Chapter 2 
ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 
HISTORICAL 
uRING 1941 aNp 1942, short and microwave 
radar sets became available in England and 
were installed along the Channel and North Sea 
coast. Very soon it was found that at certain times 
these sets were able to pick up targets such as ships 
and fixed echoes from the French coast which were 
well below the line of sight and which under the 
conditions of standard propagation would have given 
entirely negligible responses. A relationship with 
the weather soon became apparent. In 1942, enough 
had become known to establish most of the correla- 
tions between excessive ranges and meteorological 
conditions which have remained fundamental and 
which are based on the picture of refraction in the 
lower atmosphere that is now generally accepted. 
Later on similar effects with radar sets were dis- 
covered all over the world. An example in point is 
in the Mediterranean where nonstandard propa- 
gation, during certain seasons, is the rule rather 
than the exception. These conditions will be dis- 
cussed in more detail in the chapter on radiometeor- 
ology. The most extraordinary ranges, perhaps, were 
found in the Indian Ocean where radar sets operat- 
ing at frequencies of 200 me were found on occasion 
to record fixed echoes from as far away as 1,500 
miles. The mechanism of this phenomenon is not yet 
fully understood. 
In the. Pacific theater extended ranges have also 
been observed; but, on account of the vast territory 
covered, the technical difficulty of all operations, and 
the inadequacy of meteorological coverage, it is 
difficult to evaluate the results systematically. Up 
to the present, reports on the conditions responsible 
for nonstandard propagation have been received 
from many parts of the world which vary widely in 
their characteristic features and dependence upon 
season, weather. time of day,. properties of the 
ground, etc. It is possible-to lay down certain general 
rules, but on the whole the phenomena are exceed- 
ingly complex. 
During 1943 and 1944, a number of systematic 
experiments on nonstandard propagation were car- 
ried out by the British and American Services and 
affiliated organizations. Most of these were one-way 
transmission experiments that have a number of 
advantages over radar experiments, but some cf the 
latter also were undertaken .Extensive transmission 
experiments were conducted by the British in the 
Trish Sea and the Americans in Massachusetts Bay, 
the State of Washington, southern California, and 
Arizona, and in the West Indian Ocean. 
Il 
These experiments will be described in the next 
chapter. Because of the nature of the subject, it will 
be profitable to discuss the theory before the experi- 
ments and to give, in this chapter, an outline of our 
present conceptions of the theory of nonstandard 
propagation. 
REFRACTIVE INDEX 
Nonstandard propagation takes place whenever 
the rate of variation of the refractive index in the 
lower atmosphere deviates considerably from the 
“Standard” linear slope defined by equation (11), 
Chapter 1. The variation might consist either in a 
deviation from linearity, which is the most common 
case, or in a linear slope in the lowest layers that is 
widely different from the value assumed for the 
standard. The refractive index is a function of tem- 
perature, pressure, and the partial pressure of water 
vapor, given by equation (9), Chapter 1 The de- 
pendence of the refractive index on pressure leads 
to a regular decrease with height, but the change of 
barometric pressure with the weather produces only 
an insignificant effect on the gradient. The variations 
of refractive index in the lower atmosphere owe their 
existence to stratifications in which the temperature 
and moisture changes rapidly with height. 
In order to express refraction in quantitative 
terms Snell’s law for a curved earth is used as given 
by equation (14), Chapter 1: 
Nr COS a = Nolo COS ay . (1) 
Now let 
n=1+/(m— 1) withn -—1 <1 
r=a(1+2)withd«1 (2) 
a a 
ia L 
cosa = (1 — 3°) witha <1 
where a is the earth’s radius. Similar expressions 
are valid for the quantities having the subscript 0. 
Multiplying out and neglecting quantities that are 
small of the second order, one obtains 
n= m += (h-hh) = 5 (ea). (3) 
It has become customary to introduce the modified 
refractive index M by 
n+2=1+M-10-, (4) 
whereupon Snell’s law assumes the form 
(M — M,) - 10-§ = 3 (@? — ap?) . (5) 
