COMPUTING THE MODIFIED INDEX OF REFRACTION, M 



73 



LABORATORY 



10 20 30 40 50 60 70 



Figure 9. Curves of constant refractive index along the San Diego to San Pedro jiath. 



ing the magnitude and height of the strong gradients 

 along tlie path. The time interval of each sounding is 

 shown on the appropriate section. 



Again it must be emphasized that the discontinuity 

 takes the shape of a warped surface, that the gradi- 

 ents vary from point to point, and tliat the maximum 

 air density change occurs in the region of maximum 

 refractive index gradient. Interface waves in tlie 

 density discontinuity are possibly superimposed on 

 the already nonuniform structure. These small inter- 

 face waves are evident by the undulations on the top 

 surface of the stratus cloud deck. The top surface of 

 the cloud deck, which is often present, marks the air 

 mass boundary and is thus a good indicator of the 

 base of the inversion. 



It is therefore evident that meteorological observa- 

 tions required for a thorough study of propagation 

 conditions must be as extensive as possible. 



6-5 TABLES FOR COMPUTING THE 

 MODIFIED INDEX OF REFRACTION, M' 



*-^-^ Introduction 



The index of refraction of the atmosphere, modi- 

 fied for use on a plane-earth diagram, is a quantity of 

 great importance in the study of radio wave propaga- 



'By E. R. Wicher, Columbia University Wave Propagation 

 Group. 



tiou. It is defined by 

 M = \{n 



1) + 



a 



10" 



(1) 



where n = ordinary index of refraction, 



]l = height above sea level (not ground level), 

 a = radius of the earth. 

 The equation for n is obtained from Debye's theory 

 of the dielectric constant of gases. In terms of atmos- 

 pheric quantities, equation (1) assumes the form 



De Be 



+ Ch, (2) 



M=^- 



where p = barometric pressure (in millibars) 

 (1 mm Hg = 1.333 mb), 

 e ~ water vapor pressure (mb) 

 (e is of order of 1% of p), 

 T= temperature in degrees Kelvin, 

 A^79,B = 3.8 X 10% C = 0.1570, D = 11, 

 where It, the height above sea level, is measured in 

 meters. 



The constants A, B, and D have been selected to get 

 the best agreement with experimentally determined 

 values of n. The constant is 10*^ times the reciprocal 

 of the earth's radius in meters. A more detailed ex- 

 planation of this formula is given under "Constants 

 of the Index of Refraction Formula" in Section 6.5.3. 

 The formula (2) may be used to calculate M when 

 p, T, and e are known functions of height. Nomo- 

 grams have been prepared to facilitate such calcula- 

 tions. In this iiaper tables are presented which permit 



