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The Exner function is an important parameter in
atmospheric model An atmospheric model is a mathematical model constructed around the full set of primitive dynamical equations which govern atmospheric motions. It can supplement these equations with parameterizations for turbulent diffusion, radiation, moist p ...
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 HPA may refer to: Organizations * Harry Potter Alliance, a charity * Halifax Port Authority, Canada * Hamburg Port Authority, Germany * Hawaii Preparatory Academy, a school in Hawaii, US * Health Protection Agency, UK * Heerespersonalamt, the Ge ...
; R_d is the
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 p ...
for dry air; c_p is the heat capacity of dry air at constant pressure; T is the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...
; 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 ...
.


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.


See also

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Barometric formula The barometric formula, sometimes called the '' exponential atmosphere'' or '' isothermal atmosphere'', is a formula used to model how the pressure (or density) of the air changes with altitude. The pressure drops approximately by 11.3 pascals ...
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Climate model Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including atmosphere, oceans, land surface and ice. They are used for a variety of purposes from study of the dynamics of the ...
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Euler equations 200px, Leonhard Euler (1707–1783) In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler includ ...
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Fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
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General circulation model A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic terms f ...
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Numerical weather prediction Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in th ...
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Primitive equations The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations: # A ''continuity e ...
Numerical climate and weather models {{climate-stub