  The Planck survey has quantified polarized Galactic foregrounds and
established that they are a main limiting factor in the quest for the cosmic
microwave background (CMB) B-mode signal induced by primordial gravitational
waves during cosmic inflation. Accurate separation of the Galactic foregrounds
therefore binds this quest to our understanding of the magnetized interstellar
medium (ISM). The two most relevant empirical results from analysis of Planck
data are line of sight depolarization arising from fluctuations of the Galactic
magnetic field orientation and alignment of filamentary dust structures with
the magnetic field at high Galactic latitude. Furthermore, Planck and HI
emission data in combination indicate that most of the filamentary dust
structures are in the cold neutral medium. The goal of this paper is to test
whether these salient observational results, taken together, can account fully
for the statistical properties of the dust polarization over a selected low
column density region comprising 34 % of the southern Galactic cap ($b \le
-30\deg$). To do this, we construct a dust model that incorporates HI column
density maps as tracers of the dust intensity structures and a phenomenological
description of the Galactic magnetic field. By adjusting the parameters of the
dust model, we were able to reproduce the Planck dust observations at 353 GHz
in the selected region. Realistic simulations of the polarized dust emission
enabled by such a dust model are useful for testing the accuracy of component
separation methods, studying non-Gaussianity, and constraining the amount of
decorrelation with frequency.
