  The aim of this note is to derive the mixed-phase version of the moist-air
entropy potential temperature $\theta_s$ derived in Marquet (2011).
  This mixed-phase version is suitable to describe parcels where liquid water
and ice are allowed to coexist, with possible under- or super-saturations, with
possible supercooled water and with possible different temperatures for dry air
and water vapour, on the one hand, condensed water and ice, on the other hand.
  The impact of this new mixed-phase version for $\theta_s$ are evaluated by
using high latitudes, SHEBA/FIRE-ACE vertical profiles depicted in Figure 7 of
Morisson et al. (2011).
