensitive periods of the day for these two stations differ in universal time by only two hours. Examination of Svalgaard's (1973) chart of polarity as derived from Thule and Resolute Bay shows that the rate of disagreement around winter solstice is about four times that around summer solstice. This fact again suggests the times of disagreement occur when the amplitude of the effect is low, as it is in the northern polar cap during northern winter.
Finally, we note that Campbell and Matsushita have reported that the use of the horizontal component from the low latitude polar cap station Godhavn is a poor substitute for the use of the vertical component at a high polar cap station such as Thule or Resolute Bay. They found only a 60% agreement with the Thule identification. On the other hand they found a high degree of correlation >90%, when the effect was large, >10 nT. This suggests that the accuracy of Godhavn as a predictor is even more sensitive to the signal to noise ratio.
In summary, the maximum accuracy obtainable in predicting the interplanetary magnetic polarity from polar cap magnetograms is about 88%. This is approached in practice when high latitude polar cap stations are used during local summer months and when the signal to noise ratio is high. Thus, given data from high latitudes in both polar caps and a three level index, away, towards, and indeterminant, a quite useful index could be derived from terrestrial geomagnetic records.
3. The Properties of an Existing Index
The previous section dealt with the limitations on an ideal index and the creation of such an index under nearly ideal conditions. Svalgaard (1972), however, has attempted to derive such an index for the period 1926-1969, a period of over 16000 days, under far from ideal conditions. First, he has had to perform his analysis by hand and by eye, and secondly, he had to compromise his accuracy by often using a low latitude polar cap station which had a much lower correlation coefficient with the interplanetary polarity (Campbell and Matsushita, 1973). Although this index has been tested during periods where in-situ data exist, as we shall see, it is not safe to assume its properties have not changed with time. Since we do not have independent magnetic polarity data over this period to measure the constancy of its interplanetary correlation coefficient, we must examine the constancy of its other properties, and compare this with known and expected properties of the interplanetary magnetic field.
Several properties of the polarity of the interplanetary magnetic field are known from in-situ data. First, in the recent past, 1964-present, there have been roughly equal numbers of days of each polarity, ±20 days per year. This is seen in the Svalgaard index for these years. Second, the polarity of the interplanetary field divides the well known semi-annual variation of geomagnetic activity into two annual variations out of phase by 180o (Russell and McPherron, 1973; Burch, 1973). The satellite-era Svalgaard index does this also. Otherwise the polarity of the interplanetary magnetic field has no correlation with geomagnetic activity. This has been demonstrated for the Svalgaard index for 1963 to the present by Fougere (1974). However, none of these statements are true for the Svalgaard index in the presatellite-era as is demonstrated in Figure 1.
|Fig. 1. Top panel: Average Ap index for C (solid) and A days (dashed). Middle panel: Yearly average Ap index (dashed) and number of C days per year (solid). Bottom panel: Phase of the annual wave in C days. If C days exhibited the heliographic latitude dependence of the interplanetary magnetic polarity found by Rosenberg and Coleman (1969) the phase of the annual wave in C days would fall on one of the two dashed lines.|
The top panel shows the average Ap index for C days, 'toward', and A days, 'away', separately. The average Ap for C days is almost twice that for A days until about 1963, at which time they begin to track. The second panel shows the number of C days per year and the yearly average Ap index. The most striking feature of this plot is the strong correlation between the number of C days and the Ap index until about 1958. Further, although from 1963 to 1969 the C day count was almost always between 170 and 196 days as expected if C and A days were equally probable this was not true for the majority of the years before this time. Finally, the bottom panel shows the phase of the annual wave in the C day counts. An annual variation in the number of towards and away days has been found by Rosenberg and Coleman (1969). This variation is in phase (or directly out of phase) with the heliographic latitude of the Earth. Thus, the number of towards days is expected to maximize on March or September 5. If this were true also for the number of C days, the annual wave would have a phase of 65o or 115o. Indeed, it is for the last two solar cycles. However, this is not true for the first two solar cycles. We note that the correlation of C days with geomagnetic activity, which has a strong semi-annual variation but only a weak annual variation, should not in itself cause an error in the phase of the annual wave in the C day count. The disappearance of the expected phases in the first two cycles must have some additional cause. However, we cannot tell from these data whether this is due to a change in the interplanetary variation or a further change in the index.
Finally, if an index is to be used for statistical purposes to order a phenomenon that may have two or more causes, the index cannot separate those causes if it is responsive to both. In particular, we see that in the presatellite-era the index is very responsive to geomagnetic activity which in turn is controlled at least in part by solar activity. Thus, if we wish to use the index to separate solar-magnetic from solar-activity effects we could be led astray by this index.
4. Discussion and Conclusions
Despite the claim that "the inferred solar magnetic field during five sunspot cycles is available for analysis" (Wilcox, 1972), we are far from having even a qualitative measure during most of this period. This is not to say that the technique for deducing the interplanetary field polarity is not valid, for the satellite-era data show that it can be constructed to be accurate up to 85% of the time. However, the application of this technique to old data files has not been performed successfully. Thus, the high correlations seen in autocorrelation functions of this index at lags of 27 days and multiples thereof (Svalgaard, 1972) could be simply due to the well known recurrence tendency of geomagnetic activity which is apparently related to high velocity streams rather than some feature of the interplanetary magnetic field (Burton et al., 1974). Finally, in view of the above, the answer to the question "Why does the Sun sometimes look like a magnetic monopole?", (Wilcox, 1973) may still very well be instrument drift.
This work was supported by the National Science Foundation under grant GA 34148-X and by the National Aeronautics and Space Administration under contract NAS2-7251. Data used in this study were made available by the National Space Science Data Center, Greenbelt, Maryland.
Burch, J. L.: 1973, J. Geophys. Res. 78, 1047.
Burton, R. K., Russell, C. T., and McPherron, R. L.: 1974, submitted to J. Geophys. Res.
Campbell, W. H. and Matsushita, S.: 1973, J. Geophys. Res. 78, 2079.
Fougere, P. F.: 1974, Planetary Space Sci., in press.
Friis-Christensen, E., Larsen, K., Wilcox, J. M., Gonzales, W., and Colburn, D. S.: 1971, Nature Phys. Sci. 233, 48.
Friis-Christensen, E., Lassen, K., Wilhelm, J., Wilcox, J. M., Gonzales, W., and Colburn, D. S.: 1972, J. Geophys. Res. 77, 3371.
Rosenberg, R. L. and Coleman, P. J., Jr.: 1969, J. Geophys. Res. 74, 5611. Russell, C. T. and McPherron, R. L.: 1973, J. Geophys. Res. 78, 92.
Svalgaard, L.: 1972, Danish Meteorol. Inst., Geophys. Papers, R-29.
Svalgaard, L.: 1973, J. Geophys. Res. 78, 2064.
Wilcox, J. M.: 1972, Rev. Geophys. Space Phys. 10, 1003.
Wilcox, J. M.: 1973, Comments Astrophys. Space Phys. 4, 141.