i.e., made dimensionless by dividing each observed height by Hy,™„ ; 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 theoretical 

 height appears to be about 5 percent greater than the observed height for a 

 probability of 0.01 and 15 percent greater at a probability of 0.0001. It is 

 possible that the difference between the actual and the theoretical heights of 

 highest waves is due to breaking of the highest waves before they reach the 

 coastal wave gages. Hence the Rayleigh distribution may be taken as an 

 approximate distribution in shallow water, but is probably conservative. 



Equation (3-1) can be established rigorously for restrictive conditions 

 and empirically for a much wider range of conditions. If equation (3-1) is 

 used, the probability density function can be obtained in the form 



f [(H - AH) <_ H <_ (H + AH) ] = (~-) H e Ih I (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 



The average height of all waves with heights greater than H , denoted HCfi) , 

 can be obtained from the equation 



OS 



/ 



Ed) = " ^ ^ (3-8) 



/ 



A 

 H 



Alternatively, the ratio H C^/E^^r^g can be estimated from curve b in 

 Figure 3-5, where P is the probability of H being exceeded. By setting 

 H = , all waves are considered and it is found that the average wave height 

 is given by 



H = 0.886 H (3-9) 



rms 



and the significant wave height is given by 



H = 1.416H « V2~H (3-10) 



s rms rms 



In the analysis system used by CERC from 1960 to 1970, and whenever digital 

 recordings cannot be used, the average period of a few of the best formed 

 waves is selected as the significant wave period. An estimated number of 



3-6 



