110 



[chap. 4 



of more recent evidence. The latter suggests that the whole approach may- 

 break down when winds are very weak. On the other hand, when winds of 

 several meters per second or more prevail over the open sea its surface is rarely 

 if ever smooth, and the roughness appears to increase more or less continuously. 

 When turbulent shear flow is the dominant process, the assumption that 

 Ks = Ke = Km appears to be satisfactory from observation (Budyko, 1948; 

 Pasquill, 1949; Timofeev, 1951; Rider, 1954), although no sound theoretical 

 foundation for it is as yet available. Recent observational work (see Fig. 6) on 

 the dependence of cd on wind speed (roughness) over the ocean suggests a more 

 gradual increase with increasing wind, the total range being about a factor of 

 two, between a cd of about 1.0 x lO^^ for winds near 10 knots and 2.0 x 10"^ 

 for winds near 20 knots. 



0004 



0003 



0002 



K no ts 

 12 



20 



24 



28 



slightly stoble 



neulrol 



slightly unstoble 



unstoble 



2 4 6 8 10 12 14 



Wind speed (m/sec) 



Fig. 6. Relation between drag coefficient cj) and wind speed at 10 m elevation. (After 

 Deacon, Sheppard and Webb, 1956, Fig. 5. By courtesy of the Journal.) 



Top abscissa in knots, bottom in m/sec. Squares are unstable observations ; tri- 

 angles slightly unstable ; crosses neutral ; and circles slightly stable. Solid curve 

 drawn for neutral conditions. Dashed curve indicates earlier determination of cj) by 

 Montgomery (1940) with sudden transition between hydrodynamically smooth 

 (wind speed < 6.7 m/sec) and rough (wind speed > 6.7 m/sec) conditions. 



Therefore, ideally speaking, equations (18) and (19) provide totally in- 

 dependent checks on the calculation of the sum of Qs plus Qe by the energy- 

 budget method using (3). The derivation of the so-called Bowen ratio, r (7), is 

 now also clear; it is merely the result of dividing (18) by (19). Unfortunately, 

 available data are rarely adequate for this ideal to be achieved ; the common 

 situation, as we shall see, is that both methods must be used together to study 

 the energy budgets and operation of a portion of the ocean-atmosphere system. 



Furthermore, actual usage of equations (17) to (19) in budgetary and dynamic 

 analyses requires further consideration, particularly when average exchanges 

 over long periods are desired. Strictly speaking, hourly measurements of wind 



