78 



DEACON AND WEBB 



[chap. 3 



Monin and Obukhov (1954) have suggested that it may be convenient to 

 express /as a power series in z/L. Priestley (1960) has shown that, if the power 

 series coefficients are adjusted to provide the smoothest crossover to an over- 

 lying region with gradient ccz~^/^, then the second and higher powers of zjL 



1000 



100 



- 10 



Fig. 16. Scale height \L\ plotted against the bulk stability parameter |i?66| defined by 

 (33) or (34), for unstable conditions. \L\ represents approximately the height of 

 transition from superadiabatic to homogeneous structure, and 0.03|iv| the height be- 

 low which the stratification may be regarded as near-nevitral. 



(Curve derived on the assumption that in neutral conditions /\f(4 ni) = 7^//(4 m) = 

 0.1.) 



have rapidly diminishing effect and may as well be ignored for practical 

 purposes. Perhaps the most appropriate scheme, used by Webb (1960), is to 

 take a two-sided linear smoothing factor, i.e. in the case of the temperature 

 gradient to take 



dd 



Tz 



86 



74/3 



■J '- •"in 



7 z 



Z \ 1 Zm 



for Z ^ Zm, 



for z ^ Zr 



(37a) 



(37b) 



where A— —Hl{kcppu^). The coefficient 1/7 in the linear factors is the value 

 which provides a smooth crossover at Zm by making dW/dz^ and dWjdz^, as well 

 as ddjdz, continuous there. 



Since the term —zjlzm in (37b) is simply a convenient alternative form of 

 aizjL, the first-order term in the Monin-Obukhov series, we must have Zml\L\ = 

 l/7ai. This gives, assuming a trial value ai = 4.5, the same as observation in- 



