Exner function

The Exner function is a parameter used in atmospheric modeling. Depending on the application, the Exner function may be defined as

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

or as a non-dimensional form

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

where $p_0$ is a standard reference surface pressure (usually taken as 1000 hPa, but sometimes as the surface pressure); $R_d$ is the specific gas constant for dry air; $c_p$ is the specific heat capacity of dry air at constant pressure; $T$ is the absolute temperature; and $\theta$ is the potential temperature. The non-dimensional form can be used as a vertical coordinate in some numerical weather prediction applications, resulting in a simpler mathematical formulation compared to using pressure as the vertical coordinate. It is named after Felix Maria von Exner-Ewarten.

See also

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

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