However, it was known that equation (1) was quite likely to be the 

 true distribution of all wave heights as evidenced by the works cited 

 above; and in addition the forecasting method ■which was being tested 

 had worked well when compared with actual wave record observations. 



It was evident, therefore, that the observers had not been able to 

 observe and record the low waves that had actually occurred. As 

 shown in the UNIMAK example, with a significant wave height of 20,9 

 feet, 26 waves out of 67 should have had a height less than 10 feet. 

 Only 50 waves were actually recorded, and 17 waves less than 10 

 feet high were omitted. 



Histograms of the data were plotted, and the observations were 

 truncated at that height such that the distribution above that height 

 resembled a truncated distribution as given by equation (21). From 

 this truncated distribution the new corrected average height and 

 corrected significant height were computed. 



The values which res\ilted are entered in table 7 under the heading 

 Observed Significant Height (corrected). The result was to decrease 

 each value by an amount which depended upon the nature of the original 

 sample. Some heights were decreased by as much as six feet, and the 

 average decrease was 3.75 feet. The decrease is tabulated under the 

 entry labeled, Decrease. 



The forecast values and the corrected observed values then agreed 

 far better than the forecast values and uncorrected observed values. 

 Some of the largest errors were decreased a great deal. Seven of the 

 twelve forecasts were within plus or minus five feet of the observed 

 values. The forecast values still had a tendency to be lower than the 

 observed values. 



When the truncated distribution is used to determine the significant 

 wave height, the confidence limits determined from the full distribution, 

 strictly speaking, should not be used to obtain estimates of the reliability 

 of the observations. The correct procedure would be to use the mean 

 and second moment about the mean of the truncated distribution in a 

 derivation similar to the one given above. 



However, such a derivation would have to be carried out for many 

 different cases, and it is believed that the final results would not 

 improve too much on the estimates obtained from the theory derived 

 above as based on the full distribution. 



The confidence limits derived above can be applied to the results 



28 



