1292 
perature 7’ in degrees absolute, and partial pressure e of 
water vapour in millibars is 
s_79/ e , 4800¢ 
m—) x10 = 2 (p ate aa (1) 
We need to know how large the vertical gradients of 
temperature and humidity must be in order to be of 
importance in radiometeorology. Consider first a situa- 
tion in which the potential temperature is uniform 
with height; how large must the lapse rate of specific 
humidity be to make the downward curvature of a 
radio ray equal to the curvature of the earth? Let a 
be this critical lapse rate of specific humidity. Consider 
secondly a situation in which the specific humidity is 
uniform with height; how large must the negative lapse 
rate of potential temperature be to make the downward 
curvature of a radio ray equal to the curvature of the 
earth? Let 6 be this critical lapse rate of potential 
temperature, its numerical value being in fact negative. 
The values of a and 6 may be derived from (1) and 
depend somewhat on pressure, temperature, and hu- 
midity. They are of the order of 
a = 0.5 gkg™ per 100 ft, (2) 
= —5F per 100 ft. (3) 
Thus lapse rates of humidity in excess of about 16 gkg™ 
per 100 ft and inversions of temperature in excess of 
about 5F per 100 ft are of great importance in radio- 
meteorology as they cause downward bending of radio 
rays as great as or greater than the curvature of the 
earth, thereby making possible radio vision round the 
curved surface of the earth. 
On the other hand, even in a well-mixed atmosphere, 
with specific humidity and potential temperature uni- 
form with height, there is some downward bending of 
radio rays. This is the normal atmospheric refraction 
which is involved in orthodox propagation and to which 
reference has been made earlier in this article. Let 
ky be the downward curvature of radio rays when there 
is no lapse rate of specific humidity or potential tem- 
perature. It is possible to deduce xo from (1), and, like 
a and B, it depends somewhat on pressure, temperature, 
and humidity. It is convenient to compare xo with the 
curvature xe of the earth (5 X 10~° radians per 100 ft), 
and expressed in this way the value of xo is of the order of 
ko = % Ke. (4) 
Thus, even in a well-mixed atmosphere, there is down- 
ward bending of radio rays amounting to about one- 
sixth of the earth’s curvature. 
In terms of the parameters x, a, and 8 we may express 
the downward curvature x appropriate to a lapse rate 
q' of specific humidity and a lapse rate 6’ of potential 
temperature in the form 
eee (6) 
Ke — Ko a B 
This makes 
1. xk = ko when q’ = 0’ = 0, 
2. k = xe when q’ = a, 6’ = 0, 
3. kK = ke When q’ = 0, 6’ = B. 
RADIOMETEOROLOGY 
From Snell’s laws of refraction it is easily shown that 
the downward curvature « of a ray is also equal, to a 
high degree of approximation, to the lapse rate of re- 
fractive index. Thus (5) also expresses the lapse rate 
x of radio refractive index in terms of the lapse rates 
q’ and 6’ of specific humidity and potential temperature. 
In addition to these lapse rates, the actual values of 
humidity and temperature, as well as the value of the 
pressure, enter into (5) because xo, a, and 8 depend on 
these quantities to some extent, as implied by equation 
(1). But for quite a wide range of meteorological condi- 
tions it is often possible to regard ko, a, and B as con- 
stants, and (5) then expresses x purely as a function of 
q’ and 6’. 
Now under conditions when the temperature and 
humidity of an air mass have been modified by surface 
conditions, simple though not unusual profiles of po- 
tential temperature and specific humidity are as indi- 
cated in Fig. 1. It is here supposed that the air mass is 
warm and dry in comparison with surface conditions. 
It is not uncommon for the steepest gradients of tem- 
perature and humidity to occur near the surface of the 
earth, and for them to be such as to make the downward 
curvature of radio rays near the earth’s surface exceed 
the curvature of the earth. This leads to the state of 
affairs depicted in Fig. 2. Well up in the air mass the 
qT 
RAY GURVATURE EQUALS 
1/6x EARTH'S GURVATURE 
Fic. 2.—Effect of radio duct on radio rays. 
lapse rates of potential temperature and specific hu- 
midity are zero, and so, in accordance with (5), the 
downward curvature of radio rays is ko, about one-sixth 
of the earth’s curvature. A ray emanating horizontally 
from a radio transmitter 7; at such a height would show 
only a slight tendency to follow the earth’s curvature, 
as indicated in Fig. 2. Now let us bring the transmitter 
down to a level where modification of the air mass by 
surface conditions begins to be appreciable. In ac- 
cordance with (5), the positive lapse rate of specific 
humidity and the negative lapse rate of potential tem- 
perature indicated in Fig. 1 increase the downward 
curvature of rays above the standard value ko. When the 
transmitter has been brought nearly down to the earth’s 
surface, it reaches a certain level, 7, in Fig. 2, where 
the downward curvature of the ray becomes equal to 
the curvature of the earth. With the transmitter at this 
ee 
Riss Cre Vere one 
