1182 
the air are cooled by conduction, and if this process 
is carried far enough, dew forms. If there is an increase 
of specific humidity with altitude, an eddy flux of vapor 
150 
125 a i 
100 || Lal 
wn 
5 
a 75 i 
= 
50 =| 
a rl 
fo} 2 -6 -14 -22 -30 -38 -46 -54 
TEMPERATURE °F 
Fie. 3.—Number of hours of fog for various temperatures 
at Fairbanks, Alaska 1942-1947 inclusive. (After V. J. and M. 
B. Oliver {18].) 
downward is established to replace that which has 
condensed. At the same time, if there 1s any amount of 
turbulence at all, heat is conducted toward the surface 
layers along with the moisture, and some of the cooled 
air is forced aloft and slightly cooled still further by 
adiabatic expansion. This process, if continued, is sup- 
posed to cool the entire surface layer of air to saturation 
and thus fog forms. If there is no turbulent interchange 
of air or if the moisture content decreases vertically, 
then there will only be a deposition of dew. Obviously 
the presence of a cloud cover will offer counter radia- 
tion to that of the earth and permit so little cooling of 
the surface layers of air that the possibility of fog is 
practically eliminated. Likewise if the movement of air 
is sufficiently rapid for the surface roughness of the 
area concerned there will be established a turbulent 
layer deep enough so that more cooling will be required 
than is available. The intermediate condition between 
fog formation at the ground and no fog at all (given 
fog conditions with varying wind velocity) is that im 
which a stratus cloud deck forms. 
Recently, Emmons and Montgomery [5] have pointed 
out that there is another factor which has not been 
thoroughly considered. In their words, 
What has not previously been considered in explanations of 
fog formation is that air with dew point higher than the tem- 
perature of the cold surface necessarily loses water vapor by 
eddy diffusion and real diffusion toward the surface and con- 
densation on it regardless of the nature of the surface. Under 
the conditions existing when fog forms, eddy diffusion 
is equally effective in transporting both heat and water va- 
por. In the laminar layer next to the cold surface, the losses 
depend on conduction and diffusion, which are effective to 
nearly the same degree; actually the ratio of thermometric 
conductivity to diffusivity of water vapor in air is only 0.84. 
Therefore temperature and dew point both decrease, and al- 
though their difference decreases, they cannot become equal, 
4.€., saturation cannot result, by this process alone. 
It must be concluded that fog can form next to a cold 
CLOUDS, FOG, AND AIRCRAFT ICING 
surface only when there is further cooling by radiation di- 
rectly from the air or when saturation is not required. 
Likewise, in the opposite case of air in contact with 
warmer water (whether a water surface or falling precipita- 
tion) . . . air receives heat as well as water vapor, so that sat- 
uration does not necessarily result. However, in this case 
three circumstances help bring about saturation and fog; (a) 
Because diffusion is slightly more effective than conduction, 
the air gains relatively more water vapor than heat. (b) There 
may be some heat loss by radiation directly from the air (e.g., 
when warm raindrops fall through air over cold ground). (c) 
If the temperature contrast is very large (as in the case of 
sea smoke), mixing of unmodified air with air modified by 
the water may produce greater water concentration than is 
required for saturation at the temperature of the mixture. 
Strangely enough, radiation, the most important 
single element in the formation of fogs, requires less 
discussion than almost any other aspect of the subject. 
The reason for this seeming anomaly is not that radia- 
tion is of little importance, for without it the only fog 
formations would be sea fogs, fogs occurring on moun- 
tains due to upslope winds (really clouds), and perhaps 
a few isolated cases of fogs over snow cover. The 
explanation is, of course, that the difference between 
various radiative conditions usually amounts to only 
a very few degrees, and the other factors in the forma- 
tion of fog make this difference so small that it may 
usually be neglected. 
Suggestions for Research. Deficiencies in our knowl- 
edge of the physical processes of fog formation are 
present at all stages. Beginning with the nuclei, it is 
apparent that our knowledge of what constitutes them 
and how they operate is rudimentary. For example, the 
questions raised by Neiburger and Wurtele [16] con- 
cerning the role played by industrial impurities in 
lowering the relative humidity in fogs appears to cast_ 
doubt on at least one accepted idea. The submicro- 
scopic size of these particles makes it difficult to suggest 
any direct avenue of attack, but perhaps it might be 
possible to devise laboratory experiments which would 
answer some pertinent questions concerning the effects 
of various atmospheric contaminants. 
The matter of drop-size distribution appears to be 
fairly well answered, but the question raised by Heverly 
should be cleared up, perhaps by a series of observations 
taken at a number of locations such as mountain 
valleys and flat areas at some distance from water 
surfaces of any kind. Furthermore, it might be very 
instructive to have a series of such measurements made 
during the formation and dissipation of pure radiation 
fogs of shallow nature. A series of vertical measure- 
ments not only of drop size but of humidity and liquid- 
water content would also help to reveal the nature of 
fogs, particularly if the fog area were shallow enough 
to obtain a complete cross section from dense fog at the 
base to clear air at the top of the observations. 
The question of the number of fog droplets per unit 
volume has never been accurately answered. Estimates 
as low as 1 drop em~ and as high as 1000 drops cm 
have been made. Of course it is true that droplet count 
varies with the amount and kind of nuclei and with 
different kinds of fog; however, exact knowledge is 
