The 1500 Year Quasiperiodicity During the Holocene - Abrupt Climate Change: Mechanisms, Patterns, and Impacts - page 161

quasi-orthogonal empirical modes. The quasi-orthogonality
prevents leaks from one mode to another thus overcoming
a common problem in the use of the conventional band-
pass

al., 2004; Wu and Huang, 2004]. By determining the
number of degrees of freedom of this distribution, they
derived the spread function of the variances of the noise
modes. This allows a true signal mode to be discriminated
from that of white noise at any desired statistical signifi-
cance level.

filtering. The EMD modes have time-variable ampli-
tudes and frequencies. The number of modes depends on
the number of data points n as log 2 n;

i.e., it is always

small. Each mode is equivalent to a filtered signal in an

empirically determined (not imposed!) frequency band. A
mode has an envelope de

2. DATA SELECTION

ned by local maxima and min-
ima so that its mean amplitude is zero everywhere. A
mean period of a mode can easily be estimated by count-
ing the number of its maxima. Since data contain noise,
which can be subjected to the same decomposition, it is
important to know whether each mode represents a true
signal or a component of noise. EMD modes of white or
colored noise have progressively double mean periods and
the log variances of these modes are inversely proportional
to the logarithms of the mean periods. The variance of
each EMD mode must obey a

In our data analyses, we use the following paleodata in the
Holocene:
1. The temperature and salinity in the Nordic Sea are
reconstructed using measurements of two species of plank-
tonic foraminifera: Globigerina bulloids, which occupies
0 50 m seasonal mixed layer below the ocean surface, and

Globorotalia in

-

es at the base of seasonal
thermocline (100 - 200 m) during winter. The data are taken
from the RAPiD-12-1K core at 62.05°N, 17.49°Wusing Mg/
Ca-

ata, which calci

2 distribution [Flandrin et 18 O measurements [Thornalley et al., 2009].

δ

v

Figure 2. Reconstructed temperatures (top) at the thermocline depth of the ocean at 62.05°N, 17.49°W [Thornalley et al.,
2009]; (middle) off the coast of West Africa at 20.75°N, 18.58°W [deMenocal et al., 2000]; and (bottom) Cariaco Basin
core PL07-39PC at 10.70°N, 64.94°W, 790 m) [Lea et al., 2003]. (right) Wavelet decompositions of the corresponding
data in the range of millennium scales as indicated along the y axis. The solid line marks 1500 year period. The dashed line
shows the cone of in

uence of edges (the results inside the cone are the statistically signi cant at 90% level of

signi cance), as designed by Torrence and Compo [1998].