  In this paper we address a discrepancy between the surface flux evolution in
a 3D kinematic dynamo model and a 2D surface flux transport model that has been
closely calibrated to the real Sun. We demonstrate that the difference is due
to the connectivity of active regions to the toroidal field at the base of the
convection zone, which is not accounted for in the surface-only model.
Initially, we consider the decay of a single active region, firstly in a
simplified Cartesian 2D model and subsequently the full 3D model. By varying
the turbulent diffusivity profile in the convection zone, we find that
increasing the diffusivity - so that active regions are more rapidly
disconnected from the base of the convection zone - improves the evolution of
the surface field. However, if we simulate a full solar cycle, we find that the
dynamo is unable to sustain itself under such an enhanced diffusivity. This
suggests that in order to accurately model the solar cycle, we must find an
alternative way to disconnect emerging active regions, whilst conserving
magnetic flux.
