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Moberg, A. , Sonechkin, D. M. , Holmgren, K. , Datsenko, N. M. & Karlen, W. Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature 433, 613-617

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A number of reconstructions of millennial-scale climate variability have been carried out in order to understand patterns of natural climate variability, on decade to century timescales, and the role of anthropogenic forcing. These reconstructions have mainly used tree-ring data and other data sets of annual to decadal resolution. Lake and ocean sediments have a lower time resolution, but provide climate information at multicentennial timescales that may not be captured by tree-ring data. Here we reconstruct Northern Hemisphere temperatures for the past 2,000 years by combining low-resolution proxies with tree-ring data, using a wavelet transform technique to achieve timescale-dependent processing of the data. Our reconstruction shows larger multicentennial variability than most previous multi-proxy reconstructions, but agrees well with temperatures reconstructed from borehole measurements and with temperatures obtained with a general circulation model. According to our reconstruction, high temperatures--similar to those observed in the twentieth century before 1990--occurred around ad 1000 to 1100, and minimum temperatures that are about 0.7 K below the average of 1961-90 occurred around ad 1600. This large natural variability in the past suggests an important role of natural multicentennial variability that is likely to continue.
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Highly variable Northern Hemisphere
temperatures reconstructed from
low- and high-resolution proxy data
Anders Moberg
1
, Dmitry M. Sonechkin
2
, Karin Holmgren
3
,
Nina M. Datsenko
2
& Wibjo
¨
rn Karle
´
n
3
1
Department of Meteorology, Stockholm University, SE-106 91 Stockholm,
Sweden
2
Dynamical-Stochastical Laboratory, Hydrometeorological Research Centre of
Russia, Bolshoy Predtechensky Lane 11/13, Moscow 123 242, Russia
3
Department of Physical Geography and Quaternary Geology, Stockholm
University, SE-106 91 Stockholm, Sweden
.............................................................................................................................................................................
A number of reconstructions of millennial-scale climate varia-
bility have been carried out in order to understand patterns of
natural climate variability, on decade to century timescales, and
the role of anthropogenic forcing
1–8
. These reconstructions have
mainly used tree-ring data and other data sets of annual to
decadal resolution. Lake and ocean sediments have a lower
time resolution, but provide climate information at multicen-
tennial timescales that may not be captured by tree-ring data
9,10
.
Here we reconstruct Northern Hemisphere temperatures for the
past 2,000 years by combining low-resolution proxies with tree-
ring data, using a wavelet transfor m technique
11
to achieve
timescale-dependent processing of the data. Our reconstruction
shows larger multicentennial variability than m ost prev ious
multi-proxy reconstructions
1–4,7
, but agrees well with tempera-
tures reconstructed from borehole measurements
12
and with
temperatures obtained w ith a general circulation model
13,14
.
According to our reconstruction, high temperatures
similar
to those obser ved in the twentieth centur y before 1990
occurred around AD 1000 to 1100, and minimum temperatures
that are about 0.7 K below the average of 1961–90 occurred
around
AD 1600. This large natural variability in the past suggests
an important role of natural multicentennial variability that is
likely to continue.
Global temperatures are currently rising, and future scenarios
suggest large changes in precipitation patterns and temperatures
15
.
Reconstructing past climate is essential for enhanced understanding
of climate variability, and provides necessary background knowl-
edge for improving predictions of future changes. From multi-
proxy combinations
1–4,7
of climate proxy data (for example, from
tree rings, corals and ice cores), or from reconstructions based solely
on tree-ring data
5–6,16
, past surface temperatures have been inferred
by calibration to instrumental temperature data using statistical
relationships. Past surface temperature changes have also been
inferred from temperature profiles along deep terrestrial bore-
holes
12
, where physical laws rather than statistical relations are
used to estimate temperature trends. Borehole measurements
12
and some reconstructions based on tree-ring data
6,16
indicate a
larger warming trend in the past 500 yr than do multi-proxy
reconstructions
1–4,7
.
Although differences in the amplitude of centennial temperature
variability have been discussed in the literature
8,15
,thepicture
with relatively small variability (shown by multi-proxy reconstruc-
tions
1–4,7
) is arguably best known by a wider audience. One reason
for this is the prominent role that the multi-proxy reconstruction by
Mann et al.
1,2
had in the latest IPCC report
15
and in public media.
Recent findings
14
, however, suggest that considerable underestima-
tion of centennial Northern Hemisphere temperature variability
may result when regression-based methods, like those used by
Mann et al.
1,2
, are applied to noisy proxy data with insufficient
spatial representativity. It is thus important to explore other
techniques and other data types, and also to use data from more
regions than previously examined.
A view has been expressed that only tree-ring and other high-
resolution data are useful for quantitative large-scale temperature
reconstructions
3,8
. Tree-ring data, however, have a well-documented
difficulty in reliably reproducing multicentennial temperature
variability
17
. Special standardization techniques for extracting
multicentennial information exist
6,16
, but they do not ensure an
accurate reconstruction
10
. Natural archives with lower temporal
resolution (often various sediments) have potential for providing
climate information at multicentennial timescales that may not be
captured by tree-ring data
9
. Low-resolution data, on the other hand,
can sometimes have dating errors of up to more than 100 yr (ref. 9).
Such errors are intolerable at interannual to multidecadal time-
scales
8
, but if these data are used only for longer timescales the errors
become relatively small in relation to the timescales of interest.
Our aim is to combine low-frequency climate information
(contained in low-resolution proxy data) with high-frequency
information (from tree-ring data) in order to derive a 2,000-yr-
long Northern Hemisphere temperature reconstruction in which we
avoid using each proxy type at timescales where it is most unreliable,
but instead use it only where it has its greatest advantages. To
achieve this, we developed a method that allows a timescale-
dependent data decomposition by application of a wavelet trans-
form
11
technique.
The number of available 2,000-yr-long local-to-regional scale
temperature proxy series is very limited
8
. We found seven tree-ring
series and eleven low-resolution proxy series. For the period before
AD 1400, this number is similar to previous reconstructions
1–7
.
Among the eleven low-resolution series were nine already calibrated
to local/regional temperatures for different Northern Hemisphere
regions, whereas two were only available in original proxy data
units. The data set includes climatic information from the North
American and Eurasian continents and from the Atlantic and Indian
oceans (Fig. 1, Table 1; see Supplementary Information for further
details and references).
Various averages (see Methods) of the nine already calibrated
low-resolution series (Table 1, site numbers 2–10) depict, when low-
pass filtered to highlight multicentennial variability (Fig. 2a), a
temperature maximum in the ninth or tenth centuries and a
Figure 1 Locations of proxy data sites. Shown are the locations of eleven low-resolution
proxy records (blue circles, numerals 1–11, see Table 1 for site details) and seven tree-
ring series (red triangles, letters A–G). Dashed latitude lines indicate the Equator, the
Tropic of Cancer and the Arctic Circle. See Supplementary Information for further details
and references.
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minimum in the sixteenth century, with a total range of 0.6 to 0.9 K.
This is a substantially larger multicentennial temperature range
compared to previous multi-proxy reconstructions
1–4,7
, exemplified
in Fig. 2a with the Northern Hemisphere reconstruction by Mann
and Jones
7
. The conflicting views provided by the low-resolution
series and this reconstruction illustrate a clear need for further
research to determine the size of natural low-frequency climate
variability.
Simple averages of temperature proxy series, such as those shown
in Fig. 2a, can yield adequate estimates of Northern Hemisphere
century-scale mean-temperature anomalies
14
. But to obtain a
reconstruction covering a complete range of timescales we created
a wavelet transform
11
, supposed to be approximately representative
for the Northern Hemisphere (Fig. 2e), such that only information
from the tree-ring records contributes to timescales less than 80 yr
and all eleven low-resolution proxies contribute only to the longer
timescales (see Methods for details). From the wavelet transform,
which was calculated using standardized (that is, unitless) proxy
series, a dimensionless reconstruction was obtained by calculating
the inverse wavelet transform
11
. Given the small number of tree-ring
series, their contribution is best thought of as an approximation
of the statistical character of variability at ,80-yr scales. A sample
size of eleven low-resolution series is reasonable for reconstructing
.80-yr variability, given that the number of spatial degrees
of freedom on the entire globe is about five at centennial time-
scales
18
. The contribution from each low-resolution proxy series to
the total variance at .80-yr scales in the Northern Hemisphere
reconstruction is given in Table 1.
To calibrate the reconstruction, its mean value and variance
were adjusted to agree with the instrumental record of Northern
Hemisphere annual mean temperatures
19
in the overlapping period
AD 1856–1979 (Fig. 2b). This technique avoids the problem with
underestimation of low-frequency variability associated with
regression-based calibration methods
14
. Jack-knifed estimates
(light-blue curves in Fig. 2b) of the low-frequency component
(.80-yr scales, dark blue), where each of the eleven low-resolution
proxies are excluded one at a time, are all very similar, demonstrat-
ing that the reconstruction is robust to the omission of any single
low-resolution proxy series.
The reconstruction depicts two warm peaks around
AD 1000 and
1100 and pronounced coolness in the sixteenth and seventeenth
centuries, with an overall temperature range for the low-frequency
component (.80-yr scales) of about 0.65 K. This amplitude can be
compared with that in the smoothed and averaged low-resolution
series in Fig. 2a, where the data used had been calibrated to
temperatures by their original investigators. The size of the overall
amplitudes of the series in Fig. 2a (0.6–0.9 K) and Fig. 2b (0.65 K,
blue curve) indicates that the reconstructed multicentennial varia-
bility in Fig. 2b has not been inflated by the standardization, the
wavelet processing and the subsequent calibration technique. The
peaksinmedievaltimesareatthesamelevelasmuchof
the twentieth century, although the post-1990 warmth seen in the
instrumental data (green curve in Fig. 2b) appears to be
unprecedented.
Table 1 Summary information for low-resolution proxy series
No.* Site† Proxy type and
interpretation‡
Dating type
(max. dating error)
First,
last year
AD#
Sample resolution
(no. of samples)§
Variance
fraction (%) in
.80-yr scales
Proxyff NH{
...................................................................................................................................................................................................................................................................................................................................................................
1 Agassiz Ice Cap,
Ellesmere Island,
Canada,
818 N, 738 W
Ice melt, layer stratigraphy,
summer T
Annual layer,
theoretical model,
ash layers (^10%)
29, 1961 5 (393) 2.4 0.3
2 GRIP borehole,
Greenland,
738 N, 388 W
Borehole T, annual T Theoretical model 2300, 1996 50 (40) 89.2 12.5
3 Conroy Lake,
Eastern US,
468 N, 688 W
Pollen, lake sediments,
summer T
Annual laminations 35, 1968 7–40 (68) 69.2 9.7
4 Chesapeake Bay,
Eastern US,
388 N, 768 W
Shells, Mg/Ca variation,
spring T
14
C(^160 yr),
210
Pb and
137
Cs
5, 1995 1–65 (427) 30.8 4.3
5 N. Sargasso Sea,
338 N, 578 W
Foraminifera,
d
18
O,
annual SST
14
C(^160 yr) 2300, 1925 50–150 (30) 65.0 9.1
6 NE Caribbean Sea,
188 N, 678 W
Foraminifera,
d
18
O,
annual SST
14
C(^200 yr) 133, 1950 30–160 (26) 99.6 14.0
7 Lake Tsuolbmajavri,
N. Finland,
688 N, 228 E
Diatoms, lake sediments,
summer T
14
C(^ 169 yr) 2300, 1950 ,70 (29) 61.5 9.9
8 Søylegrotta Cave,
Mo i Rana,
N. Norway,
668 N, 138 E
Stalagmite,
d
18
O,
annual T
230
Th/
234
U(^46 yr) 2300, 1938 ,20 (103) 47.3 7.6
9 Shihua Cave,
Beijing, China,
408 N, 1168 E
Stalagmite, layer thickness,
summer T
Layer counting (^5 yr) 2300, 1985 1 (1985) 32.2 5.2
10 China, 20–428 N,
80–1308 E
Composite of 9 records,
annual T
Layer counting,
14
C(^200 yr)
0, 1990 10 (200) 89.8 14.5
11 Arabian Sea,
188 N, 588 E
% Globigerina bulloides,
up-welling, monsoons,
summer and winter T
14
C(^100 yr) 2300, 1986 15–180 (63) 78.6 12.7
...................................................................................................................................................................................................................................................................................................................................................................
*Numbered as in Fig. 1.
References and further site details are given in Supplementary Information.
T, temperature; SST, sea surface temperature.
#Negative numbers mean years before
AD 1.
§Sample resolution in years. Number of samples after year
AD 1 given in parentheses.
ff For each proxy, the fraction of its total variance that occurs in its .80-yr scales (wavelet scales 10–22, see Methods) is listed.
{For each proxy, its contribution (in %) to the total variance in the low-frequency component (wavelet scales 10–22) of the Northern Hemisphere (NH) temperature reconstruction is listed. These
contributions are determined by the values in the second to last column. The resulting contributions by data from different regions are geographically well distributed; Arctic 12.9, Eastern US 14.0,
Fennoscandia 17.6, China 19.7, Oceans 35.8. Furthermore, the five proxies that are annual mean temperature indicators (nos 2, 5, 6, 8, 10) together contribute 57.8% of the variance in the low-frequency
component of the NH reconstruction.
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Changes in radiative forcing due to variability in solar irradiance,
the amount of aerosols from volcanic eruptions and greenhouse gas
concentrations have been important agents causing climatic varia-
bility in the past millennium
1,8,20–25
. Reconstructions of the tem-
poral evolution of these variables have been used to drive climate
models, ranging from simple energy balance models to fully coupled
atmosphere–ocean general circulation models
8,13,14,20,22,23,25
.The
Northern Hemisphere temperature series obtained from such an
experiment with the coupled model ECHO-G
13,14,25,26
for the AD
1000–1990 period (Fig. 2c) is qualitatively remarkably similar to our
multi-proxy reconstruction, although the model shows a somewhat
larger variability. Particularly strong qualitative similarity is seen at
timescales longer than centennial (compare the two wavelet trans-
form patterns, Fig. 2e, f), but some high-frequency details are also in
good agreement (for example, the double peaks around
AD 1000
and 1100, and two short cooling periods at
AD 1460 and 1820). The
model’s variability before the twentieth century is largely deter-
mined by the combined effects of the reconstructed solar and
volcanic forcing (that is, natural forcing) that was used in the
integration
13,25
, whereas the notably strong warming in the model
data after
AD 1900 is largely due to rapidly increasing concentrations
of anthropogenic greenhouse gases
13,25,27
. The similarity between
our reconstruction and the ECHO-G model series supports the case
of a rather pronounced hemispheric low-frequency temperature
variability resulting from the climate systems response to natural
changes in radiative forcing.
As in all palaeoclimate reconstructions, there are uncertainties in
this one. Efforts to quantify uncertainties in the low-frequency
component are illustrated with blue bands of different colours in
Fig. 2d. Accounting for the total uncertainty, the cooling from the
maxima around
AD 1000 and 1100 to the minimum near AD 1600 is
between 0.3 K and 1.1 K for the .80-yr component. Only the
smallest value is similar to the corresponding temperature change
in previous multi-proxy reconstructions
1–4,7
. (Compare with the
reconstruction of Mann et al.
1,2
, which is also shown in Fig. 2d
(orange curve, yellow uncertainty range) after smoothing to show
.80-yr variability.) In contrast, the warming trend depicted by our
reconstruction in the past 500 yr is entirely consistent with estimates
of Northern Hemisphere ground surface temperature (GST) trends
from temperature measurements in nearly 700 boreholes
12
.
Although trends at individual borehole sites are very noisy, hemi-
spheric mean GST trends are robust to different aggregation and
Figure 2 Estimations of Northern Hemisphere mean temperature variations. a, Previous
multi-proxy reconstruction (MJ: from Mann and Jones
7
, black line) with ^2 s.d.
uncertainty (grey shading), and various averages (blue, green, magenta; see Methods) of
smoothed low-resolution temperature indicators (nos 2–10 in Table 1). b, Our multi-proxy
reconstruction
AD 1–1979 (red) with its .80-yr component AD 133–1925 (blue) and its
jack-knifed estimates (light blue), and the instrumental record
19
(green). c, Forced
ECHO-G model
13,14,26
. d, Low-frequency component of multi-proxy reconstruction in b
(blue curve) with confidence intervals for three separate uncertainties. The innermost
medium-blue band shows the uncertainty due to variance among the low-resolution proxy
series. The two outer bands show the uncertainty in the variance scaling factor (light blue)
and the constant adjustment (outermost blue band) separately. Each uncertainty is
illustrated with an approximate 95% confidence interval (see Supplementary Information).
Also shown are ground surface temperatures estimated from boreholes
12
with their
uncertainty interval (brown; see Methods), and the .80-yr component of a previous
multi-proxy reconstruction (MBH: from Mann et al.
1,2
, orange) with ^2 s.d. uncertainty
(yellow). e, f, Wavelet transform (see Methods) of the series in b and c where warm/cold
anomalies are red/blue. Temperature anomalies in a, b and d are with respect to the
1961–90 average.
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weighting schemes
12
(illustrated by the two brown curves in Fig. 2d),
and show a warming of ,1 K during the interval
AD 1500–2000, of
which about half fell in the twentieth century.
There are several reasons for the notable differences between our
and previous multi-proxy reconstructions. The reconstruction of
Mann and Jones
7
has a large amount of data in common with ours,
but these workers combined tree-ring data with decadally resolved
proxies without any separate treatment at different timescales.
Furthermore, our data set contains some centennially resolved
data from the oceans, while Mann and Jones used only annually
to decadally resolved data from continents or from locations very
near the coast. Different calibration methods (regression in the
work of Mann and Jones versus variance scaling in this study) are
another reason. Possible explanations for the small low-frequency
variability in the multi-proxy reconstruction of Mann et al.
1,2
have
recently been discussed in detail elsewhere
14
.
Our multi-proxy reconstruction achieves a relatively large multi-
centennial variability by separately considering the information in
tree-ring data and low-resolution proxy records. Much more effort,
however, is needed to develop new proxy data series and to
determine how proxy data should best be chosen, combined and
calibrated. The wavelet approach allows for separate weighting of
proxies at different timescales. A goal for further research could be
to determine how such weighting should be undertaken, while
simultaneously taking spatial representativity into account. New
experiments with distorted ‘pseudoproxy’ data
14,28,29
from forced
general circulation model runs, using various types of distortions,
should be useful in this context.
We find no evidence for any earlier periods in the last two
millennia with warmer conditions than the post-1990 period
in
agreement with previous similar studies
1–4,7
. The main implication
of our study, however, is that natural multicentennial climate
variability may be larger than commonly thought, and that much
of this variability could result from a response to natural changes in
radiative forcings. This does not imply that the global warming in
the last few decades
15,19
has been caused by natural forcing factors
alone, as model experiments that use natural-only forcings fail
to reproduce this warming
15,23,27,30
. Nevertheless, our ndings
underscore a need to improve scenarios for future climate
change by also including forced natural variability
which could
either amplify or attenuate anthropogenic climate change
significantly. A
Methods
Wavelet transformation
The wavelet transform
11
(WT) decomposes a time series into time–frequency space,
enabling the identification of both the dominant modes of variability and how those
modes vary with time. We used the Mexican hat
11
wavelet, after linear interpolation to
annual resolution, to decompose each proxy series into 22 wavelet ‘voices’. These are 22
separate time series, where each depict the variability in the original series at each of
the timescales near the Fourier periods 4, 4
p
2, 8, 8
p
2, …, 4,096
p
2 yr. This ranges
from the smallest possible scale for the Mexican hat wavelet up to a few times the
length of the 2,000-yr-long time interval of interest. Before calculating the WT, padding
with surrogate data to extend the proxy series from their last value to the year
AD 2300
was applied to limit boundary effects at the longest timescales. As padding data we
used the mean value for the last 50 yr with data in each series. For those records that do not
have data back at least to 300
BC, similar padding was also made at the beginning of
records.
Averaging of calibrated low-resolution temperature indicators
Nine low-resolution proxy series (Table 1) are available as calibrated local/regional
temperature indicators (numbers 2–10). Five are annual mean (nos 2, 5, 6, 8, 10), one is a
spring (no. 4) and three are summer (nos 3, 7, 9) temperature indicators.
Multicentennial variability (highlighting .340-yr scales) in these series was extracted by
first applying the WT to each series and then the inverse WT only for wavelet voices 14–
22. Timescales of .340 yr are long enough to ensure that only information at frequencies
lower than the Nyquist frequency for the most poorly resolved proxy series are used.
Figure 2a shows arithmetic (green) and cos-latitude weighted (blue) averages of all nine
indicators. Jack-knifed estimates of the cos-latitude weighted averages, where each of the
nine indicators were removed one at a time, are also shown (magenta). These series are
plotted in Fig. 2a for the period
AD 133–1925 (when all have data) such that their mean
values agree with the Mann and Jones reconstruction
7
in the interval AD 200–1925.
Minor differences between the arithmetic and cos-latitude weighted series indicate
robustness to weighting choice. The similarity among the jack-knifed estimates indicates
that the overall temperature range is relatively little affected by the removal of any
individual indicator.
Timescale-dependent reconstruction
The multi-proxy reconstruction in Fig. 2b was constructed as follows. First, the data set of
19 proxy series in Fig. 1 was divided into two half-hemispheric subsets (western and
eastern half). After wavelet transformation of each individual proxy series into 22 voices as
described above (here using standardized series obtained by subtracting the mean and
dividing by the standard deviation, after linear interpolation to annual resolution), a
scale-by-scale averaging of wavelet voices was undertaken. For each wavelet scale from 1 to
9 (Fourier timescales ,80 yr), the voices from the individual tree-ring series were averaged
and, similarly, for each wavelet scale from 10 to 22 (Fourier timescales .80 yr) the
corresponding voices from the individual low-resolution proxy series were averaged.
Merging of the tree-ring-data average voices 1–9 with the low-resolution-data average
voices 10–22 gave one complete WT with voices 1–22 for each half-hemispheric subset.
The average of these two WTs then gave the whole-hemispheric WT shown in Fig. 2e.
The rationale for dividing into half-hemispheric subsets is similar to that used in
gridding; namely, to ensure that regions with many data series are weighted the same
as regions (of the same size) with few data series. However, for our data set, little
difference would be obtained if all data were placed in one whole-hemispheric set. A
dimensionless Northern Hemisphere temperature reconstruction was obtained by
calculating the inverse transform. Finally, this time series was calibrated by adjusting
its variance and mean value to be the same as in the instrumental data
19
in the
overlapping period
AD 1856–1979 (Fig. 2b). Separate estimates of uncertainties due to
variance among individual low-resolution proxy data and in the determination of the
variance scaling factor and constant adjustment term are explained in Supplementary
Information.
Plotting GST trends
The two curves for GST trends
12
shown in Fig. 2d correspond to the upper and lower
bounds for different area- and occupancy-weighted GST reconstructions, as illustrated in
figure 3 of ref. 12. To help visual comparison with our multi-proxy reconstruction, the
GST trends are plotted with reference to the
AD 1961–90 average in Fig. 2d. This was
achieved by shifting the GST trend-curves such that they cross the zero level at 1958.5,
which is the time when the twentieth century linear trend of the Northern Hemisphere
instrumental surface air temperature
19
(anomalies with respect to AD 1961–90) crosses the
zero level. (The same technique was used in figure 5 of ref. 12.)
Received 21 July; accepted 9 December 2004; doi:10.1038/nature03265.
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Acknowledgements We thank H. von Storch, E. Zorita and F. Gonza
´
lez-Rouco for the ECHO-G
data, and H. Pollack and J. Smerdon for borehole data. All these persons and J. Esper, J.
Luterbacher and M. Rummukainen are thanked for comments on early versions of the
manuscript. We acknowledge financial support from the Royal Swedish Academy of Sciences, the
Swedish Science Council and the Russian Foundation for Basic Research.
Competing interests statement The authors declare that they have no competing financial
interests.
Correspondence and requests for materials should be addressed to A.M.
(anders.moberg@misu.su.se).
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... We mention that many time series records from real-world datasets, are known to exhibit long-term memory. This is the case of long-range memory features assumed to represent the internal variability of the climate on time scales from years to centuries [75,127,150,155]. There, the surface temperature is considered as a superposition of internal variability (the response to stochastic forcing) and a forced signal which is the linear response to external forcing. ...
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