A new interpretation of sea-surface slope probability density functions

[1] Sea-surface slope probability density functions, which are usually fitted to a GramCharlier series, can be fit equally well by a bound wave/free wave model in which the distributions of bound and free waves are Gaussian. Bound waves are generated by longer waves on the surface and travel at nearly the phase speed of the long wave while free waves are generated directly by the wind and travel at their intrinsic phase speed. These two types of short surface waves can usually be separated in measurements that yield their velocities. The integrals over the two distributions yield the probabilities of finding bound or free waves on the surface. We show that the probability of finding bound waves on the ocean is comparable to that in a wind-wave tank and much larger than the probability of whitecapping. The mean slopes of the two distributions yield the mean tilts of bound or free waves. We show that the mean tilt of the bound waves is similar to that in a wind-wave tank and close to that necessary to explain Doppler shifts in microwave backscatter from the sea surface at high incidence angles. Finally, the widths of the two distributions yield the variance of sea-surface slopes at the locations of bound and free waves. We show that these are larger at sea than in a wind-wave tank, which explains why bound waves at sea have not been recognized previously in sea-surface slope probability distributions.