Simple and Accurate Potential Temperature-Altitude Relationships for the Middle Atmosphere

Converting between altitude to potential temperature, and vice versa, is a necessary bit of "bookkeeping" for middle atmosphere researchers who must work in two or more coordinate systems. It is surprising, therefore, that no formulas can be found in middle atmosphere texts to convert a q value to height.

In this poster, simple radiative considerations are used in conjunction with Taylor series expansions to derive a family of apparently new q-to-z conversion formulas. These formulas are demonstrated to be accurate to within 10% throughout the stratosphere and mesosphere, unlike the arithmetical rule-of-thumb recently proposed by Crutzen and collaborators. The success of these surprisingly simple conversion formulas is traced to fundamental properties of ozone heating in the stratosphere.