parameter <C^> 



A preliminary analysis indicates that further useful 

 parameters of the wind-sea, including wavelength informa- 

 tion, can be obtained from a more detailed analysis of the 

 complete doppler spectrum and higher order signal moments. 

 However, the dependence of these functions on the wind-wave 

 spectrum is highly nonlinear, so that the inversion of the 

 functional relations presents a nontrivial mathematical 

 problem which can probably be solved only numerically with 

 the aid of parametrised representations of the wind-wave 

 spectrum. 



According to the solution (6), the wave field affects 

 only the onset of the reflected pulse, the asymptotic pulse 

 shape approaching the calm-surface solution (3) (as, of 

 course, must be the case if the solutions for all sea states, 

 including the limit <?^>-^o , differ only by a scale 

 factor). Although this result appears encouraging for 

 the measurement of mean sea surface, it is a particular 

 consequence of the Gaussian hypothesis, with its corollary 

 of statistically independent wave slopes and surface 

 heights. In the non-Gaussian case, the asymptotic pulse 

 shape is in general parallel to, but offset from, the calm- 

 surface solution. Physically, if the mean square wave 

 slopes tend to be higher on the wave crests than in the 

 troughs, the average energy reflected vertically from the 



25-48 



