COMPARISONS 329 



would be higher than normal, while the Cajje Kennedy example would 

 have values near or lower than normal. 



These differences are illustrated by figures 8.12 and 8.13 where the 

 bending, r, in milliradians is plotted versus altitude in kilometers. The 

 effect of horizontal changes is most pronounced for rays with initial eleva- 

 tion angles of 10 mrad. On these figures the term "vertical" ray is used 

 to designate the ray path through the horizontally homogeneous n struc- 

 ture determined from the refractive index vertically over the station. 

 The term "horizontal" ray designates the ray path through the complex 

 actual n structure. It is quite evident that a consistent difference in 

 bending of about 1 mrad exists between the "vertical" and "horizontal" 

 rays at Canterbury above 1 km for ^o = 10 mrad. This would be expected 

 since the vertical M profile (fig. 8.10) at the beach (our hypothetical 

 transmitter site) is nearly normal in gradient while as little as 10 km to 

 sea a duct exists, thus indicating a near maximum difference between the 

 "horizontal" and the "vertical" rays at any initial elevation angle small 

 enough to be affected by the duct. This is in contrast, however, with 

 the case of Cape Kennedy where, except for the region of the elevated 

 duct centered at about 1,500 m, the "vertical" and "horizontal" rays are 

 in c^uite close agreement. These two examples illustrate that horizontal 

 variations must be near the surface to be most effective. The importance 

 of the altitude of the variation is due to the fact that refraction effects 

 are very heavily weighted toward the initial layers [16]. 



Also shown on figures 8.12 and 8.13 are the values of the bending which 

 would be predicted from the Central Radio Propagation Laboratory 

 corrected exponential reference atmosphere [1]. The values shown are 

 obtained from the value of A'' at the transmitter site as corrected by the 

 vertical gradient over the first 100 m. It is noted that, for do = 10 mrad 

 at Canterbury, the value of bending predicted by the model is in essential 

 agreement with the "vertical ray" bending but under estimates the 

 "horizontal ray" (which has the largest variation of n with horizontal 

 distance) by about 1.25 mrad. For Cape Kennedy at ^o = 10 mrad, 

 the model atmosphere overestimates the bending by about 1.25 mrad for 

 altitudes in excess of 2 km. It should be emphasized that, although the 

 model exponential atmosphere appears to represent the average of the 

 two specific cases studied, the departure from this average arises from 

 quite different causes in each case. The differences in the Canterbury 

 case arise from the marked effect of horizontal variation of n as is indi- 

 cated by the agreement of the vertical ray bending with the model atmos- 

 phere. The disagreement in the Cape Kennedy case is due to the 

 presence of a very shallow surface layer of nearly normal gradient topped 

 by a strong subrefractive layer; therefore, it represents a shortcoming of 

 the model rather than an effect of horizontal changes of n. 



