Pierson 



features of the behavior of such a craft on a certain cruise for, say, the next 6 

 hours or, perhaps, even the next 24 hours, one must give up the deterministic 

 world and predict the probabilities of certain events and statistics derivable 

 from them. 



Such predictions can be quite refined statements, given sufficient knowledge 

 and understanding of a number of factors. For example, it may be possible 

 some day to make statements of the following kind: 



1. Merchant ship design A is superior to merchant ship design B for 

 cruises between New York and the English Channel because (1) if each ship were 

 to follow the least time track route on each cruise for five years, merchant ship 

 A would average five days two hours per crossing as opposed to six days one 

 hour for ship B, (2) the bow of ship A would ship water 560 (±20) times (with a 

 probability of 0.99) during the five year period and ship B would ship water 650 

 (±3) times (with the same probability) and (3) ship A would slam only 6 (±3) 

 times (with a probability of 0.99) whereas B would slam 50 (±5) times. 



2. Of five ships available for a rescue mission at a certain point, this par- 

 ticular ship should move as quickly as possible to that point. It will arrive two 

 hours (±20 minutes) sooner tiian the earliest of the other four ships. The sec- 

 ond ship to send is such and such a ship as a safety factor or as a standby re- 

 serve. 



3. All ships in a certain part of the North Pacific will encounter seas in 

 excess of the highest measured for the past decade beginning 18 hours from now 

 and ending 30 hours from now. All possible safety precautions should be taken 

 immediately. Predicted conditions for specific points in this area follow. 



Statements such as these will be possible when it is possible to describe 

 the directional spectrum of the waves at every point on the ocean as a function 

 of the winds over the ocean. The first statement can be made on the basis of 

 the historical files of weather data. The second and third require the wind field 

 to be forecasted a day or so into the future. 



It is therefore necessary to describe this directional spectrum in its infi- 

 nite variety and to predict its form at future times. Strangely enough, this 

 problem is, to a large extent, deterministic. As an analogy, to predict the vari- 

 ance of a sample to be drawn from a normal population is not the same as to 

 predict the actual values that would be drawn at random from a normal popula- 

 tion with a known variance. In this particular problem, to predict the features 

 of the directional spectrum that will be estimated from observations of waves 

 in a particular area is not the same thing as to predict the exact form of the 

 waves that will be observed in a particular area. The predicted spectrum in 

 turn permits the determination of many wave and ship motion parameters such 

 as the significant wave height, the average pitch motion, the number of slams 

 and so on. One then assumes that the predicted parameters are those that will 

 be the population parameters at the point of interest for the event of interest. 

 These parameters are then estimated directly from observation, if possible, 

 and compared with the prediction. The attempt is successful if the predicted 

 and estimated values agree within the sampling variability of the estimate. 



426 



