Altitude Adjustment Corrected Geomagnetic Coordinates

Altitude adjustment corrected geomagnetic (AACGM) coordinates are useful in space weather because they are defined such that all points along a magnetic field line have the same geomagnetic latitude and longitude. The charged particles of the ionosphere follow spiral trajectories along these field lines, so tracing them helps to understand how different regions of the ionosphere are coupled to one another. For example, precipitating electrons and ions near the magnetic poles interact with the neutral atmosphere at about 100 km to produce the aurora. Identification of the horizontal positions of the auroral boundaries are partially based on satellite measurements of particle flux in the upper ionosphere using conversion of geographic (GG) coordinates at the satellite altitude to AACGM latitude and longitude followed by conversion back to GG coordinates at the lower auroral altitude.

Derivation of the AACGM Coordinate Conversion

The International Geomagnetic Reference Field (IGRF) is a model of the Earth’s magnetic field that is produced by the International Association of Geomagnetism and Aeronomy (IAGA) and updated every five years (the latest epoch is 2010). Corrected geomagnetic (CGM) coordinates at the Earth’s surface are essentially a map of the higher-order IGRF model to a simple tilted dipole model.

AACGM coordinates are determined by field line tracing of the IGRF model from several representative altitudes down to the surface. Conversions, either GG → AACGM or AACGM → GG, are expressed by coefficients of an expansion of the coordinates in spherical harmonic functions. Extension to all altitudes up to 2000 km is accomplished by fitting each of these coefficients through the discrete set of altitudes to a polynomial function.

Complications in the Method

The mapping of IGRF to a simple tilted dipole for the surface CGM is actually performed by tracing an IGRF field line to the dipole magnetic equatorial plane and then tracing the dipole field line from that point back to the surface. However, not every such field line reaches the magnetic equatorial plane. Similarly, for low latitudes many field lines curve back and re-enter the Earth’s surface without reaching the full 2000 km altitude range. For this reason the GG → AACGM and AACGM → GG conversions are not defined for all points.

Also, the conversions are not perfect inverses of one another. That is, applying GG → AACGM → GG or AACGM → GG → AAGCM (“to and back” for either system) does not result in the same initial latitude and longitude. Considerable effort is required to smooth the data to minimize these differences, particularly near the undefined areas at low latitude and the area of rapidly changing magnetic field near the South Atlantic Anomaly (a region off the coast of Brazil where the Earth’s magnetic field is at its weakest).

Deliverable Fortran Code

AER is contracted by the Air Force Research Lab (AFRL) Space Vehicles Directorate to prepare the latest version of the AACGM coordinate conversion for each new update of the IGRF model (at 5-year epochs). The Fortran source code files in the right sidebar are primarily provided for researchers that have been directed to this page by AFRL. Each of the CGLALO files contain a standalone subroutine that converts GG → CGM (surface mapping). The BLOCKDATA files contain the coefficients (both directions) for the GG ↔ AACGM conversions, the most useful file being the update of the 2010 epoch for those who already have a program that is using one of the earlier versions. See the report at the top of the sidebar for further details of the process AER uses to determine the AAGCM coordinate updates.