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Potential temperature

The potential temperature of a parcel of air at pressure <math>P</math> is the temperature that the parcel would acquire if adiabatically brought to a standard reference pressure <math>P_{0}</math>, usually 1 bar. The special temperature is denoted <math>\theta</math> and is often given by

<math> \theta = T \left(\frac{p_{o}}{p}\right)^{\frac{R}{c_{p}}} </math> ,

where <math>T</math> is the current temperature of the parcel, <math>R</math> is the gas constant of air, and <math>c_{p}</math> is the specific heat capacity at a constant pressure.


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Comments

Potential temperature is a more dynamically important quantity than the actual temperature. Under almost all circumstances, potential temperature increases upwards in the atmosphere, unlike actual temperature which may increase or decrease.

Contexts

The concept of potential temperature applies to any compressible fluid. It is most frequently used in the Atmospheric sciences, but also in Oceanography[1].

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 a katabatic 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 of thermodynamics can be written as:

<math> dh = Tds + vdp </math>,

where <math>h</math> denotes the enthalpy change, <math>T</math> the temperature, <math>ds</math> the change in entropy, <math>v</math> the specific volume, and <math>p</math> the pressure.

For adiabatic processes, the change in entropy is 0 and the 1st law reduces to:

<math> dh = vdp </math>.

For approximately ideal gases, such as the dry air in the earth's atmosphere,the equation of state, <math> pv = RT </math> can be substituted into the 1st lawyielding, after some rearrangement:

<math> {\frac{dp}{p}} = {\frac{c_{p}}{R}\frac{dT}{T}} </math>,

where the <math> dh = c_{p}dT </math> was used and both terms were divided by the product <math> pv </math>

Integrating yields:

<math> \left(\frac{p}{p_{0}}\right)^{R/c_{p}} = \frac{T}{T_{0}} </math>,

and solving for <math>T_{0}</math>, the temperature a parcel would acquireif moved adiabatically to the pressure level <math>p_{0}</math>, you get:

<math> T_{0} = T\left(\frac{p_{0}}{p}\right)^{R/c_{p}} \equiv \theta </math>.
Meteorological data and variables

Atmospheric pressure | CAPE | CIN |Dew point | Heat index | Humidex |Humidity |Pot T | Sea surface temperature | Temperature |Theta-e | Visibility |Vorticity | Wind chill


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Atmospheric thermodynamics

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