Brief notes on Atmospheric Equilibrium in Saturated Air

While discussing the stability and instability conditions in dry air, it was pointed out that a rising air parcel cools at the dry-adiabatic lapse rate, which is always the same (10″C for every kilometer of ascent).

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On the contrary, when an ascending air parcel is saturated, its rate of cooling is wet-adiabatic. The wet or moist adiabatic lapse rate is highly variable.

Thus, the stability or instability of a saturated air mass depends on the relationship between the prevailing lapse rate and the moist-adiabatic lapse rate.


According to Petterssen, there are the following two types of lapse rates at which the moist air cools in its ascent path:-

(1) Pseudo-adiabatic lapse rate:

It is found in such an air parcel which moves up in saturated state. The condensed moisture is immediately removed from the ascending air mass.

(2) Retarded or moist adiabatic lapse rate:


It is found in such a parcel of saturated air which contains the condensed moisture.

When the prevailing lapse rate is more than the wet-adiabatic lapse rate, the saturated air is said to be in unstable equilibrium. In these circumstances, if we displace a saturated parcel upwards, it is warmer than its surroundings, and so it tends to keep moving in the direction of displacement.

Similarly, if we displace it downward, it becomes immediately colder than it’s surrounding and, therefore, it tends to continue its downward movement. On the contrary, in a saturated air mass, if the prevailing lapse rate is less than its moist-adiabatic lapse rate, the atmosphere is said to be in stable equilibrium.

If the saturated parcel is displaced upward, then at every level it finds itself colder and, hence, heavier than its surroundings. In these conditions, if the impulse is withdrawn, the ascending saturated air tends to return to its original position.


Similarly, if we displace it downward, it becomes immediately warmer than its surroundings. In the case of the impulse being removed, it tends to go back to its original position.

The third situation occurs when the saturation-adiabatic lapse rate and the prevailing lapse rate are equal. However, this situation rarely occurs and is short-lived.

Since the temperature and the density of the ascending air parcel are the same in value as those of the environment at all the levels of upward movement, it tends to stay out in its new position when the impulse is withdrawn. With the lapse rates like these, the atmosphere is said to be in neutral equilibrium.

Therefore the following criteria hold good for determining the state of equilibrium saturated air:

y < ym = stable equilibrium.

(2) The column of air is in neutral equilibrium, if the prevailing lapse rate has the same value as the wet-adiabatic lapse rate:

y = ym = neutral equilibrium.

(3) The column of air is unstable, if the prevailing lapse rate is larger than the wet-adiabatic lapse rate :

y > ym = unstable equilibrium.

where y = prevailing lapse rate.

Ym = wet-adiabatic lapse rate.

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