370 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
case where dM /dh is independent of h, and by using 
equation (6), & is conveniently obtained from the 
slope of the M —h curve. It is found that the 
vertical temperature gradient has a comparatively 
small influence on k, while fairly small variations 
of the humidity gradient will affect k appreciably. 
The other case is that of nonstandard refraction. 
Here M is not a linear function of the height. The 
most important special case is that of superrefrac- 
tion, which occurs when, in certain height intervals, 
M decreases with height instead of following the 
usual increase with elevation. Such a decrease of M 
in certain layers of the atmosphere is caused by a 
steep negative moisture gradient or steep positive 
temperature gradient, or even more by a combina- 
tion of both influences. 
With superrefraction, propagation conditions are 
greatly different from those encountered with 
standard refraction and the methods to be given 
later for the determination of the transmitted power 
do not apply. This is especially true for the field 
near or below the optical horizon. The discussion of 
nonstandard propagation is beyond the scope of this 
volume. 
High-angle coverage is generally independent of 
refraction and is therefore also unaffected by the 
variations of M in the lowest layers of the atmosphere. 
Direct Determination of k 
In Figure 9 the reciprocal of k is plotted as ordinate 
against the vertical gradient of relative humidity as 
abscissa. The values shown refer to a standard 
temperature gradient of — 0.65 degrees Centigrade 
per 100 meters; unless the temperature gradient 
differs greatly from this value, the corresponding 
values of k will not be much affected. The curves 
given refer to 100 per cent relative humidity at 
ground level, and an auxiliary table is provided 
at the top of the graph which gives figures to be 
added for other values of the relative humidity. 
The sensitivity of k to moisture gradients in warm 
climates is obvious from these data. 
GROUND REFLECTION 
Ground Reflection and Coverage 
The reinforcement of the direct ray by the ground- 
reflected ray is of great importance both in radar 
and in communication work. In favorable cases, 
the reflected ray may be of comparable intensity 
to the direct ray and thus the received intensity 
may be approximately doubled in places where the 
two rays have the same phase. This means, in many 
cases, the possibility of an appreciable increase in 
range relative to that in free space. 
Complexity of Reflection Problem 
In order to facilitate the discussion of the problems 
encountered in reflection, it is necessary to analyze 
the complex phenomena into simpler constituents. 
+f FOR 100% GROUND LEVEL HUMIDITY 
REL HUMIDITY GRADIENT 
| | % PER 100 METERS ———> 
oe 4 tet 
IS 
SSNS SASS 
t 
wy en ee CaS 
SUE SSCS 
=3 -6 
Fieure 9. Graph 1/k versus RH (relative humidity) gradient and temperature for 100 per cent RH at ground. Add 
correction tabulated to obtain 1/k for RH at ground less than 100 per cent. 
