An improved model of ionospheric electric potentials/convection patterns is presented here. This model will produce potentials for any desired level of interplanetary magnetic field (IMF), solar wind velocity, number density, and dipole tilt angle, as well as an optional value for the AL index. The following improvements have been made: (1) Terms for solar wind electric field and dynamics pressure have been added. (2) Nonlinear changes in the potentials as the magnitude of the IMF increases, owing to the decreasing effective width of the solar wind coupling region, are now allowed. (3) The lower boundary of the potential patterns is now variable according to the conditions, rather than fixed at an arbitrary location, resulting in fewer coefficients in the spherical harmonic expansion and smoother patterns. (4) The influence of magnetospheric substorms, or nightside processes, on the potential patterns is now included as a perturbation using the AL index as an optional controlling parameter. The utility of the new substorm component is demonstrated with the event on November 24, 1996, which had been chosen for the Geospace Environment Modeling (GEM) Substorm Challenge. By an examination of the potential patterns over the International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometer chain, it is shown that the IMF alone is not sufficient to predict the electric potential patterns when there are substorms present, demonstrating the influence of the substorm unloading component. This model can reproduce the very complex changes that occur in the potential patterns as the IMF orientation rotates in the GSM Y-Z plane, and it is useful for scientific studies as input for other models or validation of computer simulation results. There is also a practical application of predicting space weather in the magnetosphere, on the basis of upstream solar wind/IMF measurements. The later application will become more effective when accurate methods become available for predicting the AL indices. ¿ 2001 American Geophysical Union