Page 297 - Fundamentals of Air Pollution

II. Stability and Instability 253

Thus air cools as it rises and warms as it descends. Since we have assumed
an adiabatic process, -ATVAz defines y d, the dry adiabatic process lapse
rate, a constant equal to 0.0098 K/m, is nearly 1 K/100 m or 5.4°F/1000 ft.
If an ascending air parcel reaches saturation, the addition of latent heat
from condensing moisture will partially overcome the cooling due to expan-
sion. Therefore, the saturated adiabatic lapse rate (of cooling) y w is smaller
than y d.

C. Determining Stability
By comparing the density changes undergone by a rising or descending
parcel of air with the density of the surrounding environment, the enhance-
ment or suppression of the vertical motion can be determined. Since pres-
sure decreases with height, there is an upward- directed pressure gradient
force. The force of gravity is downward. The difference between these two
forces is the buoyancy force. Using Newton's second law of motion, which
indicates that a net force equals an acceleration, the acceration a of an air
parcel at a particular position is given by

2
where g is the acceleration due to gravity (9.8 m s ), T p the temperature
of an air parcel that has undergone a temperature change according to the
process lapse rate, and T e the temperature of the surrounding environment
at the same height. (Temperatures are expressed in degrees Kelvin.)
Figure 17-5 shows the temperature change undergone by a parcel of air
forced to rise 200 m in ascending a ridge. Assuming that the air is dry, and
therefore that no condensation occurred, this figure also represents the
warming of the air parcel if the flow is reversed so that the parcel moves
downslope from B to A.
Comparing the temperature of this parcel to that of the surrounding
environment (Fig. 17-6), it is seen that in rising from 100 to 300 m, the
parcel undergoes the temperature change of the dry adiabatic process lapse
rate. The dashed line is a dry adiabatic line or dry adiabat. Suppose that

Fig. 17-5. Cooling of ascending air. Dry air forced to rise 200 m over a ridge cools adiabati-
cally by 2°C.