amplitudes, one for each piece, are selected and averaged, the amplitude 

 value is given by table 2. For a given observation of N amplitudes, the 

 expected value of the highest amplitude is given by table 2. The very 

 high waves are rare. 



Table 2 



Greatest wave amplitude data 



Expected value 

 N of highest 



wave amplitude 



20 1.87 v^ 



50 2.12 V^ 



100 2.28 v/E 



200 2.43 yE 



500 2.60 vl: 



1000 2.73^1: 



From the probability distribution function of the highest wave of 

 N waves as given by Longuet-Higgins (1952), it is also possible to 

 compute the most probable height, the height exceeded by 95% of the 

 individual observations, and the height exceeded by 5% of the individual 

 observations. These data are given in Pierson, Neumann, and James 

 (1955). 



The average amplitude of the K percent highest waves, as shown by 

 Longuet-Higgins (1952), can be found from the appropriate truncated 

 modification of equation (1). The value of X, say X , such that K percent 

 of the waves have amplitudes greater than that value, is first found by 

 solving (4) as given by equation (5). 



Qj. l-e "^^ = I-{k/ioo) 



- x^ /E 

 e k/ = K/ioo .5. 



The result is that the probability distribution function of the K 

 percent highest wave amplitudes is given by equation (6). 



, , ^ 100 2X "X /E 



g(x) dx = "k" -f-e dx 



(for X < x < CO and zero otherwise) 



(6) 



