Radar Baak-Saatter from the Sea Surface 



In the decameter bands , the observed broadening and shiit 

 of the Bragg lines are much weaker. Instead, the Doppler spectra 

 show pronounced side band structures (cf. Fig. 11 , from Ward [ 22] 

 and similar spectra in Crombie [ 6] and elsewhere). The basic 

 difference in structure of the Doppler spectra observed in the 

 cm-dm and dkm bands lends support to theoretical considerations 

 calling for alternative expansion procedures in the two wave length 

 ranges . 



m. THE WAVE- FACET INTERACTION MODEL 



In order to treat the scattering waves as small perturbations 

 of a plane surface, it is assumed in the Bragg theory that the wave 

 amplitudes are small compared with the wave length of the incident 

 radiation. In a strict sense, the expansion is valid if this condition 

 is satisfied not only for the Bragg waves, but for the entire surface 

 displacement. Thus the theory is not rigorously applicable to short 

 electromagnetic waves of a few cm wave length, although the long 

 surface waves of high amplitude which violate the expansion condition 

 do not enter in the final scattering expressions. Various workers 

 [e.g. 3, 4, 10, 20, 21, 23] have suggested that this formal short- 

 coming may be remedied by dividing the surface-wave spectrum into 

 two parts, a high- wavenumber scattering region, and the energy- 

 containing region at low wavenumbers which defines the "sea. " The 

 "sea" is then treated as a random carrier wave which modulates 

 the scattering by the superimposed Bragg waves. If the Bragg wave 

 length TT /k' is short compared with a typical wave length 2Tr/k'^ 

 of the sea, the carrier wave may be represented locally as a plane 

 facet, and the first-order scattering theory applied in the reference 

 frame of the moving facet. 



The model involves additional conditions besides the two -scale 

 assumption that it is possible to define a facet diameter D inter- 

 mediate between the carrier and scattering wave length scales , 



(k'r' « D« (k'^r' (4) 



The finite facet size implies an indeterminacy Ak = 0(l/D) of 

 the scattering wavenumber, which corresponds to an angular spread 

 AG = O {(K'D sin 9)"'} of the backscattered beami. The wave-facet 

 interaction model is meaningful only if AG is small compared with 

 the change in effective depression angle introduced by the facet 

 slope 9^/9x = 0(k £,) , where t, is the carrier- wave amplitude. 

 This requires k^C,DK' sin G » 1 , or, since Dk*^ « i , on account of 

 [4], 



k'; sin G = k!x >» 1 (5) 



371 



