Potential temperature

In order to make the temperature of air or water of different heights or depths comparable to each other, one introduces the state variable potential temperature θ a, which is a measure of the sum of internal energy ( local temperature ) and potential energy (height / depth) is.

Calculation

The vertical movement of gas or liquid packages provide a good approximation dar. adiabatic state changes you move these completed packages adiabatically to a standard pressure p0 (1000 mbar), so, the air or the liquid due to compressibility and related work designated as potential temperature temperature.

From the adiabatic equation

Follows by integrating p0 (where T = θ ) to p and solving for θ

The individual symbols stand for the following sizes:

• Cp: specific heat capacity at constant pressure = 1003 J / ( kg · K)
• RL: specific gas constant for dry air = 287 J / ( kg · K)
• T - absolute temperature
• P - pressure

Free of condensation and evaporation, the dry potential temperature in adiabatic processes does not change. If condensation and evaporation on the other hand, leads to analogous instead the moist potential temperature one, so that temperature which would assume a parcel of air at saturation, when you put it on a normal pressure p0 feuchtadiabatisch.

Analogous to the atmosphere applies in the ocean

The individual symbols stand for the following sizes:

• β - a variable factor to be less than 1
• S - salinity
• T0 - temperature at the surface at atmospheric pressure
• γad - adiabatic temperature gradient

From the gradient of θ can be seen, the static stability of the stratification.

Relations

One of the most important features of the potential temperature is that it can be directly related to the entropy in conjunction. This isentropes are also contour lines of equal potential temperature and entropy.

Another connection is apparent with the trockenadiabatischen temperature gradient Γ or the geometric temperature gradient γ:

The difference Γ - γ is except in the case of a trockenadiabatischen atmosphere stratification ( Γ = γ ) is always positive, the dry potential temperature thus increases with the height. This is true even if T remains constant ( γ = 0), as is the case above the tropopause.

History

The concept of potential temperature was introduced in 1888 by Wilhelm von Bezold.