TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 135 
atmosphere. The present chapter deals mainly with 
refraction phenomena, but reflection and diffraction 
will be briefly considered. 
Refraction is influenced by the physical state of the 
atmosphere, in which the distributions of the temper- 
ature, pressure, and humidity are the most important 
elements. With refraction, rays are bent, and the 
electromagnetic energy flows along the curved ray 
paths. A situation frequently realized in practice is 
that in which the curvature of the rays is independent 
of height above ground. This is known as stanuard 
rejraction. The term standard propagation is used to 
designate propagation under conditions where the 
refraction is of the standard type. 
During the war years the increased number of ob- 
servations, which resulted from the world-wide use of 
radar, showed that, under certain weather conditions, 
radio field strengths may depart markedly from the 
values: expeeted with standard refraction. These 
deviations are now known to be attributable to a 
stratification of the atmosphere which is predomi- 
nantly horizontal and is produced by vertical yaria- 
tions in water-vapor content and temperature. Since 
these quantities control the index of refraction, and 
therefore the curvature of the rays, it follows that 
this curvature varies with the elevation above ground. 
Any stratification of the atmosphere tends to pro- 
duce a distribution of the radiated energy different 
from that which occurs in the standard atmosphere. 
Of particular importance is a type of stratification 
which results in a duct being formed in the atmos- 
phere. In this event, a portion of the wave energy 
may be-guided horizontally along the duct and may 
be effectively “trapped” within the duct’s upper and 
lower boundaries. This is known as “guided” propa- 
gation. The radiation energy may then travel to dis- 
tances far beyond the geometrical horizon, producing 
unusually long ranges for short wave receivers or 
radar targets. The phenomenon which tends to con- 
strain the wave energy to follow the duct is-called 
“superrefraction.’’ When this occurs, the rays in pass- 
ing through the inversion layer in the upper part of 
the duct are bent downward with a curvature which 
exceeds that of the curvature of the earth. The 
regions covered by the inversion layer and the duct 
are illustrated in Figures 15, 20, 22, and 23. The dis- 
tribution of moisture and temperature in the atmos- 
phere, responsible for the formation of ducts, is dis- 
cussed on page 152. 
As the stratification of the lower atmosphere that 
produces superrefraction is part of the weather, the 
prevailing meteorological conditions become of im- 
portance for problems of propagation and coverage. 
Meteorology as related to wave propagation is 
treated in the discussion on pages 152 -154. 
Reflection from the Ground. 
A coverage diagram is a curve, or a set of curves, of 
constant field strength in a vertical or horizontal 
plane. The horizontal coverage diagram is deter- 
mined chiefly by the antenna:pattern itself. In the 
vertical plane, however, the diagram depends pri- 
marily upon the interference between the radiation 
coming directly from the transmitter and that which 
is reflected from the ground or sea surface. This effect 
produces the lobe structure of the vertical coverage 
diagram. At the lobe maxima the two rays reinforce 
each other, while they cancel each other out, more or 
less, at the lobe minima. 
The propagation problem in its full generality 
leads to mathematical formulas of forbidding com- 
plexity. In order to understand the processes at work 
it is necessary to proceed in steps and gradually add 
refinements to the basic features of the problem. 
Consider first the field radiated from an antenna 
which is remote from the earth. This free space field 
decreases in strength in inverse proportion to the dis- 
tance, R,, from the transmitter and varies with the 
angular position in accordance with the shape of the 
radiation pattern of the transmitting antenna. Let 
this free space field strength at any point at distance 
R; be designated by Eb. 
GROUND 
Figure 2. Interference of direct and reflected rays. 
If, instead, the transmitter is placed near the 
ground, as at T in Figure 2, the field at any point in 
space is produced partly by the direct wave (giving 
the free space field Hp) and partly by the wave which 
is reflected from the ground. The resultant field is 
given by the vector sum of the two component fields. 
The magnitude of the field strength of the reflected 
beam depends upon: 
1. The antenna radiation pattern, which gives the 
relative strength of the radiation field for different 
directions. 
2. The attenuation, proportional to 1/R., resulting 
from the length of path R» of the reflected wave. 
3. The attenuation due to increased divergence of 
nearly parallel rays reflected from the curved earth. 
This is taken into account by the use of a divergence 
factor, D, which depends on range and heights of 
transmitter and receiver. 
4. The magnitude, p, that the coefficient of reflec-. 
