Exner function

The Exner function is a parameter used in atmospheric modeling. Depending on the application, the Exner function may be defined as : \Pi = c_p \left( \frac{p}{p_0} \right)^{R_d/c_p} = c_p \frac{T}{\theta} or as a non-dimensional form : \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.

The Exner function is a parameter used in atmospheric modeling. Depending on the application, the Exner function may be defined as \Pi = c_p \left( \frac{p}{p_0} \right)^{R_d/c_p} = c_p \frac{T}{\theta} or as a non-dimensional form \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.

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