Exner function

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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:

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

where p_0 is the pressure at the surface, usually taken as 1000 hPa; R_d is the gas constant for dry air; c_p is the heat capacity of dry air at constant pressure; T is the absolute temperature; and \theta is the potential temperature.


  • 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.

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