SHORT-TERM STATISTICS OF 10,000,000 WAVES OBSERVED BY BUOYS

Time records of the surface elevation measured by four Waverider buoys in the Mediterranean Sea off the coast of Spain have been analysed to inspect the statistics of crest heights and wave heights. By concatenating the normalised records we obtained a long, quasi-stationary record of 10,000,000 waves, permitting a verification of the Rayleigh distribution and its theoretical variations at rather low levels of probability (wave heights up to 10 times the standard deviation of the surface elevation). The crest heights were almost perfectly Rayleigh distributed over the entire range of observation. The distribution of the wave heights is close to a Rayleigh distribution with scale factor 0.88 (rather than 1 as in the conventional Rayleigh distribution), but it is better approximated with a Weibull distribution with a shape factor 2.162 (rather than 2, as for a Rayleigh distribution). Supplementary observations with laser altimeters in the North Sea (10,000 waves) showed nearly identical results in the range of overlap (the normalised crest heights were slightly higher, showing a nonlinear behaviour).