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Background Information Background Information
Magnetic field models

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:

  1. permanent (standard) magnetic observatories worldwide,
  2. repeat measurements (stations) at selected sites,
  3. magnetic surveys from the aircraft and ships,
  4. 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:

  1. a current system on the magnetospheric boundary (magnetopause);
  2. a current system in the neutral sheet of the geomagnetic tail (the surface that separates two lobes of the tail);
  3. 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 Kp. 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 Dst 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 Dst and Kp 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

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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.

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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.

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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