Geomagnetic disturbance, or perturbations in ground-level magnetic field vectors relative to the quasi-static terrestrial main field, induces geoelectric fields at and below Earth’s surface. This leads to geomagnetically induced currents in high-voltage electric power systems that can interfere with their operations. The sparse geospatial distribution of reliable real time ground magnetometers is not presently adequate for accurate geoelectric field estimation using traditional interpolation techniques, or even more sophisticated inverse models (for example, a spherical elementary current system) alone. To address this shortcoming, we first generate multivariate statistics on a regular grid using state-of-the-art global magneto-hydrodynamics (MHD) simulations. These synthetic data strongly resemble real observations in a statistical sense, although they do not generally reproduce the detailed time evolution of observations due to poorly known MHD boundary conditions. However, these statistics can and are used to regress on sparse observations in order to fill in, or “impute”, the unobserved points on a regular grid over North America.