The Exner function is an important parameter in

atmospheric model In atmospheric science, an atmospheric model is a mathematical model constructed around the full set of primitive equations, primitive, Dynamical systems theory, dynamical equations which govern atmospheric motions. It can supplement these equati ...

ing. The Exner function can be viewed as non-dimensionalized pressure and can be defined as: :

\Pi = \left( \frac \right)^ = \frac

where

p_0

is a standard reference surface pressure, usually taken as 1000

hPa The pascal (symbol: Pa) is the unit of pressure in the International System of Units (SI). It is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is an S ...

;

R_d

is the

specific gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment pe ...

for dry air;

c_p

is the specific heat capacity of dry air at constant pressure;

T

is the

absolute temperature Thermodynamic temperature, also known as absolute temperature, is a physical quantity which measures temperature starting from absolute zero, the point at which particles have minimal thermal motion. Thermodynamic temperature is typically expres ...

; and

\theta

is the

potential temperature The potential temperature of a parcel of fluid at pressure P is the temperature that the parcel would attain if adiabatically brought to a standard reference pressure P_, usually . The potential temperature is denoted \theta and, for a gas well-ap ...

. It is named after

Felix Maria von Exner-Ewarten Felix Maria von Exner-Ewarten (23 August 1876 in Vienna – 7 February 1930, Vienna) was an Austrian meteorologist and geophysicist Geophysics () is a subject of natural science concerned with the physical processes and properties of Earth ...

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.

References

See also