The recent addition of two radars to the existing network of six Super Dual Auroral Radar Network (SuperDARN) HF radars in the Northern Hemisphere has significantly extended the area in the high latitude where measurements of convecting ionospheric plasma are made. We show that the distribution of the electrostatic potential &PHgr; associated with the E¿B drift of ionospheric plasma can be reliably mapped on global scales when velocity measurements provide sufficient coverage. The global convection maps, or the equivalent electrostatic potential maps, are solved using an established technique of fitting velocity data to an expansion of &PHgr; in terms of spherical harmonic functions. When the measurements are extensive, and especially when they span the region between the extrema in the potential distribution, the solution for the global pattern becomes insensitive to the choice of statistical model data used to constrain the fitting. That is, the statistical model data then only guide the solution in regions where no measurements are available, and the details of the model data have little effect on the gross features of the large-scale convection patterns. The resulting total potential variation across the polar cap, &PHgr;PC, is virtually independent of the statistical model. The ability to accurately determine &PHgr;PC and the global potential &PHgr; on the basis of direct measurements is an important step in understanding solar wind-magnetosphere-ionosphere coupling. ¿ 2000 American Geophysical Union