and the relations between various wave height statistics, such as the mean, 

 significant, and RMS heights, and extreme values. In general, a group of 

 waves from the same record can be approximately described by a Rayleigh 

 distribution (see Ch. 3, Sec. II). A different distribution appears necessary 

 to describe the distribution of significant wave heights, where each sig- 

 nificant wave height is taken from a different wave record at a given locality 

 (see Fig. 4-20). An estimate of the distribution of significant heights 

 higher than the mean significant height can be especially important because 

 wave energy in the littoral zone increases with the square of the wave 

 height. A useful model is provided by a modified exponential distribution of 

 form 



n^ - H . ■ 



s s rmn 



H > H 

 s s 



= e 



where 



(4-12) 



H 



s rmn 



the significant height 



significant height of interest 



the approximate "minimum significant height" 



the significant wave height standard deviation 



(Thompson and Harris, 1972.) This equation depends on two parameters, 



H 



s rmn 



and 



which are related to the mean height. 



H = H . + a 



s s min 



(4-13) 



If Hg j^.yyi or a are not available but the mean significant height H is 

 known, then an approximation to the distribution of equation (4-12) can be 

 obtained from the data of Thompson and Harris (1972, Table 1), which suggest 



H . « 0.38 H 



s rmn i 



(4-14) 



This approximation reduces equation (4-12) to a one-parameter distribution 

 depending only on mean significant wave height 



H > H )« e 

 s si 



1.61 H - 0.61 H 

 s s 



H 



(4-15) 



Equation (4-15) is not a substitute for the complete distribution function, 

 but when used with the wave gage data in Figure 4-20, it provides an estimate 

 of higher waves with agreement within 20 percent. Greater scatter vrould be 

 expected with visual observations. 



4. Office Study of Wave Climate . 



Information on wave climate is necessary for understanding littoral 

 processes. Usually there is insufficient time to obtain data from the field, 

 and it is necessary to compile information in an office study. The primary 

 variables of engineering interest for such a compilation are wave height and 

 direction. 



4-40 



