SECT. 2] SMALL-SCALE INTERACTIONS 67 



B. Profile Coefficients 



Montgomery (1940) introduced a coefficient Fe in order to express the 

 humidity gradient conveniently in terms of the sea to air difference. We may 

 define analogous coefficients Fm and Fh for wind and temperature respectively, 

 the three then being 



Ua d in z 



r. = -!-^. (25) 



qa-qs c In z 



The F's will have a slight dependence on the height of measurement, but the 

 subscript a is omitted for convenience. They can be related to the coefficients 

 c, h and d in the bulk formulae (6), (7) and (8) by noting that in neutral condi- 

 tions K M = K H = Ke = ku^z or, in non-neutral conditions, Km = KmU^z, Kh = 

 * * 



Khu^z, and Ke = Keu^z (these being the chosen definitions of the generalized 



* 

 Karman coefficients, the iC's). The relationships are 



c = Km^Fm^ (general) = k^Fn^ (neutral case) (26) 



h = KmKhFmFh (general) = k'^FrnFu (neutral case) (27) 



* * 

 d = KmKeFmFe (general) = k'^FuFs (neutral case). (28) 



For the general case, (6), (7) and (8) may be rewritten 



* 

 U^ = KMFuUa (29) 



H = CppRffFnu^ids-da) (30) 



E = pKEFEU^iqs-qa). (31) 



C. Bulk Stability Parameter 



Using the above definitions of the profile coefficients, the Richardson number 

 from (14) becomes 



Now FhIFm^ may be expected to be a function of Ri ; it does in fact vary 

 moderately over a wide range of stability, though the relationship is perhaps 

 not perfect since it may also have some variation with wind strength. At 

 heights of about 4 to 8 m and conditions from neutral to moderate thermal 



