METEOROLOGICAL ASPECTS OF PROPAGATION PROBLEMS 
critical level, a ray emanating horizontally remains at 
the same height above the earth’s surface and does not 
fly off at a tangent. This vital level, where the down- 
ward curvature of a ray is equal to the curvature of the 
earth, forms the top of what is known as the radio duct. 
As we bring our transmitter down below the top of the 
duct, a ray emanating horizontally, say from T; in Fig. 
2, is bent downward to such an extent that it hits the 
earth and suffers successive reflections from it. The ray, 
in fact, is trapped within the duct. It is trapping of 
this sort that causes low-level radars to see low-level 
targets far beyond the geometrical horizon. 
Trapping of rays in a radio duct as illustrated in Fig. 
2, although it provides a clear insight into the phenome- 
non of superrefraction, gives a substantially oversim- 
plified picture [4]. The oversimplification does not reside 
in the meteorological aspects of the problem, however, 
and therefore we need not go into the matter in great 
detail. The principal trouble with Fig. 2 is that it sug- 
gests that, under the appropriate atmospheric condi- 
tions, superrefraction would be experienced at all radio 
wave lengths. Now it is well known that, apart from 
ionospheric refraction, with which we are not concerned, 
there is no phenomenon of superrefraction at ordinary 
broadcasting wave lengths. Propagation in the lower 
atmosphere at ordinary broadcasting wave lengths is 
almost completely independent of weather. Even under 
meteorological conditions involving a pronounced radio 
duct and producing marked superrefraction at radar 
wave lengths, propagation in the lower atmosphere at 
broadeasting wave lengths is almost completely ortho- 
dox. The reason for this dependence of superrefraction 
upon wave length is that sufficiently long wave lengths 
respond only to a crude average of the atmospheric 
gradient, but sufficiently short ones fully appreciate all 
the fine structure. Thus, to produce marked super- 
refraction on a wave length of 1 km would require a 
radio duct extending from the earth’s surface up to a 
height of the order of 30,000 ft. No approximation to 
such enormous ducts ever occurs in the atmosphere, and 
so serious superrefraction at ordinary broadcasting wave 
lengths is out of the question. On the other hand metre 
wave lengths can respond quite effectively to unusual 
gradients of temperature and humidity within the first 
few thousand feet of the atmosphere, while centimetre 
wave lengths can be seriously affected by unusual 
gradients within the first few hundred feet. It thus 
comes about that superrefraction is a phenomenon that 
is quite widespread at centimetre wave lengths, fairly 
widespread at decimetre wave lengths, only moderately 
widespread at metre wave lengths, quite exceptional at 
dekametre wave lengths, and virtually unknown at 
longer wave lengths. It therefore has to be realized 
that, in addition to meteorological parameters such as 
temperature excess, humidity deficit, wind speed, which 
control the distribution of radio refractive index in the 
lower atmosphere, there are nonmeteorological param- 
eters such as wave length, height of transmitter, height 
of receiver, which also have a big influence upon radio 
propagation. 
In Fig. 2 we have illustrated a situation in which the 
1293 
steepest gradients of temperature and humidity occur 
at the surface of the earth. This is by no means always 
the case however. For example, when superrefraction is 
produced by a subsidence inversion, the distributions 
of potential temperature and specific humidity with 
height are frequently of the type shown in Fig. 3 and 
TEMPERATURE 
ESS 
rk 
HUMIDITY 
DEFICIT 
HEIGHT 
HEIGHT 
POTENTIAL TEMPERATURE ’ SPECIFIC HUMIDITY 
Fia. 3.—Profiles of potential temperature and specific humidity 
associated with an elevated refracting layer. 
this leads to an elevated refracting layer instead of one 
resting on the surface of the earth. In such a case, the 
degree of superrefraction experienced in communicating 
between points on the earth’s surface depends on (1) 
the temperature excess and humidity deficit of the air 
mass above the layer in comparison with that below 
the layer, (2) the precise profile of refractive index in 
the layer, and (8) certain radio parameters (particularly 
wave length), but it also depends quite vitally upon the 
height of the layer above the surface of the earth. The 
lower the height at which a layer exists, the more effec- 
tive it usually is in causing superrefraction. The reason 
for this may be illustrated by supposing that the re- 
fractive index of the atmosphere suffers a small dis- 
continuous decrease as we ascend through a level S, the 
refractive index above and below this level being uni- 
form. Such a discontinuous drop in refractive index 
causes total internal reflection of a ray incident from 
below at a sufficiently glancing angle. But, on account 
of the curvature of the earth, even a ray leaving the 
surface of the earth horizontally attacks the level S 
at a nonzero angle to the horizontal, and this angle is 
larger the greater the height of the layer. As a result 
total internal reflection of a ray leaving the surface of 
the earth horizontally is impossible if the layer is too 
high. This picture, although grossly oversimplified, 
makes it clear why reflecting layers must be quite low 
in the atmosphere to produce marked superrefraction 
for communication between points on the earth’s sur- 
face. Thus a striking subsidence inversion nearly always 
causes outstanding superrefraction if its base is as 
low as one thousand feet above the earth’s surface, 
but if its base is at ten thousand feet the inversion is 
unlikely to be of much practical importance except for 
communication between airplanes. 
To summarize, we may say that superrefraction is 
usually associated with an inversion of temperature 
exceeding about 5F per 100 ft and/or a lapse rate of 
humidity exceeding about 144 gm kg per 100 ft main- 
tained over an interval of height of the order of 100 ft 
