Global Wave Forecasts Using Spacecraft Data 



been summarized by Bunting (9). These results have been used by Wachnik and 

 Zarnick (10) in the study of aircraft carrier motions. This file of climatological 

 wave conditions for the year 1959 is proving to be of great value in a number of 

 other investigations that have not yet reached the stage of publication. 



The numerical technique that was developed at that time involved the analy- 

 sis of the surface wind field over the Atlantic Ocean on the basis of reports from 

 weather ships at sea and from conventional ships, the description of the wave 

 spectra at 15 frequencies and 12 directions at each of 519 grid points, the prop- 

 agation of the various spectral components at their group velocities, certain 

 dissipation mechanisms essentially based on gross Austausch turbulence, and a 

 wave growth theory obtained from a study of the data tabulated in the reports by 

 Moskowitz, Pierson, and Mehr. 



AVAILABLE THEORIES 



At the time that the work described above was completed in 1964, theories 

 for the growth of waves due to the wind were available but they had not been 

 checked, and indications were that they did not account for the observed growth 

 of waves at sea. Since that time, some field work has led us to the conclusion 

 that perhaps these theories can be used in a modified way to describe wave 

 growth, and the purpose of this section is to review the available theoretical re- 

 sults on wind-generated gravity waves in the context of our computer-based 

 procedures. 



The shape of the spectrum of a fully developed wind sea was studied in the 

 work completed prior to December 1964. This analysis by Moskowitz (5), Pier- 

 son and Moskowitz (6), and Pierson (7) seems to have resolved a number of the 

 important discrepancies in this part of wind-generated-wave theory. The major 

 source of the discrepancies seems to have been a combination of calibration 

 effects, which explain the very low values obtained by Darbyshire (11), and dif- 

 ferences in the elevation above the surface of the sea at which the wind was 

 measured. A correction for these differences places many of the theories within 

 reasonable range of each other. 



The propagation of waves is also quite well understood, based on the work 

 of Barber and Ursell (12), Pierson (13), and the more recent study of Snodgrass 

 et al. (1) in the Pacific. There can be no doubt that each spectral component in 

 a wind sea propagates at group velocity in an appropriate direction, according 

 to where it lies in the directional spectrum, and that such components can be 

 tracked on a great-circle route for a distance comparable to half the circumfer- 

 ence of the earth. 



The problem of the growth of the spectrum of a wind-generated sea has re- 

 ceived considerable attention. Recent work, starting with that of Eckart (14), 

 and continuing through the work of Miles (15) and Phillips (16) laid the theoreti- 

 cal foundations for this problem. It has been found that the growth that can be 

 calculated from these theories is apparently too low to explain the observed 

 growth of the spectral components in a wind sea. The fascinating field study by 

 Snyder and Cox (17), however, does show that the growth of a particular spectral 



501 



