  Many scientists use coronal hole (CH) detections to infer open magnetic flux.
Detection techniques differ in the areas that they assign as open, and may
obtain different values for the open magnetic flux. We characterize the
uncertainties of these methods, by applying six different detection methods to
deduce the area and open flux of a near-disk center CH observed on 9/19/2010,
and applying a single method to five different EUV filtergrams for this CH.
Open flux was calculated using five different magnetic maps. The standard
deviation (interpreted as the uncertainty) in the open flux estimate for this
CH was about 26%. However, including the variability of different magnetic data
sources, this uncertainty almost doubles to 45%. We use two of the methods to
characterize the area and open flux for all CHs in this time period. We find
that the open flux is greatly underestimated compared to values inferred from
in-situ measurements (by 2.2-4 times). We also test our detection techniques on
simulated emission images from a thermodynamic MHD model of the solar corona.
We find that the methods overestimate the area and open flux in the simulated
CH, but the average error in the flux is only about 7%. The full-Sun detections
on the simulated corona underestimate the model open flux, but by factors well
below what is needed to account for the missing flux in the observations.
Under-detection of open flux in coronal holes likely contributes to the
recognized deficit in solar open flux, but is unlikely to resolve it.
