The significant wave period obtained by visual observations of waves 

 is likely to be the average period of 10 to 15 successive prominent waves. 

 When determined from gage records, the significant period is apt to be the 

 average period of the subjectively estimated most prominent waves, or the 

 average period of all waves whose troughs are below and whose crests are 

 above the mean water level, (zero up crossing method). 



3.22 WAVE HEIGHT VARIABILITY 



When the heights of individual waves on a wave record are ranked from 

 the highest to lowest, the frequency of occurrence of waves above any given 

 value is given to a close approximation by the cumulative form of the 

 Rayleigh distribution. This fact can be used to estimate the average 

 height of the one-third highest waves from measurements of a few of the 

 highest waves, or to estimate the height of a wave of any arbitrary 

 frequency from a knowledge of the significant wave height. According to 

 the Rayleigh distribution function, the probability that the wave height 

 H is more than some arbitrary value of H referred to as H is given 

 by 



P(H > H) = e ^ '""' (3-1) 



where Hmis is a parameter^of the distribution, and P(H > H) is the number 

 n of waves larger than H divided by the total number N of waves in 

 the record. Thus P has the form n/N. The value Hrms is called the 

 root-mean- square height and is defined by 



^rm. = V. .2. H • (3-2) 



It was shown in Section 2.238, Wave Energy and Power, that the total energy 

 per unit surface area is given by 



E = '-fil 



The average energy per unit surface area for a number of waves is given by 



Pg 1 



N 



where Hj is the height of successive individual waves, and (¥)^ is the 

 average energy per unit surface area of all waves considered. Thus H^ms 

 is a measure of average wave energy. Calculation of Hj^g by Equation 3-2 

 is somewhat less subjective than direct evaluation of the Hg because more 

 emphasis is placed on the larger, better defined waves. The calculation 

 can be made more objective by substitution of n/N for P(H > iT) in 

 Equation 3-1 and taking natural logarithms of both sides to obtain 



Ln(n) = Ln(N) - (H;^pH^ . (3_4) 



3-5 



