48 DEACON AND WEBB [CHAP. 3 



Measurement of the various fluxes by direct methods such as the eddy- 

 correlation technique together with vertical gradient observations enables the 

 equality or otherwise of the transfer coefficients to be put to the test. The trans- 

 fer coefficients for momentum, Km, and for water vapour, Ke, have been 

 measured simultaneously in two investigations using very different techniques 

 by Rider (1954) and by Deacon and Swinbank (1958). These experiments over 

 level grass surfaces gave the following ratios of KeJKm '■ 



Deacon and Swinbank 1.04+ 0.09 

 Rider 1.12+0.04. 



From this it appears that any difference there may be between the two co- 

 efficients is quite small and, in practice, the assumption of equality oi Ke with 

 Km is not likely to lead to serious error. 



The comparison of Kh and Km has also been made in a similar manner by 

 Swinbank (1955), who found Kh to exceed Km under convectively unstable 

 conditions while the reverse is true for stable conditions. It appears that the 

 magnitude of the difference depends not only on the stability conditions but 

 increases with height above the surface. Under strongly unstable conditions 

 Kh exceeds Km by some 30% at the relatively small height of 1.5 m above the 

 surface, so it may often not be satisfactory to neglect the difference between 

 these two transfer coefficients. 



In those cases for which Ks = Km, the result of dividing equation (2) by the 

 corresponding flux equation for momentum is 



Fs^ _ dsjdz 

 T du/dz 



where t is the shearing stress. Furthermore the profiles of S and of wind would 

 be similar allowing differences to replace differentials giving 



Fs = -r{S2-Si)l{U2-Ui), (4) 



in which the subscripts denote values at heights zi and 22- If, therefore, t can 

 be derived from the wind-profile, as dealt with later, then the flux oi S can be 

 obtained from measurements of s at two or more heights. 



The aim of being able to relate the fluxes to the more easily measured 

 differences between sea surface and air requires knowledge of the appropriate 

 values of the coefficient fa in equations of the form : 



Flux Oi S = fap{Ss - Sa)Ua. (5) 



Here subscripts s and a denote values at the sea surface and at some convenient 

 observing point at height a respectively. The approach via this relationship is 

 commonly called the hulk aerodynamic method to distinguish it from that based 

 on equation (2). For the various transfers equation (5) becomes: 



Momentum r = CapUa} (6) 



Heat H = hapCp{ds-6a)ua (7) 



Water vapour E — dap{qs — qa)ua- (8) 



