  Over the solar-activity cycle, there are extended periods where significant
discrepancies occur between the spacecraft-observed total (unsigned) open
magnetic flux and that determined from coronal models. In this article, the
total open heliospheric magnetic flux is computed using two different methods
and then compared with results obtained from in-situ interplanetary
magnetic-field observations. The first method uses two different types of
photospheric magnetic-field maps as input to the Wang Sheeley Arge (WSA) model:
i) traditional Carrington or diachronic maps, and ii) Air Force Data
Assimilative Photospheric Flux Transport model synchronic maps. The second
method uses observationally derived helium and extreme-ultraviolet coronal-hole
maps overlaid on the same magnetic-field maps in order to compute total open
magnetic flux. The diachronic and synchronic maps are both constructed using
magnetograms from the same source, namely the National Solar Observatory Kitt
Peak Vacuum Telescope and Vector Spectromagnetograph. The results of this work
show that the total open flux obtained from observationally derived coronal
holes agrees remarkably well with that derived from WSA, especially near solar
minimum. This suggests that, on average, coronal models capture well the
observed large-scale coronal-hole structure over most of the solar cycle. Both
methods show considerable deviations from total open flux deduced from
spacecraft data, especially near solar maximum, pointing to something other
than poorly determined coronal-hole area specification as the source of these
discrepancies.
