  Molecular clouds form from the atomic phase of the interstellar medium.
However, characterizing the transition between the atomic and the molecular
interstellar medium (ISM) is a difficult observational task. Here we address
cloud formation processes by combining HSIA with molecular line data. One
scenario proposed by numerical simulations is that the column density
probability density functions (N-PDF) evolves from a log-normal shape at early
times to a power-law-like shape at later times. In this paper, we study the
cold atomic component of the giant molecular filament GMF38a (d=3.4 kpc,
length$\sim230$ pc). We identify an extended HISA feature, which is partly
correlated with the 13CO emission. The peak velocities of the HISA and 13CO
observations agree well on the eastern side of the filament, whereas a velocity
offset of approximately 4 km s$^{-1}$ is found on the western side. The sonic
Mach number we derive from the linewidth measurements shows that a large
fraction of the HISA, which is ascribed to the cold neutral medium (CNM), is at
subsonic and transonic velocities. The column density of the CNM is on the
order of 10$^{20}$ to 10$^{21}$ cm$^{-2}$. The column density of molecular
hydrogen is an order of magnitude higher. The N-PDFs from HISA (CNM), HI
emission (WNM+CNM), and 13CO (molecular component) are well described by
log-normal functions, which is in agreement with turbulent motions being the
main driver of cloud dynamics. The N-PDF of the molecular component also shows
a power law in the high column-density region, indicating self-gravity. We
suggest that we are witnessing two different evolutionary stages within the
filament. The eastern subregion seems to be forming a molecular cloud out of
the atomic gas, whereas the western subregion already shows high column density
peaks, active star formation and evidence of related feedback processes.
