Global Wave Forecasts Using Spacecraft Data 



He has put his finger on the exact sources of the difficulties we encountered in 

 applying the then available results of Dr. Phillips and him. We are most pleased 

 to be able to report that by combining the original work of Miles (15) and Phillips 

 (16) with the material in a recent text by Phillips (29)* and with a variety of re- 

 sults on the wind profile and on the roughness length over a wind sea, Inoue (30) 

 is now able to compute a realistic wave spectral growth in which the discrepancy 

 between Miles' theory and the observations is reduced to a factor of less than 3 

 and in which the fit depends on the constant relating friction velocity to rough- 

 ness length. 



The new work of Phillips (29) provides realistic exponential growth rates 

 for the low-frequency end of a wind sea spectrum by means of wind- induced 

 components of the Reynolds stress. The original work of Miles (15) with a fac- 

 tor of less than 3 is then capable of accounting for the high-frequency end using 

 an improved version based on the work of Barnett (24) of the linear growth term 

 of Phillips. The earlier factor of 8 resulted from the need to get reasonable 

 results at low frequencies and overdrove the high frequencies. An abstract of 

 the results of Inoue (30) can be found in the Spring 1967 program of the Wash- 

 ington, D. C, meeting of the American Geophysical Union. The results should 

 appear shortly in greater detail. 



The departure of the wind profile from a simple logarithmic form was also 

 of concern to us. Cardone (31) has, we believe, made progress on this part of 

 the problem by introducing the form for the roughness length Zg proposed by 

 Kitaigorodskii and Volkov (32) and by including the effects of the Richardson 

 number and the thermal wind. Variation in stability and in Zg (as derived solely 

 from the wave spectrum) makes it possible to obtain as selective subsets all of 

 the various previously obtained curves on how the drag coefficient should vary 

 with the wind speed. The natural variability of the underlying waves and the 

 effect of atmospheric stability are quite capable of producing the wide scatter of 

 data points usually associated with attempts to study C lo- The results are again 

 given in abstract form in the program of the Washington AGU meeting and should 

 appear shortly in published form. 



There are a few more places in the structure of our numerical model where 

 traces of semiempirical techniques can be found, but they are no longer as glar- 

 ing as that factor of 8 that has now been considerably reduced. 



In reply to Dr. Hasselmajin's comments, it is instructive to point out how 

 much of the wave forecasting theory available prior to the Easton conference 

 seems to be borne out by our present results. As an example, the growth of 

 significant wave height versus either duration or fetch turns out to be remark- 

 ably close to the curves given originally by Sverdrup and Munk. Also, once the 

 difficulty of working with winds at a variety of elevations is clarified, the par- 

 tially developed spectra derivable from the co-cumulative spectra in HO 603 

 turns out to be quite close to the more recent results. All frequencies start to 

 grow at the same time, but the low frequencies take so much longer to reach the 

 explosive exponential growth stage that the spectra appear to grow from high 



'Additional references to those of the paper are given at the end of this reply. 



531 



