MAGNETOPAUSE LOCATION ON JANUARY 11, 1997
J.-H. Shue1, P. Song2, C. T. Russell3,
J. T. Steinberg4, J. K. Chao5,
G. Zastenker6, O. L. Vaisberg6, and S. Kokubun1
1Solar-Terrestrial Environment Laboratory, Nagoya University,
2 Space Physics Research Laboratory, The University of Michigan, Ann Arbor, MI, USA
3Institute of Geophysics Planetary Physics, University of California, Los Angeles, LA, USA
4Center for Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA
5Institute of Space Science, National Central University, Chungli, Taiwan
6Space Research Institute, Russian Academy of Sciences, Moscow , Russia
The magnetic cloud on January 6-11, 1997 might be the
cause of a malfunction and the following loss of
Telstar-401 satellite at 1115 UT on January 11. During
this event, around 0200 UT on January 11, there was a
sudden enhancement in the solar wind dynamic pressure
to more than 25 times of its normal value. The interplanetary
magnetic field was extremely strong and northward
(~18 nT). During the pressure enhancement, the Geotail
in the flank was in the magnetosheath, and the LANL-94
and GMS-4 geosynchronous satellites also found they were
in the magnetosheath. This event provides an excellent
opportunity to test and validate the predictability and
accuracy of the existing magnetopause location models
for the National Space Weather Program. Currently, there
are two empirical models that use the solar wind
pressure and the north-south component of the
interplanetary magnetic field to predict the
magnetopause location. The database and method
used in deriving the two models are different.
Shue et al.  may be extended to a larger
solar wind parameter range. For the purpose of the Space Weather
Forecast, there is an extrapolated version of Roelof and Sibeck .
With small differences, both Shue et al.'s model and
extrapolated Roelof and Sibeck's model predict that the
magnetopause crosses geosynchronous orbit in the subsolar
region during the event. Therefore, both of them predict correctly the
magnetopause crossings of LANL-94 and GMS-4.
The two models predict completely differently in the flank.
The Shue et al.'s model is consistent with Geotail's
measurement. The extrapolated Roelof and Sibeck's model
predicts that the Geotail satellite should remain
in the magnetosphere.
An improved version of the Shue et al.'s model is obtained, leading to
better agreement with the data.
FORMULA OF SHUE ET AL. 
Based on a database of 1673 crossings from ISEE 1 and 2, AMPTE/IRM, and IMP 8 satellites, the location of the magnetopause is fit in a form,
where r is radial distance and theta is solar zenith angle.
This form has two parameters, r0 and alpha, representing the standoff distance and the level of tail flaring, respectively. Both r0 and alpha depend on interplanetary magnetic field Bz and solar wind dynamic pressure Dp. We have
For the Space Weather Forecast purpose, the extrapolated Roelof and Sibeck's model was obtained by using tanh to map all Bz into [-7, 7] nT; and to map log2(Dp) into [0.5, 8] nPa and extrapolate it in a power law of -1/6. The upper panel of Figure 1 is a contour of r0 in terms of Bz and Dp for the Shue et al.'s model. It can be seen that r0 may reach within geosynchronous orbit even though Dp is very low if the southward IMF is extremely strong. However, the Dp predicted by the extrapolated Roelof and Sibeck's model should be reached at least 25 nPa to see geosynchronous crossings, as shown in the lower panel of Figure 1. From GOES satellites, magnetopause crossings are usually seen at Dp = ~10 nPa. Thus, their result does not agree with the observation very well. Note that the figure shows an equilibrium r0 in respect to the corresponding Bz and Dp. An uncertainty of about 0.5 Re is allowed when the magnetopause has an oscillation. The figure is also useful for space weather operation, predicting whether geosynchronous satellites are in the magnetosheath or not.
Given Bz and Dp from the WIND satellite, we can calculate magnetopause locations under a consideration of solar wind flow direction and a time delay of 24 min of the arrival of solar wind to Earth for both the Shue et al.'s model and the extended Roelof and Sibeck's model. Figure 2 shows the magnetopause location and satellites at the time of solar wind dynamic pressure at the time of its maximum. The red and blue lines represent predictions by Shue et al.  and the extended Roelof and Sibeck , respectively. The difference between the two models is small on the dayside. However, in the flank, the difference is large. Geotail and GMS 4 were in the magnetosheath (blinking red and gold dots) in respect to the model prediction by Shue et al. . Other satellites were in the magnetosphere (green dots).
The closest distance between a satellite and a model prediction is calculated in a sequence of time. Figure 3 is the distance calculation for the LANL satellite. A positive distance with a green region means LANL 94 was in the magnetosphere and a negative distance with a red region means LANL 94 was in the magnetosheath. It can be seen that the prediction between the two models has a small difference. LANL 94 reported that it crossed the magnetopause at 0152 UT on January 11 and returned to the magnetosphere at 0217 UT. The predictions by the two models agree with data very well when the uncertainty of the distance calculation (gold color) is taken into account.
Figure 4 is the distance plot for Telstar 401. At 1115 UT, the solar wind condition returned to normal values. The magnetopause moved outward to 8 Re at the subsolar point. The Telstar-401 was far inside the magnetosphere when the malfunction occurred.
The Geotail data reported that Geotail entered into the magnetosphere at around 0600 UT. In Figure 5, the prediction by the Shue et al.'s model indicates that the distance changes sign from negative (red) to positive (green) at around 0600 UT. This is consistent with the Geotail data. For the prediction by the extrapolated Roelof and Sibeck's model, all the regions are green color. Their model fails to predict Geotail to be in the magnetosheath before 0600 UT.
Figure 6 is the distance plot for Interball 1. A crossing list identified from the Interball 1 data is shown in Table 1. The region between two vertical lines in Figure 6 shows the period during the enhancement of the extremely high pressure. The prediction by the Shue et al.'s model indicates that Interball 1 was in the magnetosphere. However, the Interball 1 data have shown that Interball 1 was mainly in the magnetosheath during the period, as shown in Table 1. Thus, the Shue et al.'s model needs improvement.
Table 1. Crossing list from Interball 1 for January 11, 1997
MS/MSH 0122 UT MSH/MS 0208 UT MS/MSH 0216 UT MSH/MS 0221 UT MS/MSH 0318 UT MSH/MS 0321 UT
MS/MSH: from magnetosphere to magnetosheath MSH/MS: from magnetosheath to magnetosphere
IMPROVEMENT OF SHUE ET AL. 
The upper panel of Figure 7 shows the flaring of the magnetopause increases quickly when Dp is very high. The reason is a linear fitting of alpha to Dp in Figure 14 of Shue et al. . This have caused alpha not to reach a saturation level, as shown in the green line in the lower panel of Figure 8. Thus, it makes the flaring of the magnetopause to be increasing quickly as Dp is extreme high. Moreover, the value of r0 may go to zero when southward Bz is extremely high, as shown in the green line of the upper panel of Figure 8.
In the extended version, we use a fitting of a bell-shape function instead of a line, which is able to have r0 and alpha reach a saturation level and prevent from being unphysical values for extreme cases, as shown in the red lines of Figure 8. The standard deviation for r0 vs. Bz has been improved from 0.15 Re to 0.09 Re; The standard deviation for alpha vs. Dp has been improved form 0.032 to 0.030. We have
From the lower panel of Figure 7, it can be seen that the magnetopause shape dose not increase quickly after we use the extended formula.
Using the extended formula, we recalculate the distance, as shown in Figure 9. The prediction by the Shue et al.'s model shows that the Interball 1 satellite was in the magnetosheath during the period of the pressure enhancement, as shown in the region between two vertical lines in Figure 9, which is consistent with the data very well.
In addition, we also recalculate r0 in terms of Bz and Dp, as shown in
Figure 10. Comparing with
Figure 1, there is a significant
change at the region for the extreme high southward Bz and very low
Dp. Dp needs to be at least 9 nPa to see a geosynchronous crossing.
In this preliminary report, we have compared observations from satellites and the model calculations from Shue et al.  and the extrapolated Roelof and Sibeck  for the Jan 11, 1997 event. Both models use Bz and Dp as input without considering the dynamic magnetosphere response to solar wind changes. On one hand, the magnetosphere can be dynamic, especially under extreme conditions, creating pressure variations at the magnetospheric side of the magnetopause, and affect the location of the magnetopause. Therefore, it is not expected that the models predict every single magnetopause crossing when the magnetopause oscillates. On the other hand, for the purposes of the Space Weather Forecast, it is most important to predict the whether and when magnetopause crossings will occur and not the actual number of the crossings.
During the event, both models predict correctly the magnetopause crossings on the dayside. It is likely that these models are able to provide reasonably accurate warning of the dayside magnetopause crossings for the satellites in the vicinity.
The two models predict completely differently in the flank. The Shue et al.'s model predicts correctly the Geotail's magnetopause crossings and to significant extent of Interball's crossings. The extrapolated Roelof and Sibeck's model predicts that the Geotail satellite should remain in the magnetosphere, which is inconsistent with the in situ observations.
We have investigated the possibility to improve the model of Shue et al.
. We introduce new functional forms to represent the effects of the
solar wind pressure on the flaring of the magnetopause and IMF Bz on the
subsolar distance. The new functions provide a better implicit description of
the underlying physical conservation laws and lead to a better agreement with
the observations for this event.
We would like to thank Barbara J. Thompson, Mauricio Peredo,
and Nicky Fox, and other persons at NASA/GSFC coordinate
this event and collect related data for the homepage of ISTP.
Roelof, E. C., and D. G. Sibeck, Magnetopause shape as a bivariate function of interplanetary magnetic field Bz and solar wind dynamic pressure, J. Geophys. Res., 98, 21,421, 1993.
Shue, J.-H, J. K. Chao, H. C. Fu, C. T. Russell,
P. Song, K. K. Khurana, and H. J. Singer, A new
functional form to study the solar wind control of
the magnetopause size and shape,
J. Geophys. Res., in press, 1997.
Figure 1. Comparison of r0 between the Shue et al.  model and the extended Roelof and Sibeck  model. The red region shows that r0 is within geosynchronous orbit. The green region shows r0 is outside of geosynchronous orbit.
Figure 2. Magnetopause location and satellites at 0222 UT on January 11, 1997. The red line is the prediction of Shue et al. . The blue line is predicted by the extrapolated Roelof and Sibeck . The green line indicates geosynchronous orbit. Moreover, Green dots shows satellites that are in the magnetosphere in respect to the prediction by Shue et al. . Blinking dots with red and gold are indicated when satellites are in the magnetosheath.
Figure 3. Distance between LANL 94 and the two model predictions. A distance is calculated by using the closest distance to the model prediction. The black line represents the distance. A negative distance with a red region means that a satellite is in the magnetosheath. The green region shows the satellite is in the magnetosphere. The uncertainty of the prediction is indicated by gold color.
Figure 4. The same format as Figure 3, but for Telstar 401.
Figure 5. The same format as Figure 3, but for Geotail.
Figure 6. The same format as Figure 3, but for Interball 1. The region between two vertical lines shows the period of the enhancement of the extremely high pressure.
Figure 7. Demonstration of magnetopause locations before and after the Shue et al.'s model is extended. A value of Bz is fixed at 0 nT. Different colors show different values of dynamic pressure.
Figure 8. Refit of the upper panel of Figure 8 of Shue et al.  and the lower panel of Figure 14 of Shue et al. . Green lines represent the fitting results from Shue et al. . A bell-shape function is used to refit the data points, as indicated by red lines.
Figure 9. The same format as Figure 6, but for the extended Shue et al. . The region between two vertical lines shows the period of the pressure enhancement.
Figure 10. The same format as Figure 1, but for the extended Shue et al. .