# Liquid water potential temperature

From AMS Glossary

## 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*_{t}*R*_{υ}/(*c*_{pd}+*r*_{t}*c*_{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.

Emanuel, K. A., 1994:

*Quart. J. Roy. Met. Soc.*,**99**, 178–196Emanuel, K. A., 1994:

*Atmospheric Convection*. Oxford Univ. Press, 580 pp.*Term edited 19 February 2019.*