COMPUTATIONS OF ATMOSPHERIC REFRACTION 



381 



The answers to the several parts of the problem are summarized in the 

 next table of this chapter (immediately preceding the main body of 

 tables). Bending values for the assumed profile, from a method which 

 exponentially interpolated layers between given layers and then integrated 

 between resulting layer^, assuming only a linear decrease of refractivity 

 between interpolated layers, are included for the sake of comparison. 

 The comi^utations were performed on a digital computer. 



The reason that the answers to i)art (e) vary so radically from the 

 remaining answers for the ^o == mrad case and not so much for the 

 ^0 = 261.8 mrad case is the fact that the accuracy of the regression line 

 method increases with increasing initial elevation angle, ^o- It must be 

 remembered that the statistical regression technique, like the exponential 

 model, is an adequate solution to the bending problem for all ^o's larger 

 than about 10 mrad, and all heights above 1 km. 



The reason that the answers in part (f) and part (a) agree more closely 

 than with any other of the answers is because (3.49) is, as mentioned 

 before, Schulkin's result with only the approximation, tan dk = dk for 

 small angles, omitted. For this individual profile, the bending obtained 

 from an exponential atmosphere does not give particularly accurate bend- 

 ings; however, for 22 five-year mean refractivity profiles, figure 3.9 shows 

 that exponential bending predicts accurately within 1 percent of the 

 average bending for these five-year means. Figure 3.19 shows the rms 

 error in predicting bending at various heights as a per cent of mean bend- 

 ing (not including superrefraction). 



In summary, it is recommended that the communications engineer 

 either use the statistical regression technique or the exponential tables 

 [1] without interpolation (i.e., pick the values of height, N s, and Oq that 

 are closest to the given parameters) for a quick and facile bending result, 

 keeping in mind the restrictions on these methods. However, as men- 

 tioned before, use of Schulkin's method is recommended if accuracy is 

 the primary incentive. 



Summary of refraction results for the sample computation 



