Radar Baok-Soatter from the Sea Surface 



several features not predicted by the Bragg model. Generally, 

 there is a marked dependence of the anomalies on sea state, sug- 

 gesting that useful correlations between backscatter signatures and 

 significant sea-state parameters may be discovered by extending 

 the scattering theory to higher order. 



Two generalisations have been proposed: the wave-facet 

 interaction model [ 23 , 4, cf, also 3, 9, 10, 20, 21], in which the 

 Bragg-scattering waves are superposed on longer carrier waves, 

 and the higher-order, wave-wave interaction model originally inves- 

 tigated by Rice [ 18] . The models have been applied hitherto mainly 

 to the cross sections, which show only weak sea-state signatures. In 

 the present paper, we consider their extension to the more strongly 

 sea- state dependent Doppler spectra. 



In the cm-dm bands, good agreement with the observed 

 Doppler spectra is obtained with the wave-facet interaction model. 

 The Doppler spectra are found to be quasi- Gaussian and can be 

 characterized to good approximation by the mean frequency and the 

 frequency bandwidth. Both parameters depend on moments of the 

 wave spectrum which are governed by the high- energy, low- wave - 

 number range of the spectrum. They can therefore be used to obtain 

 independent estimates of, say, the mean waveheight and period. 



The model allows only for electromagnetic interactions. 

 Basically, the hydrodynamical modulation of short gravity waves by 

 long carrier waves is of considerable interest, not only for the 

 description of the surface wave field, but also for its energy balance. 

 The interactions generally lead to an energy loss of the long waves 

 at a rate which can be estimated from the observed upwind- downwind 

 asymmetry of the cross sections [ll] '. However, because of the 

 strong influence of white capping, the interactions cannot yet be 

 described in sufficient detail to be included realistically in computa- 

 tions of the Doppler spectra. Their effect on the Doppler bandwidth 

 is probably negligible, but the mean Doppler frequency may be more 

 strongly modified. 



The wave- facet interaction model is valid for electromagnetic 

 wave lengths shorter than about 1 m. Thus it applies in the cm-dm 

 radar band, but not in the dkm band. In the latter case, however, 

 the Bragg theory can be generalised by straightforward extension of 

 the wave-wave interaction analysis to higher order. The relevant 



' Longuet-Higgins [13] has shown that the momentum loss of short 

 waves breaking on the crests of longer waves results in an energy 

 transfer to the long waves. However, the gain in long- wave 

 kinetic energy due to this process can be shown to be slightly less 

 than the loss of potential energy arising from the simultaneous 

 mass transfer between short and long waves. The net result of 

 both processes is a weak attenuation of the long waves [ ll] . 



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