4-11 



REFRACTION EFFECTS IN THE ATMOSPHERE 



235 



Since 2{Mmin — M) seldom exceeds 100 M units, trapping occurs only 

 for rays with maximum elevation angle (which may or may not occur at 

 the ground) of the order of 10 mils, or about |°. Hence trapping is a 

 phenomenon which occurs only in almost horizontal propagation. 



The refractivity of the atmosphere for radio frequencies under about 

 4 X 10^ Mc*'' is given by the formula 



77.6/. , _ .^ ^^_g^^ 



A^ 



^'(p + 4.81 X 10^^ 



where T is the absolute temperature (°K), p the total pressure, and e 

 the partial pressure of water vapor, both in millibars. The refractivity 

 decreases with an increase in temperature, but increases with pressure, 

 and is especially sensitive to variations in vapor pressure. 



The refractivity at a given point usually fluctuates with time, so that 

 average values are used for drawing an M curve. The principal types of 

 M curves observed are illustrated in Fig. 4-50. Curve (a) is the standard 



Fig. 4-50 Various Classes of M Curves. 



M curve already referred to. The substandard M curve, shown in (b), is so 

 called because the rays are refracted less than in the standard case, and it 

 generally results in lower field strengths. Curves (c) and (d) are types 

 associated with surface ducts. The duct extends from the surface to the 

 height hi, the "nose" of the M curve. In (e) the value of M at the surface 

 is less than that at the nose, so that the duct then extends from hi to hi- 

 This is called an elevated duct. Various combinations of types can take place, 

 such as a surface duct (0 to hi) with an elevated duct (A2 to A3) shown in (f). 

 From Equation 4-87, situations where the temperature increases with 

 height together with a simultaneous decrease of vapor pressure lead to a 

 strong decrease of M with height. Such situations are favorable for duct 

 formation. Just such conditions occur at subsidence inversions. These 



«See Essen and Froome, Proc. Phys. Soc. London, B64, 873 (1951). 



