Equivalent Potential Temperature
The entropy of unsaturated air may be obtained by summing the entropy of of dry air and of water vapour. The entropy of water vapour in the air parcel is equal to the entropy it has after ascending adiabatically to the lifting condensation level temperature (see Bolton (1980) for a simple empirical formula for ). Therefore, in this case
and we may define an equivalent potential temperature according to :
so that:
where the arbitrary constant in the definition of has been used to define a reference temperature . This definition may be used for saturated air ( ) with but is then not exactly consistent with the definition of the pseudo-adiabatic reference process. Nevertheless, the term involving in eq.(17) is commonly neglected in practical definitions of (e.g. Holton, 2004) giving:
- an expression attributed to Rossby (1932).
A more recent assessment of the accuracy of equivalent potential temperature formulations can be found in Davies-Jones (2009).
References
Bolton, D. (1980) The computation of equivalent potential temperature. Mon. Wea. Rev., 108, 1046 - 1053.
Brunt, D. (1939) Physical and dynamical meteorology. By David Brunt. 2nd Ed. Cambridge University Press 1939; Publ. Wiley and Sons.
Davies-Jones, R. (2009) On Formulas for Equivalent Potential Temperature. Mon. Wea. Rev., 137, 3137 - 3148.
Dutton J.A. (1986) The Ceaseless Wind: An Introduction to the Theory of Atmospheric Motion. Dover Publications.
Holton, J.R. (2004) An Introduction to Dynamics Meteorology. : Volume 88 (International Geophysics). Academic Press, 535 pp.
Ludlam, F.H. (1980) Clouds and Storms : the behaviour and effect of water in the atmosphere. Pennsylvania State University Press, University Park and London. 405 pp.
Rossby, C. G., 1932: Thermodynamics applied to air mass analysis. MIT Meteorology Papers 1, No. 3, 48 pp.
Saunders, P. M., 1957: The thermodynamics of saturated air: A contribution to the classical theory. Quart. J. Roy. Meteor. Soc., 83 , 342–350.