Easselmann and Sohieler 



The frequencies of the backscattered waves are shifted 

 relative to the frequency of the incident radiation by the Doppler 

 frequency to- = - 2k' ' u. induced by the facet motion, where 

 K* = (k' , k^) is the wavenumber of the incident radiation and u 

 the local orbital velocity of the waves. For an approximately linear 

 wave field, u is a Gaussian variable, and the Doppler spectrum 

 also has a Gaussian shape. 



As the backscattered waves are reflected at normal incidence, 

 it follows by symmetry that the cross sections and Doppler spectra 

 are independent of polarisation. Vertical and horizontal polarisation 

 are denoted in Fig. 1 by V and H, respectively, the first index 

 referring to the incident field, the second to the backscattered field. 

 The cross-polarised return VH and HV vanishes. 



Although applied successfully by Cox and Munk [ 5] to the 

 analysis of sun glitter from the sea surface, the specular reflexion 

 model fails to describe the observed electromagnetic backscatter 

 at cm-dm and dkm wave lengths. It appears that for these wave 

 lengths surface irregularities of length scale comparable with the 

 radiation wave length cannot be neglected. Accordingly, recent 

 models have been based on the Bragg scattering theory, in which 

 these irregularities are regarded as the dominant scatterers. 



It is assumed in the Bragg model that the slopes of the 

 scattering surface waves are small and that their wave lengths are 

 comparable with those of the radiation field. The backscattered 

 field can then be expanded in powers of the surface displacement. 

 The first-order field is linear in the surface displacement and can 

 therefore be constructed by superposition from the field scattered 

 by a single gravity-wave component ^ = Z exp {ik • x - icogt } . This 

 corresponds to the classical problem of refraction by a periodic 

 lattice. The scattered field consists of two waves s = ± whose 

 horizontal wavenumbers and frequencies are given by the Bragg 

 (resonant interaction) conditions 



k' + sk^ = k- 



CO- ^ S(jO_ — CO. 



(1) 



(The vertical wavenumber component k' determining the scattering 

 angle follows from the dispersion relation |cOg| = c | k^ | , where c 

 is the velocity of light). 



Backscattering (k^ = - k' ) occurs for the gravity- wave com- 

 ponents k^= ± 2k'. The "Backscatte ring cross section is accordingly 

 of the form "^ 



366 



