Equivalent potential temperature

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Equivalent potential temperature, commonly referred to as Theta-e $\left( \theta_e \right)$ , is a measure of the instability of air at a given pressure, humidity, and temperature. Theta-e is the temperature of one parcel of air at 100 kPa (1000 mbar) after considering the energy from when the water vapor in the parcel is condensed.

Theoretically, it would be the temperature of the parcel if the following procedure were performed:

Lift adiabatically (pressure drop, and drop in temperature, but no change in heat) until it becomes saturated with water vapor,
Allow all the water vapor to condense out, releasing its latent heat, and
Drop the parcel adiabatically (pressure rise but no change in heat content) to an atmospheric pressure of 1000 millibars.

This result allows the comparison of parcels of air at different pressures, and is a measure of the instability of that air. [1]

The formula for theta-e is the following:[2]

$\theta_e = T_e \left( \frac{p_0}{p} \right)^\frac{R}{c_p} \approx \left( T + \frac {l_v}{c_{p}} r \right) \left( \frac{p_0}{p} \right)^\frac{R}{c_p}$

Where:

$T e$ = equivalent temperature
T = Temperature of air at pressure p
$p$ = pressure at the point (mbar)
$p 0$ = standard reference pressure (1000 mbar)
$R$ = specific gas constant for air (287 J/(kg·K))
$c p$ = specific heat of dry air at constant pressure (1004 J/(kg·K))
$l v$ = latent heat of evaporation ((2400 kJ/kg {at 25C} to 2600 kJ/kg {at -40C})
r = mixing ratio of water vapor in air

[edit] See also

[edit] 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

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