Earth:Exner function

Short description: Parameter in atmospheric modeling

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:

[math]\displaystyle{ \Pi = \left( \frac{p}{p_0} \right)^{R_d/c_p} = \frac{T}{\theta} }[/math]

where [math]\displaystyle{ p_0 }[/math] is a standard reference surface pressure, usually taken as 1000 hPa; [math]\displaystyle{ R_d }[/math] is the gas constant for dry air; [math]\displaystyle{ c_p }[/math] is the heat capacity of dry air at constant pressure; [math]\displaystyle{ T }[/math] is the absolute temperature; and [math]\displaystyle{ \theta }[/math] 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