Scale height

From Glossary of Meteorology

scale height

The height within which some parameter, such as pressure or density, decreases by a factor 1/e in an isothermal atmosphere.

The term is most often used in an ionospheric context, but is equally applicable to the neutral atmosphere. It is a measure of the effective "thickness" of an atmospheric layer and is expressed mathematically as
where T, m, and g are, respectively, the absolute temperature, the molecular mass, and the acceleration due to gravity; R* is the universal gas constant; and k is Boltzmann's constant.