Hasselmann and SohieZev 



perturbation parameter of the expansion is given by the ratio of the 

 amplitude of the interacting surface wave to the wave length of the 

 incident radiation. In the first order analysis, the perturbation 

 parameter is proportional to the slope of the scattering Bragg 

 wave, which is smsill for all electromagnetic wave lengths. At 

 second and higher order, however, the electromagnetic waves 

 interact with longer surface waves of higher amplitude. In this 

 case, the perturbation parameter remains small only if the electro- 

 magnetic wave length is large compared with the annplitude of the 

 entire wave field. This condition is satisfied by dkm waves, but not 

 by cm -dm waves. 



The requirements for the wave-facet and wave-wave inter- 

 action models are found to be mutually exclusive, so that the two 

 expansions cannot be matched in a common region of validity. It is 

 a fortunate coincidence that the theoretical wave length gap cor- 

 responds to the gap between the two presently available techniques 

 for measuring electromagnetic backs catter on a synoptic scale. 



The second order wave -wave interaction analysis yields a 

 continuous Doppler spectrum superimposed on the first-order Bragg 

 line. The continuum reduces to a particularly simple and useful 

 form when the Bragg wave length is short compared with the wave 

 lengths of the dominant surface waves -- the usual situation for 

 ionospheric modes. In this case, the continuum is identical with 

 the two-sided image of the surface-wave frequency spectrum, 

 centered on the Bragg line as virtual frequency origin. The energy 

 scale of the wave spectrum can be inferred from the observed 

 energy of the Bragg line, independent of transmission or other cali- 

 bration factors. 



Doppler side-band structures observed by Ward [ 22] and 

 others are not inconsistent with this interpretation. However, most 

 Doppler spectra published hitherto have been analysed from rather 

 short records , so that the continuum is generally not well deflned 

 statistically. Longer records are needed to decide whether the one- 

 dimensional frequency spectrum of the surface- wave field can indeed 

 be detected in the Doppler spectrum of backs cattered ionospheric 

 modes above the inherent ionospheric noise. 



II. THE LOWEST -ORDER SCATTERING MODELS 



For electromagnetic waves short compared with the dominant 

 waves of the sea, one might attempt to describe the scattered field 

 by a specular reflexion model. In which the sea surface Is repre- 

 sented as an ensenable of locally plane, Infinitesimal facets , each of 

 which reflects the Incident radiation according to the laws of geometric 

 optics. The cross section a for the backscattered radiation (the 

 backscattered energy per unit solid angle per unit surface area of the 

 ocean) Is then proportional to the number density of facet norm.als 



364 



