4-5] 



REFLECTION OF PLANE WAVES FROM THE GROUND 



187 



The behavior is more complicated when the ground is stratified. The 

 cases which are important to airborne radar are that of a layer of ice on top 

 of a water surface, and that of a layer of snow on land. Then multiple 

 reflections can occur between the surface and subsurface boundaries, with 

 a resulting modification of the effective reflection coefficients^; the effective 

 reflection coefficient then becomes an oscillating function of the electrical 

 thickness of the ice or snow covering. 



When the radar target is at a low altitude, a variety of phenomena are 

 generated by the interference of direct and reflected waves. Referring to 

 Fig. 4-13, if both the direct and indirect paths are illuminated equally by 

 the radar antenna, the resultant field at the target is 



Image 

 Fig. 4-13 Path Difference Between Direct and Indirect Paths. 



E = Ea{\ + p^-^-^^^) 

 where Ed is the field due to the direct wave, and Ai? 



(4-27) 

 Ih sin d is the path 



difference. 



The ratio EjEd, obtained from Equation 4-27, thus is the propagation 

 factor F due to the presence of the ground. In Paragraph 4-2, where this 

 factor was defined, it was pointed out that the received power from a radar 

 target is modified by the factor \FY. Introducing the values for K and A/? 

 in Equation 4-27, we obtain 



F = E/Ed = 1 + pe-''-"" ^*" '"-. (4-28) 



The most significant and striking phenomena resulting from the inter- 

 ference of direct and reflected rays are the lobe structure and the polarization 

 dependence below the first lobe. The formation of a set of lobes is easily seen 

 from Equation 4-28. With fixed 6 and continuous increase oi h, the resultant 

 field will pass through alternate maximums and minimums when the phase 



■^J. A. Saxton, "Reflection Coefficient of Snow and Ice at V. H. F.," Wireless Engineer 27, 

 17-25 (1950). 



