30 RADIATION 
theless, when @ for average cloudiness conditions is 
desired, equation (25) is commonly used. 
In equation (24), a is usually determined from meas- 
urements of Q for individual days on which S = 0 and 
S = 100. Very few places have an average of S = 0 
or S = 100 for a period of a month, and it is not cer- 
tain that equation (24) will yield average values of Q 
for periods which are made up of a mixture of clear, 
partly cloudy, and overcast days. A study of all suit- 
able data in the United States [83] im which only 
monthly mean values of Q and Q were used gave the 
equation 
Q = Q (0.35 + 0.618), (26) 
with a correlation coefficient of +0.88 between Q/Qo 
and S. Here Q is the cloudless-day radiation. An ex- 
amination of the data (unpublished) revealed that in 
the western part of the country a was higher than in 
the eastern part. 
That a should vary is to be expected from Haur- 
witz’s data (Fig. 10). The frequency of cloud types is 
not often available, but it can be seen that areas with 
greater frequencies of high clouds will have higher 
values of a than areas with high frequency of low clouds. 
Hence, the application of one equation such as equation 
(25) or (26) everywhere should be expected to lead to 
some imaccuracies even when the amount of cloudiness 
or of sunshine is known. Fortunately, for a considerable 
range of S, equation (25) or equation (26) will give very 
similar results for Q@/Qo. Only in very cloudy or rela- 
tively clear areas will there be a difference in the result. 
For lack of more detailed information, Kimball applied 
equation (25) to the best cloud-amount data available 
to him and computed maps showing the distribution of 
radiation over the ocean area [52]. However, if the fre- 
quency of cloud types in some ocean areas is different 
from the average for the eastern United States, results 
different from those of Kimball should be expected. 
The computations from any of these formulas can 
approximate only long-term average values. At any 
one place and time large fluctuations from the normal 
value occur. For example, at Washington, the total 
radiation on a horizontal surface for a particular Febru- 
ary, Say, may vary by as much as + 20 per cent from 
the average for all Februaries and bear very little re- 
lation to S for that particular February. Angstrém 
[11] notes that in the short interval 1923-28 the annual 
total of radiation at Stockholm varied by + 10 per 
cent from the mean for the six-year period. There is 
ample evidence therefore of large variations in the ra- 
diation that reaches the ground at particular points on 
the earth’s surface. If the variations which Danjon 
found in the earth’s albedo are verified, large fluctua- 
tions also occur in the total radiation that reaches the 
entire earth’s surface in a period of a month or even of a 
year. Except for regions where clouds are rare, areas of 
below or above normal radiation (or surface heating) 
may occur anywhere, being influenced predominantly 
by the prevalence of the amount and type of clouds. 
GENERAL SPECULATION AND CONCLUSION 
From the thoughts implied or expressed earlier, we 
can extract a few for amplification and emphasis. 
Solar Radiation at the Ground. The solar energy Q 
absorbed by a unit area of the earth’s surface is by far 
the largest portion of the absorbed energy. It is cus- 
tomary when discussing the average general circulation 
to consider that the greatest heating occurs at the 
equator where the air rises and that a whole chain of 
events takes place as a consequence. This equatorial 
heating is supposed to represent an average condition. 
Actually, even as an average condition, it is not a true 
picture for the summer hemisphere. In the Northern 
Hemisphere summer, average Q is distributed rather 
uniformly with latitude, so that there is no pronounced 
maximum of radiation near any one latitude, and the 
maximum, such as it is, probably occurs near lat 40°N 
rather than at lower latitudes. The maximum surface 
temperatures occur in the middle of the large cloudless 
land masses, not necessarily at the equator. 
Let us speculate somewhat on the possible signifi- 
cance of the fairly uniform surface heating in summer in 
middle latitudes. In the annual cycle of temperature it 
is well known that in inland areas the maximum of the 
average surface air temperature lags the maximum solar 
radiation by about four to eight weeks. Simce advection 
in summer is generally small, the heat balance at the 
ground im sziu may be an important factor i deter- 
mining the future average air temperature over a period 
of time such as a week or a month. In effect the ground 
acts as a heat reservoir; it gets hot to a considerable 
depth under the mfluence of the solar radiation which 
it receives, and it gives up its heat gradually to the 
atmosphere. 
The lag between the average surface air temperature 
and the solar radiation at the ground occurs in the mean 
or normal situation. What happens in any particular 
summertime week or month? As indicated earlier, the 
amount of solar radiation which reaches the ground in 
a period of a week or month may differ markedly from 
the normal value of solar radiation. Suppose the solar 
radiation received during a particular June is much 
higher than normal: Perhaps we can assume that the 
ground would get hotter (over and above its normal 
rate of heating) than it had been in the previous May 
and that the effect of the hotter ground would be to 
modify the air temperature towards higher temperature 
in the followmg July. 
Actually, we should of course examine the heat bal- 
ance at the ground and not the incoming solar energy 
alone. The solar energy is regularly measured im many 
places, and in the United States the network of such 
measurements is now nationwide. But the heat losses 
at the ground are not regularly measured as universally. 
In the face of such an observational deficiency, is it 
justifiable as a first approximation to assume that the 
variation of incoming solar energy in summer predomin- 
ates over other effects, such as variations im outgoing 
radiation? If this assumption is justified, and summer- 
time advection is not a predominant effect, an ano- 
