296 
the same order of accuracy as the Umkehr observations 
and can show, at least qualitatively, the variations of 
rate of heating with latitude and season. 
Calculation of Heating of the Ozone Layer. To calcu- 
late the heating of the ozone layer resulting from ozone 
absorption of direct solar radiation, one needs to know 
(1) the absorption spectrum of ozone, (2) the spectral 
distribution of solar energy, 2000-3500 A and 4500- 
6500 A, and (3) the vertical ozone distribution. 
With regard to the absorption spectrum of ozone and 
the solar spectrum, Craig [10] has given estimates based 
on the most recent and reliable data. Figure 2 gives 
N (cm NTP) 
= 2 4 8 =-3 2 Sie 2 4 8 HL 
“ 10> lo? io"! 
E,/n(cal sec !cm? cmNTP |) 
Fie. 2.—Variation of #./n as a function of N. 
E./n as a function of N, from (12), for these estimates. 
For very small values of NV the exponent in (12) is small, 
so the exponential term is close to unity; hence E,/n is 
nearly independent of NV. The curve then shows a strong 
variation of H./n with N in the range of path lengths 
that includes most of the Hartley absorption. When the 
solar energy in the Hartley region is exhausted, the 
integration in (12) effectively extends only over the 
Huggins and Chappuis bands. Here the absorption 
coefficients are small and, for values of N encountered 
in the atmosphere, the exponential term in (12) again 
approaches unity. From this graph the reader can easily 
find #2, and hence the heating from (13) at any desired 
level in the ozone layer and for any assumed solar 
zenith angle and vertical ozone distribution. 
COOLING OF THE OZONE LAYER 
Cooling of the ozone layer results from radiative 
transfer in the infrared. The atmospheric gases re- 
THE UPPER ATMOSPHERE 
sponsible for this cooling are water vapor, carbon diox- 
ide, and ozone. Several factors make calculations of the 
rate of cooling inherently more complex than calcula- 
tions of the rate of heating. In the first place, the infra- 
red radiation that affects a given level originates at all 
other levels of the atmosphere and is diffuse radiation. 
In the second place, the absorption bands in the infra- 
red consist of sharp lines with little continuous back- 
ground absorption, so that the absorption coefficient 
varies rapidly with wave length. In the third place, the 
absolute amounts of the gases in the ozone layer are 
very small, smaller than those used heretofore in most 
laboratory experiments. Finally, the range of variation 
of pressure in the region under consideration is two to 
three orders of magnitude, and pressure effects on the 
infrared absorption are marked and not completely un- 
derstood. 
Infrared Spectra of Water Vapor, Carbon Dioxide, 
and Ozone. Water vapor contains two principal ab- 
sorption bands in the infrared. The most intense, the 
rotational band, is located at the long-wave end of the 
spectrum, beyond about 20 uw, and has been studied 
spectroscopically by Randall, Dennison, Ginsburg, and 
Weber [50]. The band at 6 » has not been studied as 
exhaustively, but Fowle [17, 18] has made absorption 
measurements. 
Carbon dioxide has three bands in the infrared, in- 
tense ones at about 4 » and 15 uw and a weak band near 
10 uw. The band at 4 pu, while intense, is located in a re- 
gion of comparatively small radiation for black bodies 
at atmospheric temperatures. However, the 15-y band 
is exceedingly important in the radiative processes of 
the atmosphere, lying as it does near the peak of the 
black-body radiation at atmospheric temperatures. 
Martin and Barker [39] have studied this band spec- 
troscopically. 
Ozone has two bands, one near 10 » and a second that 
nearly overlaps the 15-u carbon dioxide band. Strong 
[54] has studied the absorption of the former band. 
Methods of Calculating Cooling. To compute the 
flux of infrared radiation arriving at a given level in 
the atmosphere, one needs to consider the radiation 
originating at all other levels and also the absorption 
of radiation during its passage from its origin to the 
reference level. In Fig. 3, let the unit area P, through 
which the downward flux is to be computed, lie on the 
horizontal plane w = 0, where the symbol wu represents 
the mass of the radiating substance in a vertical column 
of unit area. Consider an infinitesimal volume element 
in the plane w = wu, with vertical thickness du. The 
line from this element to P makes an angle @ with the 
vertical and an angle ¢ with an arbitrary reference 
direction in the horizontal. The emission of mono- 
chromatic radiation from this element is 
dI dX = kI, sec 6 du sin 6 dé de dx, (15) 
where k is the absorption coefficient and J; is the black- 
body radiation of the element at the wave length \ in 
question. The vertical flux reaching P from this element 
is cos 6 dI d\ exp (—ku sec 0). The total monochromatic 
flux reaching P from the plane wu = wu is obtained by 
