Geoscience Reference
In-Depth Information
Obukhov length
L
∗
. For small negative values of
z/L
∗
, the vertical profiles in the
CBL can be described by introducing a correction function
m
(
z
/
L
∗
) (Paulson
1970
,
Högström
1988
),
2ln
1
ln
1
x
2
+
x
+
+
2
,
m
=
+
−
2
arctg
(
x
)
(2.26)
2
2
)
1
/
4
and
b
where
x
=
(1
−
bz
/
L
=
16. With this correction function, the wind profile
∗
(2.12) becomes
⎧
⎨
u
∗
/κ (
ln(
z
/
z
0
)
−
m
(
z
/
L
)
)
for
z
<
z
p
∗
u
g
(
−
sin
α
0
+
cos
α
0
) r
z
=
z
p
u
(
z
)
=
(2.27)
⎩
2
√
2exp(
u
g
[1
−
−
γ
(
z
−
z
p
))
sin
α
0
cos(
γ
(
z
−
z
p
)
+
π/
4
−
α
0
)
for
z
>
z
p
z
p
)) sin
2
α
0
]
1
/
2
+
−
γ
−
2exp(
2
(
z
In the unstable case, eqs. (
2.13
)to(
2.15
) take the following forms:
σ
u
,
v
,
w
=
0.6
w
,
(2.28)
∗
2
u
g
γκ
α
0
z
p
sin
u
∗
=
,
(2.29)
φ
(
z
p
/
L
)
∗
1
α
0
=
arctg
,
(2.30)
(
z
p
/
L
∗
)
ln(
z
p
/
L
∗
)
2
γ
z
p
1
+
z
0
)
−
m
(
z
p
/
φ
where
φ
is the differential form of the correction function
for thermal
stratification:
L
*
)
−
1/4
.
ϕ
(
z
/
L
∗
)
=
(1
+
bz
/
(2.31)
α
u
∗
and
must be determined in the same iterative procedure as described after
eq. (
2.16
).
γ
still has the form given in eq. (
2.16
),
b
is set to 16 following Högström
(
1988
).
The alternative approaches by Gryning et al. (
2007
) and Peña et al. (
2009
) yield
the following wind profiles, which could be used in place of eq. (
2.27
),
ln
,
u
z
z
0
+
z
L
z
L
M
−
z
z
i
z
2
L
M
∗
κ
u
(
z
)
=
T
(
)
+
(2.32)
∗
ln
,
κ
d
κ
d
u
∗
κ
z
z
0
−
m
+
1
d
z
η
1
z
z
i
z
η
z
z
i
=
−
−
u
(
z
)
(2.33)
1
+
d
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