Radar Baak-Soatter from the Sea Surface 



bution for a random, linear gravity- wave field, 



p(\) = (2ir)-'^'|cr^'exp (- 1 C:!\^.. 



(8) 



The covariance matrix Cjj can be evaluated from the surface- wave 

 spectrum and the linear wave solutions. 



Cii = 



(9) 



where k^k^k = / Fg (k) (k^k^g/k) dk, etc. 



We note that the facet Doppler shift <o^ is correlated not 

 only with the facet velocity, but through the correlation (u3nj) 

 also with the facet slope. 



(10) 



For small wave slopes, the factor in square parentheses in 

 Eq. (7) Ccin be expanded in powers of nj. The integration can then 

 be carried out explicitly for each term of the expansion yielding a 

 solution of the form 



with 



X>d) = K% --P^-<-0-^yy2{-f» [1 f qf + q^ . .. . ] (U) 



{2tt(co^)) 



where q*, q?^, ... are polynomials in (to^ - soo ) of order 1, 2, ... 

 in the facet slope. 



s ^ (cOfniXcOrf-scog) ) / a ~s 



(^f") 



(l^~-:.)o/Mo^^-^5f-^(I^U '''' 



{<^i) 



373 



