  The efforts for comparing dust polarization measurements with synthetic
observations from MHD models have previously concentrated on the scale of
molecular clouds. Here we extend the model comparisons to kiloparsec scales,
taking into account hot shocked gas generated by supernovae, and a non-uniform
dynamo-generated magnetic field at both large and small scales down to 4 pc
spatial resolution. Radiative transfer calculations are used to model dust
emission and polarization on the top of MHD simulations. We compute synthetic
maps of column density $N_H$, polarization fraction $p$, and polarization angle
dispersion $S$, and study their dependencies on the important properties of the
MHD simulations. These include the large-scale magnetic field and its
orientation, the small-scale magnetic field, and supernova-driven shocks.
Similar filament-like structures of $S$ as seen in the Planck all-sky maps are
visible in our synthetic results, although the smallest scale structures are
absent from our maps. Supernova-driven shock fronts and $S$ do not show
significant correlation. Instead, $S$ can clearly be attributed to the
distribution of the small-scale magnetic field. We also find that the
large-scale magnetic field influences the polarization properties, such that,
for a given strength of magnetic fluctuation, a strong plane-of-the-sky mean
field weakens the observed $S$, while strengthening $p$. The anticorrelation of
$p$ and $S$, and decreasing $p$ as a function of $N_H$ are consistent across
all synthetic observations. The magnetic fluctuations follow an exponential
distribution, rather than Gaussian, characteristic of flows with intermittent
repetitive shocks. The observed polarization properties and column densities
are sensitive to the line of sight distance over which the emission is
integrated.
