  A framework is introduced to compare moist `potential' temperatures. The
equivalent potential temperature, $\theta_e,$ the liquid water potential
temperature, $\theta_\ell,$ and the entropy potential temperature, $\theta_s$,
are all shown to be potential temperatures, in the sense that they measure the
temperatures of certain reference state systems whose entropy is the same as
that of the air-parcel. They only differ in the choice of reference state
composition: $\theta_\ell$ describes the temperature a condensate-free state,
$\theta_e$ a vapor-free state, and $\theta_s$ a water-free state would require
to have the same entropy as the given state. Although in this sense $\theta_e,$
$\theta_\ell,$ and $\theta_s$ are all different flavors of the same thing, only
$\theta_\ell$ satisfies the stricter definition of a `potential temperature',
as corresponding to a reference temperature accessible by an isentropic and
closed transformation of a system in equilibrium; both $\theta_e$ and
$\theta_\ell$ measure the `relative' enthalpy of an air parcel at their
respective reference states; but only $\theta_s$ measures air-parcel entropy.
None mix linearly, but all do so approximately, and all reduce to the dry
potential temperature, $\theta$ in the limit as the water mass fraction goes to
zero. As is well known, $\theta$ does mix linearly and inherits all the
favorable (entropic, enthalpic, and potential temperature) properties of its
various -- but descriptively less rich -- moist counterparts. All, involve
quite complex expressions, but admit relatively simple and useful
approximations. Of the three moist `potential' temperatures, $\theta_s$ is the
least familiar, but the most well mixed in the broader tropics, a property that
merits further study as a possible basis for constraining mixing processes.
