ACTINOMETRIC MEASUREMENTS 
By ANDERS ANGSTROM 
Meteorological and Hydrological Institute of Sweden 
ACCURACY OF ACTINOMETRIC 
MEASUREMENTS 
In actmometry, as in every other field of science 
founded upon some kind of direct measurement, the 
instrumental accuracy and the method of observation 
must be closely related to the character of the scien- 
tific problem under consideration. 
Determination of the Solar Constant. Some scientists 
maintain that this so-called ‘‘constant” is subject to 
short periodic variations amounting to approximately 
0.2 per cent on the average, with a maximum amplitude 
of about 1-2 per cent. It is evident that in order to 
investigate these variations our measuring devices must 
be sufficiently accurate to measure amounts of radia- 
tion below the smallest amplitude of the variations 
which we intend to determine, in other words, the 
instrument must measure accurately to at least +0.2 
per cent. 
Heat Exchange at the Earth’s Surface. Considerably 
less accuracy is required in many other problems closely 
connected with actinometry. Suppose, for instance, 
that we wish to investigate the heat exchange at the 
earth’s surface through radiation, convection, conduc- 
tion, evaporation, etc. Here, the radiation enters into 
an equation in which the other factors mvolved can 
hardly be determined to an accuracy greater than 
5-10 per cent. Even if we could measure them more 
accurately, it would be of little benefit, since the values 
have no general applicability. Convection, conduction, 
reflection from the earth’s surface, and evaporation are 
all highly variable from place to place. Local measure- 
ments are seldom representative for more than very 
limited areas. An accuracy of +3 per cent seems in 
general quite sufficient for such purposes as actino- 
metric measurements aiming at an evaluation of the 
heat balance at the earth’s surface, ablation studies on 
glaciers and snow covers, and studies of similar geo- 
physical problems. 
Analysis of the Atmosphere. Actinometric measure- 
ments are, however, also an important means for the 
analysis of the content of the various atmospheric con- 
stituents. Through rather simple measurements of the 
total direct solar radiation and of the same radiation 
within a few selected regions of the spectrum, an evalua- 
tion can be made of the total water content in the path 
of the solar beam as well as of the turbidity (7.e., the 
content of solid or liquid particles which scatter light in 
the atmosphere). The principles on which such deter- 
minations of the turbidity and water content are 
founded will be briefly summarized in the following 
paragraphs. 
If the solar ‘“‘constant” is regarded as a true constant 
and its relatively small variations are neglected, the 
50 
variations of the incoming direct solar radiation Qm 
at a given solar elevation (air mass m) may be re- 
garded as due to four principal causes: 
1. The variable distance between sun and earth. 
2. Molecular scattering. 
3. Scattering and absorption by liquid and _ solid 
particles in the atmosphere. 
4. Selective absorption by the gases of the atmos- 
phere. 
The variations resulting from the first cause are well 
known and easily computed. The scatterme by the 
molecules may be computed from the theory of Ray- 
leigh; the scattering coefficient thus determined is a 
continuous function of the wave length, being inversely 
proportional to its fourth power. 
Scattermg by the solid and liquid particles in the 
atmosphere may, as a first approximation, also be 
regarded as a continuous function of the wave length. . 
Strictly speaking, if the physical nature of the particles 
is known in detail, the scattering coefficient may be 
computed as a function of the wave length, according 
to the classical theory of Mie. However, since we seldom 
or never have a complete knowledge concernmg the 
variable nature of the scattermg particles m the at- 
mosphere, it seems allowable to introduce a simplifica- 
tion based on empirical results. From Abbot’s extensive 
observations in various parts of the world the present 
author found that the scattering coefficient S due to 
liquid and solid particles in the atmosphere may, in 
general, be expressed by 
SS = Be, 
(1) 
where 8 has a value proportional to the number of 
particles, and a no longer has a value of 4.0 as in the 
case of the molecules but varies between 0.5 and 2.0, 
according to the size of the particles. The smaller the 
particles, the larger is the value of a. In general, an 
acceptable average value for a, that holds for ordmary 
conditions, seems to be 1.8. When the atmosphere has 
been polluted with larger particles, as after violent 
volcanic eruptions or through dust storms over deserts, 
the value of a is sometimes as low as 0.5 or even less. 
The particles influencing the visibility in the atmosphere 
near the ground are also evidently larger than the 
average particle causing the scattermg of the solar 
beam. For these lower layers Schmolinsky [10] found 
an average value of about 0.9 for a. 
These considerations hold approximately for the 
visible part of the solar spectrum, that is, for wave 
lengths in the range from 0.4 to 0.8 ». They are, how- 
ever, not applicable to the ultraviolet and the far 
infrared. Finally, the incoming solar beam is weakened 
also by the selective absorption by the various atmos- 
