Global Wave Forecasts Using Spacecraft Data 



The problem of the growth of the spectrum of a wind-generated sea is a 

 complicated one in nature for a number of reasons. The winds over the ocean, 

 either blowing offshore, or on the open ocean, are not constant in velocity for 

 the length of time required in most of the theories for full development. They 

 shift in direction and speed over time periods of the order of 6 to 12 hours. 

 They can build from 20 to 25 knots to 40 to 60 knots in a half a day, remain at 

 60 knots over an area 400 or 500 nautical miles on a side for 12 to 18 hours, and 

 then drop in speed to 15 knots in another 18 hours. The models used by ocean- 

 ographers in attempting to develop wave forecasting methods in the past, that 

 assumed a constant wind blowing for a certain duration, do not fit conditions at 

 sea very well. It has been our experience in the study of the data that are avail- 

 able that the spectra very nearly track the fully developed spectra as the winds 

 build with time, except for very high winds. The area wherein the difficulties 

 lie is in the forward face of the spectra and in getting the contribution at these 

 frequencies correct as a storm builds up and dies down. The high-frequency 

 portion of the spectrum is more or less always saturated at or near the value 

 predicted from the spectral form given by Pierson and Moskowitz (6). 



An important aspect of the problem of wave generation is the widely differ- 

 ent rates of growth reported by various investigators. The point raised by 

 Phillips concerning the presence of a background spectrum in the ocean and its 

 absence in the lee of land seems to explain these different growth rates. A very 

 low background can reduce the time to reach full development to less than half 

 that required if the waves grow from a flat calm. The spectral growth for a 40- 

 knot wind with a background present is shown in Fig. 2 according to Inoue. 



There remains the problem of how waves are dissipated at sea. If there 

 was no dissipation mechanism, the spectrum of the waves on the open ocean 

 would soon become isotropic, with spectral components traveling in all direc- 

 tions at nearly every point. This is observed not to be the case, and there is 

 some process by which waves traveling against strong wind-generated seas are 

 rapidly attenuated. The study of Snodgrass et al. (1) on the propagation of waves 

 from the South Pacific to the North Pacific found that the greatest amount of 

 attenuation was right in, or near, the generating area and that the swell could 

 then travel through the subtropical highs and the trade wind regions without very 

 much additional loss. 



It seems to us that the primary reason for the dissipation of the waves is 

 the turbulence generated by the breaking waves in a wind-generated sea. An 

 attempt has been made to model this effect by taking the simple theories pro- 

 posed by Lamb for viscous attenuation and using an Austausch coefficient in its 

 place that enhances this effect. This method very strongly attenuates waves that 

 travel against the wind. This dissipation, as discussed in a later section, seems 

 to be an important contribution to the decrease of waves after a storm passes 

 and the wind shifts. There is certainly plenty of room for improvement in this 

 particular aspect of our computer-based procedures. However, it does appear 

 to yield consistent results when tested against available sequences of wave spec- 

 tra computed from wave records obtained from both Argus Island and from the 

 British weather ships. As an example, for the square North Atlantic grid system. 

 Figs. 3, 4, and 5 show the results near the Weather Reporter for the original 



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