Empirical Orthogonal Functions Used in Decadal-Scale Magnetic Field Reanalysis
Shore, Robert¹; Whaler, Kathryn¹; Macmillan, Susan²; Beggan, Ciaran²; Olsen, Nils^3
1The University of Edinburgh, UNITED KINGDOM; ²British Geological Survey, UNITED KINGDOM; ³DTU Space, Technical University of Denmark, DENMARK

The Earth's external magnetic field is highly time-variant, rapidly changing in intensity on the scale of minutes, especially in the auroral regions. Variations of the longer period external magnetic field (e.g. over months to years) induce electric currents in the Earth's conducting mantle, which in turn induce magnetic fields that contribute to magnetic field measurements made at and above the Earth's surface. The annual and semi-annual period fields originating from magnetospheric and ionospheric currents required to estimate mantle conductivity in the depth range 1,200 to 2,000 km are subject to large uncertainty since they overlap with the periods on which the core field also changes significantly. Currently, the spatial structure of the long-period external field is poorly resolved and is commonly assumed to be the P₁⁰ solenoidal field term associated with the symmetric magnetospheric ring current.

The Swarm satellite constellation, due for launch in 2013, will provide new measurements of the Earth's magnetic field of unparalleled precision. Induction studies to estimate the distribution of mantle conductivity are a key goal of the scientific mission of the constellation, so it is important that the spatial geometry of the long-period inducing fields be properly resolved.

We use a dataset, developed for the Swarm mission, of ground-based magnetic observatory hourly means in combination with a method called Empirical Orthogonal Functions (EOFs) in order to decompose the external magnetic field over a full 11-year solar cycle. EOFs can be used to infer patterns of maximum variance in a dataset, allowing us to assess the spatial and magnitude changes of dominant spatio-temporal patterns in the external magnetic field. Specifically, our focus is on isolating the spatial pattern associated with the long-period external field oscillations. To avoid Earth rotation causing travelling waves in our spatio-temporal analysis, 24 separate EOF analyses are performed for the study period, each using one different UT hourly mean from each observatory per day. The 24 analyses are then combined to produce maps of external field variations in a coordinate frame of colatitude and local time.

We find that the annual periodicity of the external magnetic fields is dominated by a P₂⁰ term with additional spatial amplitude peaks at local noon, and between local dusk and midnight. The annual temporal amplitude oscillation of this pattern modulates with a period of the length of the solar cycle. The dominant pattern on shorter periods is a P₁⁰ term, which also has a temporal amplitude modulation according to the solar cycle. The long-period modulations of the patterns of each of the P₂⁰ and P₁⁰ oscillations have roughly equal magnitudes. In summary, we show that the seasonal variation of the external field is an important factor in the long-period inducing source, and that dawn-dusk asymmetry should be accounted for to increase the accuracy of mantle conductivity estimates.

In induction studies which use satellite data, the ionosphere contributes to magnetic fields from sources inside the satellite orbit, and cannot be used simply as an inducing source external to the measurement sphere. We are not able to specify uniquely which source regions contribute to the P₂⁰ pattern, but a combination of ionospheric and magnetospheric terms is likely. Nevertheless, the results of this study, obtained at ground level, should be useful in fulfilling the planned mantle induction objectives of the Swarm mission.