Virtual potential temperature

From Glossary of Meteorology

virtual potential temperature

The theoretical potential temperature of dry air that would have the same density as moist air.

It is used as a convenient surrogate for density in buoyancy calculations. The virtual potential temperature θv is defined by
where θ is the actual potential temperature, r is the mixing ratio of water vapor, and rL is the mixing ratio of liquid water in the air. Temperatures must be in units of Kelvin, and mixing ratios in units of gwater/gdry air. Because water vapor is less dense than dry air, humid air has a warmer θv than dry air. Liquid water droplets, if falling at their terminal velocity in air, make the air heavier and are associated with colder θv. For saturated or cloudy air, use saturation mixing ratio in place of r, while for unsaturated air, use rL = 0.
See virtual temperature.

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