Run-up distributions of waves breaking on sloping walls

Distributions of run-up are calculated by assigning to each individual wave in an irregular wave train a run-up value according to Hunt's formula. The use of this formula permits a normalization of the run-up in such a way that the run-up distributions are independent of slope angle, mean wave height and mean wave period, Expressions arc derived for the probability density and the distribution function of the run-up and of the wave steepness for arbitrary joint distributions .of wave height and period. Explicit results are obtained for wind waves by assuming wave height and period squared to be jointly Rayleigh distributed with arbitrary degree of correlation. Empirical data from the laboratory are discussed, These lend support to some of the main premises used and results obtained. A few field measurements of run-up distributions are presented; the Rayleigh distribution appears to fit these data