  A moist entropy potential temperature -- denoted by ${\theta}_{s}$ -- is
defined analytically in terms of the specific entropy for moist air. The
expression for ${\theta}_{s}$ is valid for a general mixing of dry air, water
vapour and possible condensed water species. It verifies the same conservative
properties as the moist entropy, even for varying dry air or total water
content. The moist formulation for ${\theta}_{s}$ is equal to the dry
formulation $\theta$ if dry air is considered and it verifies new properties
valid for the moist air cases, both saturated or under-saturated ones. Exact
and approximate versions of ${\theta}_{s}$ are evaluated for several
Stratocumulus cases, in particular by using the aircraft observations FIRE-I
experiment data sets. It appears that there is no (or small) jump in
${\theta}_{s}$ at the top of the PBL. The mixing in moist entropy is almost
complete in the PBL, with the same values observed in the clear air and the
cloudy regions, including the very top of the entrainment region. The
Randall-Deardorff CTEI analysis may be interpreted as a mixing in moist entropy
criterion. The iso-${\theta}_{s}$ lines are plotted on skew $T$-$\ln(p)$ and
conserved variable diagrams. All these properties could suggest some hints on
the use of moist entropy (or ${\theta}_{s}$) in cloud modelling or in mixing
processes, with the marine Stratocumulus considered as a paradigm of moist
turbulence.
