To evaluate the bulk transfer coefficients, these coefficients under neutral conditions, i.e., ch,n,
cw,n, and cm,n, would have to be evaluated. If Kh = Kw = Km is assumed, then the following expres-
sion can be obtained:
k2
ch,n = cw,n = cm,n =
(36)
ln z 2
zo
cm and cm,n can be written as
-1
1/ 2
c
2 1/2 1 + x 2
c
ch
= w = m
1 - cm,n ln
(37)
2
cm,n cm,n cm,n
k
and
-2
π
c1/2n
1 + x2
1+ x
+ 2 ln
cm
- 2 tan -1 x +
m,
= 1 -
,
(38)
ln
2
2
cm,n
2
k
where x stands for [1γ(z/L)]1/4 and γ is a constant determined experimentally. To compute these
ratios using observations at the surface and at height z, z/L can be related to a stability index such as
bulk Richardson number, Rib, defined as
(
),
2gz T - To
Rib =
(39)
(T + To ) u 2
and the Obukhov length can be transformed as
3/ 2
cm T u 2
L=
.
(40)
(
)
ch kg T - To
The value of z/L can be related to Rib by
z
k ch
=
Rib .
(41)
3/ 2
cm,n c m
L
3/ 2 c
m,n
Lumley and Panofsky (1964) indicated that, for stable conditions, the log-linear profile is appropri-
ate, and thus the dimensionless wind, temperature, and specific humidity gradients can be written
respectively as
kz u
z
= 1 + βm ,
u* z
L
ku*z
T
z
= 1 + βh , and
(42a,b,c)
- ρH
z
L
c
p
ku*z q
z
= 1 + βw ,
-E z
L
ρ
where βs are treated as constant but not equal to each other even though Lumley and Panofsky have
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