Interpolating geomagnetic observations: Techniques and comparisons

Five geomagnetic vector interpolation techniques are reviewed and compared by analyzing their performance when applied to realistic inputs simulated by a state-of-the-art geospace general circulation model. The availability of synthetic “ground truth” allows meaningful estimates of relative interpolation error as a two-dimensional function of separation between geographically sparse input coordinates. Three of these techniques - nearest neighbor, triangular barycentric, and Gaussian Process regression - are entirely based on the input data, and do not benefit from any knowledge of physics that might improve predictions in unsampled regions. Two of the techniques - spherical cap harmonic analysis and spherical elementary current system inversion - incorporate simple physical understanding into their basis functions and generally provide better predictions even when far removed from input measurements. Spherical elementary currents generate fewer interpolation artefacts in the spatial domain.