APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 



121 



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 tlic value of M plotted against height. This jl/ 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- 

 creases 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 1-5) 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 temi3erature inversion tends to lead 

 to duet formation. 



3. 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 l^oth 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 jsropagation, 

 hardly differ at all from those of neutral and unstaljle 



100 FT 



FiGXTKE 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 with elevation. Correspondingly, 

 rays are bent downward more than in the standard case 

 but not so strongly as in a duct, i.e., the rays are not 

 actually trapped. Being literally a transitional case, 



/ 



/ 



/ 



/ 



X 



y 



^^ 



■M M ■ 



Figure 13. Ti-ansitional 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 (Ail/, defined in Sec- 

 tion 8.3.3), 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 



