Liquid water potential temperature

A quantity that is conserved in reversible adiabatic motion.

This is typically approximated as

where θ is the potential temperature, T is the temperature, L_υ is the latent heat of vaporization, c_pd is the specific heat of dry air at constant pressure, and r_l is the liquid water mixing ratio.
This is sometimes further approximated as

where it is often assumed that θ/T is approximately equal to one (1), for example, for mixing processes in boundary layer clouds.
A more accurate expression is

in which χ is the Poisson constant, ε is the ratio of the gas constants of dry air and water vapor (0.622), r_υ is the mixing ratio of water vapor, c_pυ is the specific heat of water vapor, T is the temperature, and γ = r_tR_υ/(c_pd + r_tc_pυ), where r_t is the total water mixing ratio and R_υ the gas constant for water vapor. Three quantities are conserved in reversible adiabatic motion: equivalent potential temperature, total water mixing ratio, and liquid water potential temperature. Any two of these may be considered independent, with the third deducible from those two.

Betts, A. K., 1973: Non-precipitating cumulus convection and its parameterization. Quart. J. Roy. Met. Soc., 99, 178–196
Emanuel, K. A., 1994: Atmospheric Convection. Oxford Univ. Press, 580 pp.

Term edited 19 February 2019.