9<^ MALKUS [chap. 4 



equations. Undoubtedly the most exciting new observational tool contributing 

 advances to marine sciences in the past two decades is the instrumented aircraft, 

 which has provided quantitative data on phenomena ranging from sea-surface 

 waves, through cumulus clouds, hurricane, Gulf and jet stream, and whose 

 results will be drawn upon heavily in the sections to come. 



As in astrophysics, the complexity of the problems in geophysics has resulted 

 in piecemeal and fragmentary attacks ; within this complexity, specific prob- 

 lems have been isolated for their tractability to the tools and interests pre- 

 vailing. Unlike astrophysics, the practical importance of the weather and the 

 sea in man's daily life have often channelled geophysical effort and observations 

 to those areas of immediate human urgency, but equally have provided motiva- 

 tion and means of attacking problems which pure curiosity-driven science 

 might have avoided as too difficult or costly. In general, the more comprehen- 

 sive the problem, the more parts of the interacting sea-air system considered, 

 the less formal, the more descriptive, and even speculative, the treatment has 

 had to be, and the heavier demands placed upon the breadth and courage of 

 the investigator. Conversely, the more formal and rigorous the approach, the 

 less useful are the results in the practical sense of forecasting or controlling a 

 planetary phenomenon ; at present, even the convective motions in a coffee-cup- 

 sized laboratory cell are only on the threshold of tractability. The challenge is 

 to isolate simplified, prototype problems of this sort, whose rigorous treatment 

 provides key insights into the complexity of natural geophysical systems. 



Thus quantitative attacks on the joint air-sea interaction problem, with both 

 media simultaneously affecting and altering each other, are still few ; energetic 

 treatments in either meteorology or oceanography alone are just emerging. 

 The usual procedure is to isolate a single scale of phenomenon in the single 

 system, for example, the wind-driven ocean current or the growth of a cumulus 

 cloud, and to parameterize or assume the effects of the other medium (and the 

 other scales of motion in the treated medium) in some empirical or semi- 

 intuitive manner, such as in the first example through an observationally 

 computed "curl of the wind stress" or a known latent heat supply in the second. 



The problems of air-sea interaction treated to date, then, may be crudely 

 divided into four categories : 



(1) Isolated, formally tractable problems, in which the hydrodynamic 

 equations are solved for a chosen scale of motion in either ocean/air, with the 

 input or removal of energy from the air/ocean parameterized, assumed from 

 observation or ignored. Among problems treated in this way are the large-scale 

 circulation of the atmosphere (Phillips, 1956), the wind-driven ocean currents 

 (Stommel, 1948; Munk, 1950), the maintenance of the trade-winds (Malkus, 

 1956), hurricane maintenance (Malkus and Riehl, 1960), the flow of stable air 

 over a heated small island (Malkus and Stern, 1953), and, to some extent, the 

 growth of cumulus clouds (Levine, 1959; Malkus and Witt, 1959). The results 

 of these treatments are all ])redictive, and the limitations upon the degree of 

 solution of the posed ])roblem lie in the importance of the pliysical effects 

 ignored or inadequately parameterized. 



