) of a moist air parcel is the temperature at which a theoretical dry air parcel would have a total pressure and density equal to the moist parcel of air.
[1] The virtual temperature of unsaturated moist air is always greater than the absolute air temperature, however, as the existence of suspended cloud droplets reduces the virtual temperature.
[2] It has been described to increase Earth's thermal emission by warming the tropical atmosphere.
[3][4] In atmospheric thermodynamic processes, it is often useful to assume air parcels behave approximately adiabatically, and approximately ideally.
is the apparent molar mass of gas
The apparent molar mass of a theoretical moist parcel in Earth's atmosphere can be defined in components of water vapor and dry air as with
representing the molar masses of water vapor and dry air respectively.
is described by Dalton's law of partial pressures: Rather than carry out these calculations, it is convenient to scale another quantity within the ideal gas law to equate the pressure and density of a dry parcel to a moist parcel.
The only variable quantity of the ideal gas law independent of density and pressure is temperature.
This scaled quantity is known as virtual temperature, and it allows for the use of the dry-air equation of state for moist air.
Thus, analytically, a higher vapor pressure would yield a lower density, which should yield a higher virtual temperature in turn.
Consider a moist air parcel containing masses
of dry air and water vapor in a given volume
Rearranging the standard ideal gas equation with these variables gives Solving for the densities in each equation and combining with the law of partial pressures yields Then, solving for
is approximately 0.622 in Earth's atmosphere: where the virtual temperature
is We now have a non-linear scalar for temperature dependent purely on the unitless value
, allowing for varying amounts of water vapor in an air parcel.
in units of kelvin can be used seamlessly in any thermodynamic equation necessitating it.
Often the more easily accessible atmospheric parameter is the mixing ratio
Through expansion upon the definition of vapor pressure in the law of partial pressures as presented above and the definition of mixing ratio: which allows Algebraic expansion of that equation, ignoring higher orders of
due to its typical order in Earth's atmosphere of
with its constant value yields the linear approximation
in degrees Celsius and mixing ratio
, then we can write mixing ratio in terms of the specific humidity as
Virtual potential temperature is useful as a surrogate for density in buoyancy calculations and in turbulence transport which includes vertical air movement.
A moist air parcel may also contain liquid droplets and ice crystals in addition to water vapor.
can be defined as the sum of the mixing ratios of water vapor
can be defined, representing the temperature at which a theoretical dry air parcel would have the a pressure and density equal to a moist parcel of air while accounting for condensates:[8]: 113 Virtual temperature is used in adjusting CAPE soundings for assessing available convective potential energy from skew-T log-P diagrams.
The errors associated with ignoring virtual temperature correction for smaller CAPE values can be quite significant.
[9] Thus, in the early stages of convective storm formation, a virtual temperature correction is significant in identifying the potential intensity in tropical cyclogenesis.