frequency spectrum. The errors due to the spot height reading and to background 

 curvature have been eliminated, and at the moment work is under way to eliminate 

 the error due to differential shrinkage. The directional spectra have been computed 

 and indications are that such a correction can be made and that the results of the 

 wave pole observations and the stereo observations can be made consistent. 



Some tentative conclusions can be made even with the data in their present 

 form; and even if no further attempt were made in analyzing the data, many valuable 

 conclusions could be drawn. The error due to differential shrinkage shows a definite 

 pattern which can be removed qualitatively from the spectrum. The conclusions would 

 then be that the theoretical Neumann spectrum is well verified by the corrected wave 

 pole spectrum and that the directional spread of the spectrum is symmetric about the 

 wind direction and falls to half power at ±30° to the wind direction. 



Unfortunately none of the slides and drawings to accompany the final report 

 are at present in a form ready for inclusion in this report. They need correction (in 

 some cases) and further checking. Therefore the reader is requested to write for the 

 forthcoming report which will describe this work in complete detail. 



R. C. Vetter 



It may be appropriate to add, to the various ingenious methods mentioned by 

 Dr. Munk, one more method for determining some two-dimensional characteristics of 

 ocean waves. If two identical transparent copies of a vertical photograph of the sea 

 surface are super-imposed and illuminated by a beam of light, one may determine the 

 correlation function of the density variations in the transparencies by recording the 

 change in light intensity as one transparency is translated with respect to the other. The 

 two dimensional power spectrum of the density patches in the transparencies can then 

 be derived from this correlation function. This method is being used with some 

 success by Dr. Uberoi of the University of Michigan in studies of turbulence in gases. 

 Some of the same transparencies that were used in Project SWOP (see Dr. Willard 

 Pierson's comments) have been sent to Dr. Uberoi for analysis. It seems highly 

 unlikely that the two two-dimensional power spectra obtained from Dr. Pierson's 

 SWOP Project and Dr. Uberoi's method of analysis will be alike since there is no 

 simple relationship between the brightness of the sea surface and the height of waves. 

 However, it will be interesting to see in what respects the two spectra are different or 

 alike. 



A tremendous effort has gone into the determination of a two-dimensional power 

 spectrum by Project SWOP. I am sure that the results will justify this effort many 

 times over. One wonders if an easier way can be found to give similar information. 

 At present, none of the optical methods appear to be satisfactory. The value of more 

 information about the two-dimensional characteristics of real ocean waves is consider- 

 able and I am sure that everyone, including Dr. Pierson, will thank the ingenious per- 

 son who finds an easier way of getting it. 



Walter H. Munk 



Vetter's suggestion is closely related to Barber's diffraction method (PRAC- 

 TICAL METHODS, p. 3 of our paper). In particular, the reference to Cox (1955) 

 is pertinent. 



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