APEX Fortran Code

Fortran code to convert between geographic and magnetic quasi-dipole, magnetic apex, and modified magnetic apex coordinate systems based on Van Zandt et al. (1972) and Richmond [1995]. The geomagnetic main field is the International Geomagnetic Reference Field (IGRF) Version 13. The test program includes:

  • Magnetic apex parameters for a given location
  • Base vectors for scaling electric field and ion velocity components
  • Magnetic footpoints in both hemispheres for a given geographic point
  • Conversion between quasi-dipole and geographic coordinates
  • Subsolar point, solar zenith angle, magnetic local time

**Download from https://github.com/NCAR/apex_fortran.**

***In case you need the updated coefficient file with IGRF13 in an older format please download here.

References for apex coordinate systems:

  • Emmert, J.T., Richmond, A.D., & Drob, D.P. (2010). A computationally compact representation of Magnetic-Apex and Quasi-Dipole coordinates with smooth base vectors. Journal of Geophysical Research, 115, A08322. https://doi.org/10.1029/2010JA015326
  • Laundal, K.M. & Richmond, A.D. (2017). Magnetic coordinate systems. Space Science Reviews, 206, 27-59. https://doi.org/10.1007/s11214-016-0275-y
  • Richmond, A.D. (1995). Ionospheric electrodynamics using Magnetic Apex Coordinates. Journal of Geomagnetism and Geoelectricity, 47, 191-212. https://doi.org/10.5636/jgg.47.191
  • Thébault, E., Finlay, C.C., Beggan, C.D. et al. (2015). International Geomagnetic Reference Field: the 12th generation. Earth, Planets and Space 67, 79. https://doi.org/10.1186/s40623-015-0228-9


    VanZandt, T.E., Clark, W.L.,and Warnock, J.M. (1972). Magnetic Apex Coordinates: A magnetic coordinate system for the ionospheric F2 layer, Journal of Geophysical Research, 77, 2406-2411.

Other resources for apex code: