Mathematical expressions have been constructed that allow the large-scale global convection characteristics of the high-latitude ionosphere to be reproduced. The model contains no discontinuities in the ion convection velocity and as such should be useful in F region chemical models. The number of variables in the model allow such features as the dayside throat and the Harang discontinuity to be modeled. The applicability of the model to magnetospheric physics is limited by the exclusion of large-magnitude small-scale flow features associated with discrete arcs and by the inability of the model to produce separate flow cells at the same local time.