216 REFLECTION AND TRANSMISSION OF RADIO WAVES 



speed. It should be noted that near vertical incidence, c7° rises to as high as 

 + 15 db. 



These and other characteristics of sea clutter have been explained by a 

 theory developed by Katzin.^^ This theory is based on scattering by the 

 small facets of the sea surface as the basic scattering elements. At small 

 depression angles, where none of the facets is viewed broadside, the facets 

 which back-scatter most effectively are those with perimeters of about a 

 half-wavelength. The back-scattering of a facet increases with its slope, so 

 that those near the wave crests contribute most strongly, even if the 

 illumination is constant with height. 



Although at small depression angles the back-scattering is at angles far 

 removed from the facet normals, at large depression angles some of the 

 facets are viewed broadside, so that these contribute most strongly in this 

 region. The larger the facet the greater is the contribution. The angular 

 dependence at large depression angles then is governed by the slope 

 distribution of the facets. At airborne radar frequencies, the angular 

 dependence of o-° should follow the slope distribution rather closely. This 

 distribution is approximately Gaussian, but is more peaked and is skewed 

 in the upwind-downwind direction. ^^ 



At small depression angles, the theory shows that o-" is directly propor- 

 tional to wind speed, but at high angles it is inversely proportional to wind 

 speed. These features of the theory seem to be in accord with available 

 measurements. 



The evidence regarding the frequency dependence of o-'^ is not uniform. 

 Katzin^^ stated that o-° (at small d) was roughly proportional to frequency 

 in the frequency range 1.25-9.4 kMc, and gave the formula for a" upwind 

 at small depression angles, 



(7« = (2.6 X \0-'W^i'\-' (4-65) 



where W is the wind speed in knots and X the wavelength in cm. (In this 

 formula, the illumination factor F is included in o-".) Wiltse, Schlesinger, 

 and Johnson^** found a" to be substantially constant in the frequency range 

 10—50 kMc. Grant and Yaplee-* found cr" to increase with frequency 

 range 9.4-35 kMc, the increase being about as the square of frequency at 

 vertical incidence and about as the first power or less at 10° depression 

 angle. Grant and Yaplee's measurements on the different frequencies used 

 were made on different occasions, however, so that their results on the 

 frequency dependence are subject to wider variations due to different 

 surface conditions. It is quite possible that the frequency dependence of a" 



2^C. Cox and W. Munk, "Measurement of the Roughness of the Sea Surface from Photo- 

 graphs of the Sun's Glitter," J. Opt. Soc. Aju. 44, 838-850 (1954). 



3"J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, "Back-Scattering Characteristics of 

 the Sea in the Region from 10 to 50 kmc, Proc. IRE 45, 220-228 (1957). 



