Using a numerical implementation of the cowlock92 model of flow excitation in the magnetosphere-ionosphere (MI) system, we show that both an expanding (on a ~12-min timescale) and a quasi-instantaneous response in ionospheric convection to the onset of magnetopause reconnection can be accommodated by the Cowley-Lockwood conceptual framework. This model has a key feature of time dependence, necessarily considering the history of the coupled MI system. We show that a residual flow, driven by prior magnetopause reconnection, can produce a quasi-instantaneous global ionospheric convection response; perturbations from an equilibrium state may also be present from tail reconnection, which will superpose constructively to give a similar effect. On the other hand, when the MI system is relatively free of pre-existing flow, we can most clearly see the expanding nature of the response. As the open-closed field line boundary will frequently be in motion from such prior reconnection (both at the dayside magnetopause and in the cross-tail current sheet), it is expected that there will usually be some level of combined response to dayside reconnection.