a" 
_ 
ee 
4 
: 
: 
t 
‘ 
3 
we 
2 
5 
TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 141 
ground; if the humidity at the ground is less than 
100 per cent the correction read from the auxiliary 
table is added to the value of 1/k obtained from the 
graph. The standard temperature gradient of —0.65 
C per 100 m is assumed for all the curves. 
The curves of Figure 12 indicate that as the tem- 
perature increases, smaller and smaller values of rela- 
tive humidity gradients are required to produce 
changes in k of considerable magnitude. This should 
be of greater importance in the tropics where the 
moisture content is relatively high. 
Changing k from its standard value of.% has an 
important influence on the strength of the field at any 
point in space. Though it is not easy to state the re- 
sult in general terms for any position, it is possible to 
evaluate the change in field strength near the surface 
(below 60 m altitude for 600 me and somewhat higher 
for lower frequencies) and well within the diffraction 
region, for moderate changes in k. Here the decibel 
attenuation below that for the free space field is de- 
creased approximately in the ratio k2. Tf, for in- 
stance, k changes from % to 8, the original decibel 
attenuation is to be divided by 3.3. To state the mat- 
ter another way, the range at which a given field 
strength is found -will be increased approximately in 
the ratio #2. This has an important bearing on the 
problem of propagation for communication purposes 
in this region. 
Tt has been shown above that a linear variation of 
refractive index can be. converted into a change of 
earth’s curvature. The reverse process is equally 
feasible: to eliminate the earth’s curvature by using 
a modified refractive index curve. This is a general 
procedure which involves no assumption about the 
variation of refractive index with height. From tlie 
equations in this section, it is seen that the effects 
of the earth’s curvature are equivalent to those of a 
refractive index increasing linearly with height at the 
rate of 1/a. Hence one effectively flattens the earth, 
thus eliminating the curvature effect, by adding to 
the refractive index the term h/a. In other words, 
the angles between a ray and the horizontal over a 
curved earth are the same as the angles between a 
ray and the horizontal over a flat earth when the re- 
fraetive index n has been replaced by n + h/a. In 
practice, the quantity M defined by equation (7) is 
used. If M increases steadily with height, which is the 
case for the standard atmosphere, the rays appear 
curved upwards on a flat earth diagram, which is 
illustrated in Figure 13. 
Summarizing, it is seen that three types of graphi- 
TRANSMITTER 
INTERFERENCE REGION 
DIFFRACTION 
h HORIZON RAY REGION 
VME TLE) 
Ficure 13. Rays in a plane earth diagram. 
ee SEN 
TRUE EARTH 
RADIUS a 
EQUIVALENT EARTH 
RADIUS ka 
eee 
FLAT EARTH 
k=oo 
Ficurn 14. Shape of lobes as affected by method of 
representation. 
cal representations of a coverage diagram may be 
used. (These are illustrated in Figure 14 for the 
lowest lobe.) 
1. The true geometrical representation. With 
standard refractive conditions the lobes appear bent 
downwards. Refractive index n decreases with height. 
2. The equivalent earth radius representation. 
Earth’s radius changed to ka (normally k=%). For 
standard refractive conditions the lobes appear 
straight. Equivalent refractive index n’ is inde- 
pendent of height since the equivalent atmosphere is 
homogeneous. 
3. The flat earth representation. The earth’s sur- 
face and other surfaces of constant height have been 
flattened out. For standard refractive conditions 
the lobes appear bent upwards. Excess modified 
index M increases with height. 
The quantities n, n’, and M for these three cases 
are illustrated in the left-hand series of diagrams 
in Figure 15. 
The Horizon— Diffraction 
From simple geometrical considerations it can be 
shown that two points at elevations h; and he are 
within sight of each other when their distance is less 
than the horizon distance d, (Figure 16) given by 
dn = V 2kahi + V 2kahe , (18) 
