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

If you have more questions regarding the Earth's magnetosphere and geomagnetism, or would like to refresh your memory of even more general topics, covering basic astronomy and space physics, here is an extensive educational web resource, developed by David Stern.

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; a detailed overview of those systems 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]; there also exist comprehensive online resources, such as SPENVIS page.

This website offers a set of FORTRAN subroutines for transformations between various geophysical coordinate systems. The most recent revised and extended version (update of Dec.01, 2010) of the package GEOPACK-2008 is now available. IGRF-11 model coefficients are now added, extending the time span of the main field model through 2015.

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, 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?"

Links below can be used for downloading FORTRAN source codes of data-based models, developed by the author of this web resource during the last 25 years.