Corrected Geomagnetic Coordinates

The provided code calculates the Corrected GeoMagnetic (CGM) coordinates and several other main geomagnetic field parameters for specified points at the Earth's surface (geocentric coordinates) or in near-Earth space (and vice versa). The underlying main geomagnetic field models are the Definite/International Geomagnetic Reference Field (DGRF/IGRF) models for Epoch's years 1900,..1945, 1950, ..., 2005,2010,2015,2020 and the secular variation model for 2020-2025. The CGM coordinates have proven to be excellent tools in organizing geophysical phenomena controlled by the Earth's magnetic field, like auroral boundaries, high and middle latitude ionospheric currents, etc.

Required input parameters are:

Computed output parameters for the given point are:

The DGRF/IGRF model output is presented in the local geomagnetic coordinate system:

Note that the main geomagnetic field components have the following signs: H is positive everywhere on Earth, D can be eastward (+) or westward (-), Z is positive in the Northern Hemisphere, and negative - in the Southern Hemisphere.

The software package consists of several modules. The DGRF/IGRF field computation subroutine is taken from the GEOPACK-2008 software package developed by Drs. Nikolai Tsyganenko. The field line tracing and original CGM coordinate transformation modules were developed by Drs. Natalia and Vladimir Papitashvili.


By definition, the CGM coordinates (latitude, longitude) of a point in space are computed by tracing the DGRF/IGRF magnetic field line through the specified point to the dipole geomagnetic equator, then returning to the same altitude along the dipole field line and assigning the obtained dipole latitude and longitude as the CGM coordinates to the starting point. At the near-equatorial region, where the magnetic field lines may not reach the dipole equator and where, therefore, the standard definition of CGM coordinates is irrelevant. Therefore, the this code is limited to the areas less then |20| degrees geographic latitudes in both the Northern and Southern hemispheres Gustafsson et al. [1992].

Because the "local" CGM meridian is non-orthogonal to the "local" CGM latitude, we approximate the "local" direction of this the great-circle arc, connecting the given point (station) and the corresponding (North or South) CGM pole. Therefore, an azimuth of this arc with respect to the local geographic meridian (which is also the great-circle arc, connecting the station and the corresponding geographic pole) is our "meridian" angle: positive to East from the North geographic meridian and positive to West from the South geographic meridian.

According to the definition of geomagnetic coordinates under the dipole approximation, the magnetic local time (MLT) is measured by the flare angle formed by two planes: the dipole meridional plane, which contains a subsolar point on the Earth's (or any altitude) surface, and the dipole meridional plane which contains a given point on the surface (that is, the local dipole meridian). This definition cannot be applied to the CGM coordinate system because the latter is non-orthogonal and the CGM meridians do not cross the magnetic equator elsewhere [cf. Gustafsson et al., 1992]. Therefore, the dipole-based approximation is invalid in defining MLT for the CGM coordinate system.

Here we propose to utilize another approach in defining MLT for the CGM coordinate system. Let us assume that the station is located at local midnight, i.e., at some UT instance the local geographic meridian is at 00 LT and the station is "behind" the geographic pole with respect to the Sun. If the Earth rotates through an angle (measured in UT hours and minutes) so that the station's local CGM meridian (approximated by the great-circle arc) is moved to 00 MLT, then the station is "behind" the CGM pole with respect to the Sun. This UT instance (in hours and minutes) would be "a local MLT midnight in UT" which is computed in our algorithm.


Gustafsson, G., N. E. Papitashvili, and V. O. Papitashvili, A Revised Corrected Geomagnetic Coordinate System for Epochs 1985 and 1990, J. Atmos. Terr. Phys., 54, 1609-1631, 1992.

Tsyganenko, N. A., A. V. Usmanov, V. O. Papitashvili, N. E. Papitashvili, and V. A. Popov, Software for computations of the geomagnetic field and related coordinate systems, Soviet Geophys. Comm., Moscow, 58 pp., 1987.

If you have any questions/comments, contact:
Dr. Natalia Papitashvili, E-mail:, NASA/Goddard Spaceflight Center, Greenbelt, MD 20771