Modeling the Earth's Magnetosphere Using Spacecraft Magnetometer Data

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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 (IMF), "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

Space weather

Space weather is a modern field of space research, focused on the solar activity and its impact upon the near-Earth environment, spacecraft hardware, and humans. It includes investigation and prediction of solar flares, coronal mass ejections (CME), sunspots, magnetic storms, particle precipitation into the Earth atmosphere, and associated ionospheric phenomena. The flow of plasma from the Sun, known as the solar wind, is the principal factor determining the space weather in our planetary system. This is why it is very important to know in advance its principal characteristics: particle density, bulk velocity, the strength and direction of the Interplanetary Magnetic Field (IMF). The NASA Advanced Composition Explorer (ACE) satellite (operating since 1997) and the recently (2015) launched Deep Space Climate Ovservatory (DSCOVR) mission reside at the L1 libration point (1,500,000 km sunward from Earth) and provide continuous flow of information about the solar wind state nearly one hour in advance. Their real-time data are provided online by the National Oceanic and Atmospheric Administration (NOAA) Space Weather Prediction Center (SWPC).

The orientation of the IMF vector is a crucial factor that determines the state of the near-Earth space environment. Southward IMF (Bz<0 in GSM coordinates) combined with a high-speed solar wind result in magnetic storms, which may damage the spacecraft equipment, affect the navigation systems, aircraft and satellite operation. It also results in the so-called "geomagnetically induced electric currents" (GIC) in the ground infrastructures, such as pipelines and electric power grids. For example, on September 1-2, 1859, one of the largest recorded geomagnetic storms caused the failure of the telegraph systems all over Europe and North America. The intensity of geomagnetic storms is quantified by the Dst index, derived from the disturbance of the horizontal H-component of the magnetic field at low and middle latitudes. A rapid decrease of the Dst to low negative values (Dst<-50 nT) manifests the development of a storm. Anyone interested in the current state of space weather can check it at the real-time Dst trend on the webpage of the World Data Center for Geomagnetism (Kyoto).

Here is a very interesting and helpful resource for everyone with even a modest background in space physics. The site provides real-time space weather conditions such as the solar wind parameters, sunspot numbers, solar flares, solar images from SDO (Solar Dynamics Observatory) instruments and NOAA 24 and 48 hour forecasts of the flare and geomagnetic storm probabilities. Besides the space environment data, the website offers up-to-date news on spacecraft scientific missions, breathtaking pictures of auroral displays, stunning atmospheric optical phenomena, noctilucent clouds, and much more interesting information.

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.1, 2020 ) of the package GEOPACK-2008 is now available. IGRF-13 model coefficients are currently in use, extending the time span of the main field model through 2025.

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

Corrected Geomagnetic Coordinates

A source code for calculating corrected geomagnetic coordinates (CGLat, CGlon) of a location from its geodetic coordinates (latitude, longitude, elevation above ground).

Invariant Coordinates

A source code for calculating invariant geomagnetic coordinates (L-parameter, invariant latitude) of a location from its geocentric (GEO) coordinates (latitude, longitude, geocentric distance).

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 the fundamental questions:

"What is the actual structure of the geospace magnetic field according to satellite observations?"

"How it is 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.
Yearly input data files (from 1995 through December 18, 2022) and related documentation for the TS05 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.

Magnetospheric plasma

Download a source code to calculate the central plasma sheet ion parameters according to Tsyganenko and Mukai [2003] model, based on Geotail data.

Click on highlighted items below for latest developments:

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, Fortran source code for the equatorial current sheet model)
(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)
(JGRA, October 7, 2015)
(A concise description of the model, pdf~1.5MB)
(Fortran source codes and yearly input parameter files for 1995-2020)

Reconstructing the magnetosphere from data using radial basis functions (abstract)
(JGRA, published online 18 March 2016)

An empirical RBF model of the magnetosphere parameterized by interplanetary and ground-based drivers (abstract)
(JGRA, published 5 November 2016)

(Fortran source code, yearly input parameter files for 1995-2016, & data format)
ATTENTION: due to a recently discovered bug (line 270 of the original 2016 code), the source code was corrected and replaced on 11/23/2021.

A hybrid approach to empirical magnetosphere modeling (abstract)
(JGRA, published online 5 August 2017)

Empirical modeling of the quiet and storm-time geosynchronous magnetic field (abstract)
(Space Weather, Vol.16(1), pp.16-36, 2018)

(Fortran source code, model parameter file, model fitting subsample, the fitting subsample format description)
Yearly input parameter files for 1995-2016, & data format

Building the magnetosphere from magnetic bubbles (abstract)
(Geophysical Research Letters, Vol.45(13), pp.6382-6389, 2018)

Empirical modeling of dayside magnetic structures associated with polar cusps (abstract)
(Journal of Geophysical Research Space Physics, Vol.123(11), pp.9078-9092, 2018)

Secular shift of the auroral ovals: How fast do they actually move? (abstract)
(Geophysical Research Letters, Vol.46, pp.3017-3023, 2019)

Empirical modeling of the geomagnetosphere for SIR and CME-driven magnetic storms (abstract)
(Journal of Geophysical Research Space Physics, Vol.124, 5641-5662, 2019)

Magnetospheric penetration of IMF By viewed through the lens of an empirical RBF modeling (abstract)
(Journal of Geophysical Research Space Physics, Vol.125, 2020)

Reconstruction of magnetospheric storm-time dynamics using cylindrical basis functions and multi-mission data mining (abstract)
(Journal of Geophysical Research Space Physics, Vol.126, 2021)

Reconstructing substorms via historical data mining: Is it really feasible? (abstract)
(Journal of Geophysical Research Space Physics, Vol. 126, 2021)

A lifetime with models, or toils and thrills of number crunching (PERSPECTIVE article)
(Front. Astron. Space Sci., 2022)

Magnetosphere Distortions During the 'Satellite Killer' Storm of February 3-4, 2022, as Derived From a Hybrid Empirical Model and Archived Data Mining (abstract)
(Journal of Geophysical Research Space Physics, Vol. 127, 2022)

Authors and curators:

Dr. Nikolai Tsyganenko                                                         Dr. 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 updates:

April 20, 2023:
Two source codes were added (above, under "Online resources for the geomagnetc field modeling"), calculating corrected and invariant geomagnetic coordinates

December 24, 2022:
Two new paper links were added: "Magnetosphere Distortions During the 'Satellite Killer' Storm of February 3-4, 2022" and
"A lifetime with models, or toils and thrills of number crunching"

November 23, 2021:
TA16 (RBF) source code was corrected due to a newly discovered bug.

January 1, 2020:
IGRF-13 coefficients included in Geopack-2008.
A new paper link added ("Magnetospheric `penetration' of IMF By viewed through the lens of an empirical RBF modeling")

August 14, 2019: A new paper link added ("Empirical modeling of the geomagnetosphere for SIR and CME-driven magnetic storms")

March 12, 2019: A new paper link added ("Secular shift of the auroral ovals: How fast do they actually move?")

January 20, 2019: New paper links added ("Building the magnetosphere from magnetic bubbles" and "Empirical modeling of dayside magnetic structures associated with polar cusps")

December 11, 2017: A new paper link added ("Empirical modeling of the quiet and storm-time geosynchronous magnetic field")

Previous updates:

November 30, 2017: Due to requests from magnetospheric community members, a link is now added to a paper [Tsyganenko and Mukai, 2003] and
fortran source codes, referring to model calculations of the central plasma sheet plasma parameters based on Geotail data (see the "Magnetospheric plasma" section above.)

August 15, 2017: A new paper link added ("A hybrid approach to empirical magnetosphere modeling...")

October 25, 2016: a new paper link added ("An empirical RBF model of the magnetosphere ...")

April 20, 2016: update of the equatorial neutral sheet model subroutine (2015)

March 9, 2016: a new paper (RBF) link added.

October 12, 2015: a new TA15 model link added.

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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