Introduction
The Earth's real magnetic field is the sum of several contributions including
the main (core) and crustal (anomaly) fields (also referred to as the
geomagnetic field),
and the external source (magnetospheric) fields.
The magnetic field models described below are
implemented in SPENVIS.
Internal magnetic field models
As shown by Gauss in 1839, the main geomagnetic field (i.e., magnetic
potential) can be represented by a
spherical harmonic series, the first term
being the simple dipole term. A gradient of the
potential determines the magnetic vector field.
The principal data sources for models of the main geomagnetic field are:
- permanent (standard) magnetic observatories worldwide,
- repeat measurements (stations) at selected sites,
- magnetic surveys from the aircraft and ships,
- global satellite magnetic measurements.
A group of geomagnetic field modellers associated with the
International Association of Geomagnetism and Aeronomy (IAGA) Division V, Working Group 8,
periodically examines various geomagnetic field representations from which
the Earth’s main field and its secular variation can be computed. They
produce a set of coefficients to represent the main field at a particular
epoch, usually every five years, and name it the
International Geomagnetic Reference Field (IGRF).
Also, if a previous IGRF is modified using new data not available at the time
of its production, it is called a Definitive Geomagnetic Reference Field
(DGRF). Note that, when referring to these models, the designation "IGRF"
refers to all available models, viewed collectively. If a particular model is
intended, the reference must be specific, i.e. IGRF2000 or DGRF1990, rather
than simply IGRF or DGRF.
The IGRF is a series of mathematical models describing the Earth’s main field
and its secular variation.
In addition to the DGRF/IRGF model suite, the
Jensen and Cain [1962]
and
GSFC12/66
[Cain et al., 1967] models are used by the NASA AP-8 and
AE-8 trapped particle models.
External magnetic field models
The Earth's magnetic field is a sum of several contributions including the
main (core) field, the crustal (anomaly) field, and the external source
(magnetospheric) fields. The core contribution dominates the field from the
Earth's surface up to about four Earth radii.
Beyond four Earth radii, the Earth's magnetic field is increasingly affected
by the solar wind interaction with the Earth's magnetosphere. The distortions
can be described by several external source fields caused by magnetospheric
current systems. One can identify three main current systems in the
undisturbed outer magnetosphere:
- a current system on the magnetospheric boundary (magnetopause);
- a current system in the neutral sheet of the geomagnetic tail (the
surface that separates two lobes of the tail);
- a current system around the Earth (ring current) flowing in the
equatorial (minimum B) surface.
During geomagnetic storms and substorms, substantial changes occur in these
systems, in addition to the appearance of field-aligned currents flowing out
of and into the ionosphere.
The following models have been
implemented in SPENVIS:
Mead-Fairfield
For this tilt dependent model [Fairfield and Mead, 1975], four sets of
model coefficients are available
for four levels of magnetic activity as parameterized by
K_{p}.
It is valid out to 17 Earth radii. The model is expressed as second order
power series expansions in
solar magnetic coordinates,
quadratic in position and linear in tilt. The model coefficients (17) were
obtained by a least-square-fit to 12,616 vector field measurements from 451
orbits of four IMP satellites between 1966 and 1972. The effect of localized
current systems like the ring current and sheet currents in the tail are not
particularly well modelled by these quadratic expansions.
The model code can be obtained from
NSSDC.
Tsyganenko
The Tsyganenko model is a semi-empirical best-fit representation for the
magnetic field, based on a large number of satellite observations (IMP, HEOS,
ISEE, POLAR, Geotail, etc). The model includes the contributions from
external magnetospheric sources: ring current, magnetotail current system,
magnetopause currents and large-scale system of field-aligned currents.
The Tsyganenko [1987] model is provided as a "long" and a "short"
version. The Tsyganenko [1989] model T89c is tilt dependent and was
primarily developed as a tail model. The Tsyganenko [1996] model has
an explicitly defined realistic magnetopause, large-scale Region 1 and 2
Birkeland current systems, and the IMF penetration across the boundary.
The T01 [Tsyganenko, 2002ab] model represents the variable
configuration of the inner and near magnetosphere for different
interplanetary conditions and ground disturbance levels.
The T04 [Tsyganenko and Sitnov, 2005] model is a dynamical model of the storm-time
geomagnetic field in the inner magnetosphere, using space magnetometer
data taken during 37 major events in 1996-2000 and concurrent
observations of the solar wind and IMF.
The model codes can be obtained from
NSSDC.
Olson-Pfitzer quiet
This is an analytical model [Olson and Pfitzer, 1977]
of the Earth's magnetic field valid from the
dayside subsolar magnetosphere to beyond lunar orbit in the nightside
magnetotail. Only the quiet time magnetosphere is represented including the
contributions from magnetopause, tail, and ring currents. The internal (core)
field is represented by a fixed dipole. The field representation is given in
Cartesian
geocentric solar magnetospheric coordinates
using sixth-order expansions of power series and exponential terms. The 180
coefficients were determined by fitting to over 600 magnetometer measurements
from OGO 3 and 5. Shortcomings of this model are the restriction to quiet
conditions and the fact that the direction of the main dipole and the ring
current is fixed (i.e., perpendicular to the Earth-Sun direction).
The model code can be obtained from
NSSDC.
Olson-Pfitzer dynamic
Olson and Pfitzer's [Pfitzer et al., 1988] dynamic model for the
external geomagnetic field was developed for event studies in the NASA
Coordinated Data Analysis Workshops (CDAW). It extends the Olson and
Pfitzer [1974] tilt averaged and the Olson and Pfitzer [1977] tilt
dependent models by modelling the variation of the strength and size of the
major magnetospheric current systems in response to their interplanetary
sources. The model is capable of accurately representing the dayside magnetic
field at geosynchronous orbit for all magnetic conditions and the nightside
field for non-substorm conditions. The model does not accurately represent
the magnetic field in the inner tail region during storm conditions, because
it does not include the extension of the Birkeland currents into the
magnetosphere.
The dynamic model can be used to represent any set of magnetic conditions. In
the model, the pressure of the solar wind is used to determine the scale and
strength of the magnetopause currents. The ring current is driven by a
modified
D_{st} index
in which the contribution of the magnetopause currents has been removed. At
present, the tail currents are scaled in the same way as the magnetopause
currents.
On the daylight side of the Earth, the model is able to predict the strength
of the magnetic field at synchronous orbit to within 5 nT for
magnetopause standoff distances between 7 and 11 Earth radii. Since the model
does not yet include the effects of the asymmetric ring and Birkeland
currents, it is not as accurate on the night side of the Earth.
Ostapenko-Maltsev
The Ostapenko and Maltsev [1997] model was obtained by a least squares
fit of fourth order polynomials to 14,000 vector field measurements from the
database of Fairfield et al. [1994]. The model depends on the
D_{st} and
K_{p} indices,
as well as on the solar wind dynamic pressure and the z component of
the interplanetary magnetic field. The model can be obtained from
Y.P. Maltsev (maltsev@pgi-ksc.murmansk.su),
Polar Geophysical Institute, Apatity, Russia.
Paraboloid model
This proposed
ISO standard
"Model of Earth's Magnetospheric Magnetic
Field" is developed jointly by research teams from the Skobeltsyn
Institute of Nuclear Physics, Moscow State University, Russia and the
Geomagnetics Group, U. S. Geological Survey. It is intended to calculate
the magnetic induction field generated from a variety of current systems
located on the boundaries and within the boundaries of the Earth's
magnetosphere under a wide range of environmental conditions, quiet and
disturbed, affected by Solar-Terrestrial interactions simulated by Solar
activity such as Solar Flares and related phenomena which induce
terrestrial magnetic disturbances such as magnetic storms.
The model code and description can be obtained
here.
References
Alexeev, I. I., and Y. I. Feldstein, J. Atmos. Sol. Terr. Phys., 65,
331, 2001.
Cain, J. C., S. J. Hendricks, R. A. Langel, and W. V. Hudson, A proposed
model for the international geomagnetic reference field-1965, J. Geomag.
Geoelectr., 19, 335-355, 1967.
Campbell, W., Introduction to geomagnetic fields, Cambridge University Press,
Cambridge, 1997.
Chapman, S. and J. Bartels, Geomagnetism, 2 vols., pp 1049, Oxford
University Press, London, 1940.
Fairfield, D. H., and G. D. Mead, Magnetospheric Mapping with a Quantitative
Geomagnetic Field Model, J. Geophys. Res., 80, 535, 1975.
Fairfield, D. H., N. A. Tsyganenko, A. V. Usmanov, and M. V. Malkov, A large
magnetosphere magnetic field database, J. Geophys. Res., 99,
11319-11326, 1994.
Fraser-Smith, A. C., Centered and Eccentric Geomagnetic Dipoles and Their
Poles, 1600-19,85,Rev. Geophys., 25, 1, 1-16, 1987.
Jensen, D. C., and J. C. Cain, An interim geomagnetic field, J. Geophys.
Res., 67, 3568, 1962.
Langel R. A., Main Field, in Geomagnetism, 249-512, vol. I, ed. J.A. Jacobs,
Academic Press, London, 1987.
Merrill, R., M. W. McElhinny, and P. L. McFadden, The magnetic field of the
Earth, Paleomagnetism, the core, and the deep mantle, Academic Press,
San Diego, 1996.
Olson, W. P., A model of the distributed magnetospheric currents, J.
Geophys. Res., 79, 3731-3738, 1974.
Olson, W. P., and K. A. Pfitzer, Magnetospheric magnetic field modeling,
Annual Scientific Report, AFOSR Contract No. F44620-75-C-0033, 1977.
Ostapenko, A. A., and Y. P. Maltsev, Relation of the magnetic field in the
magnetosphere to the geomagnetic and solar wind activity, J. Geophys.
Res., 102, 17467-17473, 1997.
Peddie, N. W., International Geomagnetic Reference Field : The Third
Generation, J. Geomag. Geoelectr., 34, 309-326, 1985.
Pfitzer, K. A., W. P. Olson, and T. Mogstad, A time dependent source driven
magnetospheric magnetic field model, EOS, 69, 426, 1988.
Tsyganenko, N. A., Global quantitative models of the geomagnetic field in
the cislunar magnetosphere for different disturbance levels, Planet. Space
Sci., 35, 1347-1358, 1987.
Tsyganenko, N. A., A magnetospheric magnetic field model with a wrapped
tail current sheet, Planet. Space Sci., 37, 5-20, 1989.
Tsyganenko, N. A., Modeling the Earth's magnetospheric magnetic field
confined within a realistic magnetopause, J. Geophys. Res., 100,
5599-5612, 1995.
Tsyganenko, N. A., Effects of the solar wind conditions on the global
magnetospheric configuration as deduced from data-based field
models, Proc.of 3rd International Conference on Substorms (ICS-3),
Versailles, France, 12-17 May 1996, ESA SP-389, 181-185, 1996.
Tsyganenko, N. A., A model of the near magnetosphere with a dawn-dusk
asymmetry. 1. Mathematical structure, J. Geophys. Res., 107,
1179, 2002a.
Tsyganenko, N. A., A model of the near magnetosphere with a dawn-dusk
asymmetry. 2. Parametrization and fitting to observations,
J. Geophys. Res., 107, 1176, 2002b.
Tsyganenko, N. A., and A. V. Usmanov, Determination of the Magnetospheric
Current System Parameters and Development of Experimental Geomagnetic Field
Models Based on Data from IMP and HEOS Satellites, Planet. Space Sci.,
30, 985-998, 1982.
Tsyganenko, N. A., A. V. Usmanov, V. O. Papitashvili, N. E. Papitashvili,
and V. A. Popov, Software for Computations of Geomagnetic Field and Related
Coordinate Systems, Soviet Geophysical Committee, Special Report, 58 pp.,
Moscow, 1987.
Tsyganenko, N. A., and M. Peredo, Analytical models of the magnetic field
of disk-shaped current sheets, J. Geophys. Res., 99, 199-205, 1994.
Tsyganenko, N. A., and D. P. Stern, Modeling the global magnetic field the
large-scale Birkeland current systems, J. Geophys. Res., 101,
27187-27198, 1996.
Tsyganenko, N. A., and M. I. Sitnov, Modeling the dynamics of the inner
magnetosphere during strong magnetic storms, J. Geophys. Res.,,
in press, 2005.
Last update: Mon, 12 Mar 2018