Mathematical representation of the auroral oval

Abstract

A curve fitting procedure for mathematically representing the auroral oval is described. It is shown that the Feldstein ovals and quiet auroral ovals of the night side in DMSP photographs can be approximated by an offset circle, plus a small (≲ 1° magnitude) Fourier component in corrected geomagnetic coordinates. Parameters are introduced, Θ and (θo, ϕo), that indicate the dynamic motion of the auroral oval size and center location, respectively. Using the parameter Θ, an analysis of several DMSP photographs shows a strong correlation between the southward interplanetary magnetic field (−Bz) and the size of the auroral oval.

Enhanced E-layer ionization in the auroral zones observed by radio occultation measurements onboard CHAMP and Formosat-3/COSMIC

“…It is interesting to note that one focal point fits very well to the geographic pole. After transforming the ellipse into magnetic coordinates, we find that it matches the local magnetic night-time southward boundary given by the Feldstein representation of the auroral oval at midnight magnetic local time and at middle activity level 3, Feldstein et al (2008), Feldstein (1963 and Holzworth and Meng (1975). For a discussion of different auroral (boundary) models we refer to Szuszczewicz et al (1993).…”

“…Instead of using geomagnetic coordinates, we approximate the distribution of profiles first by a circle and next by an ellipse using a non-linear fit to the geographic profile positions. For comparison, an auroral oval model using a fourier series in geomagnetic coordinates is discussed in Feldstein (1963) and Holzworth and Meng (1975). We have fitted the (3-D Cartesian) positions x i of all selected ELDI profiles on the Northern Hemisphere with all local times to a circle, parameterized by its offset p from the geographical north pole and its radius r by minimizing the cost function…”

Sensing global Birkeland currents with iridium® engineering magnetometer data

“…We then define a coordinate system centered on the statistically averaged auroral zone center, displaced 3.1 ø toward midnight [Holzworth and Meng, 1975]. In this auroral centered system we divide longitude into 16, 30 ø wide sectors with centers spaced 15% giving a resolution of---2 hours.…”

N2O production by high energy auroral electron precipitation

“…where q e and q p are the equatorial and polar corrected geomagnetic latitude limits of the auroral oval, respectively, from the Holzworth and Meng [1975] scheme. The map from geographic longitude (f) and latitude (q) on the model grid to corrected geomagnetic latitude (q g (f, q)) was calculated offline.…”

“…The auroral oval is a modified version of the scheme from Holzworth and Meng [1975] based on the formulation of Feldstein [1963]. The modification for the horizontal distribution, H, was as follows:…”