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where
θ
is potential temperature,
θ
0
is a reference temperature, and
θ
v
is virtual tem-
perature.
2
The strati
cation is stable (unstable) for Ri >0(Ri < 0). Richardson number
provides the ratio between buoyancy and shear. The general problem is non-linear and
cannot be solved in explicit form. However, approximate parameterized explicit formu-
lations are available and they provide an insight of the role of strati
cation.
Curry and Webster (1999) used the bulk Richardson number parameterization for an
approximate explicit solution. They assumed that C
H
= C
E
and z
0
= z
T
(
0.1
1 mm), that
*
-
implies C
D
= C
H
= C
E
, and presented the forms
2
4
3
5
f
ð
Ri
B
Þ
j
log
z
0
C
D
¼ C
H
¼ C
E
¼
ð
4
:
14a
Þ
1
f
ð
Ri
B
Þ
¼
p
1
þ
5Ri
B
;
Ri
B
[
0
ð
4
:
14b
Þ
1
þ
15
15Ri
B
fRi
ðÞ
¼1
;
Ri
B
\
0
ð
4
:
14c
Þ
2
3
2
q
1
þ
z
0
Ri
B
4
5
j
1
þ
75
j
j
z
z
0
log
where f is the stability parameter (Louis 1979). The exchange coef
cients change quite
fast in near-neutral conditions (Fig.
4.3
). Taking z = 10 m and z
0
= 1 mm, their limiting
values for Ri
10
−
3
from the right and 1.89
10
−
3
from the left. The neutral
0 are 0.12
×
×
→
10
−
3
(Ri = 0)
reference would be 1.00
×
as
the
average. Furthermore,
10
−
3
and C
H
(Ri
B
=
10
−
3
.
C
H
(Ri
B
= 0.1) = 0.097
×
0.1) = 2.61
×
-
-
Obukhov similarity theory (Tennekes and Lumley 1972; Kagan 1995). In addition to the
Prandtl mixing length, in a strati
Advanced methods for the vertical
fl
fluxes at the surface are based on the Monin
-
ed boundary-layer there is another length scale, the
buoyant length scale or the Monin
-
Obukhov length, which is de
ned as
L ¼
H
0
u
3
j
gw
q
a
c
p
H
0
u
3
j
gQ
c
0
h
0
¼
ð
4
:
15
Þ
where
Obukhov length can be understood as the
vertical length scale to where the role of the strati
ʘ
0
is the reference temperature. Monin
-
cant. Since the
mechanical mixing length is proportional to height z, the ratio z/L becomes a natural
dimensionless length in a strati
cation is not signi
ed boundary layer.
2
An adjustment applied to the real air temperature to account for a reduction in air density due to
the presence of water vapor,
θ
v
=
θ
(1 + 0.6078q).
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