where 



Radar Back-Scatter from the Sea Surface 



<^= ^a$^g^- 2sk' ) (^,|3 = V or H. s = i) 

 and F-(k) is the surface-wave spectrum, normalised such that the 



mean square surface displacement {^} 



--1 



K,(k) dk. The cornered 



parentheses denote mean values. (The negative sign of the wave- 

 number in the definition of cr^p has been introduced so that o-J^ 

 corresponds to a spectral line with positive Doppler shift, cf. Eq. 

 (3).) Tq^ is a scattering coefficient obtained by expanding the electro- 

 magnetic boundary conditions at the free surface [ 18] ), 



T = 

 vv 



2cof , 2 Q (l-c)(€[i +cos^ e] - cos^ e) 

 — -!- sin 9 -^ -^—^ . •* . J 



(c sin 6 + V^ - cos 0) 



T = 



HH 



2u)f 



sm 9 



1 - € 



(sin 9 + 7c - cos^ 0)^ 



T = T =0 



VH HV 



where e is the dielectric constant of sea water. 



The normalized Doppler spectrum Xa/3^'^d) » defined by 

 j X„Qi<^fi) ^^d - ^aB> where co^j = oog - ^\t is given according to (1) by 

 two lines at the gravity- wave frequencies ± cog, 



with (3) 



Normally, one of the Bragg lines due to scattering from the 

 surface -wBLve component propagating in the downwind direction is 

 very much stronger than the other line associated with the wave pro- 

 pagating in the opposite, upwind direction. 



The general properties of the Bragg cross sections and 

 Doppler spectra are indicated qualitatively in the right-hand panels 

 of Fig. i. In contrast to the specular reflexion model, there is a 

 pronounced dependence on polarisation and appreciable backscatter 

 at small and intermediate depression angles. The cross -polarised 

 return again vanishes. 



367 



