Modeling the Earth's Magnetosphere Using Spacecraft Magnetometer Data

Data-based (or empirical) modeling of the geomagnetic field started as a discipline as early as in the first half of XIX century, when Gauss developed mathematical foundations of the modeling of Earth's main magnetic field and obtained first estimates of its spherical harmonic coefficients, using then available ground-based data. That approach, based on the potential (current-free) nature of the main field outside Earth, is still at the core of modern IGRF models.

With the advent of space era and understanding the crucial role of the geomagnetic field in the dynamics of the Earth's upper atmosphere and radiation belts, a need was realized to extend the models from low to high altitudes, eventually including the entire magnetosphere, an integral part of our space environment. Modeling the magnetic field in that region is much more difficult, mostly because the magnetic field from external sources (currents in the magnetospheric plasma) rapidly outweighs the main field with growing distance from Earth. The external field is not current-free and, hence, it is no longer possible to conveniently represent it by a scalar potential, uniquely defined by observations at a surface, as was the case with the main field. Rather, vector measurements of the magnetic field should now be made throughout the entire 3D modeling region, making it necessary to accumulate large amounts of space magnetometer data taken in a wide range of geocentric distances.

This task turns out to be even more complicated due to the fact that, unlike the main geomagnetic field that varies on a timescale of thousands of years, the Earth's magnetosphere is a very dynamical system, whose configuration depends on many internal and external factors. The first factor is orientation of the Earth's magnetic axis with respect to the direction of the incoming solar wind flow, which varies with time because of (i) Earth's diurnal rotation and its yearly orbital motion around Sun, and (ii) frequent "side gusts" of the solar wind. The animation on the left below shows how the magnetospheric field varies in response to the diurnal wobbling of the geodipole. The background color coding displays the distribution of the scalar difference DB between the total model magnetic field and that of the Earth's dipole alone. Yellow and red colors correspond to the negative values of DB (depressed field inside the ring current, in the dayside polar cusps, and in the plasma sheet of the magnetotail). Black and blue colors indicate a compressed field (in the subsolar region on the dayside and in the magnetotail lobes on the nightside).

Another important factor is the state of the solar wind, in particular, the orientation and strength of the interplanetary magnetic field , "carried" to the Earth's orbit from Sun due to the high electrical conductivity of the solar wind plasma. Interaction between the terrestrial and interplanetary fields becomes much more effective when the interplanetary magnetic field turns antiparallel to the Earth's field on the dayside boundary of the magnetosphere. In this case, geomagnetic and interplanetary field lines connect across the magnetospheric boundary, which greatly enhances the transfer of the solar wind mass, energy, and electric field inside the magnetosphere. As a result, the magnetospheric field and plasma become involved in a convection, as illustrated in the second animation below (right):

Geodipole Tilt Effects Steady Magnetospheric Convection
In actuality, that kind of steady convection is rarely realized. The solar wind is far from being a stationary flow: periods with a stable ram pressure are often interrupted by strong "gusts"; in addition, the interplanetary magnetic field often fluctuates both in magnitude and orientation. This results in dramatic dynamical changes of the entire magnetospheric configuration, which culminate in magnetospheric storms, accompanied by an explosive conversion of large amounts of the solar wind energy into the kinetic energy of charged particles in the near-Earth space, manifested in polar auroral phenomena and ionospheric disturbances. The third animation below (left panel) illustrates the dynamical changes of the global magnetic field in the course of a disturbance: a temporary compression of the magnetosphere by enhanced flow of the solar wind is followed by a tailward stretching of the field lines. Eventually, the increase of the tail magnetic field results in a sudden collapse of the nightside field (a substorm ) and a gradual recovery of the magnetosphere to its pre-storm configuration.

Dynamical Disturbed Magnetosphere Polar aurora on 09/30/06, Homer, Alaska, courtesy Andrei Tsyganenko

Online resources for the geomagnetic field modeling

Geophysical coordinate systems

In geophysics and space physics, individual phenomena or objects can be most conveniently described in different coordinate systems that take into account their specific properties in the most natural and simplest way. For example, the main geomagnetic field is rigidly tied to rotating Earth and, hence, can be best described in geocentric geographic (GEO) or dipole magnetic (MAG) coordinates. There exist several coordinate systems most often used in studies of the geomagnetic field and Sun-Earth connections; their detailed overview can be found in papers by Russell [Cosmic Electrodyn., v.2, pp. 184-196, 1971], Hapgood [Planet. Space Sci., v.40(5), pp. 711-717, 1992; Ann. Geophys., v.13, pp. 713-716, 1995].

This website offers a set of FORTRAN subroutines for transformations between various geophysical coordinate systems. The most recent revised and extended version (update of Jan.31, 2015) of the package GEOPACK-2008 is now available. IGRF-12 model coefficients are currently in use, extending the time span of the main field model through 2020.

The package includes 20 subroutines for evaluating field vectors, tracing field lines, transformations between various coordinate systems, and locating the magnetopause position. A new feature, not available in previous releases, is the possibility to take into account the observed direction of the solar wind, which not only aberrates by ~4 degrees from the strictly radial Sun-Earth line, but also often significantly fluctuates around that average direction. Full documentation file: (Word, 180 KB)
Double-precision version: (GEOPACK-2008_dp)

ATTENTION: see ERRATA for recent corrections/updates (last correction of Geopack-2008 made on November 30, 2010)

Two examples of a typical FORTRAN program, using the GEOPACK-2008 routines for the field line tracing

Licensing information: All programs/codes presented on this site is free software: you can download, redistribute and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version. A copy of the GNU General Public License can also be found at GNU website .

Magnetospheric magnetic field models

The data-based approach to the modeling of the geomagnetosphere has been developed over the last 3 decades, starting with the pioneering work by Mead and Fairfield [1975]. Subsequent efforts [Tsyganenko and Usmanov, 1982; Tsyganenko, 1987, 1989, 1996, 2002, 2003, Tsyganenko and Sitnov, 2005] resulted in more refined models, used since then in many studies. The principal goal of the data-based magnetosphere modeling is to extract full information from large sets of available data , bridge the gap between theory and observations, and help answer a fundamental question:

"What is the actual structure of the geospace magnetic field and how is it related to changing interplanetary conditions and the ground disturbance level?"

Follow the links below to download FORTRAN source codes of data-based models, developed by the author of this web resource during the last 25 years.

Download a source code of TS05 (aka TS04s), a dynamical empirical model of the inner storm-time magnetosphere. Click here for a detailed description of the model.

Download a source code (Fortran-77) of the T02 (aka T01_01) model of the inner and near magnetosphere. Publications: Paper I and Paper II .

See ERRATA for a list of recent corrections/updates (last correction of T02 and TS05: June 24, 2006).

Download a source code (Fortran-77) of the T96 model. More detailed information on the model: Paper I and Paper II.

Download a source code of the 1989 model (T89d_SP) (or its double-precision version (T89d_DP).)

View lists of data sets used in the derivation of the models.

Click on highlighted items below for latest developments:

Magnetospheric configurations from a high-resolution data-based magnetic field model (abstract)
(JGR-A, v.112(A6), 2007)
(PDF 2.3MB).

Dynamical data-based modeling of the storm-time geomagnetic field with enhanced spatial resolution (abstract)
(Published in JGR-A, July 30, 2008) (PDF ~21.0MB).

Note: The two papers cited above present main ideas and first results obtained using a new approach to the data-based modeling. Its essence boils down to (1) employing extensible high-resolution expansions for the field of equatorial currents and (2) a special data mining technique based on a "nearest-neighbor" search in the parameter space. More details on the advanced modeling methods and results can be found on a webpage, maintained by Mikhail Sitnov (JHU/APL).

Magnetic field and electric currents in the vicinity of polar cusps as inferred from Polar and Cluster data (abstract)
(Published in Annales Geophysicae, April 2, 2009) (PDF ~3.0MB).

On the reconstruction of magnetospheric plasma pressure distributions from empirical geomagnetic field models (abstract)
(Published in JGR-A, July 15, 2010) (Full article, PDF ~1.2MB).

Data-based modeling of our dynamic magnetosphere (abstract)
(An invited review, published in Annales Geophysicae, October 21, 2013) (Full article, PDF ~10MB).

On the bowl-shaped deformation of planetary equatorial current sheets (abstract)
(Published in Geophysical Research Letters, February 4, 2014)

Internally and externally induced deformations of the magnetospheric equatorial current as inferred from spacecraft data (abstract)
(Published in Annales Geophysicae, January 6, 2015) (PDF ~11MB).

A new forecasting model (TA15) of the magnetosphere, driven by optimal solar-wind coupling functions (abstract)
("Early view" version of JGRA paper, Oct.10, 2015)
(A concise description of the model, pdf~1.5MB)
(Fortran source codes and yearly input parameter files for 1995-2015)

Authors and curators:

Dr. Nikolai Tsyganenko                                                         Ms. Varvara Andreeva                                   

Department of Earth's Physics, University of St.-Petersburg, Petrodvoretz, St.-Petersburg 198504, Russian Federation

Phone: +7-812-428-4634

Fax: +7-812-428-7240

This site was started on February 15, 2008

Most recent update:

October 12, 2015 (a new TA15 model link added with source codes and input data)

Previous updates:

March 23, 2015 (update of TS05 model parameters for 2014, due to NSSDC revision of 2014 OMNI data)

Jan 31, 2015 (IGRF-12 coefficients included in Geopack-2008)

Nov 12, 2014 (a refurbished version of T89 source code added)

Nov 04, 2014 (TS05 model parameters through Sep 30, 2014, updated/added)

Nov 21, 2013 (TS05 model parameters through Sep 28, 2013, updated/added)

March 11, 2011 (a SAVE statement was added in the source code of the T96 model, to avoid run-time problems with some Fortran compilers).

Dec 8, 2010 (TS05 model parameters for Jan 1 - Nov 7, 2010 added);

December 1, 2010 (Earth's main field model extended by adding IGRF-11 coefficients in the Geopack-2008 s/w;

March 13, 2010 (licensing info added); February 25, 2010; June 11, 2009; March 3, 2009; April 21 and July 31, 2008.

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