In this paper we describe a quantitative model of a magnetically interconnected (open) magnetosphere, developed as a perturbation to Voigt's closed magnetosphere model with a given magnetopause shape. The ''interconnection'' (perturbation) field is obtained as a solution to a Neumann boundary value problem, with the magnetopause normal component distribution as a boundary condition. The normal component at the magnetopause is required to be time independent and is specified in accordance with one of two hypotheses: the subsolar point merging hypothesis and Crooker's antiparallel merging hypothesis. The resulting open magnetospheric configuration is used to map the magnetopause electric field down to the polar cap ionosphere. We present ionospheric convection patterns derived from three representative interplanetary magnetic field (IMF) orientations for each of the two dayside merging geometries. Both merging geometries reproduce the observed convergence of convection streamlines near noon in a convection ''throat,'' and the east-west deflection of these streamlines in response to the east-west IMF component. The major difference between the two dayside merging geometries occurs for nonsouthward IMF, and consists of a Sun-aligned convection gap that bifurcates the polar cap in the case of the antiparallel merging geometry but not in the subsolar point merging geometry. This convection gap may plausibly be associated with the ''theta aurora'' structure observed when the IMF has a northward component. ¿ American Geophysical Union 1989