On Moist Potential Temperatures and Their Ability to Characterize Differences in the Properties of Air Parcels

Abstract

A framework is introduced to compare moist “potential” temperatures. The equivalent potential temperature θe, the liquid water potential temperature θℓ, and the entropy potential temperature θs 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—θℓ describes the temperature a condensate-free state, θe a vapor-free state, and θs a water-free state—required to have the same entropy as the given state. Although in this sense θe, θℓ, and θs are all different flavors of the same thing, only θℓ 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 θe and θℓ measure the “relative” enthalpy of an air parcel at their respective reference states, but only θs measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature θ in the limit as the water mass fraction goes to zero. As is well known, θ 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, θs 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.