forward face of the spectrum should be somewhat steeper. 



If the plotted numbers in figure 11,27, for the third quadrant, are 



transferred to the first quadrant, and if the column noise and white noise are 



added to the values obtained, the result would be essentially the num.bers 



shown in figure 11.18. 



The sum of the num.bers in figure 11.27 will equal the total E value of the 

 sea plus the swell excluding a small circle near the origin. Strictly speaking, 

 the values at the borders of the rectangular area formed by the data in the first 

 and second quadrant before any reflections through the origin should be halved 

 before sm-nm-ingo However, the values on the s axis of the U(r, s) plots are 

 used only once in the direction of 240°. The values at the outer edge are so 

 small that only a mdnor error is made in not halving these values. 



Contours drawn as precisely as possible for the numbers shown in figure 

 11.27 are shown in figure 11.28. The contours are not very smooth due to 

 sampling variation. The contour analysis can be considerably smoothed when 

 this sampling variation is taken into account. 



Each of the original spectral estimates had 19 degrees of freedom. Due 

 to the corrections made so far, the smaller values of the spectral estimates 

 and the values for the transferred swell do not have 19 degrees of freedom, but 

 values near the peak: of the spectrum of the sea still have essentially 19 degrees 

 of freedomi. If a spectral estimate has 19 degrees of freedom, it can be nmlti- 

 plied by 1.88 and 0.63. Then 9 times out of 10 the true spectral value, as 



might be obtained by taking a sample with many more degrees of freedom, will 



lie between these bounds. Similarly, if the spectral estimate is multiplied by 



223 



