These results indicate that a Rayleigh distribution, as compared to the other models, tends to overpredict maximum wave heights and un- derpredict maximum crest heights. Computations obtained with the other models are quite close for maximum wave heights, and the Ha- ring model highlights a marked effect of water depth on the C,,,,/Hs ratios. 2 . Most probable C,,,,/H, ratios 5 . Bias and Standard deviation of the based-Weibull laws CONCLUSIONS The comparisons between model and data for these parameters are given in Figures 15 and 16 and show a very good agreement. We ob- serve here again from the values of bias and standard deviation given in Table 5 that the fitting is as good as the fitting of the two independ- ently corrected Rayleigh-Stokes models (Table 4). The relative stand- ard deviation is about 1% for the mode and 10% for the scale with very low bias. The measured data from the Frigg site show that the parameters of a fitted asymptotic Gumbel law of maxima is dependent of the steep- ness of the sea state. This dependency is observed very strong for the crest heights but slight for the wave heights. This effect of the non-lin- earity of the wave kinematics in infinite depth has not been taken into account in the models proposed in the past and explains some discrep- ancies between the different fitted models. 4. Classes of T, and H)3 2. Hinax/H1/3: Data mode (top) and scale (bottom) vs steepness 3 . Cinax/H)/3: Data mode (top) and scale (bottom) vs steepness 6. Hpax/H1/3: Model-Data mode ratio of Gumbel distribution vs steepness 3. Ainax/H1/3: Model-Data scale ratio of Gumbel distribution vs steep- ness 7 . Amax/Hy/3: Scale of Gumbel distribution with increasing T, and H,/3. Model (- o -) vs data (-+-) 10 . Cyyax/Hy/3: Model-Data mode ratio of Gumbel distribution vs steepness 12 . Cyyax/H1/3: Model-Data scale ratio of Gumbel distribution vs steepness 14 . Hinax/Hy/3: Model-Data scale ratio of Gumbel distribution vs steepness (mode - top, scale - bottom) 6 . Cyyax/H 1/3: Model-Data scale ratio of Gumbel distribution vs steepness (mode - top, scale - bottom)
