82 ^ DEACON AND WEBB [CHAP. 3 



Thus, as before, we find that for the layer of molecular transfer (40) is 

 applicable, while for the overlying region of turbulent transfer. 



qs-qz = {Elpku^)\ny{z + Zo)j{h + Zo)l (44) 



Finally, (40), (44) and (39) lead to 



rE{z) = {(A:Ai./7)) + ln[(3 + 2o)/(S + 2o)]}-i. (45) 



Fig. 17 shows curves plotted from (45) for three values of A, namely 7.8 and 

 11.5, as already quoted, and 27.5 as proposed by Sverdrup (1937). In deriving 

 these curves, the values of 2o inserted in (45) are those implied by the observed 

 drag relationship (22). 



In Sheppard's formulation, the transfer coefficient for water vapour is taken 

 to be Ke = D + ku^z throughout; thus molecular transfer becomes dominant 

 right near the surface, though no distinct layer of exclusively molecular transfer 

 is assumed. The turbulent transfer coefficient is taken as kU:^z rather than 

 kU:^{z + zo) on the reasonable view that the appearance of zq is a result of 

 pressure forces against the rough surface, which act to transfer momentum 

 but not vapour. Similarly, as in the preceding cases, though more simply, we 

 find 



rsiz) = [ln{ku^zlD)]-K (46) 



The curve representing (46) is shown on Fig. 17. 



It will be seen from Fig. 17 that the theories for aerodynamically rough 

 flow of Sheppard, and of Sverdrup (1937) with A= 7.8, yield values of Fe that 

 are close to that indicated by observation. Sheppard's approach is perhaps to 

 be preferred since it has the merits of simplicity and of freedom from an 

 adjustable constant. 



The bulk evaporation coefficient, ds, derived from (28), using Fe from the 

 rough-surface theories discussed above and Fm implied by the relationship (22), 

 is shown in Fig. 18. 



From the theories mentioned above, we may calculate Fh, the profile co- 

 efficient for potential temperature, by replacing D with k. Over the whole 

 range of wind speeds from 2 to 14 m/sec, its ratio to Fe is found to be close to 



FhIFe = 0.98, 



within 0.5% and 2% from the formulae of Sheppard and Sverdrup (A = 7.8) 

 respectively. Thus the observational indication of closely similar values of Fh 

 and Fe is backed by the theoretical estimate. 



In concluding this discussion of theoretical approaches, we may remark that 

 an assumption throughout is that effects of thermal stratification are absent. 

 The only attempt to introduce these effects appears to be an approximate 

 approach by Anderson et al. (1950). Their result should presumably be valid 

 provided the deviation from neutral stratification is small. 



