During a southward orientation of the interplanetary magnetic field (IMF), patches are often observed moving antisunward across the polar cap. In saying “patches” we refer to structures in which the F region electron densities are enhanced relative to lower background levels; we do not in this paper consider patches which are observed optically (see J. J. Sojka et al., Ambiguity in identificiation of polar cap F region patches, submitted to the Journal of Atmospheric and Terrestrial Physics, 1995). The patches can be modeled by a process which involves the “chopping up” of the tongue of ionization (TOI) [Sojka et al., 1993a]. Various mechanisms for chopping the TOI have been suggested; our preferred method is to introduce temporal changes in the convection electric field pattern. In any case the present study is quite independent of any particular mechanism, so long as the TOI is considered to be the source of the patches. In this study we have used the Utah State University Time-Dependent Ionospheric Model (TDIM) to model the TOI for various IMF By orientations. In our simulations the location of the TOI in the polar cap is mainly determined by the IMF By component, and hence the patch locations are also expected to be By dependent. This suggests that a polar ground-based instrument may not see patches even when they are present in the polar ionosphere. This is because the typical field of view of a ground-based instrument, such as an all-sky camera, covers less than 10% of the polar region. The TDIM simulation results were used to predict the By dependence of patches that different ground-based sites would observe. Eureka (Canada) at the magnetic pole is predicted not to observe patches for southward IMF conditions if the By component is strongly negative. Sondrestrom (Greenland) and NyAlesund (Svalbard), although at similar cusp latitudes, are expected to see quite different diurnal responses to patches. At Sondrestrom, patches are seen at noon in winter; both sites should see them in the premidnight sector. These model predictions are the “groundwork” for detailed patch observation-model comparisons at all three sites.