VISIBILITY IN METEOROLOGY 
By W. E. KNOWLES MIDDLETON 
National Research Council, Canada 
Introduction 
This discussion will be devoted to a brief study of 
those interrelations between the optical properties of 
the atmosphere and the characteristics of human vision 
which determine how far a given object can be seen at 
such and such a moment. This important distance, 
when referred to the ordinary objects which lie around 
the horizon of a meteorological observer, is called by 
meteorologists ‘“‘the visibility”; it is not with any hope 
of changing this terminology, but only in the interests 
of logical discussion, that the same quantity, applied 
now to any object, will here be given the name visual 
range. The term is self-explanatory. 
The theory of the visual range is by this time in a 
fairly satisfactory condition, largely because of very 
extensive researches conducted during World War 
II, especially in the United States. As in many other 
divisions of meteorology, however, the extreme com- 
plexity of atmospheric conditions makes it difficult to 
apply the available theory to actual instances, especially 
in the important case of visual range along inclined 
paths. Even the instrumentation necessary to measure 
the appropriate optical constants of the atmosphere has 
not been developed to the point where it is in general 
use at meteorological stations. Theory is well in front 
of practice. 
We are unable to refer the reader to any very up-to- 
date summaries of the whole field; in fact to nothing 
later than 1941 [83, 35]. In view of our restrictions on 
space we must assume that at least one of these two 
monographs is available to the reader. It is to be hoped 
that before very long a more up-to-date general account 
will be published. 
The Behavior of Light in the Atmosphere 
Light, by its interaction with the atmosphere, pro- 
duces many beautiful phenomena which are dealt with 
elsewhere in this book. Our concern here is only with 
the way in which it is attenuated in its passage through 
the air and with the manner in which it is diffused by 
scattering. 
As far as any practical interest is concerned, we may 
neglect those rare occasions when the air is nearly free 
from particles larger than the molecules of gases, in 
view of the fact that the visual range in such a pure 
atmosphere would be several hundred kilometers at sea 
level. The reader may be referred to Cabannes [10] for 
a masterly discussion of such molecular scattering. On 
all occasions when the visual range is of any practical 
importance, by far the greater part of the effect of the 
atmosphere on light is produced by particles much 
larger than molecules, which may be thought of as the 
disperse phase of an atmospheric colloid or aerosol. 
91 
These particles are of many kinds, but from our 
standpoint the most interesting of them are the liquid 
droplets, generally aqueous solutions of hygroscopic 
substances, which in various radii from about 10° to 
10— em form the obscuring matter in haze, fog, and 
mist. The actual nature of the hygroscopic nuclei in- 
volved is one of the great unsolved problems of meteorol- 
ogy, and has become the subject of a controversy, for 
the details of which the reader should consult Wright 
(52, 58, 54, 55, 56], Simpson [48, 44] and Findeisen 
[21]. Whatever their nature, they increase in size with 
increasing relative humidity, as more and more water 
condenses on them. Up to a radius of about 0.5 micron 
(5 X 10-5 em) they show selective scattering in visible 
light which makes them appear bluish by reflection, 
and we call them haze. With further increase in size, 
this selectivity practically disappears, and we have 
fog, which is typically colorless. We must now consider 
in a little more detail the scattering of light by such 
spherical particles. 
For particles of radius a in the range 0.1A < a < 
10\ (A = wave length of light), which includes most 
kinds of haze and some fogs, the theory of Mie [38]! has 
been found entirely adequate. Starting with the electro- 
magnetic theory, Mie was able to calculate the intensity 
T (lumens per steradian per particle per lumen per m? 
illuminance) in a direction making an angle ¢ with that 
of the incident light. This is a function of 27a/\ and of 
m, the index of refraction of the particles (1.33 for 
water). To show the large variation of the polar diagram 
of the scattered light with the radius of the particle, 
Fig. 1 is presented, the limiting value as a — 0 being 
shown by a dotted curve (Rayleigh atmosphere). 
By integrating [(¢) over the sphere, the total amount 
of light scattered may be calculated, and it is found that 
this is generally greater than that imcident on the 
droplet. For large droplets the ratio K of these quantities 
approaches 2, and the explanation is to be found in 
diffraction. Since K has been calculated [30, 47] as a 
function of the parameter 27a/\, the coefficient of 
attenuation by scattering for an atmosphere containing 
N droplets per m*, each of radius a, is 
b = NKra? (1) 
In such droplets, as has been shown by Zanotelli [57], 
absorption is negligible, so that the extinction coefficient 
o is also given by equation (1). 
The correctness of these ideas is now acknowledged, 
and they have been remarkably well verified in natural 
haze by Dessens [15, 16], who caught haze particles on 
minute spiders’ webs. 
For the larger droplets of fog, Bricard [8, 9] has 
meter}. 
1. Concisely set forth by Stratton [46, p. 563]. 
