WAVE HEIGHT DISTRIBUTIONS IN MULTIPLE- PEAKED SEAS 



PART I: INTRODUCTION 



1. Successful design of shore protection projects depends critically on 

 knowledge of water level variation. Sea surface elevations change because of 

 a suite of processes that include tides, storm surge, and wind waves. Wind 

 waves do significant amounts of work on coastal boundaries, in general. Of 

 particular importance is that water level changes associated with heights of 

 wind waves contribute to extremes of beach and structural runup and hence to 

 high beach erosion rates or potential for overtopping and flooding behind 

 coastal defenses. For engineering design purposes, it is useful to have a 

 statistical description of the heights of sea waves so that probabilities can 

 be assigned to particular water level extremes. With these probabilities, a 

 likelihood of project survival can be estimated. Ideally, probable distribu- 

 tions of wave heights in a given sea state can be described with a mathemati- 

 cal model. An important problem in coastal engineering is the determination 

 of a model that can represent realistic sea states with reasonable fidelity. 



2. One of the earliest and most widely used models is the Rayleigh 

 probability density function (pdf ) , first applied in ocean work by Longuet- 

 Higgins (1952). It is a one-parameter model, relying only on specification of 

 a root-mean- square (RMS) wave height to allow estimation of the probability 

 that a randomly chosen wave height will fall within a small range about a 

 specified wave height. As derived by Longuet-Higgins (1952), the Rayleigh pdf 

 is valid formally only when an ocean surface can be described by the linear 

 sum of a very large number of randomly phased and directed sinusoidal com- 

 ponents which conform to a unimodal frequency spectrum wherein all frequencies 

 are very nearly (but not quite) equal to some central, characteristic frequen- 

 cy. Unfortunately, not all sea states have unimodal, narrow-banded spectra. 

 In a rather broad study of naturally occuring sea states, Thompson (1980) 

 noted that well over half of his observed spectra were distinctly multimodal. 

 This condition means that one can expect wave height distributions to deviate 

 to some extent from a Rayleigh distribution. If such a deviation is impor- 

 tant, alternative pdf models must be sought. 



