344 REFRACTION AND REFRACTIVE INDEX MODELS 



was selected as representing roughly the lower limit of elevation angles 

 for which the bending is expected to be strongly correlated with N s (say 

 r > 0.9), while at 100 mrad (about 6°) the correlation is expected to be 

 extremely high (say r > 0.99) and the refraction should be reasonably 

 free of random profile effects. 



The results of the ray tracings and the comparison with predicted 

 values are shown in figure 8.19. As expected, the results from the South 

 Pole seem to depart significantly from the predicted values, at least for 

 the 20-mrad elevation angle. At the 100-mrad elevation angle some of 

 the calculated points lie more than one standard deviation from the pre- 

 dicted line (the theoretical prediction error is too small to show on the 

 graph clearly) ; however, in all four cases the differences are less than 50 

 ^trad, a figure which as shall be seen may represent the limit of accuracy 

 obtainable from the atmosphere in actual practice. At angles over 100 

 mrad the errors would be smaller; in fact they should tend to decrease in 

 inverse proportion to the square of the initial elevation angle, as indeed 

 they do between 20 and 100 mrad. 



A conclusion which may be drawn from the above results is that any 

 regions where the prediction model based on the Standard Sample would 

 not be expected to provide the theoretical accuracy are probably regions 

 of climatic extremes, and at least for the case of angular errors the effects 

 will be negligible for elevation angles of a few degrees or more. As an 

 interesting aside it can be noted that apparently the Antarctic may be a 

 desirable area for tracking systems location, at least with respect to 

 atmospheric refraction effects, since (most likely because of the lack of 

 substantial water vapor and the relatively homogeneous conditions) the 

 prediction error for ^o = 20 mrad in figure 8.19 is only about one-fifth as 

 large as for temperate climates, indicating a possibly more stable atmos- 

 phere (even 90 percent confidence limits for the SE in figure 8.19 yield a 

 value less than half of the theoretical temperate value of ±0.286 mrad). 



8.3.5. Comparison With Experimental Results 



Before comparing the theoretical and experimental results, it is appro- 

 priate at this point to examine what one would expect to observe on the 

 basis of propagation theory. In the case of angular errors it is expected 

 that i^ropagation through the real, turbulent atmosphere will produce 

 random variations in the shape of the incoming wavefront, so that meas- 

 urements made with systems in which the receiving antenna is alined with 

 the incoming signal will have random variations introduced in addition to 

 the ordinary refraction effects. Since these variations will probably not 

 be a function of elevation angle to any great extent, this implies that the 

 residual variance in predicting the elevation angle errors will probably 

 always be greater than predicted from theoretical (static) considerations, 

 and that there will probably be some minimum value of this variance for 



