A high-resolution model of the external and induced magnetic field at the Earth’s surface in the northern hemisphere

We describe a method of producing high-resolution models of the Earth’s combined external and induced magnetic field (EIMF) using the method of Empirical Orthogonal Functions (EOFs) applied to the SuperMAG archive of ground-based magnetometer data. EOFs partition the variance of a system into independent modes, allowing us to extract the spatiotemporal patterns of greatest dynamical importance without applying the a priori assumptions of other methods (such as spherical harmonic analysis, parameterised averaging, or multi-variate regression). We develop an approach based on that of Beckers and Rixen [2003] and use the EOF modes to infill missing data in a self-consistent manner. Applying our method to a north polar case study spanning February 2001 (chosen for its proximity to solar maximum and good data coverage), we demonstrate that 41.7% and 9.4% of variance is explained by the leading two modes, respectively describing the temporal variations of the Disturbance Polar types 2 and 1 (DP2 and DP1) patterns. A further 14.1% of variance is explained by four modes that describe separate aspects of the motion of the DP1 and DP2 systems. Thus, collectively over 65% of variance is described by the leading 6 modes and is attributable to DP1 and DP2. This attribution is based on inspection of the spatial morphology of the modes, and analysis of the temporal variation of the mode amplitudes with respect to solar wind measures and substorm occurrence. This study is primarily a demonstration of the technique and a prelude to a model spanning the full solar cycle. D R A F T January 13, 2017, 12:30pm D R A F T SHORE ET AL.: EIGENANALYSIS OF EXTERNAL FIELDS X 3