  Coronal holes (CHs) are regions with unbalanced magnetic flux, and have been
associated with open magnetic field (OMF) structures. However, it has been
reported that some CHs do not intersect with OMF regions. To investigate the
inconsistency, we apply a potential-field (PF) model to construct the magnetic
fields of the coronal holes. As a comparison, we also use a thermodynamic
magnetohydrodynamic (MHD) model to synthesize coronal images, and identify CHs
from the synthetic images. The results from both the potential-field CHs and
synthetic MHD CHs reveal that there is a significant percentage of closed field
lines extending beyond the CH boundaries and more than 50% (17%) of PF (MHD)
CHs do not contain OMF lines. The boundary-crossing field lines are more likely
to be found in the lower latitudes during active times. While they tend to be
located slightly closer than the non-boundary-crossing ones to the CH
boundaries, nearly 40% (20%) of them in PF (MHD) CHs are not located in the
boundary regions. The CHs without open field lines are often smaller and less
unipolar than those with open field lines. The MHD model indicates higher
temperature variations along the boundary-crossing field lines than the
non-boundary crossing ones. The main difference between the results of the two
models is that the dominant field lines in the PF and MHD CHs are closed and
open field lines, respectively.
