Geoscience Reference
In-Depth Information
turbulent transport is a local rate of gain due to import from above. The principal
source of TKE in this case is shear production associated with the nocturnal jet
aloft.
Banta
et al
.
(
2002
) discuss this nocturnal jet in some detail.
12.4.2 Parameterization
A test of 19 different SBL parameterizations used in weather and climate models
(
Cuxart
et al
.
,
2006
), with high-resolution LES being the standard, showed a wide
variation in performance. The scatter in the predicted eddy-diffusivity profiles, for
example, was an order of magnitude larger than that in
Figure 12.7
.
SBL parameterizations for such models are typically one-dimensional, since
SBL depth is very much less than horizontal grid mesh size. Their formulation
is particularly challenging because the nature of the effects of stable stratification
change with its strength, ultimately determining the ability of turbulence to exist.
Derbyshire
(
1999
) recommends that SBL parameterizations be expressed in terms
of the local Richardson number, pointing out that such formulations can mimic the
behavior of the very stable boundary layer.
12.5 Modeling the equilibrium height of neutral and stable ABLs
Zilitinkevich
et al
.
(
2007
) suggest that the equilibrium height
h
E
of neutral and
stable ABLs can be represented through the “Ekman formula”
h
E
∼
)
1
/
2
,
(K/
|
f
|
∼
with
f
the Coriolis parameter and
K
a characteristic eddy viscosity
u
T
T
,the
product of the velocity and length scales of the ABL turbulence. They parameterize
three ABL states: the “truly neutral” ABL with zero surface heat flux and neutral
stratification aloft; the “conventionally neutral” ABL (our “inversion-capped neu-
tral” case,
Figure 9.7
)
with zero surface heat flux and stable stratification of strength
N
aloft; and the “nocturnal stable” ABL with a negative surface temperature flux
and neutral stratification aloft. The
u
T
T
values are chosen as:
• “Truly neutral” (
Q
0
=
0
,N
=
0
)u
T
T
∼
u
h
E
.
∗
N
−
1
)
.
• “Conventionally neutral” (
Q
0
=
0
,N>
0
)u
T
T
∼
u
(u
∗
∗
• “Nocturnal stable” (
Q
0
<
0
,N
=
0
)u
T
T
∼
u
L
.
∗
u
∗
N
−
1
,was
introduced by
Kitaigorodskii and Joffre
(
1988
); it is like our
b
of
Eq. (12.41)
.That
in the nocturnal stable case,
T
∼
The turbulence length scale in the conventionally neutral case,
T
∼
L
, is our
Eq. (12.35)
.
This analysis provides the ABL height expressions
u
∗
|
h
E
∼
,
truly neutral ABL
;
f
|
