202 



TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 



17 23 Types of Modified Index Curves 



A large number of meteorological soundings of 

 the lower atmosphere have been carried out by 

 several laboratories and Service units. From these 

 measurements the modified index curves have been 

 calculated as a function of height, and it has been 

 shown that practically all these curves fall into one 

 of the six types illustrated in Figure 20. 



TRANSITIONAL 



SUBSTANDARD 



SIMPLE SURFACE 

 TRAPPING 

 'I 



ELEVATED S SHAPE GROUND-BASED S SHAPE 



DUCT 

 VlNVERSION LAYER 

 _LA _i - 



INVERSION LAYER h 



INVERSION, LAYER 

 I 



I 



M M M 



Figure 20. Types of M curves. 



For the standard atmosphere the M curve increases 

 with height as shown in curve I. For nonstandard 

 atmospheres, the M curves will take one or another 

 of the forms illustrated in curves la, lb, II, Ilia, 

 and 1 1 lb. Of particular interest are those curves in 

 which M decreases with height for a range of alti- 

 tudes. (This decrease is the result of a sufficiently 

 sharp decrease in n with height as illustrated in 

 Figure 15.) In this event an inversion layer is formed 

 in the atmosphere. 



Throughout the range of altitudes of decreasing 

 M the curvature of the rays exceeds the curvature 

 of the earth. Nearly horizontal rays which either 

 originate in, or penetrate into, this layer are trapped, 

 and, if the layer extends far enough, energy may be 

 carried to distances far beyond the geometrical 

 horizon. However, the region in which the waves or 

 rays are trapped may have a thickness or depth 

 exceeding that of the inversion layer. This region is 

 known as a duct. Its precise definition may be taken 

 from Figure 20. It is the strip between an upper 

 minimum of the M curve and either the ground or 

 the point where the vertical projection from the 

 upper minimum intersects the M curve. There are 

 two main types of ducts, the ground-based duct, 



illustrated by curves II and Illb, and the elevated 

 duct, illustrated by curve Ilia. 



The height in the atmosphere at which the varia- 

 tions in refractive index occur may vary from a few 

 feet to several hundred or even a few thousand 

 feet. These variations are likely to be found at fairly 

 low elevations in cold climates and at the higher 

 elevations in warm climates. The meteorological con- 

 ditions which yield these various M curves are 

 described in Section 17.3. 



The opposite effect occurs when the M curve takes 

 the substandard form (curve lb in Figure 20). Here 

 the lower portion of the M curve has a slope which 

 is less than standard. In this event the rays in the 

 lower atmosphere are bent downward to a lesser 

 degree than in the standard atmosphere or may 

 even be bent upward. 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 a radar and communication "blackout." 

 If the M curve is steeper than average in the lowest 

 layers, the transitional case arises (curve la). Here 

 a slight change in the temperature and moisture 

 distribution might lead to a curve of type II and 

 a duct. 



17 2A Rays in a Stratified Atmosphere 



Nonstandard vertical variations of refractive index 

 occur frequently in the lower atmosphere. In addi- 

 tion there may be gradual variations in the horizontal 

 direction. So far, the theory of propagation has not 

 reached a stage where such horizontal variations can 

 be taken into account. Unless otherwise stated it is 

 always assumed that the stratification extends hori- 

 zontally as far as the coverage of the transmitter 

 and that the variation in the M curve is entirely 

 vertical. Weather conditions often are sufficiently 

 homogeneous horizontally to warrant this assump- 

 tion, but there are exceptions, mainly near coasts 

 (see Section 17.3). 



Only those rays are affected by the vertical varia- 

 tions of refractive index in the lower atmosphere 

 which leave the transmitter at a very small angle. 

 Both theoretically and practically it has been found 

 that the effects of nonstandard refraction are negli- 

 gible for rays that leave the transmitter at an angle 

 with the horizontal of more than about 1.5°. Rays 

 that leave at an angle with the horizontal of less 

 than 1.5°, and especially those emerging at angles 



