Lapse rates and atmospheric stability

Environmental (ambient) lapse rate (ELR, $\Gamma$) is the actual rate at which air temperature falls with height at a given place and time, $\Gamma = -dT/dz$.

Dry adiabatic lapse rate (DALR, $\Gamma_d$) is the rate at which a rising parcel of dry air cools because it expands in the lower-pressure air, without exchanging heat with its surroundings:

$$\Gamma_d = \frac{g}{c_p} = \frac{9.81}{1005} \approx 9.8\ ^\circ\text{C/km} \approx 1\ ^\circ\text{C}/100\ \text{m}$$

(The saturated adiabatic rate is lower, about 4-6 $^\circ$C/km, because latent heat is released.)

Stability principle

A parcel displaced upwards cools at $\Gamma_d$. If it becomes warmer than its surroundings, it is lighter and keeps rising (unstable); if it becomes colder, it sinks back (stable).

In each sketch, \ is the DALR line (temperature of a rising parcel), . is the ELR (actual air temperature) and x is the starting point at ground level.

 (a) Superadiabatic    (b) Neutral
     ELR > DALR            ELR = DALR
 z                     z
 |   .   \             |       \
 |     .  \            |        \
 |       . \           |         \
 |         .\          |          \
 |           x         |           x
 +---------------> T   +---------------> T

 (c) Subadiabatic      (d) Inversion
     ELR < DALR            T rises with z
 z                     z
 |       \ .           |       \       .
 |        \ .          |        \     .
 |         \.          |         \   .
 |          \.         |          \ .
 |           x         |           x
 +---------------> T   +---------------> T

• (a) The air cools faster than the parcel, so the lifted parcel is warmer than its surroundings and keeps rising: unstable.
• (b) The two lines coincide, so the parcel is always at the same temperature as its surroundings: neutral.
• (c) and (d) The air is warmer than the lifted parcel, so the parcel sinks back: stable, and very stable in an inversion.

Unstable conditions occur on sunny days with light winds; stable ones on clear, calm nights. Pasquill classes A (very unstable) to F (stable) express the same idea.