# Potential temperature

The

**potential temperature**of a parcel of fluid at pressure $P$ is the temperature that the parcel would acquire if adiabatically brought to a standard reference pressure $P\_\{0\}$, usually 1000 millibars. The potential temperature is denoted $heta$ and, forair , is often given by: $heta\; =\; T\; left(frac\{P\_\{0\{P\}\; ight)^\{frac\{R\}\{c\_\{p\}$ ,

where $T$ is the current absolute

temperature (in K) of the parcel, $R$ is thegas constant of air, and $c\_\{p\}$ is thespecific heat capacity at a constant pressure.**Contexts**The concept of potential temperature applies to any stratified fluid. It is most frequently used in the

Atmospheric sciences andOceanography . [*[*] The reason that it is usedin both fluids is that changes in pressure result in warmer fluid residing under colder fluid- examples being the fact that air temperature drops as one climbs a mountain and water temperature can increase with depth in very deep ocean trenches and within the ocean*http://oceanworld.tamu.edu/resources/ocng_textbook/chapter06/chapter06_05.htm TAMU*]mixed layer . When potential temperature is used instead, these apparently unstable conditions vanish.**Comments**Potential temperature is a more dynamically important quantity than the actual temperature. This is because it is not affected by the physical lifting or sinking associated with flow over obstacles or large-scale atmospheric turbulence. A parcel of air moving over a small mountain will expand and cool as it ascends the slope, then compress and warm as it descends on the other side- but the potential temperature will not change in the absence of heating, cooling, evaporation, or condensation (processes that exclude these effects are referred to as dry adiabatic). Since parcels with the same potential temperature can be exchanged without work or heating being required, lines of constant potential temperature are natural flow pathways.

Under almost all circumstances, potential temperature increases upwards in the atmosphere, unlike actual temperature which may increase or decrease. Potential temperature is conserved for all dry adiabatic processes, and as such is an important quantity in the planetary boundary layer (which is often very close to being dry adiabatic).

Potential temperature is a useful measure of the static stability of the unsaturated atmosphere. Under normal, stably stratified conditions, the potential temperature increases with height,

: $frac\{partial\; heta\}\{partial\; z\}\; >\; 0$

and vertical motions are suppressed. If the potential temperature decreases with height,

:$frac\{partial\; heta\}\{partial\; z\}\; <\; 0$

the atmosphere is unstable to vertical motions, and convection is likely. Since convection acts to quickly mix the atmosphere and return to a stably stratified state, observations of decreasing potential temperature with height are uncommon, except while vigorous convection is underway or during periods of strong

insolation . Situations in which theequivalent potential temperature decreases with height, indicating instability in saturated air, are much more common.Since potential temperature is conserved under adiabatic or

isentropic air motions, in steady, adiabatic flow lines or surfaces of constant potential temperature act asstreamlines or flow surfaces, respectively. This fact is used in isentropic analysis, a form of synoptic analysis which allows visualization of air motions and in particular analysis of large-scale vertical motion. [*http://www.comet.ucar.edu/class/faculty/Jun05_2000/docs/schneider/htm/index.html*] [*http://weather.cod.edu/analysis/analysis.isentropic.html*]**Potential temperature perturbations**The

atmospheric boundary layer (ABL) potential temperature perturbation is defined as the difference between the potential temperature of the ABL and the potential temperature of the free atmosphere above the ABL. This value is called the potential temperature deficit in the case of akatabatic flow, because the surface will always be colder than the free atmosphere and the PT perturbation will be negative.**Derivation**The

enthalpy form of the first law ofthermodynamics can be written as:: $,\; dh\; =\; Tds\; +\; vdp$,

where $h$ denotes the

enthalpy change, $T$ the temperature, $ds$ the change inentropy , $v$ the specific volume, and $p$ the pressure.For adiabatic processes, the change in entropy is 0 and the 1st law simplifies to:

: $,\; dh\; =\; vdp$.

For approximately ideal gases, such as the dry air in the earth's atmosphere, the

equation of state , $pv\; =\; RT$ can be substituted into the 1st lawyielding, after some rearrangement:: $\{frac\{dp\}\{p\; =\; \{frac\{c\_\{p\{R\}frac\{dT\}\{T$,

where the $dh\; =\; c\_\{p\}dT$ was used and both terms were divided by the product $pv$

Integrating yields:

: $left(frac\{p\_\{1\{p\_\{0\; ight)^\{R/c\_\{p\; =\; frac\{T\_\{1\{T\_\{0$,

and solving for $T\_\{0\}$, the temperature a parcel would acquire if moved adiabatically to the pressure level $p\_\{0\}$, you get:

: $T\_\{0\}\; =\; \{T\_\{1left(frac\{p\_\{0\{p\_\{1\; ight)^\{R/c\_\{p\; equiv\; heta$.

**Related quantities**The

Brunt-Väisälä frequency is a closely related quantity that uses potential temperature and is used extensively in investigations of atmospheric stability.**References****Bibliography*** M K Yau and R.R. Rogers, "Short Course in Cloud Physics, Third Edition", published by Butterworth-Heinemann,

January 1 ,1989 , 304 pages. EAN 9780750632157 ISBN 0-7506-3215-1**External links*** http://scienceworld.wolfram.com/physics/PotentialTemperature.html

* http://meted.ucar.edu/awips/validate/thetae.htm**See also***

Wet-bulb potential temperature

*Atmospheric thermodynamics

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**potential temperature**— The temperature a parcel of dry air would have if brought adiabatically to a standard pressure level of 1,000 millibars … Aviation dictionary**potential temperature**— noun : the temperature that a sample of air attains if reduced to a pressure of 1000 millibars without receiving or losing heat to the environment … Useful english dictionary**Equivalent potential temperature**— Equivalent potential temperature, commonly referred to as Theta e left( heta e ight), is a quantity related to the stability of a column of air in the atmosphere. heta e is the temperature a parcel of air would reach if all the water vapor in the … Wikipedia**Wet-bulb potential temperature**— Wet bulb potential temperature, sometimes referred to as pseudo wet bulb potential temperature, is the temperature attained by mass of air brought adiabatically to saturation and then carried along moist adiabat to 1000 mb (hPa). This temperature … Wikipedia**Potential vorticity**— (PV) is a quantity which is proportional to the dot product of vorticity and stratification that, following a parcel of air or water, can only be changed by diabatic or frictional processes. It is a useful concept for understanding the generation … Wikipedia**Temperature**— This article is about the thermodynamic property. For other uses, see Temperature (disambiguation). A map of global long term monthly average surface air temperatures i … Wikipedia**Potential density**— The potential density of a fluid parcel at pressure P is the density that the parcel would acquire if adiabatically brought to a reference pressure P {0}, often 1 bar (100 kPa). Whereas density changes with changing pressure, potential density of … Wikipedia**potential density**— 1. The density of a unit of water after it is raised by an adiabatic process to the surface, i.e., determined from in situ salinity and potential temperature [22]. 2. Density that would be reached by a compressible fluid if it were… … Lexicon of Cave and Karst Terminology**Temperature**— Tem per*a*ture, n. [F. temp[ e]rature, L. temperatura due measure, proportion, temper, temperament.] 1. Constitution; state; degree of any quality. [1913 Webster] The best composition and temperature is, to have openness in fame and opinion,… … The Collaborative International Dictionary of English**Temperature sense**— Temperature Tem per*a*ture, n. [F. temp[ e]rature, L. temperatura due measure, proportion, temper, temperament.] 1. Constitution; state; degree of any quality. [1913 Webster] The best composition and temperature is, to have openness in fame and… … The Collaborative International Dictionary of English