A 



JL 



P(H > H) = e \"™V (3-1) 



where H is a parameter of .the distribution, and P(H > H) is the 



TVTIS A 



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 ^V^s ^^ called the 

 root-mean- square height and is defined by 



H J 

 rme \ 



1 " 2 



i I r. (3-2) 



It was shown in Chapter 2, Section II, 3, h (Wave Energy and Power) that the 

 total energy per unit surface area for a train of sinusoidal waves of height 

 H is given by 



7 PgH^ 

 ^ - 8 



The average energy per unit surface area for a number of sinusoidal waves of 

 variable height is given by 



where H- is the height of successive individual waves and (E)^ the average 

 energy per unit surface area of all waves considered. Thus ^r'ms ^^ ^ 

 measure of average wave energy. Calculation of H^,^g by equation (3-2) is 

 somewhat more subjective than direct evaluation of the Hg in which more 

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

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

 equation (3-1) and taking natural logarithms of both sides to obtain 



Ln(n) = Ln(N) - (h"^ )ft^ (3-4) 



By making the substitutions 



y(n) = Ln(n), a = Ln(N), b = - H^^^, x(n) = H^(n) 

 Equation (3-4) may be written as 



y(n) = a + bx(n) (3-5) 



The constants a and b can be found graphically or by fitting a least 

 squares regression line to the observations. The parameters N and H^,^g 

 may be computed from a and b . The value of N found in this way is the 

 value that provides the best fit between the observed distribution of 

 identified waves and the Rayleigh distribution function. It is generally a 

 little larger than the number of waves actually identified in the record. 

 This seems reasonable because some very small waves are generally neglected in 

 interpreting the record. When the observed wave heights are scaled by H^^g ; 



3-5 



