Radar Baok-Saatter from the Sea Surface 



product (w|n|) (Eq, 10), which is responsible for most of the mean- 

 frequency variation, depend on differently weighted moments of the 

 gravity-wave spectrum. The two Doppler parameters can therefore 

 be used to obtain Independent estimates of two sea- state parameters 

 --for example, the mean wave height and mean wave period.^ 



IV. HIGHER-ORDER WAVE- WAVE INTERACTIONS 



For HF waves longer than about 10 m, the Bragg model can 

 be generalised by straightforward extension of the wave- wave Inter- 

 action expansion to higher order. In this case, the perturbation 

 parameter ki^ Is normally a small quantity even when t, Is defined 

 as the surface displacement of the complete wave field, and there is 

 no need to consider the long waves of high amplitude separately. 

 In fact, the wave -facet Interaction model Is not applicable for HF 

 waves on account of the angular resolution condition (5). The In- 

 equality k^ « 1 and condition (5) are mutually exclusive, repre- 

 senting a wave length gap between the wave-facet and higher-order 

 wave-wave Interaction models extending from a few fractions of a 

 meter to about 10 meters. 



At second order, the wave-wave Interaction analysis yields 

 scattered waves through Interactions with pairs of gravity-wave 

 ■:omponents a, b satisfying the next-order Bragg conditions 



k' +aak° +(r^k'^= k' 



The second-order Doppler spectrum x (<*>d) ^^ obtained by 

 summing over all pairs of surface waves yielding a backscattered 

 component with the appropriate horizontal wavenumber k' = - k' 

 and frequency Wg = coj + w^j, "^ *~ 



x'M<od)= ^ y T^'^Fg(kVg(k'')6(cOd-'^a«a-<^b"b)di° (16) 



where k = - (rAZlfi^ + oak ) (Eq, 15). T Is a scattering function 

 determined by the^second-order coupling coefficients occurring In 

 the expansion of the boundary conditions about the undisturbed plane 

 surface (cf. Ref, (18)). (The polarisation Indices are Irrelevant for 

 the following discussion and are Ignored.) 



Significant sea-state signatures are found only for the Doppler 

 spectra and not the cross sections. On Integrating Eq. (11) with 

 respect to frequency the dependence on the moments (Wf) and 

 {iii.n.) disappears, leaving only a weak sea-state dependence 

 through the slope moments (njni) . 



381 



