METEOROLOGY — FORECASTING 247 
transmitter at an angle with the horizontal of less than 
1 degree, and therefore to only the lowest lobe in a 
radar coverage diagram. 
For the atmospheric refraction to be strong enough 
to cause trapping of microwaves it is necessary that 
the refractive index of the atmosphere decrease with 
altitude at a sufficiently rapid rate. For convenience 
in dealing with problems of nonstandard propagation, 
a quantity known as the modified refractive index has 
been defined and is usually denoted by the letter M. 
It depends on pressure, temperature, humidity, and 
height and can be readily calculated from the proper 
nomograms® or from tables,® or directly from the 
formula.® 
When values of M are computed for various eleva- 
tions from measurements of the pressure, temperature, 
and humidity at those elevations, a graph can be made 
of the value of M plotted against height. This M curve 
gives directly a graphical representation of the struc- 
ture of the atmosphere with reference to the existence 
of ducts. A decrease of M with elevation is called an 
M inversion, since under standard conditions M in- 
ereases with altitude, and indicates the existence of a 
duct. This, then, is the criterion for the meteorological 
conditions necessary for the trapping of radio waves. 
The top of the duct is taken to be that level at which 
M reaches a minimum (as in Figure 15) and the base 
of the duct the level at which a vertical projection from 
the value of M at the top of the duct intersects the 
lower portion of the M curve (as in Figure 16) or the 
ground (as in Figure 17). The term “duct width” is 
used to refer to the thickness of the duct, i.e., the ver- 
tical distance between the top and the base. 
The vertical distribution (a) of temperature and 
(b) of humidity may each contribute to the formation 
of an M inversion, in the following ways. 
1. A strong temperature inversion tends to lead 
to duct formation. 
2. A rapid decrease of humidity with altitude tends 
to lead to duct formation. 
If the first of these is predominant the duct is said 
to be dry, and if the latter is predominant the duct is 
said to be wet. Often both factors are operative to- 
gether; that is, in the M inversion there is both an 
increase in temperature with altitude and a decrease 
in humidity with altitude, the duct being more sen- 
sitive to the effect of the humidity distribution than to 
that of the temperature distribution. 
Types of M Curves. For purposes of clarification, 
the various types of M curves that may exist can be 
classified as follows: 
1. Standard type (Figure 12). In a standard atmos- 
phere M increases linearly with altitude at a rate of 
3.6 M units per 100 ft (0.118 M unit per m). Radio 
and radar waves are bent slightly downward, the paths 
of the rays actually having a radius of curvature about 
four times that of the earth; but no trapping occurs. 
Standard conditions, in their effect on propagation, 
hardly differ at all from those of neutral and unstable 
}-——__ 3.6m UNITS 
Ficure 12. Standard type of M curve. 
—_—_—| «— 
equilibrium (except in special cases as mentioned 
later) and so are frequently found in well-mixed air, 
as is likely to occur on sunny afternoons and in areas 
of turbulence. 
2. Transitional type (Figure 13). In the lower 
levels M is constant witl elevation. Correspondingly, 
rays are bent downward more than in the standard case 
but not so strongly as in a duct, ie., the rays are not 
actually trapped. Being literally a transitional case, 
TRANSITIONAL LAYER 
ee 1m ——| »—— 
Figure 13. Transitional type of M curve. 
this type of M curve is likely to occur during the 
formation or dissolution of a duct, or when the mete- 
orological factors tending to cause a duct are incom- 
pletely operative. The M deficit (AM, given on pages 
249-251), is indicated in the figure. 
3. Substandard type (Figure 14). In the lower levels 
M increases more than 3.6 M units per 100 ft, which 
corresponds to rays being bent downward only very 
slightly or, in some cases, actually upward from the 
line of sight, thus giving shorter maximum ranges on 
surface and low-flying targets. There is no trapping. 
Depending to some extent upon the elevation of the 
transmitter, the field strength in the substandard 
region may be reduced considerably below normal, even 
to the point of producing radar and communication 
“blackout.” The M deficit is negative with this type 
of curve. Associated meteorological conditions are 
usually those in which warm, moist air passes over a 
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