The results cited unfortunately are not interpreted in terms of the 

 spectrum of the waves. The records were pressure records in which 

 the spectrum is made narrower by the filtering effect of depth; also, 

 many may have been swell records with narrow band. 



It may be that records of sea waves with a broad spectrum will 

 have amplitudes distributed according to (1) and that the heights will 

 not be distributed according to (1). On the other hand, the sharper 

 peaks and shallower troughs which are the result of nonlinear effects 

 may make the heights more like equation (1) and the amplitudes skewed 

 in distribution. 



When the wave amplitudes vary erratically from crest to succeeding 

 trough, as in a sea, the theoretical distribution of the heights is a 

 very difficult problem in probability theory because the succeeding 

 trough is partially correlated with the crest.* If it were uncorrelated, 

 the p.d.f. of the sum of the two values from equation (1) could be found 

 and this would be the p.d.f. of the wave heights. This is not the case, 

 however, and the true height distribution in a sea may depend in a 

 complicated way on the spectrum of the waves. From these results 

 several conclusions can be reached. 



One conclusion, then, may well be that wave amplitudes follow 

 equation (1), but that wave heights do not follow equation (1) in some 

 circumstances. Another is that wave heights do follow equation (1) in 

 some circumstances. The third is that the assumption that wave heights 

 do follow equation (1) is about the best theoretical assumption that 

 can be made at the present time because in many cases the assumption 

 will be approximately correct, not leading to appreciable error, and 

 because the complete theory has not been solved. 



4. Spectrum Really Needed 



If an actual ocean wave record is available, its amplitude distri- 

 bution, or its height distribution, is not the most important property 

 of the record. The energy spectrum of the record is what is really 

 needed for many practical applications and without it little of real 

 theoretical value can be accomplished. 



C. Visual Height Observations 



1. Reason Needed 



There are many cases in which visual observations of ocean wave 



*As pointed out by Dr. Robin A, Wooding of New Zealand in personal 

 correspondence. 



