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- 

 square regression line to the observations. The parameters N and Harris 

 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 

 ^rms) that is, made dimensionless by dividing each observed height by 

 ^rms > then data from all observations may be combined into a single plot. 

 Points from scaled 15-minute samples are superimposed on Figure 3-3 to 

 show the scatter to be expected from analyzing individual observations in 

 this manner. 



Data from 72 scaled 15-minute samples representing 11,678 observed 

 waves have been combined in this manner to produce Figure 3-4. The theo- 

 retical height appears to be about 5 percent greater than the observed 

 height for a probability of 0.01 and 15 percent at a probability of 0.0001. 

 It is possible that the difference between the actual and theoretical 

 heights of highest waves is due to breaking of the very highest waves 

 before they reach the coastal wave gages. 



Equation 3-1 can be established rigorously for restrictive conditions, 

 and empirically for a much wider range of conditions. If Equation 3-1 is 

 accepted as an exact law, the probability density function can be obtained 

 in the form 



f[(H-AH) < H < (fi+ AH)] = l^—\ He ^^'""' . (3-6) 



The height of the wave with any given probability n/N of being exceeded 

 may be determined approximately from curve a in Figure 3-5 or from the 

 equation. 





(3-7) 



3-6 



