  The choice of free parameters in surface flux transport (SFT) models
describing the evolution of the large-scale poloidal magnetic field of the Sun
is critical for the correct reproduction of the polar magnetic flux built up
during a solar cycle, which in turn is known to be a good predictor of the
amplitude of the upcoming cycle. For an informed choice of parameters it is
important to understand the effect and interplay of the various parameters and
to optimize the models for the polar magnetic field. Here we present the
results of a large-scale systematic study of the parameter space in an SFT
model where the source term representing the net effect of tilted flux
emergence was chosen to represent a typical, average solar cycle as described
by observations. Comparing the results with observational constraints on the
spatiotemporal variation of the polar magnetic field, as seen in magnetograms
for the last four solar cycles, we mark allowed and excluded regions in the 3D
parameter space defined by the flow amplitude u0, the magnetic diffusivity eta
and the decay time scale tau, for three different assumed meridional flow
profiles. Without a significant decay term in the SFT equation (i.e., for tau
>10 yr) the global dipole moment reverses too late in the cycle for all flow
profiles and parameters, providing independent supporting evidence for the need
of a decay term, even in the case of identical cycles. An allowed domain is
found to exist for tau values in the 5-10 yr range for all flow profiles
considered. Generally higher values of eta (500-800 km^2/s) are preferred
though some solutions with lower eta are still allowed.
