  Global magnetic field models use as input synoptic data, which usually show
"aging effects" as the longitudinal 360{\deg} information is not obtained
simultaneously. Especially during times of increased solar activity, the
evolution of the magnetic field may yield large uncertainties. A significant
source of uncertainty is the Sun's magnetic field on the side of the Sun that
is not visible to the observer. Various methods have been used to complete the
picture: synoptic charts, flux-transport models, and far side helioseismology.
In this study, we present a new method to estimate the far-side open flux
within coronal holes using STEREO EUV observations. First, we correlate the
structure of the photospheric magnetic field as observed with the Helioseismic
and Magnetic Imager on board the Solar Dynamics Observatory (HMI/SDO) with
features in the transition region. From the 304A intensity distribution, which
we found to be specific to coronal holes, we derive an empirical estimate for
the open flux. Then we use a large sample of 313 SDO coronal hole observations
to verify this relation. Finally, we perform a cross-instrument calibration
from SDO to STEREO data to enable the estimation of the open flux at solar
longitudes not visible from Earth. We find that the properties of strong,
unipolar magnetic elements in the photosphere, which determine the coronal
hole's open flux, can be approximated by open fields in the transition region.
We find that structures below a threshold of 78% (STEREO) or 94% (SDO) of the
solar disk median intensity as seen in 304A filtergrams are reasonably well
correlated with the mean magnetic flux density of coronal holes (cc = 0.59).
Using the area covered by these structures (A_of) and the area of the coronal
hole (A_ch), we model the open magnetic flux of a coronal hole as |Phi_ch| =
0.25 A_ch exp(0.032 A_of) with an estimated uncertainty of 40 to 60%.
