Liquid water potential temperature
From AMS Glossary
liquid water potential temperature
A quantity that is conserved in reversible adiabatic motion.
In the simplest approximation it is given by θL, where
with θ the potential temperature, Lv the latent heat of vaporization, cpd the specific heat of dry air at constant pressure, and rl the liquid water mixing ratio. A more accurate expression is
in which χ is the Poisson constant, ε the ratio of the gas constants of dry air and water vapor (0.622), rv the mixing ratio of water vapor, cpv the specific heat of water vapor, T the temperature and γ = rtRv/(cpd + rtcpv), where rt is the total water mixing ratio and Rv 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.
Deardorff, J., and K. A. Emanuel 1994. Atmospheric Convection. Oxford Univ. Press, . 580 pp.