The Exner function is an important parameter in atmospheric modeling. The Exner function can be viewed as non-dimensionalized pressure and can be defined as:

Π = ( p p 0 ) R d / c p = T θ {\displaystyle \Pi =\left({\frac {p}{p_{0}}}\right)^{R_{d}/c_{p}}={\frac {T}{\theta }}}

where p 0 {\displaystyle p_{0}} is a standard reference surface pressure, usually taken as 1000 hPa; R d {\displaystyle R_{d}} is the specific gas constant for dry air; c p {\displaystyle c_{p}} is the specific heat capacity of dry air at constant pressure; T {\displaystyle T} is the absolute temperature; and θ {\displaystyle \theta } is the potential temperature. It is named after Felix Maria von Exner-Ewarten.

• Pielke, Roger A. Mesoscale Meteorological Modeling. Orlando: Academic Press, Inc., 1984.
• U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service. National Weather Service Handbook No. 1 - Facsimile Products. Washington, DC: Department of Commerce, 1979.