Virtual potential temperature

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 θ_v is defined by

where θ is the actual potential temperature, r is the mixing ratio of water vapor, and r_L is the mixing ratio of liquid water in the air. Temperatures must be in units of Kelvin, and mixing ratios in units of g_water/g_{dry air}. Because water vapor is less dense than dry air, humid air has a warmer θ_v than dry air. Liquid water droplets, if falling at their terminal velocity in air, make the air heavier and are associated with colder θ_v. For saturated or cloudy air, use saturation mixing ratio in place of r, while for unsaturated air, use r_L = 0.
See virtual temperature.

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