RADIATIVE TEMPERATURE CHANGES IN THE OZONE LAYER 
function in (12) gives way to the function 27His(a,N), 
where Hi(a,V) is an exponential integral, be- 
cause the returning radiation is diffuse. The path length 
N is, of course, now measured vertically upward from 
the tropopause. The factor 3 in the denominator indi- 
cates that only about one-third of the incident radia- 
tion is reflected upward from the troposphere, while the 
factor sec Z takes care of the fact that the radiation is 
incident at the angle Z from the vertical. 
Oxygen Absorption. The absorption spectrum of oxy- 
gen in the ultraviolet includes the weak Herzberg bands 
which converge near 2400 A; the much stronger Schu- 
mann band system which begins near 2000 A, converges 
at about 1750 A, and reaches its maximum intensity at 
about 1450 A; and, finally, the Hopfield bands between 
1000 and 600 A. Absorption by oxygen in the infrared 
and visible regions of the spectrum is very weak. 
The absorption coefficients of air in the Hopfield 
bands have been estimated by Schneider [53]. These 
results are only approximate, but leave no doubt that 
the solar energy in this spectral interval is already ab- 
sorbed far above the ozone layer. Between 1000 and 
1300 A the atmosphere has some strong bands and some 
transparent regions. Particularly, near the wave length 
of the Lyman-a emission line of hydrogen (1216 A), 
the atmosphere seems to be relatively transparent. 
Here, however, Preston [49] has made careful measure- 
ments of absorption coefficients of air and its con- 
stituents and finds that solar radiation could hardly 
penetrate below 60 km in important amounts. Simi- 
larly Ladenburg and Van Voorhis [35] have measured 
oxygen absorption in the Schumann region (1300-1750 
A) and their results show that the solar energy here 
also is depleted above the ozone layer. 
The only solar radiation, then, that can heat the 
ozone layer lies above 1800 A. Above about 2200 A, 
on the other hand, oxygen is comparatively unimpor- 
tant as a heating agent because ozone absorbs the bulk 
of the available energy. For the intermediate region, 
1800-2200 A, Granath [27] has measured the oxygen 
absorption in the 1900-2100 A region. The absorption 
of air has been determined by Buisson, Jausseran, and 
Rouard [6] in the interval 1855-2653 A. Because the 
measurements were made in surface air relatively free 
from ozone, one can determine the absorption of oxy- 
gen from these measurements with some degree of pre- 
cision. The absorption coefficients so derived agree well 
with Granath’s measurements in the region where they 
overlap. 
The oxygen absorption spectrum is complicated by 
a pressure dependence of the absorption in the Herz- 
berg region. Heilpern [30] discussed oxygen absorption 
at 2144 A for pressures varying between 148 and 663 mm 
Hg at a temperature of 18C and found a rather strong 
pressure dependence. 
In any case, heating caused by oxygen absorption is 
generally negligible compared to that caused by ozone 
absorption in the ozone layer. Only in the upper part 
of the layer (above 40 km), where it may approach 10 
per cent of the ozone absorption, does oxygen absorp- 
tion need to be considered by the careful investigator. 
295 
At the present stage of this type of study, the figure of 
10 per cent is considerably less than the uncertainties 
introduced by other doubtful factors. 
Solar Energy in the Ultraviolet. Until recent V-2 
rocket flights were consummated, the spectral distribu- 
tion of solar energy to the violet of 3000 A was unknown. 
This factor is, of course, necessary for the calculation 
of heating in the ozone layer. Nearly all calculations of 
this heating have been based on the assumption that 
the sun radiates as a black body at. a temperature of 
6000K. The rocket measurement has shown that the 
radiation is actually considerably less intense. 
The first source of information about the solar spec- 
trum in the region under consideration (1800-8500 A) is 
that of measurements made at the earth’s surface and 
corrected for absorption in the atmosphere. Such in- 
formation can, of course, extend down to only about 
3000 A, but even this shows that the radiated energy 
is considerably less than would be expected from the 
black-body assumption mentioned above. Several series 
of such measurements have been summarized by Moon 
[42]. Below 4000 A, the measurements indicate a steady 
decrease of emission relative to black-body emission at 
6000K until at 3000 A the ratio is only about 40 per 
cent. 
The rocket flight of October 10, 1946 obtained a 
spectrum at 55 km (already above all but about one 
per cent of the ozone) extending down to 2200 A [81]. 
The ratio of observed intensity to black-body intensity 
for a temperature of 6000K was observed to decrease 
irregularly from about 70 per cent at 3300-3400 A to 
about 6 per cent at 2200 A. The agreement with surface 
observations in the overlapping region (8000-3400 A) 
is satisfactory. An approximate spectrum based on these 
two types of information has been given by Craig [10, 
Fig. 10]. The graph of #./n against N in Fig. 2 is based 
on this distribution. 
Ozone Distribution. The vertical distribution of ozone 
is, of course, an important parameter in the determina- 
tion of rate of heating of the ozone layer at various 
levels. Unfortunately, Umkehr measurements give little 
more than the order of magnitude of the amount of 
ozone present above 30 km. Neither do these measure- 
ments give any reliable information about the seasonal 
and latitudinal variations of ozone amount above 30 
km. 
In this connection, the calculations of equilibrium 
ozone amounts may be useful. There are many uncer- 
tainties in the calculations that make them only ap- 
proximate. However, particularly above 30 km, they 
agree as to order of magnitude with the Umkehr results. 
The calculations have the advantage over the observa- 
tions that they are capable of showing, at least approxi- 
mately, the variations of ozone amount with zenith 
angle. The photochemical theory also indicates a sub- 
stantial variation of equilibrium ozone amount with 
temperature, because the photochemical factor ki2/k1s 
in (7) varies markedly with temperature [15]. Thus cal- 
culations of the photochemical-equilibrium amounts of 
ozone above 35 km, applied to the problem of computing 
the rates of radiative heating of the ozone layer, give 
