Proxy-based reconstructions of hemispheric

and global surface temperature variations

over the past two millennia

Michael E. Mann*†, Zhihua Zhang*, Malcolm K. Hughes‡, Raymond S. Bradley§, Sonya K. Miller*, Scott Rutherford¶,

and Fenbiao Ni‡

*Department of Meteorology and Earth and Environmental Systems Institute, Pennsylvania State University, University Park, PA 16802; ‡Laboratory of

Tree-Ring Research, University of Arizona, Tucson, AZ 85721; §Department of Geosciences, University of Massachusetts, Amherst, MA 01003-9298;

and ¶Department of Environmental Science, Roger Williams University, Bristol, RI 02809

Communicated by Lonnie G. Thompson, Ohio State University, Columbus, OH, June 26, 2008 (received for review November 20, 2007)

Following the suggestions of a recent National Research Council

report [NRC (National Research Council) (2006) Surface Temperature Reconstructions for the Last 2,000 Years (Natl Acad Press,

Washington, DC).], we reconstruct surface temperature at hemispheric and global scale for much of the last 2,000 years using a

greatly expanded set of proxy data for decadal-to-centennial

climate changes, recently updated instrumental data, and complementary methods that have been thoroughly tested and validated

with model simulation experiments. Our results extend previous

conclusions that recent Northern Hemisphere surface temperature

increases are likely anomalous in a long-term context. Recent

warmth appears anomalous for at least the past 1,300 years

whether or not tree-ring data are used. If tree-ring data are used,

the conclusion can be extended to at least the past 1,700 years, but

with additional strong caveats. The reconstructed amplitude of

change over past centuries is greater than hitherto reported, with

somewhat greater Medieval warmth in the Northern Hemisphere,

albeit still not reaching recent levels.

climate change  global warming

Knowledge of climate during past centuries can both improve

our understanding of natural climate variability and help

address the question of whether modern climate change is unprecedented in a long-term context (1, 2). The lack of widespread

instrumental climate records before the mid 19th century, however,

necessitates the use of natural climate archives or ‘‘proxy’’ data such

as tree-rings, corals, and ice cores and historical documentary

records to reconstruct climate in past centuries. Many previous

proxy data studies have emphasized hemispheric or global mean

temperature (3–14), although some studies have also attempted to

reconstruct the underlying spatial patterns of past surface temperature changes at global (15, 16) and regional (6, 17, 18) scales.

Most attempts to reconstruct hemispheric temperatures have

used some variant on the ‘‘composite plus scale’’ (CPS) methodology (10), in which proxy data (such as tree rings, ice cores, or

corals) considered to be sensitive to past surface temperature

variations are standardized and centered, potentially weighted, and

then composited to form a regional or hemispheric series. The

resulting series is then regressed or simply scaled against the target

instrumental series (e.g., the Northern Hemisphere mean annual

temperature series) to yield a reconstruction of hemispheric or

global mean temperature. Variants on this approach have used

proxies selected specifically for their retention of low-frequency

variability (9, 19) or have included low-resolution (decadal- or

centennial-scale) proxies that might be well suited to reconstructing

low-frequency climate variability (11) but which are consequently

difficult to calibrate robustly against the instrumental record (20).

More recently, Hegerl et al. (13) use a weighted composite of proxy

temperature series, but scaling is accomplished by a so-called

‘‘error-in-variables’’ (EIV) regression method (‘‘total least

squares’’) to allow for errors in both predictors (i.e., proxy composite) and predictand (i.e., the instrumental hemispheric mean

temperature series). Lee et al. (21) have recently compared a

number of variants on the CPS approach.

Distinct from the CPS methods are the so-called climate field

reconstruction (CFR) approaches, which instead assimilate proxy

records into reconstructions of the underlying spatial climate

patterns (15–18, 20, 22–26). Hemispheric or global means, as well

as particular indices of interest, can be computed directly from the

spatial pattern reconstructions. The CFR method offers the obvious advantage over the CPS method in that the spatial pattern of

changes are available, e.g., for comparisons with model-predicted

patterns of past climate change (27, 28). Most CFR methods make

use of nonlocal ‘‘reduced space’’ relationships between predictors

(e.g., sparse early instrumental measurements or longer-term proxy

climate data) and predictand (the full spatial field targeted for

reconstruction) through the use of large-scale covariance information (15, 17, 18, 29, 30). Such methods are useful in the context of

proxy-based climate reconstruction because they take advantage of

climate information embedded in remote proxies in the reconstruction of a continuous climate field. CFR approaches depend more

heavily on assumptions about the stationarity of relationships

between proxy indicators and large-scale climate patterns than do

simpler methods (e.g., CPS method) that are based on the assumption of local statistical relationships but make greater use of the

available statistical information. The two approaches are therefore

complementary.

If one replaces the spatial field in the CFR approach by a single

time series (e.g., hemispheric mean surface temperature), then the

approach reduces to an EIV variant on multivariate regression.

When a regularized (‘‘Reg’’) version of the expectationmaximization (EM) is used (RegEM, see ref. 31), the procedure has

the added benefit of providing an explicit regularization scheme to

protect against statistical overfitting. Previous tests with synthetic

proxy climate data derived from long model simulations demonstrate that this EIV procedure yields a very similar hemispheric

mean reconstruction to that obtained from the application of the

associated spatially-explicit CFR procedure when an estimate of

only a single time series, e.g., the hemispheric mean temperature,

is sought (32).

In this study, we employ a greatly expanded global multiproxy

database to develop hemispheric and global mean decadal surface

Author contributions: M.E.M., M.K.H., and R.S.B. designed research; Z.Z., S.K.M., S.R., and

F.N. performed research; M.E.M. analyzed data; and M.E.M., M.K.H., and R.S.B. wrote the

paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.

†To whom correspondence should be addressed. E-mail: mann@psu.edu.

This article contains supporting information online at www.pnas.org/cgi/content/full/

0805721105/DCSupplemental.

© 2008 by The National Academy of Sciences of the USA

13252–13257  PNAS  September 9, 2008  vol. 105  no. 36 www.pnas.orgcgidoi10.1073pnas.0805721105
temperature reconstructions for past centuries. We compare reconstructions based on the two distinct methods discussed above,

the CPS approach and the RegEM-based EIV estimation procedure. Both methods have been tested and validated with long-term

forced coupled model simulations (20, 32). For both methods, we

perform reconstructions both with and without dendroclimatic

proxies to address any potential sensitivity of our conclusions to

issues that have been raised with regard to the reliability of tree-ring

data on multicentury time scales (4, 11, 16, 19, 33, 34). For the CPS

approach, we employ only those proxies estimated to reflect local

temperature variations (based on a screening analysis over the

calibration interval using instrumental grid box surface temperature data). For the EIV approach, which does not require that proxy

data represent local temperature variations, results are compared

by using several alternative data-selection schemes, including one

that employs all available proxy records, another that employs only

proxy records contained within the target hemisphere, and another

that employs only the proxy data within that hemisphere that pass

the temperature-screening analysis mentioned above. Results for

all methods were compared by using both a ‘‘frozen’’ network (7–9,

13) consisting only of proxies available back to at least A.D. 1000

and a ‘‘stepwise’’ approach (15, 16) that makes use of the increasing

numbers of proxy data that become available as time progresses. All

reconstructions were validated against independent, withheld instrumental surface temperature data, and uncertainties were estimated from validation residuals. We were guided in this work by the

suggestions of a recent National Research Council report (35)

concerning an expanded dataset, updated data, complementary

strategies for analysis, and the use of thoroughly tested statistical

methods. All data used in this study and Matlab source codes for

implementing the algorithms described, as well as additional supporting information are available at www.meteo.psu.edu/mann/

supplements/MultiproxyMeans07.

Data

Proxy Data Network. We made use of a multiple proxy (‘‘multiproxy’’) database consisting of a diverse (1,209) set of annually

(1,158) and decadally (51) resolved proxy series [see supporting

information (SI) Table S1 and Dataset S1 for further details]

including tree-ring, marine sediment, speleothem, lacustrine, ice

core, coral, and historical documentary series. All 1,209 series were

available back to at least A.D. 1800, 460 extend back to A.D. 1600,

177 back to A.D. 1400, 59 back to A.D. 1000, 36 back to A.D. 500,

and 25 back to year ‘‘0’’ (i.e., 1 B.C.). Our proxy database represents

a significant extension of the database used in related earlier studies

(4, 15, 16). The proxy network covers a broad region of the globe,

including the tropics and extratropics, and terrestrial and ocean/

maritime regions, with coverage that gradually decreases back in

time (Fig. 1). The proxy data also reflect a broad range of seasonal

windows of climate sensitivity. Further details about the proxy

dataset are provided in SI Text and Figs. S1 and S2.

Reconstructions were performed based on both the ‘‘full’’ proxy

data network and on a ‘‘screened’’ network (Table S1) consisting of

only those proxies that pass a screening process for a local surfacetemperature signal. The screening process requires a statistically

significant (P 0.10) correlation with local instrumental surfacetemperature data during the calibration interval. Where the sign of

the correlation could a priori be specified (positive for tree-ring

data, ice-core oxygen isotopes, lake sediments, and historical documents, and negative for coral oxygen-isotope records), a one-sided

significance criterion was used. Otherwise, a two-sided significance

criterion was used. Further details of the screening procedure are

provided in SI Text.

The distribution of the ‘‘screened’’ proxy network for the full

interval 1850–1995 is shown in Fig. S1B. The rms local annual

temperature correlation of the full screened network isr  0.39 (r 

0.33) for predictors available back to A.D. 1800 (A.D. 1000). This

corresponds to signal-to-noise amplitude ratios (SNRs) of SNR 

0.43 and 0.35, respectively (see ref. 32). Of the 1,209 proxy records

in the full dataset, 484 (40%) pass the temperature-screening

process over the full (1850–1995) calibration interval (Fig. 1; see

also SI Text and Table S1).

Instrumental Data. We made use of the University of East Anglia

(Norwich, UK) Climatic Research Unit instrumental surface-air

temperature data from 1850 to 2006 (36) (www.cru.uea.ac.uk/cru/

data/temperature). We used both land-only and combined land and

ocean Northern Hemisphere (NH) and Southern Hemisphere (SH)

annual mean series as target series for reconstruction. In each case,

two different estimates of instrumental hemispheric means were

used: the nominal CRUTem3v land and HadCRUT3v landocean

hemispheric means (CRU and Had, respectively) and hemispheric

means calculated from spatially in-filled versions of the grid box

data (ICRU and Ihad, respectively). The global mean surface

temperature series was defined as the arithmetic mean of the

corresponding NH and SH series. A 1961–1990 reference period

was used for all series. Further details are provided in SI Text and

Fig. S3.

Results

Validation Exercises. We evaluated the fidelity of reconstructions

through validation experiments (see Methods), focusing here on NH

Fig. 1. Spatial distribution of proxy database (see SI Text for distribution of screened

network and other details). Nine different

proxy types are denoted with different symbols as shown in the map. Beginning dates of

proxy records are represented by color scale.

Mann et al. PNAS  September 9, 2008  vol. 105  no. 36  13253

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land temperature reconstructions (Fig. 2; see SI Text and Fig. S4 for

NH land plus ocean, SH, and global results). The CPS and EIV

methods (Dataset S2 and Dataset S3) are both observed to yield

reconstructions that, in general, agree with the withheld segment of

the instrumental record within estimated uncertainties based on

both the early (1850–1949) calibration/late (1950–1995) validation

and late (1896–1995) calibration/early (1850–1895) validation.

However, in the case of the early calibration/late validation CPS

reconstruction with the full screened network (Fig. 2A), we observed evidence for a systematic bias in the underestimation of

recent warming. This bias increases for earlier centuries where the

reconstruction is based on increasingly sparse networks of proxy

data. In this case, the observed warming rises above the error

bounds of the estimates during the 1980s decade, consistent with the

known ‘‘divergence problem’’ (e.g., ref. 37), wherein the temperature sensitivity of some temperature-sensitive tree-ring data appears to have declined in the most recent decades. Interestingly,

although the elimination of all tree-ring data from the proxy dataset

yields a substantially smaller divergence bias, it does not eliminate

the problem altogether (Fig. 2B). This latter finding suggests that

the divergence problem is not limited purely to tree-ring data, but

instead may extend to other proxy records. Interestingly, the

problem is greatly diminished (although not absent—particularly in

the older networks where a decline is observed after 1980) with

the EIV method, whether or not tree-ring data are used (Fig. 2 C

and D). We interpret this finding as consistent with the ability of the

EIV approach to make use of nonlocal and non-temperaturerelated proxy information in calibrating large-scale mean temperature changes, thereby avoiding reliance on pure temperature

proxies that may exhibit a low-biased sensitivity to recent temperature change.

1850 1875 1900 1925 1950 1975

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NH CPS Reconstructions vs CRU series

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Fig. 2. Comparison of CPS: hemisphere screened (A); ‘‘no dendro’’ (B); and EIV full global (C) and ‘‘no dendro’’ (D). NH reconstructions (colored curves; 95% confidence

intervals shown by lightly shaded regions of similar color) with decadally smoothed CRU NH land mean series (thick black curve). Reconstructions are shown over late

(A.D. 1950–1995) and early (A.D. 1850–1895) validation intervals corresponding to early (A.D. 1850–1949) and late (1896–1995) calibration experiments respectively.

RE validation scores are shown (Insets) as a function of the starting date of the network along with 90% and 95% significance levels based on Monte Carlo experiments.

Only reconstructions that passed validation are shown. Color bar indicates network starting dates.

13254  www.pnas.orgcgidoi10.1073pnas.0805721105 Mann et al.
The skill diagnostics (Fig. 2; see also Dataset S4) for the

validation experiments indicate that both the CPS reconstructions

(with the screened network) and EIV reconstruction (with the full

network) produce skillful NH land reconstructions back to A.D.

400. When tree-ring data are eliminated from the proxy data

network, a skillful reconstruction is possible only back to A.D. 1500

by using the CPS approach but is possible considerably further back,

to A.D. 1000, by using the EIV approach. We interpret this result

as a limitation of the CPS method in requiring local proxy temperature information, which becomes quite sparse in earlier centuries. This situation poses less of a challenge to the EIV approach,

which makes use of nonlocal statistical relationships, allowing

temperature changes over distant regions to be effectively represented through their covariance with climatic changes recorded by

the network.

A skillful EIV reconstruction without tree-ring data is possible

even further back, over at least the past 1,300 years, for NH

combined land plus ocean temperature (see SI Text). This achievement represents a significant development relative to earlier studies

with sparser proxy networks (4) where it was not possible to obtain

skillful long-term reconstructions without tree-ring data.

There are additional caveats for results based partly on tree rings

(see SI Text for details). The tree-ring series used before A.D. 1200

typically have median segment lengths between 500 and 700 years,

limiting the reliability of information on millennial time scales. Such

limitations could compromise the long-term trends in the reconstructions using these series. Interestingly, however, the long-term

(i.e., pre-A.D. 1000) behavior is largely unaffected by the removal

of tree-ring data, even though skillfulness in the reconstructions can

no longer then be inferred for earlier centuries: the long-term CPS

reconstruction is essentially unaffected back to A.D. 200, whereas

the EIV reconstruction indicates only modestly different (slightly

higher) temperatures before A.D. 600 (Fig. S7). Although this

observation may seem paradoxical, it is the greater spatial coverage,

rather than any additional low-frequency information, that leads to

the greater apparent fidelity in earlier centuries of reconstructions

employing tree-ring data. However, this increased fidelity is established primarily by relationships at decadal time scales, highlighting

the conundrum (38) that validations with modern instrumental

data are, by design, weighted toward evaluating the fidelity of

high-frequency information. Although loss of low-frequency information from tree-ring data thus does not appear to impact any of

the above conclusions, skillful reconstructions are not possible for

the earlier centuries without the spatial coverage provided by these

data.

NH Temperature Reconstructions. Although the details of the reconstructions produced for a given method and target (e.g., CPS NH

land) showed some sensitivity to which proxy data sets are used, and

precisely which instrumental series is used (e.g., CRU vs. ICRU),

all of the individual reconstructions that pass validation fall within

the uncertainties of the composite reconstruction, defined as the

average of all individual reconstructions that pass validation. In

other words, the various reconstructions are consistent within

uncertainties. This also holds true for reconstructions resulting

from the early and late calibration intervals used in validation

experiments (see SI Text and Figs. S7–S11).

Nominally, the recent observed decadal warmth recorded in the

instrumental observations exceeds the uncertainty range of the

reconstructions over at least the past 1,600 years for NH land

temperatures as reconstructed by CPS (Fig. S5) and the past 1,700

years for NH land plus ocean temperatures as reconstructed by EIV

(Fig. S6). Because this conclusion extends to the past 1,300 years for

EIV reconstructions withholding all tree-ring data, and because

non-tree-ring proxy records are generally treated in the literature as

being free of limitations in recording millennial scale variability

(11), the conclusion that recent NH warmth likely** exceeds that

of at least the past 1,300 years thus appears reasonably robust. For

the CPS (EIV) reconstructions, the instrumental warmth breaches

the upper 95% confidence limits of the reconstructions beginning

with the decade centered at 1997 (2001). It is intriguing to note that

the removal of tree-ring data from the proxy dataset yields less,

rather than greater, peak cooling during the 16th–19th centuries for

both CPS and EIV methods (see Figs. S5a and S6b, respectively),

contradicting the claim (33) that tree-ring data are prone to yielding

a warm-biased ‘‘Little Ice Age’’ relative to reconstructions using

other high-resolution climate proxy indicators.

We compared the composite CPS and EIV NH mean reconstructions (Fig. 3; see also Figs. S15 and S16) with both each other

and with other previously published NH reconstructions based on

various combinations of proxy data and differing statistical approaches (4, 6–9, 11, 12, 19, 39–41). This comparison demonstrates

rather striking agreement between alternative estimates over the

past four centuries, all of which fall well within the estimated

uncertainty range, with one exception: the borehole estimate from

Huang et al., (39) which is significantly cooler through A.D. 1800.

Back to A.D. 1000, the reconstructions all agree within uncertainties with three exceptions: the Moberg et al. (11) reconstruction is

cooler over the interval A.D. 1500–1600, the Esper et al. (19)

reconstruction is cooler over A.D. 1050–1300, and the Huang et al.

(39) estimate is significantly cooler over the period A.D. 1500–1800.

Peak Medieval warmth (from roughly A.D. 950-1100) is more

pronounced in the EIV reconstructions (particularly for the landonly reconstruction) than in the CPS reconstructions (Fig. 3). The

EIV land-only reconstruction, in fact, indicates markedly more

sustained periods of warmer NH land temperatures from A.D. 700

to the mid-fifteenth century than previous published reconstructions. Peak multidecadal warmth centered at A.D. 960 (representing average conditions over A.D. 940–980) in this case corresponds

approximately to 1980 levels (representing average conditions over

1960–2000). However, as noted earlier, the most recent decadal

warmth exceeds the peak reconstructed decadal warmth, taking

into account the uncertainties in the reconstructions.

Although the EIV and CPS reconstructions essentially agree

within uncertainties back to A.D. 1000 (Fig. 3B), there are nonetheless some significant systematic differences in the implied longterm temperature histories over that time frame. The EIV reconstructions suggest that temperatures were relatively warm

(comparable with the mean over the 1961–1990 reference period

but below the levels of the past decade) from A.D. 1000 through the

early 15th century, then fell abruptly. By contrast, the CPS reconstructions indicate more uniformly colder conditions, with peak

Medieval warmth that does not breach the mean warmth of modern

reference period (1961–1990), and a long-term, more steady decline

in temperatures before 20th century warming. We could arguably

take these two reconstructions as end members that bracket the

possible range for peak NH mean Medieval warmth, lying somewhere between 0.4°C colder and and 0.4°C warmer than the modern

reference period (1961–1990) mean, but still exceeded by the most

recent decadal warming.

Before A.D. 1000, there is somewhat less agreement between the

various reconstructions. In particular, reconstructions based on

variants of the CPS method tend to be significantly cooler than (and

outside the uncertainties of) the EIV reconstruction. Investigating

the sources of these differences, we first established that the

removal of the seven proxy series in our database identified a priori

as having potentially spurious features, has no significant impact on



Here and elsewhere in the paper, ‘‘recent’’ is taken to correspond to the past decade unless

noted otherwise.

**For the purpose of this paper, we adopt the definition of ‘‘likely’’ used by the Intergovernmental Panel on Climate Change (IPCC): i.e., that the probability of the assertion

being true is estimated as between 66% and 90%.

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the CPS (or EIV) reconstructions (SI Text and Fig. S8). However,

we observed that the pronounced cooling between approximately

A.D. 750 and A.D. 1000 in the current CPS reconstruction is based

on prominent excursions in a relatively small number (see Fig. S9)

of the 15 NH proxy series available in the screened network back

through the 9th century and that the amplitude of the cooling is

somewhat sensitive to the removal of individual proxy records (see

Fig. S10). Analysis of synthetic ‘‘pseudoproxy’’ proxy networks (SI

Text, Figs. S12–S14, and Tables S2–S4) indicates that such apparent

pronounced hemispheric temperature anomalies in the reconstructions can arise as purely spurious features with the CPS approach,

given such sparse networks, an artifact of the statistics of averaging

a small number of noisy local temperature estimates. By contrast,

we find in these experiments that the EIV reconstructions are

significantly more skillful, given a particular synthetic data network.

Where the two methods no longer yield reconstructions that agree

within uncertainties, it is therefore likely that the EIV reconstruction is the more reliable, although with the caveat that this finding

has been demonstrated only under the assumptions implicit in the

pseudoproxy analyses (e.g., that proxies have a linear, if noisy,

relationship with local temperature variations). For this reason, we

place greatest confidence in the EIV reconstructions, particularly

back to A.D. 700, when a skillful reconstruction as noted earlier is

possible without using tree-ring data at all.

SH and Global Temperature Reconstructions. Conclusions for SH

mean temperatures are somewhat weaker (Figs. S5 and S6), plausibly due to the relative paucity of proxy data in the SH (Fig. 1).

Nominally, recent warmth appears anomalous in the context of the

past 1,500 years from the CPS reconstructions, but skillful CPS

reconstructions are not possible without tree-ring data before A.D.

1700, implying additional caveats as discussed above. Recent

warmth exceeds that reconstructed for at least the past 1,800 years

in the EIV reconstructions, and this conclusion extends back at

least 1,500 years without using tree-ring data. However, the estimated uncertainties are compatible with the possibility that recent

SH warmth might have been breached during brief periods in the

past. Similarly, for global mean temperature, the CPS reconstruction suggests that recent warmth is anomalous for at least the past

1,500 years, but with the caveat that tree-ring data are required for

a skillful long-term reconstruction. The EIV reconstruction indicates recent warmth that exceeds the reconstructed warmth (past

1,500 years with caveats related to the use of tree-ring data, and the

past 1,300 years if tree-ring data are excluded), but like the SH, the

uncertainties are compatible with the possibility of brief periods of

similar warmth over the past 1,500 years. More confident statements about long-term temperature variations in the SH and globe

on the whole must await additional proxy data collection.

Conclusions

We find that the hemispheric-scale warmth of the past decade for

the NH is likely anomalous in the context of not just the past

1,000 years, as suggested in previous work, but longer. This

conclusion appears to hold for at least the past 1,300 years

200 400 600 800 1000 1200 1400 1600 1800 2000

0

Northern Hemisphere

Temperature Anomaly ( C)

CPS land with uncertainties

EIV land with uncertainties

EIV land+ocn with uncertainties

Mann and Jones (2003)

Esper et al. (2002)

Moberg et al. (2005)

CRU Instrumental Record

HAD Instrumental Record

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

0

Temperature Anomaly ( C)

CPS land with uncertainties

EIV land with uncertainties

EIV land+ocn with uncertainties

Mann and Jones (2003)

Esper et al. (2002)

Moberg et al. (2005)

CRU Instrumental Record

HAD Instrumental Record

CPS land+ocn with uncertainties

Briffa et al. (2001)

Crowley and Lowery (2000)

Mann et al. (1999)

Jones et al. (1998)

Oerlemans (2005)

Huang et al. (2000) Borehole

Mann et al. (2003) Optimal Borehole

Fig. 3. Composite CPS and EIV NH land and land plus ocean temperature reconstructions and estimated 95% confidence intervals. Shown for comparison are

published NH reconstructions, centered to have the same mean as the overlapping segment of the CRU instrumental NH land surface temperature record

1850–2006 that, with the exception of the borehole-based reconstructions, have been scaled to have the same decadal variance as the CRU series during the

overlap interval (alternative scaling approaches for attempting to match the amplitude of signal in the reconstructed and instrumental series are examined in

SI Text). All series have been smoothed with a 40-year low-pass filter as in ref 33. Confidence intervals have been reduced to account for smoothing.

13256  www.pnas.orgcgidoi10.1073pnas.0805721105 Mann et al.
(consistent with the recent assessment by ref. 2) from reconstructions that do not use tree-ring proxies, and are therefore not

subject to the associated additional caveats. This conclusion can

be extended back to at least the past 1,700 years if tree-ring data

are used, but with the additional strong caveats noted. When

differences in scaling between previous studies are accounted

for, the various current and previous estimates of NH mean

surface temperature are largely consistent within uncertainties,

despite the differences in methodology and mix of proxy data

back to approximately A.D. 1000. The reconstructions appear

increasingly more sensitive to method and data quality and

quantity before A.D. 1600 and, particularly, before approximately A.D. 1000. Conclusions are less definitive for the SH and

globe, which we attribute to larger uncertainties arising from the

sparser available proxy data in the SH. Given the uncertainties,

the SH and global reconstructions are compatible with the

possibility of warmth similar to the most recent decade during

brief intervals of the past 1,500 years. A targeted effort to

recover additional high-quality, long paleoclimate proxy records

from the SH could reduce these current existing uncertainties.

Similarly, reducing uncertainties for the period before A.D. 1000

for the NH will require additional proxy records of sufficient

length that preserve climate signal on the millennial time scale.

Methods

Detailed descriptions of the CPS and EIV procedures are provided in SI Text.

Reconstructions were based on calibration over the full 146-year interval

1850–1995. Statistical validation was achieved by using a split calibration/

verification procedure wherein data were calibrated alternatively on both the

most recent (1896–1995) and oldest (1850–1949) 100-year subintervals,

whereas the remaining 46 years were used to validate the reconstruction.

Results from the early and late validation experiments were then averaged for

the purpose of estimating skill metrics and uncertainties. So-called ‘‘reduction

of error’’ (RE) and ‘‘coefficient of efficiency’’ (CE) skill scores for the decadal

reconstructions were used as metrics of validation skill as in past work (20, 32).

Because of its established deficiencies as a diagnostic of reconstruction skill

(32, 42), the squared correlation coefficientr2 was not used for skill evaluation.

Statistical significance of RE and CE scores were estimated by Monte Carlo

simulations based on the null hypothesis of first-order autoregressive ‘‘red

noise’’ (20, 32). Only those reconstructions that passed validation at the P 

0.05 (i.e., 95% significance) level based on both metrics were retained. Uncertainties were estimated from the residual decadal variance during the

validation period based (32, 42) on the average validation period r2 (which in

this context has the useful property that, unlike RE and CE, it is bounded by 0

and 1 and can therefore be used to define a ‘‘fraction’’ of unresolved variance). Although use of validation residuals for uncertainty estimation avoids

the potential overfit bias associated with use of calibration residuals, an

important caveat nonetheless remains that such statistical uncertainty estimates do not account for the possible degradation in the proxy record before

the validation interval, which is potentially an issue in earlier centuries in

particular.

ACKNOWLEDGMENTS. We are indebted to G. North and G. Hegerl for their

valuable insight, suggestions, and comments and to L. Thompson for presiding

over the review process for this paper. M.E.M. and Z.Z. gratefully acknowledge

support from the Atmospheric Sciences program of the National Science Foundation (Grant ATM-0542356). R.S.B. acknowledges support from the Office of

Science (Biological and Environmental Research), U.S. Department of Energy,

Grant No. DE-FG02-98ER62604. M.K.H. and F.N. were supported by National

Oceanic and Atmospheric Administration Grant NA16GP2914 from Climate

Change Data and Detection.

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