258 TRANSHORIZON PARAMETERS 



values in excess of the measured ones) point to the influence of anisotropic 

 layers or eddies of varying size and degrees of stability. This interpre- 

 tation is consistent with numerical calculations based on the properties of 

 "intermediate" size layers, suggested in the analysis of Friis, Crawford, 

 and Hogg [22]. 



Calculations of the field strength produced by extended stable layers, 

 using sonde data and a model profile with a linear lapse of n with height, 

 are in reasonable agreement with the experimental results. However, 

 there is probably no unique profile characteristic of elevated layers. 



6.3. A New Turbulence Parameter 



6.3.1. Introduction 



We shall here attempt to unify past work utilizing the surface value 

 of the refractive index and the concept of atmospheric stability. To do 

 so we shall first review the concepts of atmospheric stability from the 

 viewpoint of temperature structure. In the process we shall show that 

 past efforts have neglected the important role of the conditions at the 

 earth's surface; then we shall extend this work to derive an analogous 

 expression for the radio refractive index. 



6.3.2. The Concept of Thermal Stability 



The stratification of the earth's atmosphere by and large reflects the 

 control of the earth's gravitational field. This average structure is, 

 however, constantly disturbed by the intrusion of thermal plumes of 

 heated air rising from the differentially heated surface of the earth, as 

 well as by the mechanical mixing produced by the passage of air currents. 

 It is customary to assume that parcels of air are forced upwards through 

 the normal stratified atmosphere without mixing with the environmental 

 air mass. Since the parcel is forced to rise, be it by convection or by 

 mechanical mixing, it is also assumed that it expands and cools without 

 exchange of heat, i.e., adiabatically. In such a process it can be shown 

 that the pressure, P, is given by 



where T is the temperature (°K); g, the acceleration of gravity; R, the 

 gas constant for air; and, where a, the constant lapse of temperature with 

 height is 



(6.12) 



