# Modeling the Earth's Magnetosphere Using Spacecraft Magnetometer Data

This is a webpage by N. A. Tsyganenko, dedicated to empirical modeling of the Earth's magnetospheric magnetic field. Here one can find the latest studies and download source codes of data-based models, developed by the author of this web page (and his co-authors) during the last 30 years.

For convenience, the Fortran source codes are grouped into categories 'Magnetic field', 'Plasma', and 'Current sheet' in the sidebar on the left.

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## Empirical modeling​

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):

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.

## 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 ($B_z<0$ 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 SpaceWeather.com 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.