46 RADIATION 
An initial attempt of this type was made by approxi- 
mating the function X by the sum of two exponential 
functions. This would mean that the absorption spec- 
trum of the water vapor is not gray but “bichromatic.” 
The investigation of the radiation equilibrium of the 
atmosphere was carried out by Emden [15] for gray 
radiation and led to an isothermal stratosphere of 
—68C. The calculation of the same problem for bi- 
chromatic absorption of water vapor does not lead to 
an isothermal stratosphere but yields a steady decrease 
in temperature with altitude down to —144C at the 
boundary of the atmosphere [81]! If it still were at all 
necessary to deal the death blow to the untenable 
theory of the radiation equilibrium of the water vapor 
in the stratosphere, this calculation would do so. 
Another approximation of X is fundamentally more 
accurate. If we set X = a In(w + 6), where a and b 
are numerical values, we obtain an approximation 
that is especially good for small values of w and small 
amounts of CO:. Then dX = adw/(w + 6), and from 
this simple formula the radiation equilibrium can be 
developed as a kind of integral equation and can be 
brought closer to numerical solution. This method 
appears important especially for the temperature 
distribution in immediate proximity to the ground be- 
cause, under conditions of both midday adiabatic strat- 
ification and nocturnal ground inversion, this tempera- 
ture distribution is a function not only of the austausch 
but also of radiation. Results of these calculations are 
not yet available. 
Radiation in the Stratosphere 
Investigation of radiation phenomena in the strato- 
sphere is more difficult than in the troposphere for sey- 
eral reasons. First of all, the absorbing media are under 
very low pressure, and therefore a check must be made 
in every case to ascertain to what extent the absorption 
coefficients, as measured in the laboratory, may be 
used. In the second place, the concentration of the 
various gases is not known exactly. Finally, the radia- 
tion cannot be considered any longer as an individual 
process out of the context of the general physical phe- 
nomena. In the troposphere also, radiation participates 
everywhere, to be sure, in the general weather pattern, 
and in the presentation above, emphasis has been on 
showing that radiation participates decisively in all 
meteorological processes. However, the substances 
themselves are not changed in their molecular struc- 
ture by absorption or emission. If, for instance, water 
vapor is brought to condensation and fog forms as 
a result of strong radiational cooling, it changes only 
its aggregate state, not its chemical structure. In the 
stratosphere, however, ozone offers an example of more 
drastic changes. It is only by the absorption of the solar 
radiation in the ultraviolet bands that the formation of 
O; from O02 becomes possible, and it is under the in- 
fluence of longer waves in the ultraviolet that the ozone 
again dissociates. It is indeed true that it is not the 
long-wave heat radiation but the short-wave solar radi- 
ation that controls the formation and dissociation of the 
absorbing medium. In addition, however, both proc- 
esses participate in the heat balance with their thermal 
implications. Therefore, the radiation processes in the 
stratosphere cannot be separated from the multitude of 
physical atomic processes at those altitudes. If, in spite 
of this, such an attempt is made, it will necessarily be 
in full consciousness of the unreliability involved. 
Above 10-km altitude the importance of water vapor 
as a decisive absorbing medium decreases more and 
more, and CO, and O; become significant. The water- 
vapor content of the air in the stratosphere is extremely 
small according to measurements by Dobson [13], Bar- 
rett [5], and others. For several kilometers above the 
tropopause the frost point falls steadily at the rate of 
its decrease with altitude in the troposphere, so that 
the relative humidity at 2 km above the tropopause 
has decreased to below 1 per cent. However, if we 
accept this low humidity as a generally valid fact, the 
radiation effect of the water vapor in the stratosphere 
no longer exerts any notable effect, smce its total 
content drops to 10 g em. Dobson, however, thinks 
that its effect is to be considered equivalent to that of 
CO2, but gives no numerical values for the amount of 
absorbed radiation. \ 
Carbon dioxide has a very intensive absorption band 
around 15 p. An extremely weak band around 10 yp 
absorbs only one per cent for layer thicknesses that 
equal the content of the whole atmosphere. An addi- 
tional band at 4 pu lies at the boundary of the spectrum. 
The absorption curve in the 15-p band is known. The 
dependence on pressure is usually estimated by the 
effect on the 4-u band which is known from measure- 
ments by Wimmer [51]. From this Moller has derived 
a reduction factor 1 = (p/po)°", whereas Hlsasser uses 
the +/p/po law in the same manner as for the water 
vapor, and Goody a proportionality to p. A calculation 
of the processes is possible by means of the Moller dia- 
gram. Moller calculated the CO,-radiation emitted by 
an isothermal stratosphere and found a maximum effect 
at an altitude of 26 km with a cooling of 1.5C to 2C 
per day. Since his assumption of a CO:-content of 0.03 
per cent is somewhat too high, the maximum lies prob- 
ably a little lower. 
In this calculation it was assumed that the ozone has 
no effect. But, as mentioned already, ozone has a very 
intensive absorption band around 14 yu which is situated 
at the same point as that of CO. and shows a curve 
with respect to wave length which is similar to that of 
CO. The line structure of ozone which probably differs 
from that of COs, is unknown, however, and probably 
does not enter into the calculations. Since half of the 
ozone lies at altitudes above 20 km, the radiation of the 
CO is extensively shielded by its absorption, and the 
outgoing radiation in this range of wave lengths takes 
place only at higher altitudes and then as an emission of 
the ozone. Thus, these processes interact strongly with 
each other, and for this reason scarcely any attempts 
have been made to investigate them in greater de- 
tail [83]. 
Furthermore, the experimental bases for the ozone 
spectrum are not yet sufficient. In addition to the 
14-» band, there is another band around 9.6 pn, which 
