INFLUENCE OF SMALL LAYERS 255 



irregularities on the layer, A/i say, must not exceed ±X/8a for the layer 

 to be considered smooth; i.e., 



Ah < ±7 m (X = L67 m) 

 Ah < ±17 m (X = 4.18 m). 



These values apply for a = 0.03 rad, corresponding to a layer height of 

 2.5 km; for lower layers Ah will be greater due to the decrease in a. 



These conditions are not likely to be satisfied in all the examples studied 

 and the analysis therefore overestimates the value of lp| in this respect. 

 (Some discussion of this point has been given by Bauer and Meyer [42].) 

 The limitations of sonde soundings, and the effects of layer tilt and surface 

 irregularities therefore provide a partial explanation of the scatter of 

 points in figure 6.16. Further detailed measurements of layer structure 

 are obviously desirable. 



6.2.7. The Influence of Small Layers 



The above discussion has dealt with the particular case of extended 

 elevated layers such as are often associated with temperature inversions. 

 However, it seems quite possible that these layers are merely the more 

 extreme examples of anisotropic irregularities which are thought to be 

 prevalent in the troposphere. There is already some preliminary evidence 

 supporting this concept in the results of refractometer and radar soundings 

 and recent theoretical work [22, 28, 40] has developed this approach in 

 detail. The relationship of this work to earlier analyses in terms of a 

 "scattering" model is discussed in the references quoted and need not 

 concern us here. For our purpose it is sufficient to utilize the essential 

 features of the argument as the basis for a simple calculation. 



It seems reasonable to assume that even in an atmosphere which sonde 

 data would lead us to classify as "well-mixed" there are often layer-type 

 irregularities. Detailed evidence on the spatial form and stability of this 

 type of layer or "feuillet" is so far lacking, but an inspection of some 

 refractometer results suggests that horizontal dimensions of a few kilo- 

 meters represent a realistic assumption. Such a layer might exist as a 

 separate entity for, say, several minutes (as compared with a period of 

 several hours for the extended layer in a stable inversion). 



For the following analysis, let us consider two layers of horizontal 

 dimensions, x, of 2 and 10 km respectively with the following character- 

 istics: 



An = 10-5 

 /i = 100 m 



a = 0.01-0.03 rad (i.e., layer height of 0.4 to 2.5 km on the Illinois 

 paths). 



