C. T. Russell1, G. L. Siscoe2, E. J. Smith3

1Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024
2Department of Atmospheric Sciences, University of California, Los Angeles, California 90024
3Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91103


Originally published in:GEOPHYSICAL RESEARCH LETTERS, VOL. 7, NO. 5, PAGES 381-384, MAY 1980


Abstract. Three hourly correlation coefficients and the lag at maximum correlation are computed using one minute averages of ISEE-1 and -3 magnetometer data during the period in which ISEE-3 moved from the earth to its halo orbit around the libration point. The maximum correlation coefficients are highly variable ranging from close to zero to almost unity. The lags, while on the average approximating the expected corotation delay. have very large departures from this value. These results suggest that the normals to the planes separating fields of differing orientation often make large angles to the ecliptic plane and/or that the interplanetary magnetic field has a significant amount of bending on a scale length the order of 200 earth radii. Furthermore, there often appears to be a significant amount of propagating structure in the IMF. Thus, ISEE-3 magnetic field measurements should be used with caution if precise timing of arrival at the earth or precise directions of the field upon arrival are important.


The launch of ISEE-3 in August 1978 into a halo orbit about the sunward libration point approximately 200 earth radii (Re) in front of the earth has for the first time permitted a systematic study of the the earth. It is important to assess both the temporal and spatial scale sizes of the interplanetary magnetic field (IMF) because one would like to be able to use the data from ISEE-3, which is continuously in the solar wind, as a monitor of the IMF for studies of geomagnetic processes and for predictions of geomagnetic activity. If ISEE-3 were stationed on the earth-sun line or, more correctly, sampled the element of solar wind that impacted the nose of the magnetosphere. we would be interested only in temporal variations. However, as shown in Figure 1, ISEE-3 departs from the earth-sun line by up to over 100 Re. In this report, we examine the correlation of the magnetic field at ISEE-3 and ISEE-1 from ISEE-3 launch until day 280, during which period ISEE-3 moves from the earth to over 200 Re in front of the earth and over 100 Re to the dawn side of the earth-sun line.

Fig. 1a. Solar ecliptic X-Y projection of ISEE-3 trajectory to halo orbit about libration point. Numbers denote day of year in 1978.
Fig. 1b. Solar ecliptic Y-Z projection of ISEE-3 trajectory.

All data used in this study were obtained from the ISEE data pool tapes, summary tapes prepared at Goddard Space Flight Center using simplified algorithms. The magnetometers have been described by Frandsen et al. (1978) and Russell (1978). Since reports have been published of magnetospheric response to variations in the interplanetary magnetic field of the order of minutes or less in duration (e.g., Kivelson et al., 1973; Caan et al., 1977), we compared ISEE-1 and -3 at the highest resolution possible using the summary or data pool tapes, i.e., 64-second averages. For each three hour interval we computed the cross-correlation coefficient from lagged cross products of each component and of the total field, with lags ranging from zero to three hours (cf. Chapter 7. Bendat and Piersoll, 1958). Since records are available nearly continuously from both spacecraft a total of three hours of data were available for computation of the cross product independent of the size of the lag. We then examined the correlation coefficient versus lag for each three hour period and determined the lag with the best correlation, and recorded the correlation coefficient for each of the components at that lag. During the month and a half interval of data used in this study, less than one-half of the three hour intervals were usable. Most of the unusable data refer to periods when ISEE-1 was in the magnetosheath or magnetosphere. Some periods were unusable because of missing data from one of the spacecraft. We did not use any interval in which at the lag of peak correlation more than half the data were missing in the cross product. However, there were 44 3-hour intervals, or greater than 20% of the otherwise acceptable data which were unusable because no clear maximum correlation coefficient could be determined. Such rejected intervals had more than one peak correlation time or the time of maximum correlation differed between components by more than the half-width of the correlation peak. We examined the effect of missing data within the three hour intervals and found no effect on either the average correlation coefficient or its variance as a function of the percent data available in the three hour period. Three hours were arbitrarily chosen for analysis in an attempt to balance statistical accuracy and temporal resolution. The treatment below is based on the 152 intervals for which we found a clear maximum correlation coefficient.

Correlation Coefficients

Figure 2 shows the correlation between the Bz or north-south components on the two spacecraft as a function of time. By day 230 ISEE-3 was 100 Re in front of the earth, thus the apparent slight increase in median correlation coefficient with time seen after day 230 is probably associated with the motion of the spacecraft off the earth-sun line. The most striking feature of the correlation is its variability. Sometimes the field behaves almost identically at the two spacecraft. Other times, the behavior is quite different, resulting in a zero correlation coefficient. If the correlation coefficient were high when the variance in the field was high and low when it was low. then ISEE-3 would still be a good monitor because times of high variance are the times of most geophysical interst. However, this is not the case as we illustrate below.

Fig. 2. Correlation coefficient for Bz at maximum ISEE 1/3 correlation using one minute averages over 3 hours intervals for period of study.

The temporal behavior of the other two components is very similar. Figure 3 gives a histogram of the occurrence of correlation coefficients for all three components. Although the most probable correlation is about 85%, only 1/4 of the coefficients equalled or exceeded this value. In fact 1/2 of the coefficients were less than 73% and 1/4 were less than 52%.

Fig. 3. Histogram of component correlation coefficients. Lower Quartile, QL upper quartile, QU, and median are indicated.

To assist the understanding of the meaning of these statistics we have selected three intervals during which the correlation was first good, then intermediate, and then poor. Time histories of the magnetic field for each of these periods are shown in Figures 4a, 4b and 4c. We examine first the period of good correlation on day 249. The x, y, and z traces have been offset by 5 and shifted in time by the lag that aligns the most prominent field variation. As shown in Table 1, the correlation coefficients range front 0.83 to 0.98 at this time. However, we note that from 00-03 UT no clear maximum correlation was found. This lack of correlation is due to the lack of coherence of the large amplitude rapid variations even though the general trends are similar. We return to this point later.

Fig. 4a. One minute averages of magnetic field observed at ISEE-1 (heavy line) and ISEE-3 (light line) on day 249, 1978. The traces have been offset vertically by 5 and shifted in time by the amount necessary to align the most prominent features.

Fig. 4b. ISEE-1 and 3 magnetic field measurements on Day 261, 1978.

The next interval on day 261, shown in Figure 4b, has an intermediate correlation. As shown in Table 1, the coefficients ranged from 0.37 to 0.96 at this time. No maximum correlation could be obtained from 09 to 12 UT because each component had a maximum correlation at a quite different lag. During this particular interval the Bz correlation is seen to be excellent by inspection of Figure 4b or Table 1, yet at the same time the Bx correlation is poor. The general trends are similar but the detailed field variation is different.

Figure 4c shows an interval on day 252 when the correlation was poor. The correlation coefficients range from -0.01 to 0.92. It was impossible to define a lag of maximum correlation from 12-15 UT. We note especially that even though the traces have been offset by 5, the Bz traces often overlap, indicating 5 differences in the Bz component lasting close to half a day. Both magnetometers were operating normally during this period. The difference is real and due to structure in the IMF. This interval also illustrates dramaticallv the variable time delays apparent in the records from hour to hour and front component to component during the same hour.

Fig. 4c. ISEE-1 and 3 magnetic field measurements on Day 252, 1978.


It is just as important to know when a certain orientation of the IMF is going to reach the earth as it is to know what that orientation will be. Figure 5 shows the lag corresponding to the maximum corre lation coefficient. During the interval being studied ISEE-3 alwavs preceded ISEE-1. The delay ranged from 3 minutes to 90 minutes. Figure 6 shows the ratio of the observed lags to the expected lag due to solar wind propagation and the corotation of the solar wind stream. This choice for the expected lag is equivalent to assuming all discontinuities in the solar wind have normals in the ecliptical plane perpendicular to the Archimedean spiral direction of the IMF. As can be seen from Figure 6 this assumption appears to be quite appropriate on average but the deviations from this assumption are quite large. We cannot predict the time of arrival of such IMF structures with much confidence using these simple assumptions. Since the observed deviations from expectations are of the order of one half hour and frequently exceed this number. we could not use such data in studies of the triggering of substorms or motion of the polar cusp even if we had confidence that the field directions observed at ISEE-3 would be convected to the magnetopause.

Fig. 5.The lag between ISEE-1 and 3 at the time of the maximum correlation for the period studied.
Fig. 6. The lag normalized by the expected corotation delay.

The Effect of Averaging

As noted above some of the periods of poor correlation may be due to the presence of large amplitude fluctuations with periods of a few minutes that are not coherent between the two spacecraft while the low frequency behavior is coherent. If this were true in general we might be able to restrict our use of ISEE-3 data to that of a monitor of longer term variations and not for detailed and precise timing studies. To check this possibility we reran two weeks of ISEE-3 and ISEE-1 data using overlapped 10 minute averages. Figure 7 compares the correlation coefficient as a function of lag for the 1 minute and 10 minute averages for the first 9 hours of Figure 4a. The first three hour interval now has clearly defined maxima for all three components. However, we note that the time of the maximum is still quite different from component to component and ranges from 32 to 40 minutes. The correlation coefficients for the next two intervals are not much changed at all. In fact the major change is a further delay in arrival which is not due to errors in computing lags with the averaged data but which is a real physical effect. A simple interpretation of this phenomenon is that the high frequency structures are MHD waves propagating towards the earth which arrive at the earth sooner than the convected structure. We would expect such structures to propagate with velocities of about 50 to 100 km/sec and arrive at the earth about 5 to 8 minutes prior to a nonpropagating structure given that the phase fronts of the convecting and non-convecting structures were parallel. If they are not the reduction in lag could vary considerably from these numbers. We note that this reduction in lag was a common feature in the two weeks of data surveyed with 10 minutes averages.

Fig. 7. Correlation coefficients versus lag for three intervals on Day 249. The heavy line shows the correlation coefficient when 10 minute averages are used; the dots when 1 minute averages used.

Concluding Remarks

This analysis indicates that ISEE-3 is often a poor monitor of the interplanetary field as it will be later seen at the earth on time scales comparable to those on which substorms are initiated. The correlation between the temporal variation of the IMF observed at ISEE-3 and that at ISEE-1 is highly variable. Sometimes the correlation coefficients are high but sometimes they are quite low. Furthermore, the time of arrival at the earth is quite variable about the expected time of arrival. At times it is impossible even to define a time of arrival. Often the lag corresponding to the maximum correlation coefficient differs markedly from component to component. Finally at times even the three hourly average field differs markedly, by up to 5 in the data studied.

The possible reasons for these differences seem clear enough. We cannot treat interplanetary magnetic field lines as being straight on length scales of 100 Re nor can we treat them as time stationary for periods of the order of one hour. The field lines are probably curved and contain large amplitude waves that propagate. Further, the planes of discontinuity are not expected to be normal to the ecliptic along the Parker spiral. These effects are large enough to diminish ISEE-3's ability to monitor small scale, minutes to tens of minutes duration, structure in the IMF. If we restrict our attention to longer periods, greater than 10 minutes, then the situation improves somewhat but not enough to invalidate our conclusion.

We should not be surprised by these conclusions because they are in accord with previous work using the shorter baselines available with the earth orbiting Explorer 33, 34 and 35 satellites. Chang and Nishida (1973) found a correlation length of about 80 Re for the IMF Burlaga and Ness (1969) studied the orientation of six discontinuitv surfaces and found that the orientations differed by about 35 for two of them over distances of about 75 Re. Denskat and Burlaga (1977) also found a variable peak correlation and component dependent lag in near-earth data. Akasofu and Chao (1979) using Mariner 5 data 460 Re from earth and hourly averages of the field also found an extremely variable lag. The major event during their interval of study arrived two hours late or 2.6 times the length of time expected from solar wind propagation delay.

We have not identified any effects of upstream waves on the correlation coefficients in our analysis. During the interval treated herein the apogee of ISEE-1 was in the afternoon sector where upstream wave effects are minimal. Further, such effects should not cause changes in the lag. Nevertheless, such effects are of interest and we will pursue them in future studies.

Lest this paper be misconstrued as to diminish the importance of ISEE-3 measurements, we emphasize that the ISEE-3 observations provide invaluable data on the behavior of the solar wind at 1 AU and together with the other two ISEE spacecraft will lead to a better understanding of the nature of the interplanetary magnetic field and its variation. Further, it provides the facility for making real time predictions of impending geomagnetic activity. While fallible these predictions can be useful and should improve in accuracy as the magnitude of the event increases. In some applications precise knowledge of the time delay before the event is not necessary. On the other hand ISEE-3 magnetic field data cannot fill the need for accurate representation of the IMF immediately upstream of the earth which is the key to many present studies of magnetospheric processes.


Acknowledgments. The authors wish to thank S. J. Bame for providing via the data pool tape the ISEE-3 solar wind data used in this study. This research was supported at UCLA by the National Aeronautics and Space Administration under contract NAS 5-25772, and represents one aspect of the research done at JPL for NASA under contract NAS 7-100.


Akasofu, S.-I. and J.K. Chao, Prediction of the occurrence and intensity of magnetospheric substorms, Geophys. Res. Letters. 6, 897-899, 1979.

Bendat, J.S. and A.G. Piersol, Measurement and Analysis of Random Data, 390 pp, John Wiley and Sons, New York, 1958.

Burlaga, L.F. and N.F. Ness, Tangential discontinuities in the solar wind. Solar Phys., 9, 467, 1969.

Caan, M.N.. R.L. McPherron and C.T. Russell, Characteristics of the association between the interplanetary magnetic field and substorms, J. Geophys. Res., 82, 4837-4842, 1977.

Chang, S.C. and A. Nishida. Spatial structure of transverse oscillations in the interplanetary magnetic field, Astrophys. Space Sci., 23, 301-314, 1973.

Denskat. K.U. and L.F. Burlaga. Multispacecraft observations of microscale fluctuations in the solar wind, J. Geophys. Res., 82,2693-2704,1977.

Frandsen. A.M.A., B.V. Connor, J. Van Amersfoort and E.J. Smith, The ISEE-C Vector Helium Magnetometer, ISEE Trans. Geoscience Electronics GE-16, 195-198, 1978.

Kivelson, M.G., C.T. Russell, M. Neugebauer, F.L. Scarf and R. W. Fredricks, The dependence of the polar cusp on the north-south component of the interplanetary magnetic field, J. Geophys. Res. 78, 3761-3772, 1973.

Russell, C.T., the ISEE-I and -2 fluxgate magnetometers, IEEE Trans. Geoscience Electronics GE-16, 239-242, 1978.


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