1 



N-I 



a2 = J- z2(nAt) 



^ N-I 



n=i 



(28) 



where a is the standard deviation of LVTS. All peaks and valleys in the 

 LVTS are identified and their positions in time are retained. Small, incon- 

 sequential peaks and valleys are then deleted with a computer algorithm 

 described in Appendix C and in Thompson (1980). Peaks and valleys smaller 

 than one standard deviation, cr , are deleted. The remaining peaks and 

 valleys are useful indicators of the occurrence of wave groups, although even 

 these must be reviewed in conjunction with the original time series, y(nAt), 

 to best identify groups of high waves. 



The LVTS can be used to define a simple parameter which is indicative of 

 the extent of wave grouping in a record. The dimensionless parameter 



^=72 



(29) 



where G is grouping parameter, o^ the variance of y(nAt); n = 1, 2, ..., 

 N, represents the ratio of the standard deviation of the LVTS (which is in 

 units of length squared) to the variance of the original time series (which 

 also is in units of length squared) . G is small for a record of reasonably 

 high, uniform waves and relatively large for a record containing well-defined 

 groups of high waves. The grouping parameter defined in equation (29) is 

 believed to be similar in practice to a parameter defined by Funke and Mansard 

 (1979), but equation (29) is preferred in this study for reasons discussed in 

 Section II. 



b. Autocorrelation. The use of autocorrelation requires the definition 

 of individual waves in the original time series. The computer algorithm (see 

 App. C) is used to identify meaningful crests and troughs in the original time 

 series, y(nAt). Wave height is defined as the difference in elevation between 

 a crest and preceding trough. Wave period is defined as the time difference 



between successive troughs, 

 puted as 



Ej( 



The autocorrelation between wave heights is com- 



T) 



I H(j) H(j - x) 



J=T+1 ^ 



I h2(j) ^l h2(j) 



j=T+l j = l 



(30) 



where 



Rh(t) 



T 



H(j) 



autocorrelation between wave heights 



lag between wave heights (number of waves) 



difference between height of j ' th wave and the mean wave 

 height for the record 



number of waves in record 



39 



