Effects of Meteorology on Air Pollution - Air Pollution and Global Warming: History, Science, and Solutions - page 137

During an adiabatic expansion, kinetic energy of
air molecules is converted to work to expand the
air. Because temperature is proportional to the kinetic
energy of air molecules (Equation 3.1), an adiabatic
expansion cools the air. In sum, rising air expands and
expanding air cools; thus, rising air cools during an adia-
batic expansion. The rate of cooling during an adiabatic
expansion near the surface of the Earth is approximately
9.8 K or ◦ C per kilometer increase in altitude. This rate
is called the dry or unsaturated adiabatic lapse rate
(

Example 6.1
If the observed temperature cools 14 ◦ Cbetween
the ground and 2 km above the ground, what
is the environmental lapse rate? Is it larger or
smaller than the dry adiabatic lapse rate?

Solution
The environmental lapse rate in this example is
e =+ 7 ◦ Ckm −1 ,whichisless than the dry adia-

batic lapse rate of

9.8 ◦ Ckm −1 .

d =+

d ) .Lapse rates are opposite in sign to changes in
temperature with height; thus, a positive lapse rate
indicates that temperature decreases with increasing
height.
If the balloon in our example rises in air saturated
with water vapor, the resulting adiabatic expansion
cools the air and decreases the saturation vapor pres-
sure of water in the balloon, causing the relative humid-
ity to increase to more than 100 percent and water
vapor to condense to form cloud drops, releasing latent
heat. The rate of temperature increase with increas-
ing height due to this latent heat release in saturated
air parcels is typically 4 ◦ Ckm − 1 ,butitincreases to
8 ◦ Ckm − 1 in the tropics. Subtracting this latent heat
release rate from the dry adiabatic lapse rate gives a
net lapse rate during cloud formation of between 6 and
2 ◦ Ckm − 1 .Thisrate is called the wet, saturated, or
pseudoadiabatic lapse rate (

6.6.1.2. Stability
One purpose of examining dry, wet, and environmental
lapse rates is to determine the stability of the air, where
the stability is a measure of whether pollutants emit-
ted will convectively rise and disperse or build up in
concentration near the surface.
Figure 6.8 illustrates the concept of stability. When a
parcel of air (the balloon, in our example) that is unsat-
urated with respect to water is displaced vertically, it
rises, expands, and cools dry adiabatically (along the
dashed line). If the environmental temperature profile
is stable (right thick line), the rising parcel is cooler and
more dense than is the air in the environment around
it at every altitude. As a result of its lack of buoyancy,
the parcel sinks, compresses, and warms until its tem-
perature (and density) equals that of the air around it.
In reality, the parcel overshoots its original altitude as
it descends, but eventually comes back to the original
altitude in an oscillatory manner. In sum, a parcel of
pollution at the temperature of the environment that is
accelerated vertically in stable air returns to its original
altitude and temperature. Stable air is associated with
near-surface pollution buildup because pollutants per-
turbed vertically in stable air cannot rise and disperse.
In unstable air ,anunsaturated parcel that is per-
turbed vertically continues to accelerate in the direction

w ) .Itisthenegativerate
of change of temperature with increasing altitude dur-
ing an adiabatic expansion in which condensation also
occurs. The wet adiabatic lapse rate is applicable only in
clouds.
The opposite of an adiabatic expansion is an adia-
batic compression ,which occurs when a balloon sinks
adiabatically from low to high pressure. The compres-
sion is due to the increased air pressure around the
balloon. During an adiabatic compression, work is con-
verted to kinetic energy (which is proportional to tem-
perature), warming the air in the balloon.
Although dry and wet adiabatic lapse rates describe
the extent of cooling of a balloon rising adiabati-
cally, the environmental lapse rate describes the actual
change in air temperature with altitude in the environ-
ment outside a balloon. It is defined as

2.2

2

1.8

d

Stable

1.6

Unstable

1.4

e

e

1.2

e =−

T

(6.1)

1

z

0.8

0 5 10 15 20 25 30

where z is the actual change in air temperature

with a change in altitude. An increasing temperature
with increasing altitude gives a negative environmental
lapse rate.

T /

Temperature ( o C)

Figure 6.8. Stability and instability in unsaturated air,
as described in the text.