A method has been developed to derive the electric potentials in the high-latitude ionosphere resulting from any arbitrary combination of the interplanetary magnetic field (IMF) magnitude and orientation, solar wind velocity, and dipole tilt angle. This model is based on spherical harmonic coefficients that were derived by a least error fit of measurements from multiple satellite passes. These harmonic coefficients have been found to have systematic variations that can be reproduced by a combination of a Fourier series and a multiple linear regression formula. Examples of the model output are shown. In principal, this technique could be used as a fundamental building block to forecast geomagnetic disturbances, or “space weather”, from satellite measurements in the upstream solar wind.