If the Rayleigh distribution of wave heights is valid, the representative wave heights can all be converted one to another through the known relationships. In shallow water, it has been pointed out by many researchers that the wave height distribution deviates from the Rayleigh distribution. However, it is not clear whether this deviation can lead to significant errors on the estimation of representative wave heights or not. Experimental data from small-scale, large-scale, and field experiments were used to examine the errors of the relationships derived from the Rayleigh distribution on estimating representative wave heights. The examination indicates that if Hrms is given, the relationships give overall very good estimations on H̄ and H1/3, good estimation on H1/10 but fair estimation on Hmax- The effect of wave breaking was empirically incorporated into the relationships. The new relationships give better estimation than the relationships derived from the Rayleigh distribution.
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