A high-resolution, well-dated foraminiferal

The key to gaining information on climate analogues and periodicities, on decadal to multi-centennial and millennial timescales, is the measurement of proxy records over recent millennia, with multi-annual resolution and matching accuracy in dating.

Among the different timescales of natural climatic variability, the
centennial scale is particularly interesting, being comparable to the scale of
human life and to the modern variation related to anthropogenic forcing

The instrumental observations, covering only a couple of centuries

Marine cores with very high sedimentation rates allow for investigation of climate
variations on scales of decades to millennia. In order to avoid possible
artefacts produced by the composition of different proxies, we measured the
oxygen isotopic ratio

In a previous paper

The record has now been extended to cover the last 2700 years. The aim of the
present work is to investigate the spectral features of the prolonged series
in order to detect the modes describing the climate variability over the
interval 707–200 BC, in comparison with the following two millennia.
Moreover, the results of a recent study by our group concerning Northern Hemisphere
(NH) temperature and based on a reliable and extended data set

Since the 1990s, the Torino cosmogeophysics group has been studying
shallow-water Ionian Sea sediment cores, drilled from the Gallipoli Terrace
in the Gulf of Taranto, and has carried out their absolute dating. The
Gallipoli Terrace is a particularly favourable site for high-resolution
climatic studies, due to a high sedimentation rate and to the possibility of
accurate dating, offered by the presence along the cores of volcanic markers
related to eruptive events that occurred in the Campanian area, a region for which
documentation of the major eruptions is available. Historical documents are
quite detailed for the last 350 years (a complete catalogue of
eruptive events, starting from 1638, is given by

The markers of the eruptions were identified along the cores as peaks of the
number density of clinopyroxene crystals, carried by the prevailing westerly
winds from the volcano to the Ionian Sea, and deposited there as part of
marine sediments. The time–depth relation for the cores retrieved from the
Gallipoli Terrace

The cores were sampled every 2.5

The series presented here was measured in the GT90/3 core
(39

In a previous paper

In Fig.

Thus, several classical and advanced spectral methods were applied to the

The SSA spectrum is shown in the main panel of Fig.

Eigenvalue spectrum from the SSA of the

At a first glance, we can notice a break between the initial steep slope
(first 12 eigenvalues) and an almost flat floor. However, to reliably extract
signal from noise, an MC-SSA test

The inset in Fig.

The significant components are a trend (EOF 1) explaining 17.7 % of
total variance, and five oscillatory components of about 600 (EOFs 2–3), 380
(EOFs 4–5), 170 (EOFs 6–8), 130 (EOFs 9-12) and 11 years (EOFs
10–11), respectively explaining 12.0, 6.7, 4.6, 2.3 and 2.4 % of the
total variance. The periods associated to each oscillation were evaluated by
MEM. Figure

Significant components extracted by SSA from the

Reconstructed components from the SSA of the

Thus, the SSA analysis of the longer

The long-term variability features characterizing the

In order to compare the variability detected in the

This data set was analysed using multi-channel singular-spectrum analysis

Application of SSA requires uniformly spaced time series; therefore, all the
time series were interpolated to a common annual resolution. We then applied
MSSA over the largest-possible common interval, spanning AD 1000 to 1935
(936 years;

High variance was found in the NH data set at both multi-decadal and
centennial timescales, relative to what would be expected under the
red-noise hypothesis. The significant reconstructed components are RCs 1–2
(trend), 6–8 (170 years), 9–10 (110 years), 12–13 (80 years), 16–17 (45 years) and 18–19
(60 years)

In our previous paper

Characteristics of the 26 temperature time series in the NH data
set. The columns in the table give a two-letter acronym; a full name based
on the location; longitude; latitude; the archive from which the series was
extracted; the proxy type; the time span; the sampling interval,

A centennial-scale periodicity is also in common between our local proxy
record and NH temperature anomalies. However, spectral analysis of the
700-year-long local alkenone-based temperature record does not detect
a centennial component (figure not shown) and therefore we can deduce that
this climatic variability mode is not present locally. Its presence in the

Focusing on the two dominant modes of NH temperature, in
Figs.

The trend (RCs 1–2) marks the MWP and the LIA climatic features and is
present in both latitude belts. The cooler temperatures associated with the
LIA appear first in mid-latitudes and propagate on to higher latitudes. The
bicentennial oscillation (RCs 6–8; 170-year period), when averaged over the
two different latitude belts, exhibits comparable amplitudes and a good phase
agreement, as shown especially by the lower panel of Fig.

Figure

The individual series of the NH data set show, however, a certain difference
in trend amplitudes (see the upper panel of Fig.

Reconstructed components RCs 1–2 of the NH temperature data set,
representing the long-term trend; colour bar is for amplitude from

Reconstructed components RCs 6–8 of the NH temperature data set,
representing a bicentennial oscillation; colour bar for amplitude from

On the other hand, the MWP–LIA increase in the trend component of

Using the alkenone-based MWP–LIA temperature variation of
0.5

We can thus state that the trend component of

Comparison between the reconstructed components extracted by SSA
from the

Turning now to the bicentennial component, we compare the

A 2700-year-long, high-resolution record of foraminiferal

The construction of a data set of 26 temperature-proxy records, extending
back at least to AD 1000 with at least decadal resolution and selected
requiring that the temperature calibration of each proxy record be provided
by the authors who published the record itself, allowed for the
variability detected in the

Singular-spectrum analysis (SSA) is a non-parametric spectral estimation
method which was originally designed to obtain information about non-linear
systems from short and noisy time series without appealing to the process
governing equations

SSA grounds on the Mañé–Takens delay embedding theorem, according to
which the dynamics of a chaotic dynamical system can be reconstructed from a
single time series by its time-delayed embedding

In contrast to a classical Fourier decomposition, the new orthogonal basis is data-adaptive and not restricted to pure sine and cosine functions. Thus, SSA turns out to be a more flexible and less limited spectral analysis method, especially when dealing with highly noisy, volatile, and often nonstationary experimental time series.

In more detail, given a time series

Selecting the window length

From the augmented time series

The Toeplitz approach by

Next, the symmetric covariance matrix is diagonalized,

By projecting the time series

Although PCs exhibit no exact phase information, it is possible to analyse
various aspects of the time series that belong to the direction

No information is lost during the reconstruction process, since the
superposition of all individual RCs,

A critical step when performing spectral analysis
is the distinction of significant oscillations from random fluctuations.

That way, Monte Carlo SSA (MC-SSA) can be used to establish whether a given time series is linearly distinguishable from any well-defined process, including the output of a deterministic chaotic system.

The coefficients

The authors thank S. M. Bernasconi (Geological Institute, ETH, Zurich,
Switzerland) for the mass spectrometer measurements of