COMPARISON WITH EXPERIMENTAL RESULTS 345 



very large elevation angles. Thus, in some cases, the residual errors will 

 probably not decrease steadily with increasing elevation angle, but will 

 tend to flatten out at some point and assume a more or less constant value 

 above that point. These effects will be complicated in comparing one set 

 of data with another by such things as differences in the location or time 

 of day or season in which data are taken, and instrumental effects such as 

 aperture averaging. 



The case of range errors is more straightforward. The effects of 

 turbulent atmospheric inhomogeneities are expected to average out over 

 regions of abnormally high or low density, when considering the transit 

 time of particular points on the wave front. Hence the effect on the 

 residual range errors is expected to be small, and the observed values are 

 expected to compare rather well with the predicted (theoretical )values. 



Turning first to the comparison of observed and predicted elevation 

 angle errors, figure 8.20 shows some data on the mean refraction of 1.85- 

 cm radio waves received from the sun, a target at essentially infinite range 

 so that the elevation angle error is identical with the total angular bending 

 of the radio ray, r. The data shown in figure 8.20 were obtained by 

 tracking the sun with a precise radio sextant developed by the Collins 

 Radio Company, and were collected in August through December of 1959 

 at Cedar Rapids, Iowa [20]. These data represent essentially instan- 

 taneous measurements. The mean of all observations at each elevation 

 angle is plotted for elevation angles ranging from 2 to 65°, and the mean 

 value of N s associated with each point is about 332; the curve for the 

 mean bending of the CRPL Standard Sample corresponds to the mean 

 value of A^s of 334.6 for that sample and hence the data should be com- 

 parable. The standard deviation "wings" refer to the standard deviation 

 of the individual "instantaneous" data, not to the standard error of 

 estimate of the mean value. The close agreement observed for elevation 

 angles between 2 and 35° constitutes not only a confirmation of the use- 

 fulness of the Standard Sample, but also a verification of the accuracy 

 of ray-tracing theory in estimating radio wave refraction in the actual, 

 and thus heterogeneous, atmosphere. The standard deviation of the 

 Collins data (shown on the lower part of fig. 8.20) is generally lower than 

 for the standard sample, but this is to be exjjected in view of the larger 

 range of climatic variation contained in the CRPL Standard Profile 

 Sample. The apparent discrepancies in the measurements made at eleva- 

 tion angles over 40° are apparently due to some slight inaccuracies in the 

 calibration procedure used on the radio sextant during the period of data 

 acquisition.'* In fact, the data shown in figure 8.20 are almost precisely 



'' The data for the highest elevation angles in figure 8.20 were necessarily collected 

 during the early part of the period when the sun was higher in the sky. In a private 

 communication, Anway states that the mean A'^s applicable to the data at 60° to 65° 

 was 358 rather than 332; this difference would account for about one-third of the 

 discrepancies noted, reducing the residual bias to a maximum of about 40 Mi'ad. 



