=2i= 
of the process. If computed spectra are used to estimate these moments, 
many of the higher moments are obscured by high frequency white noise in 
the estimate or made questionable by the high frequency nonlinear part of 
the spectrum so that the results predicted from them are doubtful. If the 
various theoretical forms for the spectra that have been proposed are used, 
the fourth or fifth moment of the frequency spectrum becomes questionable 
and the meaning of the second or third moment in the wave number spectrum 
is obscure. 
These problems are further complicated by the fact that sea 
surface slopes depend on the very high frequency capillary waves. With 
capillary waves, breakers, whitecaps and turbulence in the upper layers of 
the water, any results on curvature, as they depend on the higher moments 
of the spectrurn, are highly doubtful for a storm sea. 
The actual sea surface has gross features that are not in accord 
with the short crested Gaussian model. No artist, for example, depicts 
wind waves as irregular sinusoidal waves. Wave profiles along a line as a 
function of distance show sharp crests and long shallow troughs that do 
not occur in the model. This point will be discussed further in a later part 
of this paper. 
Purpose of paper 
The purpose of this paper is to derive three new random sea - 
way models that appear to have some properties of actual seas not illus - 
trated by previous models, to derive a few of these properties and discuss 
other possible properties, and to show how these models appear to be 
more realistic by comparing them with selected observations. These new 
models explain some of the difficulties that arise with the higher spectral 
moments. They may also be capable of giving some information about 
whitecaps, breaking waves, and sharp crested waves. Since all mathe - 
matical models of nature fail in one way or the other when the conditions 
and assumptions in the derivation are not met, these models will provide 
a second choice when observations of waves are to be compared with theo- 
retical results. Some questions are raised that can only be answered by 
additional theoretical work and by precise measurements of waves. The 
theoretical properties of these models can be compared with the theoretical 
