Page 295 - Fundamentals of Air Pollution

II. Stability and Instability 251

Fig. 17-4. Radiation heat balance. The 100 units of incoming shortwave radiation are
distributed: reflected from earth's surface to space, 5; reflected from cloud surfaces to space,
20; direct reaching earth, 24; absorbed in clouds, 4; diffuse reaching earth through clouds,
17; absorbed in atmosphere, 15; scattered to space, 9; scattered to earth, 6. The longwave
radiation comes from (1) the earth radiating 119 units: 101 to the atmosphere and 18 directly
to space, and (2) the atmosphere radiating 105 units back to earth and 48 to space. Additional
transfers from the earth's surface to the atmosphere consist of latent heat, 23; and sensible
heat, 10. Source: After Lowry (4).

assess their effects. When the atmosphere resists vertical motions, it is
called stable; when the atmosphere enhances vertical motions, it is called
unstable or in a state of instability.
In incompressible fluids, such as water, the vertical structure of tempera-
ture very simply reveals the stability of the fluid. When the lower layer is
warmer and thus less dense than the upper layer, the fluid is unstable and
convective currents will cause it to overturn. When the lower layer is cooler
than the upper layer, the fluid is stable and vertical exchange is minimal.
However, because air is compressible, the determination of stability is
somewhat more complicated. The temperature and density of the atmo-
sphere normally decrease with elevation; density is also affected by mois-
ture in the air.
The relationship between pressure p, volume V, mass m, and temperature
T is given by the equation of state:

where R is a specific gas constant equal to the universal gas constant divided
by the gram molecular weight of the gas. Since the density p is m/V, the
equation can be rewritten as

or considering specific volume a = 1/p as