Estimating external magnetic field differences at high geomagnetic latitudes from a single station

Providing an accurate estimate of the magnetic field on the Earth's surface at a location distant from an observatory has useful scientific and commercial applications, such as in repeat station data reduction, space weather nowcasting or aeromagnetic surveying. While the correlation of measurements between nearby magnetic observatories at low and mid-latitudes is good, at high geomagnetic latitudes (58deg < |\theta_{gm}| < 75deg $) the external field differences between observatories increase rapidly with distance, even during relatively low magnetic activity. Thus, it is of interest to describe how the differences (or errors) in external magnetic field extrapolation from a single observatory grow with distance from its location. These differences are modulated by local time, seasonal and solar cycle variations, as well as geomagnetic activity, giving a complex temporal and spatial relationship. A straightforward way to describe the differences are via confidence intervals (CI) for the extrapolated values with respect to distance. To compute the CI associated with extrapolation of the external field at varying distances from an observatory, we used 695 station-years of overlapping minute-mean data from 37 observatories and variometers at high latitudes from which we removed the main and crustal fields to isolate unmodelled signals. From this dataset, the pairwise differences were analyzed to quantify the variation during a range of time epochs and separation distances. We estimate the 68.3%, 95.4% and 99.7% confidence levels (equivalent to the 1sigma, 2sigma and 3sigma bounds) from these differences for all components. We find that there is always a small non-zero bias, which we ascribe to instrumentation and local crustal field induction effects. The computed CI are typically twice as large in the north-south direction compared to the east-west direction and smaller during the solstice months compared to the equinoxes.