Geoscience Reference
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Figure 17.8. Sequence of surface temperature in the geometry with the barrier mounted. Top row from left to right: at 37, 39, and
43 rotations. Bottom row from left to right: at 45, 47, and 48 revolutions.
often surprisingly few “modes” and thus the CEOF anal-
ysis is an efficient technique for dimension reduction.
We computed CEOFs over the full annulus and over
subregions. The first 10 eigenvalues denoting the variance
comprised in the corresponding CEOFs of the annulus
region upstream of the barrier are shown in Figure 17.10a.
We find that the first two local CEOFs explain more than
50% of the total variance in the region upstream of the
barrier. For the CEOFs of the full annulus we find a very
similar spectrum with contributions of 28.8% and 19.4%
for CEOF1 and CEOF2, respectively. PC1 and PC2, that
is, the temporal behavior of CEOF1 and CEOF2, are
shown in Figures 17.10b and 17.10c for the upstream
region. Note that real and imaginary parts are in quadra-
ture, indicating propagating anomalies. Obviously, PC2
comprises for a significant part the slow periodic variation
of the radial temperature difference mentioned above. In
contrast, PC1 shows a strong wave oscillation and only a
weak modulation due to the slow variation of the temper-
ature difference. We find about 9 wave oscillations per 100
rotations. The PCs of the full annulus look very similar to
the one of the upstream part; however, the order of PC1
and PC2 is reversed. That is, for the full annulus the first
PC mainly contains the low-frequency forcing.
We now focus on the dominant spatial structure of
the anomalies. CEOF2 of the full annulus and CEOF1
of the local domain are shown in Figures 17.11a-d. The
CEOFs shown correspond to the PCs that mainly contain
the waves and not the low-frequency forcing. Real parts
(a)
(b)
Ω
b
a
d
Figure 17.9.
(a) Annulus with the barrier. (b) Photograph of the
barrier.
single complex orthogonal function and not in two real
functions. Therefore, amplitude and phase information is
contained in a single CEOF. More specifically, we will
apply a combined CEOF Analysis to find connected prop-
agating anomalies of surface temperature and velocity
[ Harlander et al. , 2012a]. Frequently, the dominant com-
ponents of a high-dimensional process are captured with
 
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