Pierson, Tick, and Baer 



for a 2-hour time step, so that in 16 hours the component will decay to l/e of 

 its original value. A frequency of 0.20 sec"^ is attenuated 16 times faster, so 

 that the local chop traveling against the wind rapidly disappears, whereas a fre- 

 quency of 0.05 takes more than 10 days to be attenuated to l/e of its original 

 value. 



The effect of this attenuation is shown in Figs. 3 and 4, where it has not 

 been included in one computation and it has been included in a second computa- 

 tion. The effects of propagation accoxint for a major part of the variation at the 

 weather ship, but attenuation appears to be needed to explain the full sequence of 

 observations. This attenuation is only effective if the spectral component is 

 traveling against the wind. In Figures 3, 4, and 5, for example, the wind shifted 

 after the peak of the December 17 cyclone, and this kind of dissipation provides 

 for closer agreement between theory and observation. For the peak of Decem- 

 ber 22-23, the wind speed decreased, but the winds did not change direction, so 

 that the dissipation term did not operate. Although, without dissipation, the peak 

 waves are too high, the decrease after the peak is at the same rate and is due 

 to the effects of propagation in all of the figures. The correct determination of 

 the effect of dissipation will be extremely important, because Eq. (7) indicates a 

 quite different behavior, depending on the initial value of s^( f . ) . It would be 

 highly desirable to replace the above dissipation computation by some measure 

 of breaking waves and white caps in the wind sea, but this problem is not yet 

 clearly enough understood for this to be possible. 



Propagation on a Global Scale 



To forecast both local sea and swell, the winds from essentially the entire 

 ocean area are needed at some time. Thus if the spectral component is travel- 

 ing at 33 knots, the effects of the winds 12 hours ago and 400 miles away from 

 the forecast point will be needed. Similarly, day-old information is needed from 

 800 nautical miles away and 2-day-old information from 1600 nautical miles. 

 Other components travel at a different velocity, so that data over most of the 

 ocean is needed to make a single forecast. By judicious scanning of all of these 

 wind fields, one might conceivably drop many of the areas and reduce the prob- 

 lem to manageable size for a single forecast point. However, for many require- 

 ments, such as ship routing, wave forecasts are needed for such large areas 

 that it is worthwhile to consider forecasting for at least a large region of the 

 ocean and perhaps for all the oceans. 



One of the problems is how to represent the wave conditions over such a 

 large area. From the previous discussion it is obvious that the spectrum can 

 have an infinite number of different shapes, so that no simple system can repre- 

 sent the condition at a particular location. We have therefore searched for a 

 simple function which could represent the spectrum and be remembered in the 

 computer by a reasonable number of parameters. Many such functions are 

 available, but they are not amenable to the components being propagated inde- 

 pendently. We have therefore been forced to use individual discrete frequency 

 and directional components to represent the spectrum. After rather extensive 

 testing, we found that 15 frequencies and 12 directions did well for the North 

 Atlantic. An increase to 24 directions is planned in the present development 



512 



