There are a number of disadvantages to this procedure. The total 

 number of waves which pass must still be counted. How can the one-third 

 highest waves be counted if the two- thirds lowest waves are not 

 counted also, so that it will be known that the one- third highest waves 

 are actually some one-third of a total number of waves? 



Also if the significant height is computed, a large number of the 

 waves which pass cannot be utilized in computing a statistic about the 

 height. Many fewer usable values are obtained during a given time 

 duration for the observation. A lot of time is wasted doing nothing. 



With the aid of the truncated distribution for K equal to 33 percent, 

 the mean of the distribution and the standard deviation could be found. 

 Then the steps used above to determine confidence limits for samples 

 from the complete distribution could be used on the mean and second 

 moment of the truncated distribution to determine the confidence 

 limits of a significant height determined from N observed values. The 

 results would be more reliable for a given N because some (but not 

 all) of the correlation effect would be removed. However it would take 

 three times as long to observe the N elements of the sample. 



Exactly similar procedures could be used with any other percentage 

 of the highest waves. However, in each case the total number of waves 

 which pass must be observed. 



8. Truncated Distribution at a Fixed Height 



The second way to truncate the distribution is to eliminate all waves 

 less than a certain fixed height and observe every wave in excess of 

 this fixed height. For a given state of the sea the observer might 

 record all heights greater than, say, 4 feet. For a higher sea all 

 waves in excess of 10 feet could be recorded. 



It is then possible to compute the average of the observed values 

 and from this the true average of all the heights, including those 

 which were not recorded, and any other desirable height parameter. 

 The theoretical derivation is given in the following paragraphs. 



Let the minimum height recorded be equal to H . . Then f 

 equals H /2, and the theory will be worked out using amplitudes! 



The results must be doubled at the finish to obtain the height parameters 

 needed. 



/ "^2X3 -xVe dx-- i-e- ^'"^'"-A 



^ r 



Since / 2X^ -X /E dx = I-P- "^ "^'"/^ (20) 



E 

 'min. 



21 



