On the Correct Use of the Wet Adiabatic Lapse Rate in Stability Criteria of a Saturated Atmosphere

A rigorous stability analysis of a saturated atmosphere is carried out and is compared with the parcel method. It is shown that the stability parameter n̄ω2 (the Brunt-Väisälä frequency) one obtains by the two methods is identical. It is further shown that the replacement of the dry adiabatic by the wet adiabatic lapse rate in studying the stability of a saturated atmosphere is inadequate in certain circumstances. In particular, for an atmosphere at rest with negative temperature gradients, such a replacement may lead to erroneous prediction of instability. Similarly, for an atmosphere with a background wind, the same replacement will lead to underestimation of stability for sufficiently negative temperature gradients.