ELEVATED LAYERS AT TEMPERATURE INVERSIONS 253 



and preliminary calculations based on this work were made to determine 

 the most suitable model in the present application. It was evident from 

 these calculations that a simple linear profile would yield the best agree- 

 ment with the measured data, and this model was therefore adopted in 

 the subsequent analysis. 



Consider the layer profile shown in figure 6.15, i.e., a linear decrease of 

 An over a height interval h, with transition regions of height d. This 

 model and others have been discussed by several authors, but the most 

 detailed treatment is that of Brekhovskikh [39]. His analysis shows that 

 for this linear model: 



I p I = An • X/Sirh sin^ a 



~ An • X/Sirha^. (6.5) 



This equation is valid if: 



(a) An • \ <K rha^ 

 and (b) 4ad « X. 



In the present problem, with values of X of 1.7 to 4.2 m, An '^ 10"^, 

 a ^ 0.02 condition (a) is satisfied for layer thicknesses greater than about 

 20 m. In addition, condition (b) is fulfilled for the stated conditions if the 

 thickness of the transition region is less than a few meters. These condi- 

 tions do not seem inconsistent with available refractometer data on 

 elevated layers, but a rigorous justification of the model is impossible at 

 the present time. In any case, there is almost certainly no unique profile 

 representative of all elevated layers. We assume here, therefore, the 

 linear profile of figure 6.15 merely as a simple analytical model. It may 

 be noted here that the value of | p | given by (6.5) agrees with that quoted 

 by du Castel [40] but is half the value obtained in an earlier analysis [28]. 



Equation 6.5 was used to calculate reflection coefficient of the layers 

 on each occasion on which these were observed in the sonde ascents. The 

 results, expressed in terms of a reflection loss are compared with the 

 measured values of field strength in figure 6.16. The general agreement 

 is satisfactory for the assumed model. As might be expected, there is 

 a considerable scatter in the data and two considerations are important in 

 assessing the significance of these results. These concern sonde response 

 and layer structure. The work of Wagner [41] on the response of radio- 

 sondes shows that, for an elevated inversion layer with An = 3 X 10~*, 

 h = 100 m, a sonde with a 10 sec time constant in the sensing elements, 

 and rising at 5 m/sec will give an indicated value for An of approximately 

 half the true value. The above procedure, using sonde data, therefore 

 underestimates the value of |p| for an idealized infinite layer. 



