# 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.

## 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.