Liquid water potential temperature

From Glossary of Meteorology

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, Lυ is the latent heat of vaporization, cpd is the specific heat of dry air at constant pressure, and rl 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), rυ is the mixing ratio of water vapor, c is the specific heat of water vapor, T is the temperature, and γ = rtRυ/(cpd + rtc), where rt is the total water mixing ratio and Rυ 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.