Ionospheric currents are driven by several different physical processes and exhibit complex spatial and temporal structure. Magnetic field measurements of ionospheric sources are often spatially sparse, causing significant challenges in visualizing current flow at a specific time. Standard methods of fitting equivalent current models to magnetic observations, such as line currents, spherical harmonic analysis, spherical cap harmonic analysis, and spherical elementary current systems (SECS), are often unable to capture the full spatial complexity of the currents or require a large number of parameters which cannot be fully determined by the available data coverage. These methods rely on a set of generic basis functions which contain limited information about the geometries of the various ionospheric sources. In this study, we develop new basis functions for fitting ground and satellite measurements, which are derived from physics-based ionospheric modeling combined with principal component analysis (PCA). The physics-based modeling provides realistic current flow patterns for all of the primary ionospheric sources, including their daily and seasonal variability. The PCA technique extracts the most relevant spatial geometries of the currents from the model run into a small set of equivalent current modes. We fit these modes to magnetic measurements of the Swarm satellite mission at low and middle latitudes and compare the resulting model with independent measurements and with the SECS approach. We find that our PCA method accurately reproduces features of the equatorial electrojet and Sq current systems with only 10 modes and can predict ionospheric fields far from the data region.
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