The average height of all waves with heights greater than H (H) can be 

 obtained from the equation. 



/ h' e ' "^'"^ ' d H 



H(H) = 



H 



/ H eVHrmJ dH 



(3-8) 



H 



or from curve b in Figure 3-5. By setting H = 0, all waves are con- 

 sidered, and it is found that the average wave height is given by 



H = 0.886 H 



rms ' 



and the significant wave height is given by 



H = 1.416H „, « vTh 



(3-9) 



(3-10) 



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 equivalent waves in the record is obtained by dividing the 

 duration of the record by this significant period. The highest waves 

 are then ranked in order with the highest wave ranked 1. The height of 

 the wave ranked nearest 0.135 times the total number of waves is taken as 

 the significant wave height. The derivation of this technique is based on 

 the assumption that the Rayleigh distribution law is exact. Harris (1970) 

 showed that this procedure agrees closely with values obtained by more 

 rigorous procedures which require the use of a computer. These procedures 

 are described in Section 3.23, Energy Spectra of Waves. 



The following problem illustrates the use of the theoretical wave 

 height distribution curves given in Figure 3-5. 



************** EXAMPLE PROBLEM ************** 



GIVEN : Based on an analysis of wave records at a coastal location, the 

 significant wave height Hg was estimated to be 10 feet. 



FIND : 



(a) Hjo (Average of the highest 10 percent of all waves) 



(b) H-^ (Average of the highest 1 percent of all waves) 



3-10 



