DEPARTURES-FROM-NORMAL METHOD 77 



3.9. The Initial Gradient Correction Method 



The importance of the initial gradient in radio propagation, where the 

 initial elevation angle of a ray path is near zero, has long been recognized. 

 For example if dn/dh = — 1/a (the reciprocal of the earth's radius), then 

 the equation for r is indeterminate, an expression of the fact that the 

 ray path remains at a constant height above the earth's surface. This is 

 called ducting, or trapping of the radio ray. The effect of anomalous 

 initial A^-gradients on ray propagation at elevation angles near zero, and 

 for gradients less than ducting ( | dN/dh \ < 157 N units/km, or dN/dh > 

 — 157 A^ units/km) may also be quite large. A method has been devel- 

 oped for correcting the predicted refraction (from the exponential refer- 

 ence atmosphere) to account for anomalous initial A'^ gradients, assuming 

 that the actual value of the initial gradient is known [2]. 

 The result is 



Th = Th (Ns, So) + [riooiN*, do) - T100{N„ do)], (3.45) 



where th (N s,do) = r at height h, for the exponential reference atmosphere 

 corresponding to A''^, and N s* is the A''s for the exponential reference 

 atmosphere that has the same initial gradient as the observed intiial 

 gradient; t^qq is r at a height of 100m. 



This procedure has the effect of correcting the predicted bending by 

 assuming that the observed initial gradient exists throughout a surface 

 layer 100 m thick, calculating the bending at the top of the 100-m-thick 

 layer, then assuming that the atmosphere behaves according to the ex- 

 ponential reference profile corresponding to the observed value of A^^ for 

 all heights above 100 m. This approach has proved quite successful in 

 predicting T for initial elevation angles under 10 mrad, and will, of course, 

 predict trapping when it occurs. 



3.10. The Departures-From-Normal Method 



A method of calculating bending by the use of the exponential model 

 of N{h) together with an observed N{h) profile can sometimes be advan- 

 tageously employed [15]. This method is primarily intended to point out 

 the difference between actual ray bending and the average bending that is 

 predicted by the exponential N{h) profile and is a powerful method of 

 identifying air mass refraction effects. 



The exponential model described in section 3.8 can be expected to 

 represent average refractivity profile characteristics at any given location, 

 but it cannot be expected to depict accurately any single refractivity pro- 

 file selected at random, even though it may occasionally do so. In order 



