23. The constraint on the upper frequency £3 is related to the time 

 step At used to simulate a time series. If a frequency is too high, there 

 will be too few time steps per wave. The probability will then be small that 

 the crests and troughs of these waves will be represented in the discrete 

 sample. For practical purposes, about 20 time steps per wave is a reasonable 

 sampling. A crest or trough is then always within one -fortieth of a wave 

 period of some discrete time step. The fractional error in crest or trough 

 estimation is then the ratio of the cosine of one-fortieth of a wave cycle 



(9 deg) to the cosine of zero degrees. This ratio is about 0.988, correspond- 

 ing to an error of about 1.2 percent in crest elevation estimation or about 

 2.4 percent overall. A frequency upper limit of 20 time steps then requires 

 f2 < 1/(20 At) . 



24. Another parameter of use is one that gives a measure of spectral 

 width. A wave height distribution is theoretically Rayleigh if the cor- 

 responding frequency spectrum is narrow-banded. A measure of such spectral 

 width has been given by Cartwright and Longuet-Higgins (1956) as the parameter 

 e defined by 



€ = 1 - -^^^2_ (18) 



mQm^ 



where m^ , m2 , and m^ are determined through Equation 17. A small e 

 indicates a narrow spectrum, and an € near 1 indicates a broad spectrum. 



25. Further parameters associated with spectral definitions are given 

 in Part III, wherein test data generation is described. Parameters associated 

 with averages of particular subsets of wave heights (for example, average of 

 the highest one-third) are defined in Part IV, where model test criteria are 

 described. 



13 



