Virtual Temperature

     A fictitious temperature that dry air would need to attain in order to have the same density as the moist air at the same pressure is considered virtual temperature. The fact that moist air is less dense than dry air was first clearly stated by Sir Isaac Newton in his “Opticks.” However, the basis for this relationship was not generally understood until the latter half of the 18^th century.

At any rate, due to that fact, and at the same temperature and pressure, the virtual temperature is always greater than the actual temperature. The use of virtual temp allows us to use the gas constant for dry air, R_d, saving us from constantly having to calculate gas constants for moist air—the value of which would vary with water vapor content.

            However, virtual temperature correction is usually neglected except in certain calculations relating to the boundary layer. Nonetheless, in moving from a given pressure surface to another pressure surface located above or below it, the geopotential height (used as the vertical coordinate in most atmospheric applications in which energy plays a role—i.e. large scale motions) is related geometrically to the thickness of the intervening layer which, in turn, is directly proportional to the mean virtual temperature of the layer. The mean virtual temperature is used for determining the thickness of a layer between two pressure surfaces (p₁ and p₂).

where e is vapor pressure, p is pressure, and ε is approximately equal to 0.622.