thus waves with a significant height of 40 feet could, if many more wave 

 records had been taken near the ship in the same general area (say, within 

 an area 10 miles on a side) actually be more precisely represented by a 

 significant height that nine times out of ten would be sonnewhere between 

 44 feet and 36 feet. 



The bias in the hindcasting procedure is negligibly small, and the rms 

 error of 4.25 feet is nearly the same as the sampling variability of the 

 higher waves. Of the 38 hindcasts, about 75% fall within -4.Z5 feet of the 

 observed value. A forecast, if it could be made, that the significant height 

 of the waves at a certain point on the ocean at a certain time would be be- 

 tween 31 and 39 feet would be a very useful forecast. 



A correct hindcast of the significant height implies a correct hindcast 

 of the total volume under the directional wave spectrum; that is, it im- 

 plies that the sum of the numbers in Table 1 is correct. However, the 

 errors in height produce larger percentage errors in variance. A five 

 percent error in significant height implies a ten percent error in variance, 

 and a twenty percent error in height (too high) implies a forty -four percent 

 error in variance. 



It was not possible to verify the results of Table 1. However, the sumi 

 column of Table 1 could be verified. Figure 3 shows a portion of such veri- 

 fications for ZO, 21, and 22 December 1959- The agreement between the 

 hindcasted and observed frequency spectra is quite good for the first day 

 and for the last two observations on 22 December. The waves grew in the 

 hindcast for 06Z 22 December too rapidly to provide a good verification 

 although a few hours earlier the hindcast spectrum probably would agree 

 quite well with the spectrunn that was observed. 



The final output of this project was 60 reels of magnetic tape containing 

 approximately one million spectra of the form of Table 1. They represent 

 the essential information on the state of the sea for a 15 nnonths period 

 every six hours at 519 points on the North Atlantic Ocean. 



Use of Results. 



The primary purpose of this work was described in the introduction 

 Toward this goal the data will be used to compute the motions of aircraft 

 carriers in the waves, and since the wind is also given, the landing con- 

 ditions can be found. Its usefulness extends far beyond its original purpose 

 to many problems in the design of vehicles and platforms to be used on the 

 open sea. It is immediately obvious that the procedure has operational 

 significance. Interest has already been indicated by those connected with 

 the design of merchant ships. It would also be possible to improve on 

 various ship routing procedures by testing various models on these data. 

 Numerous studies based on these results can be made. The accuracy at 

 low frequencies in the spectral hindcasts is currently not too good. For 

 mine warfare problems, our present results would need improvenaent be- 

 fore the waves could be refracted to shallow water and used to predict 



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