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A 







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/ 













/ 



f 









\ 









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h 





/ 







Mr 









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1 







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Figure 8 - Wave Record Showing Elevation^ and Wave Height h, 



It is not necessarily true that a sea for which the wave heights follow the probability 

 density function [1] will have a normal distribution of f(0) where ^(<) is the instantaneous 

 wave elevation. 



Reference 8 gives the ratio 





\ 



An 



[2] 



jfi^ denotes the mean value of the first pN of the A' wave heights when arranged in descend- 

 ing order of magnitude, where p is a fraction between and 1. Thus the average of the 

 "significant waves" is h^^^^\ It should be noted that, experimentally, it is difficult to find h 

 from measurements of h inasmuch as the average depends to a considerable degree upon the 

 lower limit to which the wave heights are measured; see Reference 4 for a discussion of this 

 effect. 



The distribution plotted in Figure 7 is fitted with the mathematical curve given in 

 Equation [1], The value of h^ which gives the best fit is h^ = 60.0.* As stated on page 10 the 

 random walk theory holds only if the sea has a narrow spectrum. It may well be that the 

 spectrum of the sea for the wave height distribution shown in Figure 7 will not remain narrow 

 due to the fact that the sampling extended over a period of years. 



MEANS AND STANDARD DEVIATIONS 



Means and standard deviations were computed for the distributions shown in Figures 1 

 and 2 and are given in Table 1. It will be observed that the average of the data obtained from 

 merchant-ship observations is much lower than the average of the Weather Bureau data. From 

 the standard error of the mean (the standard deviation of the distribution of the means of 

 samples) of the four yearly Weather Bureau samples, it may be stated that there are 99.7 



♦The best fit was determined by a Chi square test. 



