wave field), but it does reduce instrument noise. All analysis is done in dis- 

 crete frequency space, and results are defined in terms of N = 28 frequency 

 bands from/! = 0.054 Hz (the low-frequency bound) to f N = 0.319 Hz (the 

 high-frequency bound) in steps of A/ = 0.00977 Hz. The discrete frequency 

 spectrum is given the symbol S(fJ so that characteristic wave height is 



H = 4 



E ■*(/•„) A/ 



(1) 



Characteristic wave period, or peak period T is defined as the inverse of 

 the peak frequency/ deduced from the frequency spectrum; i.e., the discrete 

 frequency at which S(f n ) is maximum. This is the conventional definition of 

 peak period, and is used here to be consistent with other wave studies. Thus, 



T = 1//. 



p J p 



There are a number of ways to define peak direction 6 . The one used 

 here is the peak of the discrete frequency-direction spectrum S(f n ,8J at the 

 peak frequency; i.e., the discrete direction at which S(f ,0J is a maxi- 

 mum. Discrete directions m range from 0, = -90 deg to M = 9J = 90 deg 

 in A0 = 2-deg increments. These angles represent the directions from which 

 wave energy arrives relative to shore-normal, with -90 deg being waves trav- 

 elling parallel to the beach from the south, deg being waves arriving along 

 the shore-normal axis, and +90 deg being waves travelling parallel to the 

 beach from the north. A constraint on linear array analysis is that it cannot 

 detect waves travelling seaward, so all waves are assumed to arrive from the 

 seaward semicircle of azimuths. 



A characteristic directional spread of wave energy 86 p also is a very useful 

 parameter for these data. It is also defined from S(f n ,6J as being the angle 

 that subtends the central half of the energy in the directional distribution at the 

 peak frequency. Symbolically, an integral function I{f,8) can be defined as 



W) = \ 



IMld* (2) 



where I(f, -90°) = and I(f, 90°) = 1 identically because the integral of 

 S(f,8) with respect to direction defines S(f) . The arc that contains the central 

 half of the energy at a given frequency begins at the angle 0^ for which 

 Kfj^) = 0.25 and ends at the angle 75 for which I(f,6 75 ) = 0.75. If 0^ 

 and 75 are determined at / = / , the peak directional spread is simply 



50, = 75 - 0,^ (3) 



This parameter is robust in that it can be computed for any finite directional 

 distribution and is meaningful in that it gives a small number for narrowly 



Chapter 3 Storm Data 



13 



