presently being considered. Such corrections were indeed made to obtain the 

 results of Figure 11 . In practice, the function H (cr) in this region would be 

 approximated reasonably well by 



H {'^)=d^g^<r~^ . (13) 



This is the equilibrium spectrum proposed by Phillips (1958b), with d3 equal 

 to an empirically determined, universal constant. However, the amount of noise 

 present in the experimental E (<«')'s is an order of magnitude greater than the 

 correction term under discussion » There is enough uncertainty in this noise level 

 so that, in general practice, it was not realistic to attempt this relatively fine 

 scale correction. This, of course, implies, and rightfully so, that the estimates 

 that will be made of the high frequency portion of the spectrum are not particularly 

 accurate,. This should come as no great surprise, however, since the very nature of 

 the instrument response (Section 2.3, Figure 4) indicates that reasonably exact esti- 

 mates of high frequency spectral components are not possible with the airborne sea- 

 swell recorder. 



6.4 Definition of the Spectral Field 



In presenting the final estimates of spectral energy at various distances 

 from the coast, it has been convenient to speak in terms of true frequency, f = *''/2ir, 

 and the true frequency spectrum, ¥ {f ,'^ , x) = 2 ir F (<r,\|/ , x). Figures 12 and 

 13 show contours of the quantity F (f, o, x) for the various directional assumptions and 

 plane headings. This is similar to the type of presentation that has often been used by 

 Munk and his co-workers in tracking swells from distance storms (eog., Munk, etool., 

 1963). Henceforth, all references to the spectrum will be directed toward the quantity 

 F(f,o,x)o 



The contours on each f-x diagram are based on approximately 22 values of 

 F vs f for each of 27-30 different x's ( ~ 600 points/diagram) » The x-axis is directed 

 downwind and x equals zero at the coast line. The grid spacing along the x-axis was 



3.5 nautical miles for the inner region and 7.0 nautical miles for the outer region^ 

 Along the f-axis the grid spacing decreased from .01 1 cps near f s; .08 cps to o004 

 cps at f w .20 cps. The philosophy used in contouring was to show as much detail as 

 possible with a minimum of smoothing. In this way it was felt that the data would be 

 presented as objectively as possible « As luck would have it, no data were obtained 

 for the region between about 15 and 25 nautical miles from the coast. This made it 

 impossible to discuss the growth of the higher frequency waves „ 



In viewing the f-x diagrams there are several important items to bear in mind. 

 A cut along the f-axis at constant x will give the spectrum F(f,o) at x. Similarly, a 

 cut along the x-axis at constant f will give the spatial history of the f-spectral 



32 



