An Empirical Orthogonal Function Reanalysis of the Northern Polar External and Induced Magnetic Field During Solar Cycle 23

We apply the method of data-interpolating empirical orthogonal functions (EOFs) to ground-based magnetic vector data from the SuperMAG archive to produce a series of month length reanalyses of the surface external and induced magnetic field (SEIMF) in 110,000 km$^{2}$ equal-area bins over the entire northern polar region at 5 min cadence over solar cycle 23, from 1997.0 to 2009.0. Each EOF reanalysis also decomposes the measured SEIMF variation into a hierarchy of spatiotemporal patterns which are ordered by their contribution to the monthly magnetic field variance. We find that the leading EOF patterns can each be (subjectively) interpreted as well-known SEIMF systems or their equivalent current systems. The relationship of the equivalent currents to the true current flow is not investigated. We track the leading SEIMF or equivalent current systems of similar type by intermonthly spatial correlation and apply graph theory to (objectively) group their appearance and relative importance throughout a solar cycle, revealing seasonal and solar cycle variation. In this way, we identify the spatiotemporal patterns that maximally contribute to SEIMF variability over a solar cycle. We propose this combination of EOF and graph theory as a powerful method for objectively defining and investigating the structure and variability of the SEIMF or their equivalent ionospheric currents for use in both geomagnetism and space weather applications. It is demonstrated here on solar cycle 23 but is extendable to any epoch with sufficient data coverage.