the choice of time interval, number of lags, resolution and degrees of 

 freedom in the analysis of a wave record as a function of time at a fixed 

 point (Pierson and Marks [1952]) except that far more data processing 

 and numerical computation is necessary. As an example, to double the 

 resolution with the same grid spacing and same number of degrees of 

 freedom would require 40 lags and four times the number of spot heights. 

 The covariance surface would then require about 48 million multipli- 

 cations and additions. The time required would be more than twelve 

 times greater than was actually used. To have reduced the aliasing by 

 halving Ax, would have required four times the number of spot heights, 

 40 lags, and the above number of multiplications. Moreover, the total 

 energy over 3/4 of the area of the spectrum would have been only 10 

 percent of the total energy of the sea surface. 



For these reasons, Hydro was requested to read spot heights on a 

 square grid with 30 feet between intersections. Essentially all of the 

 details of the analysis were decided by this one choice of grid interval. 



References 



Marks, W. , and J. Chase [1955]; Observation of the growth and decay 

 of a wave spectrum. Contribution No. 769i from the Woods Hole 

 Oceanographic Institution. 



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