34 



STANDARD PROPAGATION 



Figdee 4. Phase lag, <j>, of the reflection coefficient 

 versus reflection angle, \p, from \p = to \p = 5.5° for 

 sea water. 



From the practical viewpoint the following sum- 

 mary may give an overall picture of the more out- 

 standing features of ground and sea reflection. 



For horizontal polarization over the sea the reflec- 

 tion coefficient may be taken as unity and the phase 

 shift as 180 degrees for frequencies up to and includ- 

 ing the centimeter range, for practically all angles of 

 reflection. Over land there is a slight decrease of the 

 amplitude of the reflection coefficient with increasing 

 angle; for instance, for a frequency of 200 mc, at 

 an angle of 15 degrees the reflection coefficient has 

 decreased to 0.9 or slightly more for moist soil and 

 to 0.8 or slightly more for dry soil. These statements 

 apply when the ground or sea surface is reasonably 

 smooth. In order to decide whether a surface is 

 smooth or rough, Rayleigh's criterion, explained 

 below, is usually applied. When the surface is rough 

 or wavy, irregular scattering predominates and re- 

 duces the intensity to a small part of the value 

 attained with a smooth surface. 



For vertical polarization the curve of the magnitude 

 of the reflection coefficient versus the angle goes 

 through a minimum (see Figure 2) . When the imagi- 

 nary term of the complex dielectric constant is 

 negligible so that the ground behaves like a pure 

 dielectric material, the reflection coefficient goes to 

 zero at a certain angle (Brewster angle). Ordinary 

 soil nearly fulfills this condition. For instance ; at a 

 frequency of 200 mc the Brewster angle occurs at 



about 12 degrees with moist soil and at about 21 

 degrees with dry soil. 



For the ocean surface, and vertical polarization, 

 the imaginary part of the dielectric constant cannot 

 be neglected, and the reflection coefficient as a func- 

 tion of the angle does not vanish at any angle but 

 goes through a minimum, the pseudo-Brewster angle. 

 The actual variation of amplitude and phase lag is 

 represented in Figures 2 and 3 for the small angles of 

 reflection which are most important in practice. 



When the ground is rough the reflection coeffi- 

 cient for both types of polarization is reduced to a 

 very small value. For 10-cm waves and still more for 

 shorter ones, most types of land are rough. A reflec- 

 tion coefficient of 0.2 may be taken as representative 

 for an average ground covered with vegetation. A 

 slightly ruffled sea is a fairly good reflector for 10-cm 

 waves but appears somewhat rough at shorter wave- 

 lengths. 



Standard Refraction 



Numerous experiments have resulted in the fol- 

 lowing formula for the refractive index of moist air: 



in - 1) • 10 6 = 



79 

 T 



p — e 



4,800e \ 

 T ) 



(9) 



where n = the index of refraction, 



p = the barometric pressure in millibars 



(1 mm mercury = 1.3332 mb), 

 e = partial pressure of water vapor in milli- 

 bars, 

 T = absolute temperature. 

 The mixing ratio, s, which is practically equal to 

 specific humidity, is connected with e by the relation 



e = 0.00161ps . 



(10) 



A recent analysis 278 has shown, moreover, that this 

 expression for refractive index must, on theoretical 

 grounds, be substantially independent of frequency 

 down to the shortest waves employed in microwave 

 engineering. 



In an average atmosphere temperature, pressure, 

 and water vapor density decrease with height, and, 

 in the lowest few kilometers where most of the short 

 and microwave propagation takes place, it may be 

 assumed to a good approximation that the decrease 

 of refractive index with height is linear though the 

 rate of decrease is somewhat dependent on the cli- 

 mate. In middle latitudes it is given by 



