A new magnetic coordinate system for conjugate studies at high latitudes

TLDR

Studying magnetically conjugate phenomena at very high latitudes requires a magnetic coordinate system that is smooth, well defined at the geographic poles, and allows accurate comparisons at different altitudes. The authors propose a variation of the corrected geomagnetic coordinate system that is smooth and well defined globally. The system is derived by tracing magnetic field lines with the IGRF85 model (updated to 1988) to produce an analytic expression linking geographic coordinates, including altitude, to magnetic coordinates. The authors derived spherical‑harmonic expansions of the coordinate transformation, showing that the coefficients vary smoothly with altitude, enabling simple interpolation between 0 and ~600 km, and identified a seasonal magnetic‑local‑time shift of about one hour that should be considered in applications.

Abstract

Studying magnetically conjugate phenomena at very high latitudes requires a magnetic coordinate system that is smooth and well defined at the geographic poles. In addition, it should provide for accurate comparisons at different altitudes. In this report we present a variation on the corrected geomagnetic coordinate system that is well defined and smooth over the entire globe. It provides an analytic expression relating geographic coordinates, including altitude, to the magnetic coordinates. The coordinate system is produced by tracing magnetic field lines using the IGRF85 reference magnetic field model with time derivatives updating the model to 1988. An expansion of the relationship in terms of spherical harmonics has been determined, which then provides the required well‐defined and smooth relationship over the entire globe. Independent expansions for different altitudes show a smooth functional relationship of the coefficients of the expansion with altitude, and therefore simple interpolation schemes can be used to provide an appropriate expansion at any altitude between 0 km and approximately 600 km. By reversing the process, the inverse expansions relating the magnetic coordinates to geographic coordinates have also been determined. The effects of the seasonal variation in the Sun's declination along with the variation in the Sun's apparent position due to the eccentricity of the Earth's orbit result in a variation of nearly 1 hour of magnetic local time for a fixed UT over the course of a year. In many applications this variation may be important and should be included when presenting data in terms of magnetic latitude and MLT.