Geoscience Reference
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the mean from each time series g k (t), we form the 7 × 7 co-
variance matrix and compute its eigenvalues and eigenvec-
tors. The sum of the eigenvalues is the total variance of all the
components, which includes the seasonal cycle. It turns out
that the first two eigenvalues account for 98% of the variance;
the trajectory of Arctic sea ice is essentially two-dimensional.
The first two principal components are given by
PC 1 = 0 . 56g 1 + 0 . 76g 2 + 0 . 33g 3 + 0 . 03g 4
PC 2 = 0 . 35g 1 + 0 . 56g 2 0 . 69g 3 0 . 29g 4
0 . 07g 5 0 . 02g 6 .
(1)
The two-dimensional trajectory in principal component
space is shown in figure 2. The annual cycles go clockwise,
drifting slowly over time toward increasing values of PC 2 .
notice from equation (1) that PC 2 is roughly “thin ice minus
thick ice.” Thus the trajectory indicates increasing thin ice
and decreasing thick ice.
To investigate the effect of the number of ice thickness
bins on the principal component analysis, we also analyzed
a 56-year run (1948-2003) of a version of the PIOMAS
model with 11 ice thickness bins. We found that the first two
principal components account for 91% of the total variance.
Figure 1. The sea ice thickness distribution from PIOMAS is aver-
aged over the 6.6 million km 2 of the central Arctic Ocean shown
by the gray cells.
Report on Emissions Scenarios A1B scenario [ Meehl et al. ,
2006] which assumes a moderate level of conservation and
technical advance to limit emissions (i.e., greenhouse gas
levels rise more slowly after about 2050). The distribution
and thickness of Arctic sea ice have improved in CCSM3
relative to earlier versions. The model simulates sea ice ex-
tent, thickness, and trends reasonably well in the late 20th
and early 21st centuries [ Holland et al. , 2006a]. The model
is run for 230 years, of which we analyze the last 150 years
(1950-2099). The sea ice thickness distributions are aver-
aged in a manner similar to those from PIOMAS: monthly in
time and Arctic-wide in space. The spatial domain is essen-
tially the same as that shown in figure 1 (although slightly
more area along the northern edge of the Canadian Archi-
pelago is included).
3. AnALySIS
3.1. Principal Component Analysis
Consider the trajectory of sea ice from the PIOMAS model,
which is a curve in seven-dimensional space. It is natural to
ask whether this curve occupies the full seven dimensions,
or whether it is primarily confined to a lower-dimensional
subspace. Thus we look for linear combinations of the com-
ponents g 1 through g 7 that account for as much variance as
possible, i.e., principal component analysis. After removing
Figure 2. Trajectory of Arctic sea ice in principal component (PC)
space. The annual cycles go clockwise, drifting slowly over time
toward increasing values of the second principal component.
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