Volume 1 - The Atmospheric Studies Group at TRC

w'
θ ' = −u
θ
(3-14)
*
*
w'
q'
= −u
q
(3-15)
*
*
The gustiness component of the speed is related to large-scale eddies in the
convective boundary layer, and is proportional to the convective scaling velocity w * :
2 2 2 2
S u + v + U g
= (3-16)
U g
= 1.25w
(3-17)
*
3
3 g ' u*
g zi
u*
zi
w* = w'
θ
v
zi
= − ( θ*
+ 0. 61T q*
) = −
(3-18)
T
T
κL
1
L
κg
= θ*
u T
2
*
( + 0.61T q )
*
(3-19)
where z i is the mixing height (m), κ is the von Karman constant (0.4), L is the Monin-
Obukhov length (m), and g is the acceleration due to gravity (m/s 2 ) .
The bulk transfer coefficients are defined for the reference height z r in terms of the
neutral (1/L=0) transfer coefficient (c xn ) and the corresponding empirical stability
function for the mean profile, Ψ x :
c
x
cxn
=
cxn
1−
Ψx
( zr
L)
κ
(3-20)
c
xn
κ
= (3-21)
ln
( z z )
r
0x
The stability functions are those given in Equations 3-1 through 3-11, where Ψ M is
used for the wind speed, and Ψ H is used for θ and q. Scalar roughness lengths are
related to the roughness Reynolds number R r :
R r
= u *
z 0
ν
(3-22)
z0 S
= z 0
(3-23)
−0.6
( a bR )
z θ (3-24)
0
= z0q
= MIN ,
r
where a=1.1·10 -4 and b=5.5·10 -5 .
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