Geoscience Reference
In-Depth Information
Table 17.1.
Variance in % explained by the zonal wave modes
m
=1,2,
...
, 12.
Ta
Ro
1
2
3
4
5
6
7
8
9
10
11
12
6.79E+06
4.00E+00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
9.49E+06
2.82E+00
0.0
4.8
8.7
7.1
3.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.24E+07
2.21E+00
0.0
37.0
6.8
5.8
4.1
0.7
0.0
0.0
0.0
0.0
0.0
0.0
1.24E+07
2.19E+00
0.0
51.1
9.1
8.2
5.7
1.9
0.0
0.0
0.0
0.0
0.0
0.0
1.54E+07
1.76E+00
0.0
48.9
6.3
11.5
6.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.91E+07
1.40E+00
0.0
46.0
4.3
10.7
4.9
2.9
0.0
0.0
0.0
0.0
0.0
0.0
2.30E+07
1.19E+00
0.0
0.0
36.5
0.0
0.0
24.7
0.0
0.0
9.6
0.0
0.0
0.0
2.74E+07
9.67E-01
0.0
0.0
52.6
0.0
0.0
23.0
0.0
0.0
3.4
0.0
0.0
0.0
3.20E+07
8.64E-01
0.0
0.0
50.0
0.0
0.0
21.3
0.0
0.0
4.5
0.0
0.0
0.0
3.75E+07
7.24E-01
0.0
0.0
48.1
0.0
0.0
24.0
0.0
0.0
5.3
0.0
0.0
0.0
4.29E+07
6.40E-01
0.0
0.0
45.6
0.0
0.0
24.9
0.0
0.0
4.5
0.0
0.0
0.0
4.85E+07
5.62E-01
0.0
0.0
44.1
0.0
0.0
26.8
0.0
0.0
7.3
0.0
0.0
0.0
5.50E+07
4.89E-01
0.0
0.0
0.0
25.7
0.0
0.0
0.0
36.1
0.0
0.0
0.0
6.1
6.17E+07
4.40E-01
0.0
0.0
41.4
0.0
0.0
28.4
0.0
0.0
8.4
0.0
0.0
0.0
6.88E+07
3.85E-01
0.0
0.0
34.6
0.0
0.0
28.4
0.0
0.0
7.7
0.0
0.0
0.0
7.56E+07
3.54E-01
0.0
0.0
33.1
0.0
0.0
27.1
0.0
0.0
8.5
0.0
0.0
0.0
8.89E+07
3.08E-01
0.0
0.0
37.4
0.0
0.0
24.1
0.0
0.0
10.3
0.0
0.0
0.0
9.73E+07
2.80E-01
0.0
0.0
37.5
6 0.0
0.0
25.3
0.0
0.0
9.9
0.0
0.0
0.0
1.10E+08
2.51E-01
0.0
0.0
26.9
0.0
0.0
29.1
0.0
0.0
7.9
0.0
0.0
0.0
1.19E+08
2.30E-01
0.0
0.0
27.2
0.0
0.0
21.6
0.0
0.0
5.0
0.0
0.0
0.0
1.29E+08
2.11E-01
0.0
0.0
0.0
24.5
0.0
0.0
0.0
35.4
0.0
0.0
0.0
7.7
1.39E+08
1.97E-01
0.0
0.0
30.8
0.0
0.0
27.1
0.0
0.0
7.1
0.0
0.0
0.0
1.49E+08
1.84E-01
0.0
0.0
25.7
0.0
0.0
25.7
0.0
0.0
7.2
0.0
0.0
0.0
1.72E+08
1.59E-01
0.0
0.0
24.3
0.0
0.0
22.9
0.0
0.0
6.3
0.0
0.0
0.0
1.95E+08
1.39E-01
0.0
0.0
27.0
0.0
0.0
18.2
2.9
0.0
3.7
2.5
0.0
0.0
3.04E+08
9.01E-02
0.0
0.0
0.0
20.1
0.0
0.0
0.0
24.9
0.0
0.0
0.0
3.9
4.77E+08
5.73E-02
0.0
0.0
3.00
19.51
0.0
0.0
0.0
9.29
3.37
0.0
0.0
0.0
Note:
Left two columns give the Taylor and Rossby number. The table corresponds with Figure 17.6, right.
Figure 17.6 illustrates that EOF decomposition is a
powerful tool to classify regime transitions. Such an EOF-
based classification is not restricted to laboratory data but
should work as well for data from the real atmosphere.
In this section, we have presented the application of
multivariate statistical methods to velocity data, and we
have highlighted the particular abilities of the CEOF anal-
ysis and the MSSA to detect interactions. In the next
section, we will apply the CEOF analysis to a more com-
plex experiment with broken azimuthal symmetry and
time-dependent boundary conditions. Moreover, in addi-
tion to the velocity, surface temperature has been mea-
sured as well.
17.3.2. Baroclinic Waves in Rotating Annulus with
Barrier: CEOF Analysis
Several experiments with the differentially heated rotat-
ing annulus have been performed with modifications to
the standard geometry (flat bottom, constant gap width).
These geometric modifications were introduced to better
represent certain aspects of natural flows, e.g., to further
understand the dynamics of zonal flow over topography
[
Weeks et al.
, 1997]. In ocean basins, the zonal flow is
blocked by continents. Thus, several authors studied the
case when a radial barrier is mounted in the annulus to
understand better the western intensification of flows in
