Six Magnetic Field Models Compared:
Mapping Geosynchronous Orbit
to the Auroral Zone
Geoffrey D. Reeves
Loretta A. Weiss, Michelle F. Thomsen and David J. McComas
Los Alamos National Laboratory, Los Alamos NM
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- Introduction
- IGRF Internal Field Only
- Hilmer-Voigt Model: Dependence on equatorward edge of auroral oval
- Hilmer-Voigt Model: Dependence on magnetopause stand-off distance
- Hilmer-Voigt Model: Dependence on ring current (Dst)
- Tsyganenko 1989 Model: Dependence on Kp
- Tsyganenko 1987 Model: Dependence on Kp
- Tsyganenko 1982 Model: Dependence on Kp
- Olsen Pfitzer Static Model: No adjustable parameter
Understanding magnetic field mapping between the ionosphere and the equatorial magnetosphere has long been an important goal of space plasma physics. In no specialty is this more true than in substorm physics. One of the great debates in substorm physics in particular and in magnetospheric physics in general is what physical process is responsible for the onset of magnetospheric substorms. This question hinges directly on the magnetic connection between auroral signatures seen from the ground and in situ measurements of plasma processes in the equatorial magnetosphere.
Much research has focused on multi-point, multi-spacecraft measurements of substorm phenomena from the ground and from space. From a multitude of measurements we attempt to synthesize a picture of particular substorms. Often this synthesis relies heavily (if not decisively) on assumptions about the mapping along magnetic field lines between the ground and space. Typically we rely on models of the magnetic field for answers.
Many models of the Earth's magnetic field exist. Most researchers have a particular model they can call their "favorite". There are usually a handful of claims that each model can make on being "the best" which one can quote to support one's favorite model. Field models are difficult to evaluate though.
Here we attempt such an evaluation. There are many ways that one can compare magnetic field models. We provide a very specific comparison by looking at how six different magnetic field models map geosynchronous orbit into the auroral ionosphere. Field line mapping provides a very different test than comparing against local measurements of the magnetic field because it integrates along the entire field line. It is appropriate because it is magnetic mapping which we wish to compare.
(Note:
We emphasize that we are not comparing local field vectors. Therefore when we say the field is "stretched" this refers to the relative displacement of the foot point equatorward rather than the equatorial field magnitude or off-equatorial field inclination.)
Why Geosynchronous Orbit?
It is difficult to present mapping comparisons for 6 models over a large range of L-shells so we have concentrated on geosynchronous orbit at 6.6 Re. Geosynchronous orbit is interesting because it lies in a transition region where both internal and external magnetic field contributions are important and because many important substorm processes are observed there. Indeed many of us now suspect that the substorm onset mechanism may actually be found near geosynchronous orbit. One reason for this suspicion comes from the magnetic field models themselves. As the figures in this paper show geosynchronous orbit typically maps to an oval which looks essentially identical to the auroral oval.
Another reason for choosing geosynchronous orbit is that it supports another area of research which we are pursuing. Using Magnetospheric Plasma Analyzer (MPA) data from two geosynchronous spacecraft and data from the plasma analyzers on three low-altitude DMSP spacecraft we are testing the mapping between geosynchronous orbit and the auroral zone directly. This is done by comparing low and high-altitude spectra to determine when DMSP crosses the geosynchronous L-shell. We use this technique for a statistical comparison of measured mapping with the six magnetic field models presented here. The spectral comparison and measured mapping results will be presented at IUGG in Boulder on Thursday July 13, 1995 and will be available on line sometime thereafter.
Technique
We map field lines separated by 10 deg longitude starting on the geographic equator at an altitude of 6.6 Re. Essentially we map a ring at geosynchronous altitude to the ionosphere. We define the foot point as the position on the field line at an altitude of 100 km. We use a Runge-Kutta algorithm with an adaptive step size and strict error checking to map the field line. In this study all models were compared for March 7, 1991 at 0 UT but the models are valid for arbitrary dates and times.
We compare six different field models.
- IGRF Internal Field Model Only
- Hilmer-Voigt
- Tsyganenko 1989
- Tsyganenko 1987
- Tsyganenko 1982
- Olsen Pfitzer
All of the external field models (2-6) include the IGRF as the internal field.
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- It is essential to use the full IGRF field. Using a dipole for the internal field can cause a larger error in mapping than any differences in external field models.
- It is sufficient to use 6 harmonics. Higher harmonics make negligible contributions to the location of the foot points of geosynchronous orbit.
- The effect of higher harmonics varies with location. There is little difference over western Canada and large differences over Iceland and central Russia.
- All field models in this study use the IGRF field for the internal field.
- The IGRF field rotates with the earth and does not depend on local time.
- The external fields which are superimposed on the IGRF field mainly depend on local time.
- Therefore foot points depend on both local time and longitude.
IGRF Figures & Text
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- The Hilmer-Voigt model has three adjustable parameters:
- The Equatorward Edge of the Auroral Oval
- The Magnetopause Stand-Off Distance
- Ring Current Strength (measured by Dst)
- We adjusted each of these parameters independently, keeping the others fixed, to assess their individual effects. Normally the model would be used with values reflecting actual magnetospheric conditions.
- The equatorward edge of the auroral oval affects all local times but the largest effects are at local midnight.
- The "nominal" latitude of the equatorward edge is 65 deg.
- The IGRF field alone gives foot points which are poleward of even the 55 deg. version of Hilmer-Voigt.
- Hilmer-Voigt allows values of the equatorward edge between 55 deg. and 69 deg.
- The code will adjust input values to fit model parameters. e.g. 55 deg. is reset to 55.89 deg.
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- Here we examine the dependence of the foot point on the magnetopause stand-off distance.
- The magnetopause stand-off distance has the largest effect in the noon local time sector as expected.
- The model is designed so there is no dependence of the foot point on stand-off distance at local midnight.
- The "nominal" magnetopause stand-off distance is 10 Re.
- Stand-off distances from 6 to 12 Re were investigated.
- Stand-off distances less than 10 Re compress the day-side field and move the foot points poleward. Stand-off distances greater than 10 Re stretch the day-side field and move the foot points equatorward.
- A stand-off distance of 6 Re moves the foot point poleward of the IGRF foot point and correctly shows that part of geosynchronous orbit lies outside the magnetopause.
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- Here we examine the dependence of the foot point on the strength of the ring current measured by Dst
- Dst values between +50 and -200 were investigated.
- The "nominal" value of Dst is -50.
- Positive values of Dst move the foot points poleward of their nominal positions.
- All other values of Dst give foot points which are essentially indistinguishable.
- To compare with the Tsyganenko family of models we note that high Kp correlates with both a compressed magnetopause and a stronger ring current. However, in the Hilmer-Voigt model the dependence on stand-off distance is stronger than the dependence on Dst. Therefore in high Kp conditions the Hilmer-Voigt model predicts that, on average, the dayside foot points should move poleward and the nightside foot points should move equatorward compared to low Kp conditions.
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- The Tsyganenko 1989 model accepts 6 values of Kp. The first 5 values are 0 to 4. The last value covers all Kp conditions Kp>4+.
- Higher values of Kp move the foot points equatorward compared to low values of Kp for all local times. The Tsyganenko 1989 model does not show the effects of magnetopause compression during active conditions on the foot points of geosynchronous orbit.
- The foot points predicted by the Tsyganenko 1989 model are always equatorward of the foot point predicted by the internal IGRF model alone.
- For quiet conditions the Tsyganenko 1989 model has foot points which are substantially equatorward of the IGRF model foot points indicating that the field model is "stretched" even under Kp=0 conditions. (This is similar to the dependence of the Hilmer-Voigt model on equatorward edge in the midnight local time region.)
- We suspect that, in order to get sufficient stretching at midnight for high Kp conditions the field is over-stretched at other local times and for low Kp conditions. (Note that relatively few dayside observations are included to constrain the model.)
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- The Tsyganenko 1987 model is, qualitatively, very similar to the Tsyganenko 1989 model.
- Kp can take on 6 values, 0-4 and >4+.
- High Kp moves the foot points equatorward for all LT.
- No dayside compression at high Kp.
- Foot points always equatorward of IGRF foot points.
- The field is substantially stretched at midnight for Kp=0
- The Tsyganenko 1987 model differs from the Tsyganenko 1989 model in the quantitative dependence of the foot points on Kp.
- The Tsyganenko 1987 model stretches the field less at midnight for high Kp than the Tsyganenko 1989 model.
- The strangest feature of the Tsyganenko 1987 model is that for the highest values of Kp the effect of field line stretching is minimum at local midnight and maximum on the dawn and dusk flanks.
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- The Tsyganenko 1982 model [Tsyganenko-Usmanov, 1982] is quite different from the 1987 and 1989 versions.
- Kp can take on 11 values, 0, 0+, 1-, 1, 1+, etc. up to 3+. The 11th value covers all conditions Kp>3+.
- All dayside foot points in the Tsyganenko 1982 model are poleward of the IGRF foot points. This is consistent with compression of the field on the day side. However, the low Kp foot points are poleward of the high Kp foot points which is equivalent to less compression for higher Kp conditions. (Statistics show more compression is correlated with high Kp conditions.)
- For the same value of Kp the foot points in the Tsyganenko 1982 model are further equatorward than the foot points in the Tsyganenko 1989 model indicating that the 1982 model is more stretched at midnight. This includes Kp=0 which is more stretched than in the other Tsyganenko models.
- Unlike the Tsyganenko 1987 model, the dependence of the foot point on Kp is maximum at midnight (as expected).
- The dependence of the foot point on Kp at midnight is similar in magnitude to that in the Tsyganenko 1989 model for Kp=0-4 but the Tsyganenko 1989 model goes to higher Kp values.
- Because Kp can take on 11 values in the Tsyganenko 1982 model it is more continuously adjustable than the Tsyganenko 1987 or 1989 models.
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- The Olsen Pfitzer static magnetic field model does not have an adjustable parameter for magnetospheric conditions.
- As the accompanying plot shows the foot points of geosynchronous orbit are almost identical to the foot points in the Tsyganenko 1989 model with Kp=1.
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