Geoscience Reference
In-Depth Information
Table 9.1.
Experimental parameters in the LES of a laboratory analogue for MJO-like tropical dynamics.
Symbol
Laboratory Scale
Atmospheric Scale
Description
L
2 m
4000 km
Length scale
U
0.05 m
/
s
50.0 m
/
s
Velocity scale
0.093 m
−1
s
−1
β
10
−11
m
−1
s
−1
2.3
×
Coriolis
β
1.566 s
−1
0.01 s
−1
N
Brunt-Väisällä frequency
u
e
(v
e
=0,
w
e
=0
)
0.05 m
/
s
50.0m
/
s
Ambient flow
x
0
4.3 m
8600 km
Zonal domain length
y
0
4.0 m
8000 km
Meridional domain width
H
0
0.11 m
17000 m
Vertical domain height
T
1
,
T
2
120 s, 100 s
2.7 days, 2.3 days
Forcing periods
a
0.2 m
400 km
Forcing amplitude
λ
=
x
0
/s(s
=6
)
0.717 m
1430 km
Forcing wavelength
L
D
=
NH
0
/βL
0.926 m
1850 km
Equatorial deformation radius
T
D
=
L
D
/U
18.5 s
10 h
Equatorial deformation time
Reproduced from
Wedi and Smolarkiewicz
[2010].
for a simulation of upto 8 h, representing a laboratory-
scale “climate” realization. Equally, the proposed labo-
ratory analogue experiment presents immense technical
challenges since it would require to emulate a zonally
periodic equatorial
β
-plane while maintaining constant
vertical stratification for several hours in the presence of
bottom heating and zonally propagating meanders of the
meridional sidewalls.
The laboratory-scale climate simulations described
here thus broadly fit into the class of implicit large-
eddy simulations (ILESs). ILESs dispense with explicit
subgrid-scale models and exploit truncation properties
of high-resolution (nonoscillatory) finite-volume meth-
ods to mimic the spectral viscosity of standard LESs
[
Domaradzki et al.
, 2003;
Margolin et al.
, 2006;
Piotrowski
et al.
, 2009].
The simulations capture details of the formation of
solitary structures and of their impact on the convec-
tive organization [
Wedi and Smolarkiewicz
, 2008, 2010].
The horizontal structure and the propagation of anoma-
lous stream function patterns, a diagnostic typically
used in tracing the equatorial MJO, are similar to
archetype solutions of the Korteweg-deVries equation,
which extends the linear shallow-water theory, commonly
used to explain equatorial wave motions, to a weakly
nonlinear regime for small Rossby numbers. In this way,
Wedi and Smolarkiewicz
[2010] attributed the origin and
evolution of periodically reoccuring anomalous flow pat-
terns in the equatorial troposphere to resonant nonlinear
wave dynamics. As a result, the MJO may be understood
as a quasi-horizontal and quasi-nondivergent synoptic-
scale motion that is driven, or rather preconditioned,
by coupling with extratropical weather and that persists
at planetary scale due to nonlinearity. Such motion is
governed by a particular solution of the conservation law
for absolute vorticity
2
ψ
+
f
[
Charney
, 1963]. Conse-
quently, the process of convection is found to be impor-
tant but chronologically secondary to the MJO evolution.
There are MJO case studies [
Hsu et al.
, 1990] that sup-
port this view. Moreover,
Vitart and Jung
[2010] recently
confirmed a substantial influence of the Northern Hemi-
sphere extratropics on the skill in predicting the MJO by
relaxing the Northern Hemisphere (and in particular the
North Pacific) to the “known” analyzed state. The predic-
tive skill is even further improved when also the Southern
Hemisphere is relaxed toward the analysis (Vitart, per-
sonal communication). The latter suggests that the MJO
is a global phenomenon not only in appearance but also
in its initiation and propagation properties.
∇
9.3.1.1. Numerical Model.
The numerical model is as
described in Section 9.2.2.1. In addition, the Coriolis force
terms on the equatorial
β
-plane
2
are now given as
1
=
C
+
βy(v
2
3
= 0. Diabatic and
frictional terms, emulating boundary layers adjacent to
r
=
y
,
z
boundaries, are of the form
v
e
)
,
2
=
βy(v
1
v
e
)
,and
−
C
−
−
C
F
ρ
(r)
:=
τ
−
1
e
−
r/h
(ρ
−
ρ
j
(r)
:=
τ
−
1
v
j
v
j
e
−
r/h
(v
j
ρ
b
)
and
b
)
, with subscript
b
denot-
ing a prescribed boundary value; the attenuation time
scales are
τ
ρ
=
z
2
/κ
and
τ
v
j
= 0.125
τ
ρ
(assuming diffu-
sivity of heat in water,
κ
= 1.39
F
−
10
−
7
m
2
/
s) and height
scale
h
=2
z
,where
z
is the vertical grid size. Given the
model's formulation in density, heating is included indi-
rectly via the gradient of density at the lower boundary,
×
2
The shallow atmosphere (or “traditional” approximation) has been
applied here for consistency with simulations using the integrated
forecasting system (IFS), the operational global forecast model at
ECMWF; see also
Wedi and Smolarkiewicz
[2009].
