38 RADIATION 
assumes that in the region from 13.1 » to 16.9 p» the 
CO, always absorbs so strongly that we can assume 
total absorption, and that therefore the radiation 
emitted in that range by an atmospheric layer is equal 
to the black-body radiation at a temperature existing 
at the surface of such a layer. Méller [35] assumes a 
width of only 3 uw for this range, that is, from 13.5 to 
16.5 », and estimates that within these wave lengths 
the absorption by water vapor is equal to that ‘by 
CO, only when the specific humidity is 100 g¢ ke or 
more. Outside of these boundaries, however, the ab- 
sorption by H.O is greater than that by CO». Accord- 
ingly, the CO: absorption at 273K is 18.4 per cent 
according to Elsasser and 14.6 per cent according to 
Moller. In addition, Moller gives a scale in his chart 
which permits determination of the radiation effect of 
CO» for large temperature variations at low altitude 
(close to the ground) or for very low CO», content of the 
air (stratosphere). 
Another point of comparison consists of the numerical 
values assigned to the absorption coefficient ky by 
Elsasser and by Moller. In the 6-1 band Moller’s values 
are somewhat higher. The same applies to the absorp- 
tion increase from 10 » to the rotation band, while in 
the core of this band the values are lower. Elsasser 
first calculated his graph with the coefficients of his 
table. Later, however, he corrected it according to 
measurements of total absorption and concluded from 
these measurements that the ky values around 6 yu 
were originally too low, while those for 50 » were too 
high. This makes the agreement of the ko values even 
better than a comparison of the numerical values would 
indicate. 
Lately, an important objection has been raised 
against both radiation diagrams. The absorption func- 
tions for a spectral line, L¢(kom), which are used by 
both authors, contain the assumption that a = Av/é = 
5.6, wherein 6 was set at 0.5 em and the distance 
between lines, Av, was assumed to be 2.8 em as the 
mean of the range investigated by Randall and his 
collaborators. According to recent measurements by 
Adel [1] on two lines near 16 and 18.6 p, it was found 
that 6 = 0.23 em; from this it follows that a = 12. 
The absorption function for a line L? is also shown in 
Fig. 1 for a = 12. The author suspects that the applica- 
tion of the new function will not lead to any important 
differences from the previous radiation charts, since 
the differences of ko at 10 », as compared to those at 
6» and 50 un, are so large as to render all refinements 
negligible. 
The Downcoming Radiation of the Atmosphere 
The simplest possible application of the radiation 
charts arises in the calculation of the downcoming 
radiation R of the atmosphere and of the effective 
nocturnal radiation H = oT)! — R of the ground. 
Only a few direct comparisons of the measured and the 
calculated values are available. 
Wexler [50] compared measurements made in Alaska 
and North America under winter conditions with radia- 
tion values calculated from Elsasser’s diagrams and 
found that on the average the calculated outgoing 
radiation values were about 0.035 cal em~ min higher 
than the observed values. This deviation, for which 
Wexler has no explanation, must probably be ascribed 
to the use of the earlier edition of Elsasser’s diagram 
which, in the range of water-vapor content in ques- 
tion, furnishes a value for downcoming radiation ap- 
proximately 10 per cent lower than the later edition 
of this chart. 
F. A. Brooks [7] and Robinson [48] carried out com- 
parative calculations for some cases of their numerous 
observations, but used them essentially to compute a 
radiation diagram on an empirical basis (see p. 40). 
However, in part of these observations in the free 
atmosphere only the total water-vapor content was 
used. So far, in most cases, no aerological measurements 
were made concurrently with the radiation measure- 
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R/aT4 
(0) 4 8 12 16 20 24 
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Fie. 3—Scattering of the relative atmospheric radiation 
R/oT* according to Bolz and Falckenberg |6]. Seventy per cent 
of all measured values lie in the hatched region, and 
ninety-eight per cent of all values lie within the region bounded 
by the dashed line. 
ments. Therefore only the variables measured on the 
ground such as pressure, temperature, vapor pressure, 
and cloudiness were used to organize the measurements 
and to develop interpolation formulas. The best known 
are those by Angstrém and Brunt which give the 
ratio R/oT>* as a function of the vapor pressure at 
ground level only where 7 is the air temperature at 
the point of observation. Numerous authors have 
derived the constants of this formula from their meas- 
urements, but the scattering of the constants given by 
the different authors is as great as the scattering of the 
individual measurements around the curves plotted by 
each author [28]. Only recently Bolz and Falckenberg 
[6] gave constants for Angstrém’s formula which re- 
sult in values for the downcoming atmospheric radia- 
tion which are 7 per cent higher than the constants so 
far assumed as best values (Fig. 3). 
If we assume a relative humidity that does not vary 
with height and a normal lapse rate of 6C km, we 
obtain the values for R (at Tp = 283K) given in Table 
II, according to Méller. These figures are higher than 
