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\title{
GLOBAL-SCALE TEMPERATURE PATTERNS AND CLIMATE FORCING OVER THE PAST SIX 
CENTURIES}
\author{Michael E. Mann \& Raymond S. Bradley, \\
        Department of Geosciences,\\
        University of Massachusetts\\
        \\
        Malcolm K. Hughes,\\
        Laboratory of Tree Ring Research,\\
        University of Arizona,\\
         {to appear in \em Nature}}
\date{}
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%\noindent

{\bf
Reconstructions of annual global surface temperature patterns
over several centuries are now possible,
based on the 
multivariate calibration
of widely distributed high-resolution proxy climate indicators.
These reconstructions provide insight into both the spatial
and temporal nature of climatic variations during the
past six centuries.
Time-dependent correlations of these temperature reconstructions with time 
series 
representing
greenhouse gases, solar irradiance, and volcanic aerosols,
suggest that each of these forcings has played a role in 
the climatic variability 
of the past several centuries, with
greenhouse gases appearing to emerge as the dominant
forcing during the 20th
century. Northern
hemisphere mean annual temperatures for three of the past eight years
are warmer than any other year since (at least) 1400 AD, at
a greater than 99.5\% level of confidence.
}

Knowing both the spatial and temporal patterns of climatic
change over the past several centuries remains a key
to assessing a possible anthropogenic impact
on post-industrial climate$^1$. In addition to the possibility
of warming due to enhanced
greenhouse gases during the past century, there is evidence
that both solar irradiance and explosive volcanism have played
an important
part in forcing climate variations over the past several 
centuries$^{2,3}$.
The unforced ``natural variability'' of the climate
system may also be quite important on multidecadal and century 
timescales$^{4,5}$.
If a faithful empirical 
description of climate variability
can be obtained for the past several centuries, a more confident
estimation can be made of the roles of
different external
forcings and internal sources of variability on past and recent climate.
Because widespread
instrumental climate data are available for only about one century,
we must use proxy climate indicators combined with any
very 
long instrumental records that are available
to obtain such an empirical description of large-scale climate variability 
during
past centuries.
A variety of studies have sought to employ a ``multiproxy''
approach to study long-term climatic variations, in which a 
widely-distributed set 
of proxy  and instrumental
climate indicators are analyzed$^{1,5-8}$ to yield insights into
long-term global climatic variations.
Building on such past studies, we take a new 
statistical approach to reconstructing global patterns of annual
temperature back through the 15th century, based on
the calibration of multiproxy
data networks by
the dominant patterns of temperature variability
in the instrumental record. 

Using these statistically-verifiable yearly 
global temperature reconstructions,
we analyze the
spatiotemporal patterns of climatic change over the past
half-millenium, and then
take an empirical approach
to estimating the relationship between global temperature changes,
variations
in volcanic aerosols, solar irradiance, and greenhouse
gas concentrations during the same period.

\section*{\bf Data}

We employ a multiproxy network consisting of 
widely distributed high-quality annual resolution proxy climate
indicators individually collected and formerly analyzed
by many
paleoclimate researchers (details and references are
available; see 
Supplementary information).
The network includes (see Figure 1a) the collection of annual resolution
dendroclimatic, ice core, ice melt, and long historical 
records
used by Bradley and Jones$^6$ combined with other
coral, ice core,
dendroclimatic,
and long instrumental records. 
The long instrumental records have been 
formed into annual mean anomalies relative to the 1902-1980 
reference period,
and gridded onto a 5 degree by 5 degree grid (yielding 11 temperature
gridpoint series and 12 precipitation gridpoint series dating back to
1820 or earlier) similar to that
shown in Figure 1 (bottom).
Certain densely
sampled regional dendroclimatic datasets have been represented
in the network by a smaller number of leading principal components
(typically 3-11 depending
on the spatial extent and size of the dataset). This form of representation 
insures a reasonably homogeneous spatial sampling in the
multiproxy network (112 indicators back to 1820).

Potential limitations
specific to each type of proxy data series must be carefully
taken into account 
in building an appropriate network. 
Dating errors in a 
given record (e.g., incorrectly assigned annual layers or rings)
are particularly detrimental if mutual information is sought to
describe climate patterns on a year-by-year basis.
Standardization of certain biological proxy records relative to 
estimated growth trends, and the limits
of constituent chronology segment lengths,
(e.g. in dendroclimatic reconstructions) can restrict
the maximum timescale of climatic variability that
is recorded$^9$.
However, the dendroclimatic data used
were carefully screened for conservative standardization
and sizeable segment
lengths.
Moreover, the mutual information
contained in a diverse and widely distributed set of independent climatic
indicators can more faithfully capture the consistent 
climate signal that is present, reducing
the compromising effects of
biases and weaknesses in the individual indicators.

Monthly instrumental land air and sea surface temperature$^{10}$ gridpoint data 
(Figure 1--bottom) from the period 1902-1995 are used
to calibrate the proxy dataset.
Although there are notable spatial gaps, this network
covers significant enough portions of the globe to form
reliable estimates of Northern Hemisphere (``NH'') mean temperature,
and certain regional indices of particular importance such as
the ``NINO3'' eastern tropical Pacific surface temperature index
often used to describe the El Ni\~{n}o phenomenon.
The NINO3 eastern equatorial Pacific sea 
surface temperature index is constructed from the
8 gridpoints available within the conventional NINO3 box shown
between 5S to 5N, 90W to 150W.

\section*{\bf Multiproxy Calibration}

While studies have demonstrated that well-chosen regional paleoclimatic
reconstructions can act as surprisingly representative surrogates
for large-scale climate$^{11-13}$,
multiproxy networks nonetheless,
appear to provide the
greatest opportunity for large-scale paleoclimate 
reconstruction$^6$
and climate signal detection$^{5,1}$.
There is a rich tradition of 
multivariate statistical calibration approaches to 
paleoclimate reconstruction,
particularly in the field of dendroclimatology where
the relative strengths and weaknesses of 
various approaches to multivariate calibration have been 
well-studied$^{14,15}$. 
Such approaches have been
applied to 
regional dendroclimatic networks to
reconstruct regional patterns of
temperature$^{16,17}$ and atmospheric circulation$^{18-20}$
or specific climate phenomena such as the Southern Oscillation$^{21}$.
Largely because of the inhomogeneity of the information
represented by different types of indicators in a true ``multiproxy'' network, 
we found conventional approaches (e.g.
Canonical
Correlation Analysis or ``CCA'' of the proxy and instrumental datasets) to be
relatively ineffective.
Our approach to climate
pattern reconstruction
relates closely to
statistical approaches which have recently been
applied to the problem of filling in sparse
early instrumental climate fields, based on calibration
of the sparse sub-networks against
the more widespread patterns of variability
that can be resolved in shorter
datasets$^{22,23}$.
We first decompose the 20th century instrumental
data into its dominant patterns of variability,
and subsequently calibrate the individual
climate proxy indicators against the time
histories of these distinct patterns during their mutual
interval
of overlap. One can think of the instrumental patterns as
``training'' templates against which we calibrate or ``train'' the much longer proxy data 
(i.e., the ``trainee'' data) during the shorter calibration period 
which they overlap.
This calibration allows us to subsequently solve
an ``inverse problem'' whereby
best estimates of surface temperature patterns are deduced back in time before
the calibration period, from the
multiproxy network alone. 

Implicit in our approach are at least three fundamental
assumptions. We assume (1) that the indicators in our
multiproxy trainee network are linearly related to one
or more of the instrumental training patterns. In
the relatively unlikely event that a proxy indicator
represents a truly local climatic phenomenon which
is uncorrelated with larger-scale climatic variations,
or represents a highly non-linear response to climatic
variations,
this assumption will not be satisfied.
We further assume (2) that
a relatively sparse but widely distributed sampling 
of long proxy and instrumental
records may nonetheless sample most
of the relatively small number of 
degrees of freedom in climatic patterns at
interannual and longer timescales. Regions not
directly represented in the trainee network may
nonetheless be indirectly represented  through
teleconnections with regions that are.
The  El Ni\~{n}o-Southern Oscillation (ENSO),
for example, exhibits global-scale patterns of
climatic influence$^{24}$, and is an example of a
prominent pattern of variability which, if captured,
can potentially describe variability in regions not
directly sampled by the trainee data. 
Finally, we assume (3) that
that the patterns of variability captured by
the multiproxy network have analogues in the patterns
we resolve in the shorter instrumental data.
This latter assumption represents a fairly weak
``stationarity'' requirement--we don't require that
the climate itself be stationary. In fact, we expect that
some sizeable trends in the climate may be resolved by
our reconstructions.
We do, however, assume that the fundamental {\em spatial patterns} of
variation which the climate has exhibited during the past 
century
are similar to those by which it has varied during past recent centuries.
Studies of instrumental
surface temperature patterns suggest that such a form
of stationarity holds
up at least on multidecadal timescales, during the 
past century$^{23}$. 
The statistical cross-validation exercises we describe later
provide the best evidence 
that these key underlying assumptions hold.

We isolate the dominant patterns of the
instrumental surface temperature data
through principal component analysis$^{25}$ (PCA).
PCA provides
a natural smoothing of the temperature field in
terms of a small number of dominant patterns of variability
or ``empirical eigenvectors''.
Each of these eigenvectors
is associated with a characteristic spatial pattern or 
``Empirical Orthogonal Function'' (EOF) and
its characteristic evolution in time or ``Principal Component'' (PC).
The ranking of the eigenvectors orders the fraction of variance they 
describe in the (standardized) multivariate data during the calibration period.
The first 5 of these eigenvectors describe a fraction
$\beta=0.93$ (ie, 93\%) of the
of the global-mean (``GLB''), temperature variations, 85\% of
the northern hemisphere-mean (``NH'') variations, 
67\% of the NINO3 index, and
76\% of the non trend-related (``DETR'') NH variance
(see ``Methods--statistics'' section
for a description of the $\beta$ statistic used here as a measure
of resolved variance).
A sizeable fraction of the total multivariate 
spatiotemporal variance (``MULT'') in the raw (instrumental)
data (27\%) is
described by these 5 eigenvectors, or about 30\% of the
standardized variance
(1=12\%, 2=6.5\%, 3=5\%, 4=4\%, 5=3.5\%).
Figure 2 shows the 
EOFS of the first 5 eigenvectors.
The associated time histories of these patterns
(PCs) and their reconstructed
counterparts (``RPC''s) are discussed in the next section.
The first eigenvector, associated with the 
significant global warming trend of the 
past century, describes much
of the variability in the global (GLB=88\%) and hemispheric (NH=73\%) means.
Subsequent eigenvectors, in contrast, describe much of the spatial variability
relative to the large-scale means (ie, much of the remaining multivariate
variance ``MULT'').
The second eigenvector is the dominant 
ENSO-related component, describing 41\% of
the variance in the NINO3 index. This eigenvector
exhibits a modest
negative trend which, in the eastern tropical Pacific,
describes a ``La Ni\~{n}a''-like cooling trend$^{26}$, which
opposes warming in the same region
associated with the global warming pattern of the first eigenvector.
The third eigenvector is associated largely with interannual-to-decadal scale 
variability in the Atlantic basin and carries the well known temperature 
signature of the North Atlantic Oscillation (NAO)$^{27}$ and decadal tropical
Atlantic dipole$^{28}$.
The fourth eigenvector describes a primarily multidecadal timescale variation with ENSO-scale
and tropical/subtropical Atlantic features,
while the fifth eigenvector
is dominated by multidecadal variability in the entire Atlantic basin and 
neighboring regions that has been widely noted elsewhere$^{29-34}$. 

We calibrate each of the indicators in the multiproxy data network
against these empirical 
eigenvectors  at annual mean resolution during the
1902-1980 training interval.
While the seasonality of variability is potentially
important--
many extratropical proxy indicators for example reflect
primarily warm-season variability$^{6,7}$--we seek
in the present study to resolve only annual mean conditions,
exploiting the seasonal climatic persistence, and
the fact that the mutual information from data reflecting various
seasonal windows should provide complementary information
regarding annual mean climatic conditions$^{10}$.
Following this calibration, we apply an overdetermined optimization procedure 
to determine the best combination of eigenvectors represented by the multiproxy
network back in time on a year-by-
year basis, with
a spatial coverage dictated only by the spatial extent
of the instrumental training data. From the reconstructed
PCs or ``RPC''s, spatial patterns and all relevant averages or indices can be 
readily determined.
The details of the entire statistical
approach are described
in the
 ``Methods--calibration'' section.

The skill of the temperature reconstructions (ie,
their statistical validity) back in time
is established through a variety of complimentary
independent cross-validation or
``verification'' exercises (see ``Methods--verification'' below).
We summarize the key results of these experiments below (a Table detailing the 
quantitative results of the calibration and verification procedures is provided 
in {\em Natures's} on-line supplementary
information):

1) In the reconstructions from 1820 onward based on the full multiproxy network 
of 112 indicators, 11 eigenvectors are skillfully resolved (\# 1-5,7,9,11,14-16)
describing  ($\sim$70-80\% of the variance in
NH and
GLB mean series in both calibration and verification (verification
is based here on the independent 1854-1901 dataset which was
witheld, as described in the 
``Methods--verification'' section).
Figure 3
shows the spatial patterns of calibration $\beta$,
and verification $\beta$ and the squared correlation
statistic $r^2$, demonstrating highly significant 
reconstructive
skill over widespread regions of the reconstructed spatial domain.
30\% of the full spatiotemporal variance in the
gridded dataset is captured in calibration, and 22\% of the
variance is verified in cross-validation. Some of the degradation
in the verification score relative to the calibration score may reflect the 
decrease in instrumental data quality
in many regions before the 20th century rather than a true decrease in resolved 
variance.
These scores thus compare favorably to the 40\% total
spatiotemporal variance that is described by simply filtering
the raw 1902-1980 instrumental data 
with 11 eigenvectors used in calibration, suggesting
that the multiproxy calibrations are describing a level
of variance in the data reasonably 
close to the optimal ``target'' value. While a verification NINO3
index is not available from 1854-1901, correlation of the reconstructed NINO3 
index with the available Southern
Oscillation index (SOI) data from 1865-1901 of $r=-0.38$ ($r^2=0.14$) compares 
reasonably with its target value given by the correlation between the actual 
instrumental NINO3 and SOI index from 1902-1980 ($r=-0.72$). 
Furthermore, the correspondence 
between the reconstructed NINO3 index warm events and Quinn and Neal's$^{35}$ historical
El Ni\~{n}o 
chronology back to 1820 (see ``Methods--verification'') is 
significant at the 98\% level.

2)The calibrations back to 1760 based on 93 indicators,
continue to resolve at least 9
eigenvectors (1-5,7,9,11,15) with no degradation of calibration or verification 
resolved variance in NH, and only slight degradation in MULT (calibration 
$\sim$27\%, verification $\sim$17\%). Our reconstructions are thus largely 
indistinguishable in skill back to 1760.

3)The network available back to 1700 of 74 indicators (including only 2 
instrumental or historical indicators) skillfully resolves 5 eigenvectors 
(1,2,5,11,15) and shows some significant signs of decrease in
reconstructive skill. In this case, about 60-70\% of NH variance is resolved
in calibration and verification, and about 14-18\% of MULT in calibration,
and 10-12\% of MULT in verification.  The verification $r$ of NINO3 with
the SOI is in the range of $r \sim$-0.25 to -0.35, which is statistically 
significant (as is the correspondence with the Quinn historical chronology back 
to 1700) but notably inferior to the later calibrations. In short, both spatial
patterns and large-scale means are skillfully resolved, but with significantly
less resolved variance than in later calibrations.

4)The network of 57 indicators back to 1600 (including 1 historical record) 
skillfully resolves 4 eigenvectors (1,2,11,15). 67\% of NH is resolved in
calibration, and 53\% in verification. 14\% of MULT is resolved in calibration,
and 12\% of MULT in verification. A significant, but modest level of 
NINO3-scale 
variability is resolved in the calibrations.

5) The network of 24 proxy indicators back to 1450 resolves 2 eigenvectors (1,2) 
and $\sim$40-50\% of NH in calibration and verification. Only $\sim$10\% of MULT 
is resolved in calibration and $\sim$5\% in verification. There is no skillful 
reconstruction
of ENSO-scale variability. Thus spatial reconstructions are of marginal 
usefulness this far back, though the largest-scale quantities are still 
skillfully resolved.

6) The multiproxy network of 22 indicators available back to 1400 resolves only 
the first eigenvector, associated with 40-50\% of resolved variance in NH in
calibration and verification. There is no useful resolution of spatial patterns
of variability this far back. The sparser networks available before 1400
show little evidence of skill in reconstructing even the first eigenvector,
terminating useful reconstruction at the initial year 1400 AD.

7) Experiments using trainee networks 
containing only proxy
(i.e., no instrumental or historical) indicators
establish the most truly independent cross-validation of the reconstruction
since there
is in this case neither spatial nor temporal dependence
between the calibration and verification datasets. Such statistically
significant verification is demonstrated at the gridpoint level (
calibration and verification resolved variance$\sim$15\%
for the ``MULT'' statistic),
at the largest scales (calibration and verification resolved variance $\sim$60-65\% for
NH) and the ENSO-scale (90-95\% statistical
significance for all verification diagnostics).
In contrast, networks containing only the 24
long historical or instrumental records available back to 1820
resolve only $\sim$30\% of NH
in calibration or verification, and the modest multivariate calibration and
verification resolved variance scores of MULT ($\sim$10\%) are artificially inflated
by the high degree of spatial correlation between the
instrumental ``multiproxy'' predictor and instrumental predictand data. 
No evidence of skillful ENSO-scale reconstruction
is evident in these latter reconstructions. 
In short, the inclusion of the proxy
data in the ``multiproxy'' network is essential for the most skillful reconstructions.
Certain sub-components
of the proxy dataset however
(e.g., the dendroclimatic indicators)
appear to be especially important
in resolving the large-scale temperature patterns, with notable 
decreases in the NH scores 
obtained if all dendroclimatic indicators
are witheld from the multiproxy network. On the other hand, 
the long-term trend in NH is relatively robust to the inclusion
of dendroclimatic
indicators in the network, suggesting that potential tree growth
trend biases are not influential in 
multiproxy pattern reconstructions.
The network of all combined proxy and long instrumental/historical indicators provide the
greatest cross-validated estimates of skillful reconstruction, and are used in obtaining
the reconstructions described below.

\section*{\bf Temperature Reconstructions}

The reconstructions henceforth discussed are derived using all indicators available,
and using the
optimal eigenvector subsets determined in the calibration experiments
described above (11 from 1780-1980, 9 from 1760-1779, 8 from 1750-1759, 5 from 1700-1749,
4 from 1600-1699, 2 from 1450-1599, 1 from 1400-1449).
To better illustrate the workings
and effectiveness of
the proxy pattern reconstruction procedure,
we show as an example (Figure 4) the actual, EOF-filtered, and reconstructed
temperature patterns for a year (1941) during the calibration interval. This
year is a known ENSO year, associated with a warm eastern tropical Pacific, 
and a cold central
North Pacific. Pronounced cold anomalies are also found over large-parts of Eurasia.
The proxy-reconstructed pattern captures these features, although in a relatively 
smoothed
sense (describing about 30\% of the full variance in
that pattern), and is remarkably similar to the raw data once it has been filtered by retaining
only the 11 eigenvectors 
(\#s 1-5,7,9,11,14-16) 
used in pattern reconstruction. It is thus visually apparent
that the multiproxy network is quite capable of
resolving much of the structure resolved
by the eigenvectors retained in the calibration process.

It is interesting to consider the temporal variations
in the first 5 reconstructed PCs (Figure 5a).
The positive trend in RPC \#1 during the 20th century is clearly
exceptional in the context of the long-term variability
in the associated eigenvector, and indeed describes much of the
unprecedented warming trend evident in the NH reconstruction.
Equally interesting is the negative trend in RPC \# 2 during
the past century which is also anomalous in the context
of the longer-term evolution of the associated eigenvector.
The recent negative trend is associated with
a pattern of cooling 
in the eastern tropical Pacific (superimposed on warming
associated with the pattern of eigenvector \#1) which may be a modulating
negative feedback on global warming$^{26}$.
RPC \#5 exhibits notable multidecadal
variability throughout both the modern and pre-calibration
interval,
associated with the wavelike trend
of warming and subsequent cooling of the North
Atlantic this century discussed
earlier$^{29-33}$ and the longer-term multidecadal oscillations
in that region detected in a previous analysis of proxy climate
networks$^5$.
This variability may be associated with
ocean-atmosphere processes related to the North Atlantic thermohaline
circulation$^{34,4}$.

The long-term trends in the reconstructed annual mean NH series (Figure 5b)
are quite similar to those of the decadal Northern Hemisphere summer temperature
reconstructions of Bradley and Jones$^6$,
exhibiting pronounced cold periods during the mid 17th and 19th centuries, and
somewhat warmer intervals during the mid 16th and late 18th centuries,
with almost all years prior to the 20th century well below the
20th century climatological mean. 
Taking into account the
uncertainties in our NH reconstruction (see ``Methods--calibration''),
it appears that the years 1990, 1995 and now 1997 (this value recently
calculated and not shown) each exhibit anomalies that
are greater than any other year back to 1400 at 3 standard errors, or, roughly a 
99.7\%
level of certainty.
It should be kept in mind that hemispheric mean values
are
not associated with globally or hemispherically uniform trends.
An example of the global pattern
for an historically documented$^{35}$ ``very strong''  El Ni\~{n}o year (1791)
is shown in Figure 6a demonstrating the classic warm eastern tropical 
Pacific and cold central North Pacific
SST patterns.
Analysis of ENSO variability in these reconstructions is discussed
in more detail elsewhere$^{36}$.
The reconstructed pattern for 1816 is also shown (Figure 6b) exhibiting 
quite anomalous cold
throughout much of the northern hemisphere
(even relative to this generally cold decade) but 
with a quadrapole pattern of warmth near Newfoundland and the
Near East, and enhanced cold
in the eastern United States and Europe
consistent with  the anomalous atmospheric
circulation associated with the
North Atlantic Oscillation (NAO) pattern. Such a pattern is indeed observed in 
empirical$^{37}$
and model-based studies$^{38}$ of the atmospheric response to
volcanic forcing. We infer in the 1816 temperature pattern
a climatic
response to the explosive Tambora eruption of April 1815 based
on both the anomalous hemispheric coolness and the superimposed
NAO-like
pattern.
Reconstructed time series RPCs \#1-5, the NH series, NINO3 index and 
reconstructions for specific gridpoints can be obtained through the NOAA 
paleoclimatology web site {\em http://www.ngdc.noaa.gov/paleo/paleo.html}.

\section*{\bf Attribution of Forcings}

Finally, we take an empirical approach to detecting
the possible effects
of external forcings on the climate.
We take the reconstructed NH series
as a diagnostic of the global climate, and
examine its relationship with three candidate external forcings 
during the period 1610-1995 including
(i) CO$_2$ measurements$^{39}$ as
a proxy for total greenhouse
gas changes, (ii) reconstructed solar irradiance variations$^{2}$
and (iii) the weighted historical dust veil index (DVI)
of explosive volcanism used by Jones and Bradley$^{40}$
(see Figure 31.1 therein) updated with recent data$^{41}$.
While we caution the reader that 
historical series for these forcing agents 
are imperfectly known or measured, they do nonetheless
represent our best estimates of the time-histories of the
corresponding forcings.
The reader is referred to more detailed discussions of
the estimation, and potential
sources of uncertainty or bias in these series$^{2,39,40}$.
Industrial aerosol forcing of the climate has also been
suggested  as an important forcing of recent climate$^{42-43}$,
but its physical basis is still controversial$^{44}$, and
difficult to estimate observationally. Noting that in any case,
this forcing is not believed to be important before about 1940,
its omission should be inconsequential in our long-term
detection approach.
Our empirical signal detection 
is complementary to that of  model-based
``fingerprint'' signal detection studies$^{42,43,45}$;
while our empirical approach relies on the faithfulness
of the reconstructed forcing series and on the assumption
of a linear and contemporaneous
response to forcings, it does not suffer the potential
weaknesses of
incomplete representations of
internal feedback processes$^{26}$, poorly
constrained parameterizations
of climatic responses$^{44}$, and underestimated
natural variability$^1$ in model-based studies. To the extent that
the response to forcing is not contemporaneous, but rather is delayed
owing to the inertia of the slow-response components of the climate
system (e.g., the ocean and cryosphere), our detection approach will
tend to underestimate the response to forcings, making the approach
a relatively conservative one.

We estimate the climatic response to the three forcings
based on an evolving multivariate regression method (Figure 7).
This time-dependent correlation approach
generalizes on previous studies of (fixed) correlations
between long-term northern hemisphere temperature
records and possible forcing agents$^{2,3}$.
Normalized regression (that is, correlation) 
coefficients $r$ are simultaneously estimated between each of the 
three
forcing series and the NH series from 1610 to 1995 in a 200 year moving window.
The first calculated value centered at 1710 is based on data from
1610 to 1809, and the last value, centered at 1895, is based on 
data from 1796 to 1995--i.e.,
the most recent 200 years. A 200 year window width was chosen
to insure that any given window contains enough samples to provide
good signal-to-noise ratios in correlation estimates. Nonetheless,
all of the important conclusions drawn below are robust to choosing
other reasonable
(e.g.,
100 year) window widths.

We test the significance of the correlation coefficients ($r$)
relative to a null hypothesis of random correlation arising from
natural climate variability,
taking into account the reduced
degrees of freedom in the correlations 
owing to substantial trends and low-frequency
variability in the NH series.
The reduced degrees of freedom are
modeled in terms of first-order
Markovian ``red noise'' correlation structure of the data series,
described by the lag-one autocorrelation coefficient
$\rho$ during a 200 year window.
This parameter ranges from
$\rho=0.48$ in the first window (1610-1809) to $\rho=0.77$ 
in the final window (1796-1995) of the moving correlation,
the considerably larger recent value
associated with the substantial global warming trend of the
past century. This latter trend has been shown to be inconsistent with
red noise$^{46}$ and could thus itself
be argued as indicative of externally forced variability.
An argument could, in this sense, be made for using the smaller pre-industrial
value $\rho=0.48$ of the NH series in estimating
the statistical degrees of freedom appropriate for 
the null hypothesis of
natural variability.
Nonetheless, we make the conservative choice of adopting the
largest value $\rho=0.77$ as representative of the natural
serial correlation in the series. We employ Monte Carlo
simulations to estimate the likelihood of chance spurious
correlations of such serially correlated noise 
with each of the 3 actual forcing series.
The associated confidence limits are approximately constant
between sliding 200 year windows. For (positive) correlations
with both CO$_2$ and solar irradiance, the confidence
levels are both approximately 0.24 (90\%), 0.31 (95\%),
0.41 (99\%), while for the ``whiter'', relatively trendless 
DVI index, the confidence levels for (negative) correlations are somewhat lower
(-0.16, -0.20, -0.27 respectively).
A one-sided significance test is employed in each case
because the physical nature of the forcing dictates
a unique expected sign to the correlations
(positive for CO$_2$ and solar irradiance variations,
negative for the DVI fluctuations).

The correlation statistics indicate
highly significant detection of solar irradiance
forcing in the NH series during 
the ``Maunder Minimum'' of solar activity 
from the mid 17th to early 18th century which corresponds
to an especially cold period. In turn, the steady increase in solar irradiance
from the early 19th century through the mid 20th century coincides with the
general warming over the period, exhibiting peak correlation during the
mid 19th century. 
The regression against solar irradiance indicates a sensitivity to changes in 
the ``solar constant'' of about 0.1K/(W/m$^2$), which is consistent with 
recent model-based studies$^{42}$.
Greenhouse (CO$_2$) forcing, on the other hand, shows no
sign of significance until a large positive correlation
sharply emerges as the moving window slides into the 20th
century.
The partial correlation with
CO$_2$ indeed dominates over that of solar irradiance
for the most recent 200 year interval, as increases in temperature 
and CO$_2$ 
simultaneously accelerate through 1995, while solar irradiance levels off after
the mid 20th century. It is reasonable to infer that greenhouse gas forcing
is now the dominant external forcing of the climate system.
Explosive volcanism exhibits the expected
marginally significant negative correlation
with temperature during much of 1610-1995 period,
most pronounced in the 200 year window centered near 1830 which includes
the most explosive volcanic events.

A variety of general circulation$^{42,47}$ and energy balance model 
experiments$^{43,45,48}$ as well as statistical
comparisons of 20th century global temperatures with forcing
series$^{49}$ suggest
that, although both solar and greenhouse gas
forcings play some role in explaining
20th century climate trends, greenhouse gases appear to play an increasingly 
dominant role during the 20th century.
Such a proposition
is consistent with the results of this study.

As larger numbers of high quality proxy reconstructions
become available in diverse regions of the globe it may be
possible to assimilate a more globally representative multiproxy
data network. Given the high level of skill possible in large-scale
reconstruction back to 1400 with the present network, it is reasonable
to hope that it may soon
be possible to faithfully reconstruct mean global temperatures
back over the entire
millenium, resolving for example the enigmatic medieval period$^7$. 
Geothermal measurements from boreholes$^{50}$ recover 
long-term temperatures trends without many of the complications of traditional
proxy indicators and, in combination with traditional multiproxy networks, may prove helpful in 
better resolving trends over many centuries.
With a better knowledge of how the
climate has varied prior to the 20th century, we will be able
to place even better constraints on the importance
of natural
and anthropogenic factors governing the climate of the past
few centuries, factors which will no doubt continue to affect
climate variability in the future, in addition to any 
anthropogenic effects.

\section*{Methods}
{\bf Statistics} We use as our primary diagnostic of
calibration and verification reconstructive skill
the conventional 
``resolved variance'' statistic,
$$
\beta = 1-\sum \left(y_{ref}-\widehat{y} \right)^2
/ \sum y_{ref}^2
$$
where $y_{ref}$ is the reference
series (e.g., the raw data in the case of calibration or
the verification dataset in the case of verification)
and $\widehat{y}$ is the series being compared to it 
(e.g., the proxy-reconstructed data for either calibration
or verification).
We compute $\beta$ for each gridpoint, and for
the NH, GLB, and MULT quantities.
The sum extends
over the time interval of comparison, and for the multivariate
case (MULT), over all gridpoints as well.
We also computed a calibration $\beta$
statistic for the detrended NH series  (DETR) to distinguish
between explanatory variance associated with the noteable trend of the 20th century,
and that related to departures from the trend.

$\beta$ is
a quite rigorous measure of the similarity between
two variables,
measuring their correspondence
not only in terms of the relative departures
from mean values (as does the correlation coefficient
$r$) but also in terms of the means and absolute variance
of the two series.
For comparison 
correlation ($r$) and squared-correlation ($r^2$) statistics 
are also determined.
The expectation value for
two random series is $\beta=-1$. Negative values of $\beta$
may in fact be statistically significant for sufficient temporal
degrees of freedom.
Nonetheless, the threshold $\beta=0$ 
defines the simple ``climatological'' model
in which a series is assigned its long-term mean. In this sense,
statistically significant negative values of $\beta$ might still be
considered questionable in their predictive or reconstructive
skill. Due to the more rigorous ``match'' between two series
sought by $\beta$, highly significant values of $\beta$ are 
possible even
when $r^2$ is only marginally significant.

Significance
levels were determined for $r^2$ from standard one-sided
tables, accounting for decreased degrees of freedom due
to serial correlation. Significance levels for $\beta$ were
estimated by Monte Carlo simulations, also
taking serial correlation into account.
Serial correlation is assumed to follow from the null
model of AR(1) red noise, and degrees of freedom are
estimated based on the lag-one autocorrelation coefficients 
($\rho$)
for the two series being compared. While the values of
$\rho$ differ from gridpoint-to-gridpoint, this variation
is relatively small, making it simplest to use the ensemble
average values of $\rho$ over the domain ($\rho \approx 0.2$). 

{\bf Calibration} With the spatial sampling of $M=1082$
continuous
monthly gridpoint surface temperature anomaly (ie, de-seasonalized) temperature data used
(Figure 1b),
the $N=1128$ months of data available from 1902-1995 
were sufficient for a unique, overdetermined  eigenvector decomposition 
(note that 
$N'=94$ years of
the annual mean data would, in contrast, not be sufficient).

For each gridpoint, the mean was removed, and the series
was normalized by its standard deviation. A standardized data
matrix {\underline{\bf T}} of the data is formed by weighting each
gridpoint by the cosine of its central latitude to ensure
areally-proportional contributed variance, and a conventional
Principal Component Analysis (PCA) is performed,
$$
{\underline{\bf T}} = \Sigma_{k=1}^K \lambda_k
 {\bf u_k}^{\dagger} 
{\bf v_k}
$$
decomposing the dataset into its
dominant spatiotemporal eigenvectors.
The M-vector or empirical orthogonal function (EOF) ${\bf v}_k$ 
describes the relative spatial pattern of
the $k$th eigenvector, the N-vector ${\bf u}_k$ or principal
component (PC) describes its variation over time, and the
scalar 
$\lambda_k$ describes the associated fraction of resolved
(standardized and weighted) data variance. 

In a given calibration exercise,
we retain a specified subset of the annually-averaged 
eigenvectors,
the annually-averaged PCs denoted by ${\overline{u}^k}_n$,
where $n=1,\ldots,\overline{N}$, $\overline{N}=79$ is the
number of annual averages used of the $N$ month length dataset.
In practice, only a small subset $N_{eofs}$ of the highest rank
eigenvectors
turn out to be usefull in these exercises from the standpoint
of verifiable reconstructive skill. 
An objective criterion was used to determine the particular set of
eigenvectors which should be used in the calibration as follows.
Preisendorfer's$^{25}$ selection rule
``rule N'' was applied to the multiproxy network to determine
the approximate number $N_{eofs}$ of significant independent climatic patterns that
are resolved by the network, taking into account the spatial correlation
within the multiproxy dataset. Because the ordering of various eigenvectors
in terms of their prominence in the instrumental data, and their prominence as 
represented by the multiproxy network, need not be the same, we allowed for
the selection of non-contiguous sequences of the instrumental eigenvectors.
We chose the optimal group of $N_{eofs}$ eigenvectors, from among a larger
set (e.g., the first 16) of the highest-rank eigenvectors, as the group of
eigenvectors which maximized the calibration explained variance.
It was encouraging from a consistency standpoint that this subset typically corresponded quite
closely to the subset which maximized the {\em verification}
explained variance statistics (see below), but the objective criterion
was, as it should be, independent of the verification process.
We emphasize, furthermore, that statistical significance was robustly established,
as neither the measures of statistical skill nor the 
reconstructions themselves were highly sensitive to the precise criterion for 
selection.
In addition to the above means of cross-validation, we also tested the network 
for sensitivity to the inclusion or elimination of particular trainee data 
(e.g., instrumental/historical records, non-instrumental/historical records, or 
dendroclimatic proxy indicators).

These $N_{eofs}$ eigenvectors
were trained against
the $N_{proxy}$ indicators, by finding the least-squares
optimal
combination of the $N_{eofs}$ PCs
represented by each individual proxy indicator during
the $\overline{N}=79$ year training interval from 1902-1980 (the training 
interval is terminated at 1980
because
many of the proxy series terminate at or shortly after 1980).
The proxy series and PCs were formed into
anomalies relative to the same 1902-1980 reference period
mean, and the proxy series were also normalized by their standard deviations
during that period.
This proxy-by-proxy calibration
is well posed (i.e., a unique optimal solution exists)
as long as $\overline{N} >N_{eofs}$ (a limit never approached
in this study) and can be expressed as the least-squares solution to the
overdetermined
matrix equation,
$$
{\bf \underline{U}} {\bf x} = {\bf y^{(p)}}
$$
$$
{\bf \underline{U}} = \left[
\begin{array}{cccc}
  {\overline{u}^{(1)}}_1 & {\overline{u}^{(2)}_1} & \ldots & {u^{(N_{eofs})}_1} 
\\
  {\overline{u}^{(1)}}_2 & {\overline{u}^{(2)}_2} & \ldots & {u^{(N_{eofs})}_2} 
\\
\vdots \\
  {\overline{u}^{(1)}}_{\overline{N}} & {\overline{u}^{(2)}_{\overline{N}}} & \ldots & {u^{(N_{eofs})}_{\overline{N}}} 
\\
\end{array} \right] 
$$
is the matrix of annual PCs, and
$$
{\bf y^{(p)}} = \left[
\begin{array}{c}
{y^{(p)}}_1 \\
{y^{(p)}}_2 \\
\vdots \\
{y^{(p)}}_{\overline{N}} \\
\end{array} \right]
$$
is the time series $\overline{N}-$vector for proxy record $p$.

The $N_{eofs}$-length solution vector ${\bf x} ={\bf G^{(p)}}$ is 
obtained by solving the above over-determined optimization problem by
singular value decomposition (SVD) for each proxy
record $p=1,\ldots,P$. This yields a 
matrix of coefficients relating the different
proxies to their closest linear combination of the $N_{eofs}$ PCs,
$$
{\bf \underline{G}} = \left[
\begin{array}{cccc}
  {G^{(1)}}_1 & {G^{(1)}}_2 & \ldots & G^{(1)}_{N_{eofs}} \\
  {G^{(2)}}_1 & {G^{(2)}}_2 & \ldots & G^{(2)}_{N_{eofs}} \\
\vdots \\
  {G^{(P)}}_1 & {G^{(P)}}_2 & \ldots & G^{(P)}_{N_{eofs}} \\
\end{array} \right] 
$$
This set of coefficients will not provide a single consistent
solution, but rather represents an overdetermined relationship
between the optimal weights on each of the $N_{eofs}$ PCs and
the multiproxy network.

Proxy-reconstructed patterns are thus
obtained during the pre-calibration interval by the year-by-year
solution of the overdetermined matrix equation,
$$
{\bf \underline{G}} {\bf z} = {\bf y_{(j)}}
$$
where ${\bf y_{(j)}}$ is the predictor vector of values of each of the $P$ proxy
indicators during year $j$. The predictand solution vector ${\bf z} = {\bf 
\widehat{U}}$ contains the least-squares
optimal values of
each of the $N_{eofs}$ PCs for a given year. 
This optimization
is overdetermined (and thus well constrained) as long as $P>N_{eofs}$
which is always realized in this study. It is noteworthy that,
unlike conventional paleoclimate transfer function approaches, there
is no specific relationship between a given proxy indicator and a given 
predictand (ie, reconstructed
PC). Instead, the best common choice of values for the small number of 
$N_{eofs}$ predictands is determined from the mutual information present in the 
multiproxy network during any given year. The reconstruction approach is thus 
relatively resistant to errors or biases specific to any small number of 
indicators during a given year. 

This yearly reconstruction process leads to annual 
sequences of the optimal reconstructions of the
retained PCs, which we term the reconstructed principal
components or ``RPCs'' and denote by ${\bf \widehat{u}^k}$.
Once the RPCS are determined,
the associated temperature patterns are readily obtained through
the appropriate eigenvector expansion,
$$
{\underline{\bf \widehat{T}}} = \Sigma_{k=1}^{N_{eofs}} \lambda_k
 {\bf \widehat{u}_k}^{\dagger} 
{\bf v_k}
$$
while quantities of interest (e.g., NH) are calculated from the
appropriate spatial averages, and appropriate calibration and
verification resolved variance statistics are calculated from
the raw and reconstructed data.


Several checks were performed
to insure a reasonably unbiased calibration procedure. The 
histograms of calibration residuals were examined for possible heteroscedasticity,
but were found to pass a $\chi^2$ test for Gaussian distributedness
at reasonably high levels of significance
(NH: 95\% level, NINO3: 99\% level).
The spectrum of the calibration residuals for these quantities, were, furthermore, found
to be approximately ``white'', showing little evidence for preferred or
deficiently resolved
timescales in the  calibration process. 
Having established reasonably unbiased calibration residuals,
we were able to calculate uncertainties in the reconstructions 
by assuming that the unresolved variance is Gaussian distributed over time. This
variance increases back in time 
(the increasingly sparse multiproxy network calibrates 
smaller fractions of variance), yielding error bars which expand back in time.

{\bf Verification} Verification resolved variance statistics ($\beta$) were determined 
based on two distinct verification datasets
including
(a) the sparse subset of the gridded data
($M'=219$ gridpoints) for which independent values are available
from 1854-1901 (see Figure 1b) and
(b) the small subset of 11 very long instrumental
estimated temperature gridpoint averages (10 in Eurasia,
1 in North America--see Figure 1a) constructed
from the longest available station measurements.
Each of these ``gridpoint'' series shared at least
$70\%$ of their variance with the corresponding
temperature gridpoint available from 1854-1980,
providing verification back to at least 1820 in all cases
(and back through the mid and early
18th century in many cases). Note that this latter verification
dataset is only temporally but not spatially independent of the multiproxy 
network itself, which contains these long instrumental gridpoint series as a 
small subset
of the network.
In case (a), NH and GLB verification statistics are 
computed as well as the multivariate (``MULT'') gridpoint
level
verification statistic, although these quantities represent
different spatial samplings than in the full calibration dataset
owing to the sparser sampling of the verification period.
Case (b) provides a longer-term
albeit an even less spatially-representative multivariate
verification statistic (``MULTb''). In this case, the spatial sampling does
not
permit meaningful estimates of NH or GLB mean quantities.
In any of these diagnostics, a positive value of $\beta$ is statistically
significant at greater than 99\% confidence as established from Monte Carlo simulations. 
Verification skills for the NINO3 reconstructions are estimated by other means, since the actual NINO3
index is not available far beyond the beginning of the calibration period.
The (negative) correlation $r$ of NINO3 with the 
Southern Oscillation Index (``SOI'') annual-mean from 1865-1901 (obtained
from P.D. Jones,
personal communication)
and a squared congruence statistic $g^2$ measuring the categorical match between the distribution of warm
NINO3 events and the distribution of warm episodes according to the 
Quinn and Neal$^{35}$ historical chronology (available back through 1525) 
were used for statistical cross-validation
of our reconstruction NINO3 index, with significance levels estimated from standard one-sided tables
and Monte Carlo simulations respectively. The results of all calibration
and verification experiments
are provided in Supplementary Information.


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\section*{Acknowledgements}

This work benefited greatly from helpful discussions with Mark Cane, Ed Cook, 
Mike Evans, Alexey Kaplan, and 
collaborators
at the Lamont Doherty Earth Observatory.
We acknowledge discussions with K. Briffa,
T. Crowley, P.
Jones, S. Manabe, R. Saravanan, and K. Trenberth, as well as the comments of
G. Hegerl
and two anonymous
reviewers.
We are indebted to Rosanne D'Arrigo, David Fisher, Gordon Jacoby, Judith Lean,
Alan Robock, David Stahle, Charles Stockton, Eugene Vaganov, Ricardo
Villalba, and the numerous contributors to the International Tree-Ring
Data Bank. 
We are also grateful to
Frank Keimig, Martin Munro, Richard Holmes, and Caspar Ammann 
for their technical assistance.
This work was supported by the National Science Foundation and
the Department of Energy. M.E.M. acknowledges
support through the Alexander Hollaender Distinguished Postdoctoral
Research Fellowship program of the Department of Energy. This work
is a contribution to the NSF- and NOAA-sponsored Analysis of Rapid
and Recent Climatic Change (ARRCC) project.

\newpage

\section*{Figure Captions}

\begin{description}

\item[ ]
Figure 1. Data used in this study. 
(top) 
Distribution of annual resolution proxy indicators
used in this study. Dendroclimatic reconstructions are
indicated by ``tree'' symbols, ice core/ice melt proxies
by ``star'' symbols, coral records by ``C'' symbols. Long historical
records and instrumental ``gridpoints'' series are shown by squares 
(temperature), or diamonds (precipitation).
Groups  of ``+'' symbols indicate principal components of dense tree
ring sub-networks, with the number of such symbols indicating
the number of retained principal components.
Sites are shown dating back to
at least 1820 (red), 1800 (blue-green),
1750 (green), 1600 (blue), and 1400 (black).
Certain sites (e.g., the Quelccaya ice core) consist of
multiple proxy indicators (e.g., multiple cores,
and both $\delta^{18}o$ isotope and accumulation measurements).
(bottom)
Distribution of the (1082) nearly continuous available land air/sea 
surface temperature
gridpoint data available from 1902 onward indicated
by shading. The squares indicate the subset of 219 gridpoints
with nearly continuous records extending back to 1854 that
are used for verification.
Northern Hemisphere (NH) and global (GLB) mean temperature are estimated as 
areally-weighted (ie, cosine latitude) averages over the Northern
hemisphere and global domains respectively.

\item[ ]
Figure 2. Emirical orthogonal functions (EOFs) for the 
five leading eigenvectors 
of the global temperature
data from 1902-1980. The gridpoint areal weighting factor used
in the PCA procedure has
been removed from the EOFs so that relative temperature anomalies can be 
inferred from the patterns.

\item[ ]
Figure 3. Spatial patterns of reconstruction
statistics. Top, calibration $\beta$ (top--based
on 1902-1980 data); middle,
verification (based on 1854-1901 data) $\beta$; bottom,
verification $r^2$
For the $\beta$ statistic, values that are
insignificant at the 99\% level are shown in gray,
while negative, but 99\% significant values are
shown in yellow, and significant positive values
are shown in two shades of red.
For the $r^2$ statistic,
statistically insignificant
values (or any gridpoints with unphysical values of correlation
$r<0$)
are indicated
in gray. The color scale indicates values significant
at the 90\% (yellow), 99\% (light red), and 99.9\% (dark red)
levels (these significance levels are slightly higher for the calibration
statistics which are based on a longer period of time).
A description of significance level estimation is provided in
the Methods section.

\item[ ]
Figure 4. Comparison of the proxy-based spatial reconstructions
of the anomaly pattern for 1941 vs the raw data.
based on (top) actual, (middle) EOF-filtered, and (bottom) proxy-reconstructed data. 
Anomalies (relative to 1902-1980 climatology) are indicated by 
the color scale shown.

\item[ ]
Figure 5. Time reconstructions (solid lines) along with raw data.
(a) Principal Components (RPCs) 1-5 
(b) Northern hemisphere mean temperature (NH) in $^o$C.
In both cases, the zero line corresponds to the 1902-1980 calibration mean of 
the quantity. For (b), raw data is shown through 1995 and 
positive and negative 2$\sigma$ uncertainty limits are 
shown by the light dotted lines surrounding the solid reconstruction, 
calculated 
as described in the Methods section. 

\item[ ]
Figure 6. Reconstructed annual temperature patterns
for two example years
(i) 1791 (ii) 1816. The colors indicate 
regions which exceed (either positively or negatively) the
threshold indicated in $^o$C. 
The zero baseline is defined by the 1902-1980
climatological mean for each gridpoint.

\item[ ]
Figure 7. Relationship of Northern hemisphere  mean (NH) temperature 
with 3 candidate forcings between 1610 and 1995.
(i) reconstructed NH temperature series from 1610-1980 update with raw data from 
1981-1995.
(i) greenhouse gases represented by atmospheric CO$_2$ measurements.
(ii) reconstructed solar irradiance.
(iii) weighted volcanic dust veil index (DVI).
(iv) evolving multivariate correlation
of NH series with the
3 forcings (i) (ii) and (iii). 
The time axis denotes the {\em center}
of a 200 year moving window. 
One-sided (positive) 90\%,95\%,99\% significance levels (see text)
for correlations
with CO$_2$ and solar irradiance 
are shown by horizontal dashed lines, while the one-sided (negative)
90\% significance threshold for correlations w/ the DVI series
is shown by the horizontal dotted line.
The gray bars indicates two different 200 year window of data, with
the long-dashed vertical lines indicating the center of the corresponding
windows.
%and intersecting the 3 curves at their corresponding values. The
%upper gray bar spans the window from 1751-1950 (centered
%at ``1850''), while
%the lower gray bar indicates the final data window from 
%1796-1995 (window centered at ``1895'') correspond to the final estimates
%from the moving multivariate correlation.
\end{description}

\end{document}

%While generalizations of our approach which exploit temporal
%autocovariance and error covariance estimation$^{29}$ could
%provide for an even more efficient calibration of the
%multiproxy network, we established a  satisfactory
%statistical efficiency of our particular approach through 
%synthetic experiments based on small trainee networks 
%of ``pseudo-proxies'' constructed as linear 
%combinations of the actual PCs immersed in additive noise.
%These synthetic experiments demonstrated
%that the reconstructed fields asymptotically
%approach their exact counterparts as the number of
%trainee records and resolvable eigenvectors is increased.
%These experiments also demonstrate that any climatic
%indicator
%with a linear relationship to any combination
%of large-scale
%temperature eigenvectors such as sea level pressure
%or precipitation indicators, adds incremental value
%in the calibration
%process.

%
%of temperature$^{32,33}$, and precipitation/drought$^{34,35}$.
%Other studies have demonstrated that particularly
%well-chosen regional proxy climate reconstructions can 
%act as surprisingly representative surrogates for larger-scale
%features such as hemispheric mean temperature${36,13}$,
%ENSO$^{37,38}$ or North Pacific$^{39}$ and North Atlantic$^{40,41}$
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