  The surface flux transport (SFT) model of solar magnetic fields involves
empirically well-constrained velocity and magnetic fields. The basic evolution
of the Sun's large-scale surface magnetic field is well described by this
model. The azimuthally averaged evolution of the SFT model can be compared to
the surface evolution of the flux transport dynamo (FTD), and the evolution of
the SFT model can be used to constrain several near-surface properties of the
FTD model.
  We compared the results of the FTD model with different upper boundary
conditions and diffusivity profiles against the results of the SFT model. Among
the ingredients of the FTD model, downward pumping of magnetic flux, related to
a positive diffusivity gradient, has a significant effect in slowing down the
diffusive radial transport of magnetic flux through the solar surface. Provided
the pumping was strong enough to give rise to a downflow of a magnetic Reynolds
number of 5 in the near-surface boundary layer, the FTD using a vertical
boundary condition matches the SFT model based on the average velocities above
the boundary layer. The FTD model with a potential field were unable to match
the SFT results.
