LONG-WAVE RADIATION 39 
comparative values [28] that can be calculated ac- 
cording to 
Ra = oP! (0.79 — 0.174 X 10-98) (Angstrém) 
3 = oF! (0.48 + 0.60 Ve). (Brunt) 
Three influences may cause the discrepancies and 
also the large scattering of individual measurements 
around the interpolation formulas. They are (1) the 
consideration of temperature, which is all too imac- 
curate, (2) the neglect of ground inversions, and (3) the 
additional effect of absorbers other than H.0 and COs. 
These three influences will now be considered in turn. 
1. The formulas of Angstrém and Brunt give the 
radiation of the atmosphere as proportional to T>'. 
This law is taken into account in Moller’s diagram by 
the fact that the area under a given isotherm 7’, which 
represents the radiation of an isothermal atmosphere 
with w = © and CO,-content = ©, is equal to the 
black-body radiation o7*. An isothermal atmosphere 
of OC with the limited vapor content 3 g cm™~™ has a 
radiative power R = 0.826 oF '; a layer of equal con- 
tent at +40C gives R/oT)' = 0.804 and at —40C, 
R/cT:! = 0.866. The variation of this factor, frequently 
Tapip I]. CatcutateD Downcomine RapratTion Ff 
AND EFFECTIVE TERRESTRIAL RaprIatTion H 
(For T) = +10C, ground-level vapor pressure «, and 
total water-vapor content W) 
ay (Gald))3 Sao e eee 123 | 8.7% | Gail |) SG Wiles OO) 
ii’ (@ Guipe)e so eecenes 0.224) 0.67 | 1.12 | 1.56 | 2.24 | 3.64 
R (cal em? min=)...| 0.334] 0.369} 0.385) 0.396 0.408) 0.425 
E (cal em? min“). ..| 0.196) 0.161) 0.145) 0.134) 0.122) 0. 105 
H/oT (per cent)..... 37 [30 27 25 23 20 
called emissivity, is caused by the changes of the 
ordinates of the J-lines in the diagram with w. The 
yariation may also be expressed by the assumption 
that the radiation of such a limited vapor mass in- 
creases more slowly with 7 than with 7’. Accordingly, 
it appears that we can set 
R/oTo = C [1 — y(To — 273), 
in which 7’) = observed temperature near the earth’s 
surface, and 
C= (R/oTo) To = 273 
is a function of the water content W of the atmosphere. 
W g cm 
vy 107! deg 
0.2] 0.5 | 1 2 3 4 
—2.0/ 1.0 |] 4.0 | 7.0 | 85 | 9.5 
It can be seen that measurements at high atmos- 
pheric temperatures, when they are taken as represen- 
tative for OC, yield too low a downcoming radiation, 
except when the vapor content of the atmosphere is 
exceptionally low. Brunt prefers presentation by an 
exponential law and finds the radiation as proportional 
to 7? without indication of the vapor content. In the 
little-known formula of Robitzsch [45] for atmospheric 
radiation, R varies as oT)’. 
2. On nearly all cloudless nights during which radia- 
tion measurements are made there exists a ground 
inversion, the magnitude and temperature of which are 
usually unknown. However, the layers next to the 
ground also furnish a considerable portion of radiation 
from above. (The values in parentheses in the following 
statement are percentages of the black-body radiation.) 
According to an estimate by Moller [28] for a normal 
atmosphere, 37 (28) per cent of the radiation proceeds 
from the layer 0-10 m, 71 (53) per cent from 0-100 m, 
and 88 (66) per cent from 0-500 m. Accordingly the 
effect of a ground inversion is great; an attempt at 
estimating this effect is shown in Table III. The down- 
coming atmospheric radiation R and the effective ter- 
restrial radiation H are given for an atmosphere of 
hy = QBS enncl Wi’ = i & ea’. 
This table indicates that a ground inversion can 
reduce the effective terrestrial radiation to 45 its nor- 
mal value, and under the extreme conditions found by 
Mosby during the polar night, to as low as 14. There- 
fore, any comparison between calculation and observa- 
tion becomes impossible if the vertical temperature 
Taste II]. Downcomrnc ATMOSPHERIC RapiaTION R AND 
EFrectivE TERRESTRIAL RapIATION # IN RELATION TO 
VERTICAL TEMPERATURE DISTRIBUTION 
F op Temperature 
T hick 5 
So ickness incieass (cal em=2min—) | (cal cm min7) 
100 9.4 . 360 _ -099 
200 8.8 356 . L038 
300 8.2 .353 . 106 
400 7.6 -ool . 108 
500 7.0 300 . 109 
1000 to. 344 ate 
6C km Bod 125 
Lapse rate { adiab. .333 .126 
distribution, especially that part close to the ground, 
is not known. Frequently, the temperature immedi- 
ately contiguous to the ground will mcrease with alti- 
tude even more rapidly than assumed in the examples 
in Table III, and can thus cause an even larger positive 
deviation of the atmospheric radiation. Generally there 
will be no inversion over mountain stations, although 
so-called mountain inversions do occur. The diurnal 
variation of the temperature gradient may also explain 
the diurnal variation of the atmospheric radiation and 
its dependence on the air mass as demonstrated by 
Faleckenberg [16]. 
3. Robinson [43] has carried out very careful evalua- 
tions of the measurements at Kew which included 
soundings of the free atmosphere. He found that on 
only few of the clear nights could the radiation values 
easily be fitted on a smooth curve that represented 
the relationship between radiation and the vapor con- 
tent of the atmosphere. For other nights & rose to 0.038 
cal, that is, more than 10 per cent higher. Such supple- 
mentary radiation appeared at times within an hour, 
It is impossible to seek an explanation in the variation 
of the content of CO»: or O;. It is rather more plausible 
to conceive a sudden development or advection of 
ground inyersions or of very thin invisible cloud veils. 
Robinson suspects, rather, an additional radiation 
