Exner function

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:

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

where ${\displaystyle p_{0}}$ is a standard reference surface pressure, usually taken as 1000 hPa; ${\displaystyle R_{d}}$ is the gas constant for dry air; ${\displaystyle c_{p}}$ is the heat capacity of dry air at constant pressure; ${\displaystyle T}$ is the absolute temperature; and ${\displaystyle \theta }$ is the potential temperature.

References

• 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.

See also

• Barometric formula
• Climate model
• Euler equations
• Fluid dynamics
• General circulation model
• Numerical weather prediction
• Primitive equations