In the format provided by the authors and unedited.

1

Supplementary Information for

Internal and external forcing of multidecadal Atlantic climate variability over the

past 1200 years

Jianglin Wang1, Bao Yang1★, Fredrik Charpentier Ljungqvist2,3, Jürg Luterbacher4,5,

Timothy J. Osborn6, Keith R. Briffa6, Eduardo Zorita7

1Key Laboratory of Desert and Desertification, Northwest Institute of Eco-Environment

and Resources, Chinese Academy of Sciences, 730000 Lanzhou, China 2Department of History, Stockholm University, SE-106 91 Stockholm, Sweden 3Bolin Centre for Climate Research, Stockholm University, SE-106 91 Stockholm,

Sweden 4Department of Geography, Climatology, Climate Dynamics and Climate Change,

Justus Liebig University of Giessen, Senckenbergstrasse 1, D-35930 Giessen, Germany 5Centre for International Development and Environmental Research, Justus Liebig

University Giessen, Senckenbergstrasse 3, D-35390 Giessen, Germany 6Climatic Research Unit, School of Environmental Sciences, University of East Anglia,

Norwich NR4 7TJ, UK 7Institute of Coastal Research, Helmholtz-Zentrum Geesthacht, D-21502 Geesthacht,

Germany

★e-mail: yangbao@lzb.ac.cn

Contains:

1. Supplementary Methods

2. Supplementary Tables

3. Supplementary Figures

4. Supplementary References

Internal and external forcing of multidecadalAtlantic climate variability over the past

1,200 years

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NGEO2962

NATURE GEOSCIENCE | www.nature.com/naturegeoscience 1

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1. Supplementary Methods

Proxy contributions to the reconstruction. In each nest of the PCR reconstruction,

the contribution of the proxy is given by its beta-weight1,2 during the calibration period.

The beta-weight of the proxy was transformed from the regression coefficients of the

PCs and the spatial loading of the proxy in the retained eigenvector. The beta-weight

for proxy i, β(i), is calculated as:

β (i) = ∑ BjUj(i)

n

j=1

where n is the number of retained PCs that participated in the Multiple Linear

Regression (MLR), Bj is the regression coefficient for the retained PC j, and Uj(i) is the

space loading of the proxy i in the retained eigenvector j.

Supplementary Fig. 1 shows the median beta-weight of the 38 ensemble members

during the calibration intervals for a number of nests. It shows that the magnitude and

sign of beta-weight for each proxy exhibits a similar behavior with that revealed by

correlations between the instrumental AMV index and proxy records (Supplementary

Table 1). The signs of beta-weights are relatively robust regardless of number of proxy

records included in the reconstruction (Supplementary Table 2), whereas their

magnitude (contribution) tend to increase as the number of proxy records available

decreases. Especially, the robust signs of beta-weights for hydroclimate-sensitive proxy

records indicate a stable relationship with the AMV, supporting the rationality of

inclusion of these hydroclimate-sensitive proxy records in our reconstruction (see also

Supplementary Fig. 3 for a sensitivity test for the exclusion or inclusion of hydroclimate

proxies). The robust signs of beta-weight for all proxies over time suggest the stability

of the teleconnection between the AMV and proxy network, which is also supported by

a number of sensitivity tests using a reduced network of proxy records (Supplementary

Figs. 2, 3, 6, 7), pseudo-proxy experiments (Supplementary Figs. 8–11), and persistent

positive correlations between the reconstructed AMV and the NH temperature

throughout the past twelve centuries (Supplementary Figs. 24, 25).

Sensitivity tests for the reconstruction choices. Several alternative AMV

3

reconstructions were performed to test the sensitivity to some of the choices in

reconstruction method. The robustness of the reconstruction was assessed by using

these alternative choices:

(1) Including only the 29 proxy records whose correlation coefficients with the summer

AMV index have an absolute value of no less than 0.15 (i.e., |r| ≥0.15) over the

overlap period, instead of using all 46 proxy records (Supplementary Fig. S2).

(2) Excluding all 16 hydroclimate-sensitive proxy records (indicated by “Precip”,

“PDSI”, “PHDI” or “Stream flow” signal in Supplementary Table 1), and the

remaining 30, temperature-sensitive, proxy records were used for an alternative

reconstruction (Supplementary Fig. 3).

(3) Using one half of the instrumental AMV index (across the period 1856–1967) as

calibration intervals, and the remaining half of the instrumental data as verification

intervals, instead of two third (one third) of instrumental data as calibration

(verification) intervals in the final reconstruction. This alternative reconstruction

and the RE and R2 statistics were calculated as the median value of the 57 member

ensembles in each nest, different from the 38 member ensembles for the final

reconstruction (Supplementary Fig. 4).

(4) Using the annual (January-December, JD) AMV index as the instrumental target,

instead of the summer (MJJAS) AMV index used in the final reconstruction

(Supplementary Fig. 5).

(5) Using a reduced proxy network with 10 or 20 percent of proxy records randomly

removed in each time, which was repeated 1000 times. The intervals for the median

±1 standard deviation of the 1000 reconstruction ensemble members were

calculated and compared with the final reconstruction (Supplementary Fig. 6).

(6) Comparing the nested reconstructions before splicing them, based only on the

variable length of contributing proxy records (Supplementary Fig. 7).

Overall, the sensitivity tests reveal that the AMV reconstruction is relatively robust

and not particularly sensitive to specific reconstruction choices. For instance, the

alternative reconstruction using a reduced network, including only 29 proxy records

that have |r| ≥0.15 with instrumental AMV index, is found to decrease the verification

4

skill of the reconstruction, but has only a minor effect on the multidecadal variability

shown in our final reconstruction (Supplementary Fig. 2). Similar results also hold if

another subset of the network, excluding 16 hydroclimate records and only including

30 temperature records (Supplementary Fig. 3), was used to develop the reconstruction.

Alternative reconstructions, using a different length of the instrumental data as

calibration/verification intervals (Supplementary Fig. 4) or different seasonal target

(Supplementary Fig. 5), show very similar multidecadal behaviors with that described

by the final reconstruction. Furthermore, jackknifing tests using a reduced network by

randomly removing the 10–20 percent of proxy records indicate robustness of the

network sampling, and that our reconstruction does not depend on some specific proxy

records (Supplementary Fig. 6). Additionally, there are no substantial differences

between the reconstructions produced with or without nesting approaches. Even if only

19 proxy records extending back to AD 800 were used, it still shows similar

multidecadal variability with our final reconstruction using 46 proxy records

(Supplementary Fig. 7).

Pseudo-proxy experiments. The skill of the reconstruction method can be tested in the

virtual climate provided by climate simulations covering the past millennium with

state-of-the art models. Within this framework, artificial proxies are constructed based

on the temperature (or precipitation or soil moisture) simulated in climate simulations.

These artificial proxies are the simulated climate variables in grid-cells co-located with

the real proxy sites and degraded with stochastic noise to attain a correlation between

the degraded timeseries and the simulated timeseries that matches the correlation

between the real proxies and their corresponding instrumental records. For a

comprehensive review of this method the reader is referred to ref.3.

The climate model also simulates an index of Atlantic Multidecadal Variability,

defined (in the same way as in the real world) as the seasonal averaged of the sea-

surface temperatures in the North Atlantic. Once the artificial proxies (pseudo-proxies)

are generated mimicking the real proxy network, the same statistical reconstruction

method can be applied to pseudo-reconstruct the index of the AMV, using the data

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within the instrumental period to estimate the model parameters (model calibration) and

then reconstructing the AMV index over the whole length of the simulation. This

pseudo-reconstruction can be directly compared with the AMV simulated by the

climate model, thereby assessing the properties (skill, bias, uncertainties) of the

reconstruction method.

For each pseudo-proxy set up (e.g., a certain proxy nest), we have produced an

ensemble of pseudo-reconstructions by generating, 1000 realizations of identically and

independently distributed Gaussian noise (white noise). Each white noise record in this

ensemble is added to the climate variable simulated by the climate model in the grid-

cell collocated with the real proxy record, thereby creating a pseudo-proxy record. The

final product is a 1000-member ensemble of pseudo-proxy records.

The amplitude of the added white noise is chosen so that the correlation between

the real proxy and the corresponding real instrumental record is also replicated between

the pseudo-proxy and the simulated climate variable. Therefore, the connection

between the instrumental records and the real proxies is maintained in the pseudo-

reconstructions. For each ensemble member, we produce a pseudo-reconstruction by

applying the same statistical reconstruction method to the pseudo-proxy records. The

distribution of these 1000-member ensemble of pseudo-reconstructions can be used to

estimate their mean, their bias with respect to the true (simulated) target variable, and

the uncertainty range reflecting the uncertainty due to the non-climate noise present in

the real proxies.

Here, we have tested the two extreme proxy nests used in the real reconstructions,

as two limiting cases through the all proxy nests, i.e. the full proxy network of 46 series

and the smallest early proxy network of 19 proxies that reach back to AD 800. Both

pseudo-reconstructions are performed for the whole simulation period (AD 850–2005).

The climate simulation used in these pseudo-reconstructions is from the climate

model MPI-ESM-P4, participating in the Climate Model Intercomparison Project phase

5 (CMIP5)5. Details of this simulation can be found in ref.6 and of the characteristics of

the simulated North Atlantic circulation in ref.7. Only the more important details are

given here. The climate model consists of the atmospheric model ECHAM6 with a

6

spatial resolution of about 1.8° longitude × 1.8° latitude and 40 levels in the atmosphere,

coupled to the ocean-sea-ice model OM, with an average resolution of about 1°

longitude × 1° latitude. The model was forced by estimations of variations in the Total

Solar Irradiance8, volcanic aerosols9, atmospheric greenhouse trace gases4, land use

changes10, and orbital forcing in the period 850–2005.

The pseudo-reconstructions using both proxy nests provide similar results, with the

largest nest achieving slightly better results for all measures of skill, e.g., correlation

between simulated and pseudo-reconstructed AMV index, reduction of error. The

correlations at multidecadal and longer timescales attain vary high values

(Supplementary Figs. 8, 9). The reduction of error also indicates a reasonable (smallest

nest) to very good (largest nest) reconstruction skill (Supplementary Figs. 10, 11). This

reconstruction method based on Principal Component regression is burdened by loss of

variability at decadal and longer timescales, a feature that is common to many other

statistical reconstruction methods based on regression3,11. However, this loss of

variability quite likely does not affect the conclusions of the study since it would equally

affect the forced and unforced components of AMV.

Adjusting the degrees of freedom. Considering the serial correlation in proxy records

and instrumental data, the number of degrees of freedom was adjusted prior to testing

significance of correlation. The adjusted degrees of freedom, namely the effective

degrees of freedom (Neff), was computed as follows to determine the decorrelation time

(DT)12.

DT =1 + Rx ∗ Ry

1 − Rx ∗ Ry

Neff =N

DT

where DT is decorrelation time; Rx and Ry are the lag-1 serial correlations of the series

x and y; N is the length of the series x and y.

In the case of low-pass filtered data, the Neff was also constrained as degrees of freedom

7

is reduced by a factor of DT, but the DT should be calculated as:

DT =1

2 ∗ f

where f is the filter frequency.

This calculation of DT is based on a convenient assessment of the Nyquist frequency,

i.e., the Nyquist (highest) frequency should equal twice the filter frequency in the

smoothed series.

Superposed epoch analysis. To examine the response of the AMV to external forcing

(e.g., solar activity and volcanic eruption), we performed superposed epoch analysis

(SEA)13. The reconstructions of global volcanic Aerosol Optical Depth (AOD)9 and

Total Solar Irradiance (TSI)14 that were used in Fig. 5.8 in the Intergovernmental Panel

on Climate Change Fifth Assessment Report (IPCC AR5)15 were selected in our study.

Additional reconstructions of solar16 and volcanic17 forcing were also selected to test

the sensitivity of the SEA results.

To assess volcanic-forced AMV anomalies, the SEA approach was performed by

generating composites of the AMV index from lag –5 to lag 15 years corresponding to

the timing of large volcanic events, relative to the average of 5 years (lag –5 to lag –1

years) before each volcanic event. For interannual composites, we selected the 15

strongest volcanic events based on the two reconstructions of past volcanism9,17,

respectively.

Due to the possible influence of the external forcing at multidecadal timescales18-20,

the SEA approach was performed on the 30-year low-pass filtered AMV reconstruction.

The multidecadal composites were calculated as the average of individual AMV time-

series from lag –30 to lag 30 years, with respect to the mean of the values from lag –30

to –1 years. In the case of multidecadal volcanic composites, only the 5 strongest event

years were selected, except that an event year was not selected if it is within 29 years

of another event year that has a larger volcanic forcing. In the case of multidecadal solar

composites, the two solar forcing reconstructions14,16 were 30–160 year band-pass

filtered to extract multidecadal variability (similar as the method used in refs15,21), and

8

then the 5 event years (i.e., peak negative solar forcing) with values less than –1.5

standard deviation (SD) were selected in each solar forcing reconstruction.

For each interannual and multidecadal composite, the 95% confidence interval was

estimated as the composite mean ± 2 standard error (SE) of individual time-series for

multiple events. All of the event years selected for solar and volcanic anomalies are

shown in Supplementary Table 3.

The results of SEA are shown in Fig. 3 and are discussed in main text.

Multiple linear regression (MLR). The MLR, as described in the PCR calculation,

has previously been used in refs22,23 to assess the externally-forced variability of the

North Atlantic SST. Here, we used the MLR to estimate which degree of changes in the

reconstructed AMV can be fitted by external forcings. We calculated the internally-

generated component of the AMV (which we define as the AMO) by subtracting our

estimate of the forced component from the reconstruction. The two solar and two

volcanic reconstructions used in the SEA were selected as predictors to participate into

the MLR. The reconstruction of volcanic AOD in ref.9 was multiplied by –1 so that has

a sign consistent with that of the radiative forcing (W/m2) of the other reconstructions.

All of these time-series were smoothed using a 30-year low-pass filter to extract the

variability at multidecadal time-scales. Due to expected time lags in its response, we

calculated the cross-correlation between the AMV index and the solar and volcanic

forcing (Supplementary Fig. 17) over the common period 850–2000 of all series. We

used the lagged time-series with the highest correlation to enter into the MLR. The

MLR created four estimated AMV time-series by considering all combinations of the

two volcanic and two solar forcing reconstructions (Supplementary Fig. 20a).

Anthropogenic forcing (i.e., CO2 concentration24) was also included in the MLR,

although it hardly improves any of the skill of the regression (Supplementary Fig. 20c).

Finally, the composite mean and ±1 SD intervals of the four estimated AMV series

was calculated to represent the externally-forced component of the AMV. The

internally-generated variability component of the AMV was calculated by subtracting

the forced variability component from the reconstructed AMV index (Supplementary

9

Fig. 20e).

An advantage of our approach is that it does not depend on the amplitude of the

solar forcing reconstruction, which is quite uncertain, and different reconstructions with

strong, medium or weak variations have been produced. The correlation and regression

approaches are unaffected by changes in forcing amplitude. Although they are affected

by uncertainty in the shape of the forcing series, and the timing of the maxima and

minima, this uncertainty is much smaller than the uncertainty in the amplitude of

change.

Composite of Northern Hemisphere temperature reconstructions. We calculated a

composite of 13 published NH temperature reconstructions using a similar method as

in ref.25. The 13 reconstructions were selected to meet three criteria: 1) extending to at

least AD 1000; 2) having a high temporal resolution (annual to decadal); and 3) not

being superseded by a later version. The details of each reconstruction are provided in

Supplementary Table 4.

The 13 reconstructions were filtered with a low- or band-pass filter to extract the

time scale considered. Each filtered series was then normalized to have a zero mean

and unit SD over the instrumental interval (i.e., 1850–1960). After that, the composite

mean and ±1 SD intervals were calculated in each year.

It should be noted that the proxy dataset used here to reconstruct AMV and the

data used for some of the NH temperature reconstructions are very possibly partly

overlapped, which may cause an overestimation of similarity between the AMV and

NH temperature if use this composite of NH temperature. To address the overlap of

proxy records in our AMV and these published NH temperature reconstructions, we

calculated another NH temperature timeseries, using only 22 temperature-sensitive

tree-ring records selected from ref.26, which are not used in our AMV and AMO

reconstructions. The details of each tree-ring record are provided in Supplementary

Table 5, and they were combined to represent NH temperature variability using a similar

method as above, except that all tree-ring chronologies were normalized over their

common period 1775–1988, and the ±1 SE intervals were used to account for the

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uncertainty associated with changes in the number of available tree-ring records.

The internally-generated variability component for the two composite of NH

temperature was calculated using a similar method as for the AMV, i.e., the externally-

forced component was obtained by MLR with the forcing time-series and was then

removed from the composite NH time-series (see Supplementary Figs. 21c, 22c).

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2. Supplementary Tables

Supplementary Table 1. Metadata of the 46 proxy records from the circum-North

Atlantic (100°W–35°E, 20°N–80°N) available from the PAGES 2k Consortium27 and

individual authors.

Region Name/Site LON LAT Proxy type Period used Signal Season Cora Ref

The

North

Atlantic-

Arctic

region

GISP2 -38.1 72.1 Ice core δ18O 818-1987 SAT Annual 0.19 27,28

Finnish Lapland 25.0 69.0 Tree-ring width 800-2000 SAT July 0.25 27,29

Forfjorddalen 18.5 69.1 Tree-ring width 877-1994 SAT JJA 0.11 27,30

B16 -37.6 73.9 Ice core δ18O 1478-1992 SAT Annual 0.20 27,31

B18 -36.4 76.6 Ice core δ18O 871-1992 SAT Annual 0.03 27,31

NGRIP1 -42.3 75.1 Ice core δ18O 800-1995 SAT Annual 0.10 27,32

Camp Century -61.1 77.2 Ice core δ18O 1242-1967 SAT Annual 0.16 27,33

Agassiz Ice Cap -73.1 80.0 Ice core δ18O 800-1972 SAT Annual 0.27 27,34

Crête -37.3 71.1 Ice core δ18O 800-1972 SAT Annual 0.23 27,35

Dye-3 -43.8 65.2 Ice core δ18O 800-1979 SAT Annual 0.15 27,35

Torneträsk 20.0 67.5 Tree-ring MXD 800-2010 SAT MJJA 0.38 36

Forfjorddalen-x 15.7 68.8 Tree-ring MXD 978-2005 SAT JJA 0.09 37

Laanila 27.3 68.5 Tree-ring MXD 800-2005 SAT JJA 0.41 37

Khibiny 33.5 67.5 Tree-ring BI 821-2005 SAT JJA 0.25 37

Arjeplog 17.9 66.5 Tree-ring BI 1200-2010 SAT JJA 0.40 38

Jämtland 15.0 63.1 Tree-ring MXD 800-2011 SAT AMJJAS 0.36 39

B18-s -36.0 76.0 Ice core snow accumulation 871-1992 Precip Annual -0.18 40

NGRIP-s -42.0 76.0 Ice core snow accumulation 800-1995 Precip Annual 0.18 41

GISP2-s -38.5 73.0 Ice core snow accumulation 800-1987 Precip Annual 0.08 42

Europe Nsc12 25.0 68.0 Tree-ring MXD 800-2006 SAT JJA 0.28 27,43

Tat12 20.0 49.0 Tree-ring width 1040-2011 SAT MJ 0.19 27,44

Car09 25.3 47.0 Tree-ring width 1163-2005 SAT JJA 0.27 27,45

Aus11 10.7 47.0 Tree-ring width 800-2003 SAT JJA 0.39 27,46

Swi06 7.5 46.0 Tree-ring MXD 800-2004 SAT JJAS 0.31 27,47

Fra12 7.5 44.0 Tree-ring width 969-2007 SAT JJA 0.30 27,48

Pyr12 1.0 42.5 Tree-ring width and MXD 1260-2005 SAT MJJAS 0.21 27,49

Alb12 20.0 41.0 Tree-ring width 968-2008 SAT JJ -0.02 27,50

CEu10 13.0 49.0 Documentary 1500-2007 SAT JJA 0.36 27,51

Sodankylä 27.0 67.0 Tree height increment 800-2007 SAT JJA 0.12 52

Southern Finland 28.5 61.5 Tree-ring MXD 800-2000 SAT MJJAS 0.24 53

Swiss Alps 8.0 47.0 Tree-ring δ13C 800-2004 PDSI JJA 0.04 54

Tyrol 12.5 48.0 Tree-ring MXD 1053-2003 SAT JAS 0.27 55

SW Turkey 31.0 37.0 Tree-ring width 1339-1998 Precip MJ 0.01 56

SC England -1.4 51.5 Tree-ring width 950-2009 Precip MJJ 0.09 57

Germany 9.0 51.5 Tree-ring width 996-2005 PDSI JJAS 0.07 58

Austria 10.0 45.5 Tree-ring width 800-2008 Precip AMJ 0.11 46

Col du Zad -5.1 33.0 Tree-ring width 984-1984 PDSI FMAMJ 0.02 59

12

Eastern

North

America

Quebec-w -74.0 57.3 Tree-ring width 910-2012 SAT JA 0.35 60

Quebec-x -76.0 57.3 Tree-ring MXD 1373-1988 SAT MJJAS 0.44 55

Potomac River -77.5 39.3 Tree-ring width 950-2001 Stream

flow

MJJAS 0.16 61

S Manitoba -97.1 49.5 Tree-ring width 1409-1998 Precip Annual -0.01 62

Mesoamerica -100.0 20.0 Tree-ring width 800-2008 PDSI June -0.02 63

Niagara Escarpment -81.5 45.1 Tree-ring width 800-1989 Precip JJ 0.25 64

Big Cypress State Park -93.0 32.3 Tree-ring width 997-1988 Precip JJ 0.00 65

Albemarle Sound -76.0 36.0 Tree-ring width 934-2005 PDSI July 0.03 66

Jamestown-Roanoke -75.6 40.8 Tree-ring width 1185-1984 PHDI July -0.19 67

a Correlation of proxies with the summer (MJJAS) AMV index during the overlapping period.

13

Supplementary Table 2. Calibration and verification statistics for the reconstructed

AMV index in each nest.

No. Proxies, number of proxy records; No. PCs, number of principal components;

Unchanged sign of proxy weights (%), the percentage of proxies that have median beta-

weights with no change of sign with respect to the most replicated nest, 1500–1967. R2,

RE and RMSE are shown as the median value of the 38 ensemble members derived by

a sliding approach for calibration and verification (see Methods in main text). Numbers

in brackets refer to the minimum and maximum of R2, RE, RMSE into the 38-member

statistics.

Nest

Period

No.

Proxies

No.

PCs

Unchanged sign of

proxy weights (%)

Calibration R2 Verification R2 Verification RE Verification

RMSE

800-817 19 7 73.68 0.40 (0.24, 0.50) 0.18 (0.01, 0.31) 0.37 (-0.31, 0.60) 0.16 (0.15, 0.20)

818-820 20 7 85.00 0.39 (0.23, 0.50) 0.21 (0.01, 0.34) 0.40 (-0.31, 0.60) 0.16 (0.15, 0.20)

821-870 21 7 85.71 0.39 (0.23, 0.50) 0.21 (0.01, 0.36) 0.42 (-0.28, 0.60) 0.16 (0.05, 0.20)

871-876 23 8 78.26 0.40 (0.26, 0.51) 0.18 (0.01, 0.30) 0.36 (-0.50, 0.58) 0.16 (0.05, 0.20)

877-909 24 9 87.50 0.41 (0.26, 0.54) 0.23 (0.01, 0.37) 0.43 (-0.51, 0.59) 0.16 (0.14, 0.20)

910-933 25 9 88.00 0.41 (0.26, 0.55) 0.24 (0.01, 0.39) 0.45 (-0.55, 0.61) 0.16 (0.14, 0.19)

934-949 26 10 84.61 0.42 (0.27, 0.54) 0.22 (0.01, 0.35) 0.40 (-0.53, 0.60) 0.16 (0.15, 0.19)

950-967 28 11 78.57 0.43 (0.32, 0.53) 0.21 (0.02, 0.32) 0.35 (-0.50, 0.56) 0.17 (0.15, 0.20)

968 29 11 86.21 0.41 (0.25, 0.52) 0.20 (0.01, 0.35) 0.33 (-0.45, 0.59) 0.17 (0.15, 0.19)

969-977 30 12 83.33 0.44 (0.32, 0.53) 0.16 (0.01, 0.26) 0.27 (-0.66, 0.54) 0.18 (0.15, 0.22)

978-983 31 12 80.65 0.45 (0.35, 0.54) 0.12 (0.00, 0.24) 0.29 (-0.87, 0.49) 0.18 (0.15, 0.22)

984-995 32 12 81.25 0.45 (0.35, 0.53) 0.12 (0.01, 0.24) 0.27 (-0.84, 0.49) 0.18 (0.15, 0.21)

996 33 12 78.79 0.44 (0.34, 0.54) 0.15 (0.01, 0.25) 0.29 (-0.86, 0.49) 0.18 (0.15, 0.22)

997-1039 34 12 76.47 0.43 (0.33, 0.52) 0.16 (0.02, 0.26) 0.29 (-0.54, 0.50) 0.17 (0.15, 0.22)

1040-1052 35 13 80.00 0.43 (0.32, 0.52) 0.15 (0.02, 0.26) 0.25 (-0.60, 0.49) 0.17 (0.15, 0.23)

1053-1162 36 14 75.00 0.45 (0.34, 0.54) 0.15 (0.02, 0.27) 0.25 (-0.70, 0.51) 0.18 (0.15, 0.22)

1163-1184 37 13 75.68 0.44 (0.32, 0.53) 0.13 (0.01, 0.26) 0.25 (-0.53, 0.53) 0.17 (0.16, 0.22)

1185-1199 38 14 78.95 0.45 (0.32, 0.54) 0.10 (0.01, 0.23) 0.20 (-0.73, 0.50) 0.18 (0.16, 0.21)

1200-1241 39 15 79.49 0.50 (0.36, 0.57) 0.19 (0.03, 0.30) 0.24 (-0.83, 0.54) 0.17 (0.16, 0.20)

1242-1259 40 14 87.50 0.38 (0.25, 0.50) 0.22 (0.02, 0.35) 0.32 (-0.50, 0.54) 0.17 (0.15, 0.21)

1260-1338 41 15 92.68 0.43 (0.32, 0.51) 0.25 (0.09, 0.37) 0.31 (-0.48, 0.53) 0.17 (0.15, 0.21)

1339-1372 42 15 90.48 0.40 (0.30, 0.51) 0.27 (0.07, 0.43) 0.42 (-0.31, 0.60) 0.16 (0.14, 0.21)

1373-1408 43 16 93.02 0.46 (0.39, 0.56) 0.37 (0.14, 0.52) 0.48 (-0.32, 0.64) 0.15 (0.13, 0.21)

1409-1477 44 16 93.18 0.47 (0.39, 0.56) 0.39 (0.18, 0.52) 0.46 (-0.37, 0.64) 0.15 (0.13, 0.21)

1478-1499 45 17 88.88 0.47 (0.41, 0.58) 0.41 (0.17, 0.56) 0.47 (-0.45, 0.63) 0.15 (0.13, 0.21)

1500-1967 46 17 100.00 0.45 (0.38, 0.54) 0.36 (0.14, 0.53) 0.44 (-0.29, 0.62) 0.15 (0.13, 0.21)

1968-1972 45 17 91.11 0.45 (0.39, 0.54) 0.31 (0.12, 0.49) 0.42 (-0.20, 0.62) 0.16 (0.14, 0.21)

1973 44 17 79.55 0.49 (0.41, 0.56) 0.25 (0.06, 0.38) 0.34 (-0.25, 0.66) 0.16 (0.14, 0.19)

1974-1978 43 17 76.74 0.49 (0.39, 0.55) 0.26 (0.04, 0.39) 0.34 (-0.25, 0.65) 0.17 (0.15, 0.19)

14

1979-1984 42 16 76.19 0.49 (0.40, 0.55) 0.20 (0.01, 0.30) 0.25 (-0.57, 0.61) 0.17 (0.16, 0.20)

1985-1987 40 15 75.00 0.49 (0.38, 0.54) 0.14 (0.00, 0.27) 0.15 (-0.95, 0.59) 0.18 (0.17, 0.21)

1988 38 14 73.68 0.47 (0.38, 0.53) 0.15 (0.00, 0.29) 0.16 (-0.29, 0.58) 0.18 (0.16, 0.21)

1989 36 13 75.00 0.45 (0.34, 0.53) 0.08 (0.00, 0.20) 0.05 (-1.14, 0.50) 0.19 (0.18, 0.22)

1990-1992 35 13 77.14 0.43 (0.35, 0.46) 0.08 (0.00, 0.20) 0.03 (-0.76, 0.50) 0.19 (0.16, 0.21)

1993-1994 32 11 81.25 0.38 (0.29, 0.44) 0.13 (0.00, 0.24) 0.20 (-0.82, 0.50) 0.19 (0.17, 0.21)

1995 31 11 83.87 0.38 (0.29, 0.40) 0.14 (0.04, 0.26) 0.20 (-0.26, 0.51) 0.17 (0.15, 0.21)

1996-1998 29 10 82.76 0.35 (0.25, 0.39) 0.12 (0.02, 0.25) 0.17 (-0.33, 0.50) 0.18 (0.15, 0.22)

1999-2000 27 10 77.77 0.37 (0.23, 0.42) 0.12 (0.00, 0.25) 0.14 (-0.62, 0.52) 0.18 (0.16, 0.21)

2001 25 9 80.00 0.35 (0.21, 0.42) 0.09 (0.00, 0.20) 0.14 (-0.82, 0.51) 0.19 (0.17, 0.21)

2002-2003 24 8 87.50 0.24 (0.17, 0.36) 0.09 (0.00, 0.19) 0.25 (-0.79, 0.43) 0.19 (0.17, 0.24)

2004 22 8 77.27 0.21 (0.16, 0.31) 0.10 (0.00, 0.23) 0.26 (-0.60, 0.40) 0.18 (0.16, 0.24)

2005 20 7 70.00 0.21 (0.16, 0.31) 0.10 (0.00, 0.21) 0.25 (-0.42, 0.41) 0.17 (0.16, 0.23)

2006 13 5 76.92 0.17 (0.09, 0.23) 0.07 (0.00, 0.15) 0.20 (-0.16, 0.43) 0.17 (0.15, 0.23)

2007 12 5 75.00 0.16 (0.08, 0.22) 0.06 (0.00, 0.21) 0.21 (-0.20, 0.43) 0.17 (0.15, 0.23)

2008 9 3 88.88 0.12 (0.05, 0.19) 0.05 (0.00, 0.21) 0.23 (-0.26, 0.39) 0.17 (0.15, 0.24)

2009 6 2 100.00 0.11 (0.04, 0.18) 0.06 (0.00, 0.20) 0.22 (-0.30, 0.38) 0.17 (0.15, 0.25)

2010 5 2 100.00 0.11 (0.02, 0.19) 0.09 (0.00, 0.19) 0.21 (-0.36, 0.42) 0.17 (0.15, 0.23)

15

Supplementary Table 3. The event years of volcanic and solar forcing for the past

twelve centuries (800–2000 AD) selected in the superposed epoch analysis (SEA) in

order of time.

Reconstruction Volcanic event years

Interannual timescale

(the 15 largest eruptions)

Volcanic event years

Multidecadal timescale

(the 5 largest eruptions)

Reconstruction Solar irradiance minima

Multidecadal timescale

(the 5 weakest activity years)

Ref.17 939, 1108, 1171, 1230, 1258,

1276, 1286, 1345, 1458, 1601,

1641, 1695, 1783, 1809, 1815

1108, 1258, 1458, 1783,

1815

Ref.16 899, 1027, 1280, 1458, 1815

Ref.9 1229, 1258, 1259, 1286, 1456,

1457, 1641, 1695, 1696, 1809,

1810, 1815, 1816, 1817, 1884

1258, 1456, 1641, 1696,

1816

Ref.14 1055, 1446, 1563, 1690, 1826

16

Supplementary Table 4. The 13 Northern Hemisphere (NH) temperature

reconstructions selected to calculate the composite of NH temperatures in

Supplementary Fig. 23.

Identifier Time span (AD) Resolution Ref

Christiansen and Ljungqvist (2012) [Ch12loc] 1–1973 Annual 68

D’Arrigo et al. (2006) [Da06cps] 713–1995 Annual 69

Frank et al. (2007) [Fr07cps] 831–1992 Annual 70

Hegerl et al. (2007) [He07tls] 558–1960 Decadal 71

Juckes et al. (2007) [Ju07cvm] 1000–1980 Annual 72

Ljungqvist (2010) [Lj10cps] 1–1999 Decadal 73

Mann et al. (2008) [Ma08civ] 200–2007 Decadal 74

Mann et al. (2008) [Ma08cps] 200–1995 Decadal 74

Mann et al. (2009) [Ma09full-nh] 500–2006 Decadal 75

Moberg et al. (2005) [Mo05wave] 1–1979 Annual 76

Schneider et al. (2015) [Sc15cps] 1000–2002 Annual 55

Shi et al. (2013) [Sh13pcar] 1000–1998 Decadal 77

Wilson et al. (2016) [Wi16cps] 750–2011 Annual 78

17

Supplementary Table 5. The 22 temperature-sensitive tree-ring records used to

calculate the composite of NH tree-ring records in Fig. 4 in main text. To provide

independence from the dataset used in the AMV reconstruction, the 8 tree-ring records

used for both ref.26 and our AMV reconstruction were excluded from the full network

of 30 clusters. For more details of each record, see Table S1 in ref.26.

Site name LAT (°N) LON (°E) Proxy type Span time (AD)

Aktash Valley 49-52 84-88 Tree-ring width 1581–1994

Ary-Ongorbynf River 66-72 111-123 Tree-ring MXD 1535–1991

Athabasca 51-53 -116- -118 Tree-ring width and MXD 950–1994

Churchill 58-59 -95- -93 Tree-ring MXD 1775–1987

Coastal Alaska 55-62 -154- -131 Tree-ring width 713–2000

Fifth River 68 -141 Tree-ring MXD 1098–2002

French Alps LADE 44-46 6-7 Tree-ring width 810–2009

Indigirka 70 148 Tree-ring width 500–1993

Kola Peninsula 64-70 29-33 Tree-ring MXD 1578–1992

Labrador 55-58 -63- -61 Tree-ring width 1670–2001

Lac Romanel 54-55 -78- -67 Tree-ring MXD 1410–1989

Polar Ural 65-70 65-85 Tree-ring MXD 880–2006

Qilian Mountains 38-39 99-100 Tree-ring width 670–2012

Sarejmek 41-43 75-79 Tree-ring MXD 1626–1995

Sartan River 64-72 127-155 Tree-ring MXD 1495–1991

Seward Peninsula 65-68 -162- -157 Tree-ring width 1140–2002

Solongotyn Davaa 47-49 97-100 Tree-ring width 913–1999

Taymir 67-73 88-105 Tree-ring width -2013–2003

Thelon 64-68 -116- -103 Tree-ring width 1175–2004

Vikran 68-70 15-19 Tree-ring width 1230–1997

Yamal 66-68 69-70 Tree-ring width -2690–2005

Zolotica 59-67 41-61 Tree-ring MXD 1695–1991

18

3. Supplementary Figures

Supplementary Fig. 1. Maps of location and contribution (beta-weight) of each

proxy record to reconstructed segments. a. Nest 1500–1967 using 46 records. b. Nest

1373–1408 using 43 records. c. Nest 1200–1241 using 39 records. d. Nest 1040–1052

using 35 records. e. Nest 978–983 using 31 records. f. Nest 950–967 using 28 records.

19

g. Nest 871–876 using 23 records. h. Nest 800–817 using 19 records. Here we only

show beta-weights for a number of nests for backward models and do not show any of

them for forward models (i.e. after AD 1967).

20

Supplementary Fig. 2. Comparison of the final AMV reconstruction with an

alternative reconstruction. The alternative reconstruction only used 29 proxy records,

having |r| ≥0.15 with MJJAS AMV index, instead of the all 46 proxy records in the final

reconstruction. a. Comparison between the final and the alternative reconstruction over

the past twelve centuries with respect to the 1856–1967 mean. b. As a, but 30-year low-

pass filtered. c. R2 and RE statistics, and the number of records for the final

reconstruction. d. As c, but for the alternative reconstruction. In each case, the AMV

reconstruction, R2 and RE statistics are reported as the median value of the 38 ensemble

members calculated by a sliding calibration/verification approach. For more details of

statistics, see Methods in main text.

21

Supplementary Fig. 3. As Supplementary Fig. 2, but compares with an alternative

reconstruction that excluded 16 hydroclimate-sensitive proxy records and only used 30

temperature-sensitive proxy records.

22

Supplementary Fig. 4. As Supplementary Fig. 2, but compares with the alternative

reconstruction that used a half (another half) of instrumental data for calibration

(verification), instead of two third (one third) of instrumental data for calibration

(verification) used in the final reconstruction.

23

Supplementary Fig. 5. As Supplementary Fig. 2, but compares with the alternative

reconstruction that used the annual (January-December, JD) AMV index as the

reconstruction target, instead of the summer (MJJAS) AMV index used in the final

reconstruction.

24

Supplementary Fig. 6. Jackknife tests. The comparison of the final reconstruction

with the intervals of the median ±1 standard deviation (SD) of the 1000 alternative

reconstructions, based on a truncated proxy network with removal of 10% or 20% of

proxy records in each time, for the annual (a) and 30-year smoothed (b) reconstructions.

The upper and lower confidence intervals represent the median ±1 SD of 1000

alternative reconstructions based on a reduced proxy network. The statistics (i.e.,

minimum, median and maximum) for cross correlations among 1000 reconstructions

are shown on the bottom left corner of the panel.

25

Supplementary Fig. 7. Comparison of the PCR nesting procedure. The curves show

annual (a) and 30-year low-pass filtered (b) reconstructions. The AMV reconstruction

(black) is producing using a nested PCR procedure to account for the variable length of

proxies available in the reconstruction. For comparison we also show a number of PCR

reconstructions without nesting, based only on the proxy records that extend

continuously back to AD 800 (19 records), AD 871 (23 records), AD 950 (28 records),

AD 978 (31 records), AD 1040 (35 records), AD 1200 (39 records), AD 1373 (43

records), and AD 1500 (46 records). For the reconstructions without nesting, we only

show a number of them for backward models and do not show any of them for forward

models (i.e. after AD 1967).

26

Supplementary Fig. 8. Pseudo-proxy test of the statistical reconstruction method

with the full proxy network: histogram of correlation coefficients between the AMV

index simulated in the MPI-ESM-P climate simulation and the AMV reconstructed with

a 1000-member ensemble of pseudo-proxies covering the full proxy network, at

interannual timescales and after 30-year low-pass smoothing. The period of calibration

of the statistical method is 1856–2005. The correlations have been computed over the

period 850–1855.

27

Supplementary Fig. 9. Pseudo-proxy test of the statistical reconstruction method

with the smallest proxy network: histogram of correlation coefficients between the

AMV index simulated in the MPI-ESM-P climate simulation and the AMV

reconstructed with a 1000-member ensemble of pseudo-proxies covering the smallest

proxy network, at interannual timescales and after 30-year low-pass smoothing. The

period of calibration of the statistical method is 1856–2005. The correlations have been

computed over the period 850–1855.

28

Supplementary Fig. 10. Pseudo-proxy test of the statistical reconstruction method

with the full proxy network: histogram of Reduction of Error (RE) between the AMV

index simulated in the MPI-ESM-P climate simulation and the AMV reconstructed with

a 1000-member ensemble of pseudo-proxies covering the full proxy network, at

interannual timescales and after 30-year low-pass smoothing. The period of calibration

of the statistical method is 1856–2005. The RE values have been computed over the

period 850–1855, with respect to the 1856–2005 mean.

29

Supplementary Fig. 11. Pseudo-proxy test of the statistical reconstruction method

with the smallest proxy network: histogram of Reduction of Error (RE) between the

AMV index simulated in the MPI-ESM-P climate simulation and the AMV

reconstructed with a 1000-member ensemble of pseudo-proxies covering the smallest

proxy network, at interannual timescales and after 30-year low-pass smoothing. The

period of calibration of the statistical method is 1856–2005. The RE values have been

computed over the period 850–1855, with respect to the 1856–2005 mean.

30

Supplementary Fig. 12. Spectral properties of the reconstructed AMV over the

period 800–2010. The multi-taper method (MTM) of spectral analysis was performed

on the reconstructed annual-resolution summer AMV index to identify major

periodicities. The statistical confidence level was tested against a red noise

background79. The periodicities at multidecadal time-scales that are significant at the

90% confidence level are marked with green numbers on the figure, though we do not

expect pure oscillatory modes and instead interpret the group as representing a broad

band of enhanced stochastic variability on timescales from 60 to 90 years.

31

Supplementary Fig. 13. Comparison with the published AMV reconstructions.

Comparison of our reconstruction (black) with that from Mann et al.75 (red) and from

Gray et al.80 (green) for their original (a), 10-year low-pass filtered (b), and 30-year

low-pass filtered (c) data. All time-series are shown as normalized anomalies with

respect to their common period AD 1567–1990. The correlation coefficients of our

reconstruction with others are indicated on the panel.

32

Supplementary Fig. 14. Wavelet analysis for the reconstructions of AMV in our

study and other previous studies. a. The wavelet power spectrum for the AMV

reconstruction in this study. b. As a, but for the reconstruction of Mann et al.75. c. As a,

but for the reconstruction of Gray et al.80. In all cases of Gaussian wavelet analysis, the

power spectrum was calculated based on 10-year low-pass filtered reconstructions

(Supplementary Fig. 13b), and the cross-hatched region is the cone of influence, where

zero padding has reduced the variance. Black contour is the 95% significance level for

a red-noise (autoregressive lag-1) background spectrum81.

33

Supplementary Fig. 15. Wavelet coherence (WTC) between the AMV

reconstructions reported in our study and other studies. a. The WTC between the

AMV reconstructions in this study and in Mann et al.75. b. As a, but for the AMV

reconstructions in this study and in Gray et al.80. c. As a, but for the AMV

reconstructions in Mann et al.75 and in Gray et al.80. In each case, the WTC was

calculated based on 10-year low-pass filtered reconstructions (Supplementary Fig. 13b).

The 95% significance level (against red noise) is shown as the thick black line contour82.

Arrows show the phase relation between the two reconstructions, where pointing to the

right is in phase and to the left is in out-of-phase.

34

Supplementary Fig. 16. Comparison with the multidecadal North Atlantic

Oscillation (NAO) reconstruction83. The two reconstructions were 30-year low-pass

filtered and normalized over the common period AD 1049–1995. The two

reconstructions share some similar multidecadal variations. It should be noted that our

reconstruction is representative of summer season, but Trouet et al. reconstruction is

winter biased.

35

Supplementary Fig. 17. Cross-correlations of the reconstructed AMV with

external forcings. The correlations were calculated using 30-year low-pass filtered

series with different lags. a. Correlations with the reconstruction of solar forcing in

ref.16 b. Correlations with the reconstruction of solar forcing in ref.14. c. Correlations

with the reconstruction of volcanic forcing in ref.17. d. Correlations with the

reconstruction of volcanic forcing in ref.9. The time-series of volcanic aerosol optical

depth estimated in ref.9 was multiplied by –1 so that it has a sign consistent with that of

radiative forcing as in ref.17. The 0.05 significance levels (grey shading) were calculated

based on the adjusted degrees of freedom using the approach described in

Supplementary Methods.

36

Supplementary Fig. 18. As Supplementary Fig. 17, but for correlations between the

composite of NH temperatures and the external forcings. The composite of NH

temperatures (Supplementary Fig. 23a) was calculated using the 13 published NH

temperature reconstructions (Supplementary Table 4) by applying the approach

described in Supplementary Methods.

37

Supplementary Fig. 19. As Supplementary Fig. 17, but for correlations between the

composite of 22 temperature-sensitive tree-ring records and the external forcings. The

composite of tree-ring records (see Fig. 4a in main text) was calculated using 22 tree-

ring records (Supplementary Table 5) by applying the same approach as for the

composite of the NH temperature reconstructions.

38

Supplementary Fig. 20. Estimating the forced component of AMV by Multiple

Linear Regression (MLR) against external forcings. a. Comparison of our AMV

reconstruction (black) with the estimated AMV timeseries using different combinations

of solar and volcanic forcings. b. Comparison of our AMV reconstruction (black) with

the composite (red; origin, ±1 standard deviation) of four estimated AMV timeseries. c.

Same as a, but the anthropogenic CO2 concentration forcing24 was included in the MLR.

d. As b, but for comparison with the composite of four estimated AMV time-series

when the CO2 concentration forcing was included in the MLR. e. The internal

variability component of the AMV (which we define as the AMO), calculated as the

difference between the two timeseries in panel d. The MLR was performed using 30-

year low-pass filtered time-series and the related time-series had been lagged to obtain

the highest correlation (Supplementary Fig. 17). The regression equations are given in

panels a and c using these symbols: solar(St), solar forcing in Steinhilber et al.16;

solar(Am), solar forcing in Ammann et al.14; volcanic(Si), volcanic forcing in Sigl et

al.17; volcanic(Cr), volcanic forcing in Crowley and Unterman9.

39

Supplementary Fig. 21. Estimating the forced component of NH temperature by

Multiple Linear Regression (MLR) against external forcings. a. Comparison of the

composite of NH temperature reconstructions (black) with the estimated NH

temperatures using different combinations of forcing factors (solar, volcanic and CO2

concentration forcings). Other details are the same as Supplementary Fig. 20c. b.

Comparison of the composite of NH temperature reconstructions (black) with the

composite (red; origin, ±1 standard deviation) of four estimated timeseries. c. The

estimated internal variability component of NH temperature, calculated as the

difference between the two series in panel b.

40

Supplementary Fig. 22. As Supplementary Fig. 21, except that the composite of NH

temperature reconstructions was replaced by the composite of 22 tree-ring records.

41

Supplementary Fig. 23. Comparison of the AMV and AMO reconstructions with

a composite of Northern Hemisphere (NH) temperatures. The AMV reconstruction

(red) compared with a composite of 13 NH temperature reconstructions (black line,

composite mean; gray shading, composite mean ±1.0 standard deviation) on

timescales >30 years (a) and 30–90 years (b). c. and d. As a and b, respectively, except

the internal variability components (i.e., AMO and NH internal variability) were

calculated by subtracting our estimate of the externally-forced components from both

the reconstructed AMV and NH temperatures (Supplementary Figs. 20e, 21c). The

correlation coefficient and its significance level (using the effective degrees of freedom,

Neff) between the two compared time-series are indicated on the panel. See Fig. 4 in

main text for an additional comparison between the AMV and a composite of 22

temperature-sensitive tree-ring records, independent of the proxy dataset used in our

AMV reconstruction.

42

Supplementary Fig. 24. The 150-year running correlations between the

AMV/AMO and the NH temperature. The correlations were calculated using the two

timeseries in each panel of Supplementary Fig. 23. The positive correlation between

AMV/AMO and the NH temperature is relative robust over the past twelve centuries,

with only some slight interruptions in the early-11th, early-16th and late-18th centuries.

The strong correlations in the 12th, 15th and 17th centuries are comparable with that

for the last 150 years. Similar results were also obtained if using the composite of 22

tree-ring records instead of the composite of the NH temperature reconstructions

(Supplementary Fig. 25).

43

Supplementary Fig. 25. As Supplementary Fig. 24, but for correlations between the

AMV/AMO and the composite of 22 tree-ring records. The correlations were calculated

using the two timeseries in each panel of Fig. 4 in main text.

44

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