RADIATIVE TEMPERATURE CHANGES IN THE OZONE LAYER 
temperature maximum near 55 km was reasonable. 
In 1936 [25], he revised these calculations on the basis 
of later determinations of the vertical distribution of 
ozone. Finally, in 1947 [26] he published revised results 
based on further information about absorption in the 
infrared. Only the last results are included here. 
Gowan gives his results in the form of radiative- 
equilibrium temperatures at various levels in the ozone 
layer. These are the temperatures that would exist 
according to his calculations if the radiative gains of 
the layer were just balanced by the radiative losses, 
with no effects of atmospheric circulations. The assump- 
tions made by Gowan are: 
1. Solar Energy. For all calculations except one, 
Gowan assumes that the sun radiates as a black body 
at 6000K in the ultraviolet. In this one case, the emis- 
sion is taken as that of a black body at 4000K. 
2. Vertical Distribution of Absorbing Gases. Ozone 
is assumed to vary vertically according to the Umkehr 
measurements of G6tz, Meetham, and Dobson at Arosa 
for a total amount of ozone of either 0.20 em NTP or 
0.28 em NTP. Water vapor is assumed to be either 10 per 
cent or 40 per cent saturated at the tropopause with 
constant mixing ratio in the ozone layer. Carbon dioxide 
is assumed to be present throughout the ozone layer in 
a concentration of 0.03 per cent by volume (corre- 
sponding to tropospheric conditions). 
TasLe I. Rapratrve-EQuiILisrium TEMPERATURES aT 50°N 
(After Gowan [26])* 
Summer Winter 
Amount 03 
(cm NTP) -280 280 280 200 280 -280 
Amount H20 (%) 0 10 40 10 10 10 
Solar temperature 
°K 6000 6000 6000 6000 4000 6000 
Height (km) Temperature (°K) 
50-55 452 |415 448/344 441/410 445/323 347/406 439 
45-50 429 |410 424/361 421/409 422/321 333/364 875 
40-45 399 |385 397/350 394/382 390/311 319/305 314 
35-40 B89 1324 332/295 327/320 330/291 301|278 285 
30-35 296 |285 295)262 291/281 292)272 282|262 273 
25-30 275 |258 272/244 265|257 268)252 266)246 256 
20-25 254 |241 249/240 239)239 247/236 245/280 238 
15-20 239 1232 232/232 221)229 225|229 229)221 221 
11-15 228 |218 217/211 209)215 208/217 215|208 209 
* The two columns under each group of assumptions repre- 
sent the alternative results if water vapor absorption is (right 
column) or is not (left column) corrected for a pressure de- 
pendence. 
3. Absorption Spectra In the ultraviolet, absorption 
coefficients of oxygen are taken from the measurements 
of Granath [27], those of ozone from the measurements 
of various investigators [16, 36]. In the infrared, the 
emissivity of carbon dioxide is taken from laboratory 
measurements, as summarized by Elsasser [14], and 
extrapolated on log-log paper to smaller values of path 
length. Similarly the absorption coefficients of Fowle 
and Hettner [17] for water vapor are extrapolated on 
log-log paper. Summerfield’s measurements at the 10-u 
hand of ozone are utilized. The water vapor coeflicients 
are corrected according to the square-root pressure law 
in some cases. The calculations apply to a latitude of 
299 
50°N in summer or winter according to various com- 
binations of the assumptions listed above. Table I gives 
the results. 
These results show reasonable agreement with obser- 
vations. The temperature increases with height to the 
top of the ozone layer, although the maximum is not 
usually reached in these calculations. The temperatures 
are considerably higher than those that actually occur 
in the ozone layer; this is due in part to the assumption 
of solar black-body radiation at 6000K. Recent rocket 
measurements show much less energy. 
Penndorf’s Calculations of Rate of Heating and Cool- 
ing because of Ozone Alone. Penndorf [48] has com- 
puted the rates of heating and cooling of the ozone layer 
that would result from the effects of ozone alone. He 
takes the solar emission curve in the ultraviolet as that 
of a black body at 5910K and assumes the vertical 
distribution of ozone to be that measured by the Um- 
kehr effect at Arosa. He imtegrates the temperature 
changes over the period of a day. 
Penndorf’s results show maximum heating resulting 
from ozone absorption of solar ultraviolet radiation to 
lie between 45 and 50 km. The cooling effect of long- 
wave radiation is a maximum at 50 km. The absolute 
value of the rate of heating is 10-50 times greater than 
that of the rate of cooling, at least from 30 to 50 km. 
This discrepancy is probably at least partially due to 
two factors: (1) smaller solar emission in the ultraviolet 
than the assumed amount; and (2) the cooling effects 
of carbon dioxide and water vapor are not included. 
Karandikar’s Calculation of Heating of the Ozone 
Layer. Karandikar [32] has given a rather complete dis- 
cussion of the rate of heating of the ozone layer. He 
considers not only heating caused by ozone absorption 
of ultraviolet solar radiation, but also the heating caused 
by absorption of solar radiation in the infrared bands 
of ozone, carbon dioxide, and water vapor. He assumes 
the sun to radiate as a black body at 6000K. The ver- 
tical distribution of ozone is based on available Umkehr 
measurements, that of carbon dioxide on a constant 
proportion by volume (0.03 per cent) throughout the 
ozone layer. Several alternative assumptions are made 
about the total amount of water vapor present, the 
vertical distribution of the water vapor being taken to 
follow Dalton’s law. 
The results show a maximum of absorbed energy 
between 40 and 50 km. For a solar zenith angle of 0°, 
the maximum absorption occurs at 40-45 km. For a 
solar zenith angle of 75°, the maximum absorption 
occurs at 45-50 km and is only about half as intense 
as for the smaller zenith angle. Karandikar’s computa- 
tions show that the heating produced by infrared ab- 
sorption of solar energy can be safely neglected above 
30 km in comparison with the heating produced by 
ultraviolet. absorption of ozone. Below 30 km, on the 
other hand, the former process becomes predominant, 
water vapor playing the most important role. 
Craig’s Calculations of Heating and Cooling. The 
writer has carried through some unpublished calcula- 
tions of heating and cooling of the ozone layer. They 
are mentioned here to show the results that have been 
