# 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 θ with θ the potential temperature, in which χ is the Poisson constant, ε the ratio of the gas constants of dry air and water vapor (0.622),

_{L}, where*L*_{v}the latent heat of vaporization,*c*_{pd}the specific heat of dry air at constant pressure, and*r*_{l}the liquid water mixing ratio. A more accurate expression is*r*_{v}the mixing ratio of water vapor,*c*_{pv}the specific heat of water vapor,*T*the temperature and γ =*r*_{t}*R*_{v}/(*c*_{pd}+*r*_{t}*c*_{pv}), where*r*_{t}is the total water mixing ratio and*R*_{v}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.