An accurate description of the state of the ionosphere is crucial for understanding the physics of Earth's coupling to space, including many potentially hazardous space weather phenomena. To support this effort, ground networks of magnetometer stations, optical instruments, and radars have been deployed. However, the spatial coverage of such networks is naturally restricted by the distribution of land mass and access to necessary infrastructure. We present a new technique for local mapping of polar ionospheric electrodynamics, for use in regions with high data density, such as Fennoscandia and North America. The technique is based on spherical elementary current systems (SECS), which were originally developed to map ionospheric currents. We expand their use by linking magnetic field perturbations in space and on ground, convection measurements from space and ground, and conductance measurements, via the ionospheric Ohm's law. The result is a technique that is similar to the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) technique, but tailored for regional analyses of arbitrary spatial extent and resolution. We demonstrate our technique on synthetic data, and with real data from three different regions. We also discuss limitations of the technique and potential areas for improvement.