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Identifying Signatures of Natural Climate Variability in Time Series of Global-Mean Surface Temperature: Methodology and Insights

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Global-mean surface temperature is affected by both natural variability and anthropogenic forcing. This study is concerned with identifying and removing from global-mean temperatures the signatures of natural climate variability over the period January 1900-March 2009. A series of simple, physically based methodologies are developed and applied to isolate the climate impacts of three known sources of natural variability: the El Nino-Southern Oscillation (ENSO), variations in the advection of marine air masses over the high-latitude continents during winter, and aerosols injected into the stratosphere by explosive volcanic eruptions. After the effects of ENSO and high-latitude temperature advection are removed from the global-mean temperature record, the signatures of volcanic eruptions and changes in instrumentation become more clearly apparent. After the volcanic eruptions are subsequently filtered from the record, the residual time series reveals a nearly monotonic global warming pattern since similar to 1950. The results also reveal coupling between the land and ocean areas on the interannual time scale that transcends the effects of ENSO and volcanic eruptions. Globally averaged land and ocean temperatures are most strongly correlated when ocean leads land by; 2-3 months. These coupled fluctuations exhibit a complicated spatial signature with largest-amplitude sea surface temperature perturbations over the Atlantic Ocean.
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Identifying Signatures of Natural Climate Variability in Time Series of Global-Mean
Surface Temperature: Methodology and Insights
DAVID W. J. THOMPSON
Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
JOHN M. WALLACE
Department of Atmospheric Sciences, University of Washington, Seattle, Washington
PHIL D. JONES
Climatic Research Unit, University of East Anglia, Norwich, United Kingdom
JOHN J. KENNEDY
Met Office Hadley Centre, Exeter, United Kingdom
(Manuscript received 11 February 2009, in final form 23 May 2009)
ABSTRACT
Global-mean surface temperature is affected by both natural variability and anthropogenic forcing. This
study is concerned with identifying and removing from global-mean temperatures the signatures of natural
climate variability over the period January 1900–March 2009. A series of simple, physically based method-
ologies are developed and applied to isolate the climate impacts of three known sources of natural variability:
the El Nin
˜
o–Southern Oscillation (ENSO), variations in the advection of marine air masses over the high-
latitude continents during winter, and aerosols injected into the stratosphere by explosive volcanic eruptions.
After the effects of ENSO and high-latitude temperature advection are removed from the global-mean
temperature record, the signatures of volcanic eruptions and changes in instrumentation become more clearly
apparent. After the volcanic eruptions are subsequently filtered from the record, the residual time series
reveals a nearly monotonic global warming pattern since ;1950. The results also reveal coupling between the
land and ocean areas on the interannual time scale that transcends the effects of ENSO and volcanic erup-
tions. Globally averaged land and ocean temperatures are most strongly correlated when ocean leads land by
;2–3 months. These coupled fluctuations exhibit a complicated spatial signature with largest-amplitude sea
surface temperature perturbations over the Atlantic Ocean.
1. Introduction
The time history of observed twentieth-century
global-mean surface temperature reflects the combined
influences of naturally occurring climate variations and
anthropogenic emissions of greenhouse gases and sul-
fate aerosols. A technique used extensively in the In-
tergovernmental Panel on Climate Change (IPCC)
assessment reports for distinguishing the signal of an-
thropogenic forcing from natural variability involves
comparing (a) the observed spatial signature of climate
change with (b) the signature of anthropogenic climate
change inferred from climate models forced with pre-
scribed increasing greenhouse gas concentrations [i.e.,
the ‘‘optimal fingerprinting’’ technique; Hegerl et al.
(2007) and references therein]. Here, we infer the an-
thropogenic signal and other key aspects of twentieth-
century global-mean surface temperature variability by
subtracting from the observed global-mean land and
ocean temperature records the variance associated with
known sources of natural climate variability.
Previous studies have estimated the variance in
global-mean temperature attributable to natural climate
Corresponding author address: David W. J. Thompson, Dept. of
Atmospheric Science, Colorado State University, Fort Collins, CO
80523.
E-mail: davet@atmos.colostate.edu
6120 JOURNAL OF CLIMATE VOLUME 22
DOI: 10.1175/2009JCLI3089.1
Ó 2009 American Meteorological Society
variability but have relied largely on statistical fits to
prescribed climate indices. The signal of the El Nin
˜
o–
Southern Oscillation (ENSO) in global surface tem-
peratures has been estimated using linear regression
based on lagged indices of the Southern Oscillation in-
dex or equatorial Pacific sea surface temperatures (e.g.,
Jones 1988; Mass and Portman 1989; Robock and Mao
1995; Kelly and Jones 1996; Wigley 2000; Santer et al.
2001; Trenberth et al. 2002), maximum covariance anal-
ysis between surface temperatures in the tropical Pacific
and over the continents (Yang and Schlesinger 2001),
complex ‘‘patterns-based filters’’ derived from linear in-
verse models (Penland and Matrosova 2006; Compo and
Sardeshmukh 2008, manuscript submitted to J. Climate),
and regression analyses with geographically dependent
lag (Chen et al. 2008). The signal of volcanic eruptions
has been prescribed as linear cooling followed by expo-
nential warming (Wigley 2000; Santer et al. 2001).
In this study we exploit a series of novel methodolo-
gies to identify and filter out of the unsmoothed monthly
mean time series of global-mean land and ocean tem-
peratures the variance associated with ENSO, dynam-
ically induced atmospheric variability, and volcanic
eruptions. The impacts of ENSO and volcanic eruptions
on global-mean temperature are estimated using a sim-
ple thermodynamic model of the global atmospheric–
oceanic mixed layer response to anomalous heating. In
the case of ENSO, the heating is assumed to be pro-
portional to the sea surface temperature anomalies over
the eastern Pacific; in the case of volcanic eruptions, the
heating is assumed to be proportional to the strato-
spheric aerosol loading. The impacts of dynamically
induced atmospheric variability on global-mean tem-
perature are estimated on the basis of the covariance
between the land–sea temperature difference in the
Northern Hemisphere and the sea level pressure field.
The filtering methodology reduces the high-frequency
variability in global-mean temperatures not by smooth-
ing the data, but rather by subtracting out physically
based estimates of the time-dependent signatures of
known sources of natural climate variability. Hence, the
resulting residual global-mean temperature time series
has the same monthly time resolution as does the orig-
inal data.
The results of the filtering process provide several new
insights into twentieth-century global-mean temper-
ature variability. After ENSO and the dynamically
induced variability are removed from global-mean tem-
peratures, the residual time series highlights a spurious
drop in SSTs in 1945 and sharpens substantially the
signal of major volcanic eruptions in surface tempera-
tures. After the signature of the volcanic eruptions is
removed, the residual global-mean temperature time
series exhibits nearly monotonic warming since ;1950.
The results also 1) reveal a significant level of coupling
between ocean and land temperatures that remains even
after the effects of ENSO and volcanic eruptions have
been removed; 2) serve to highlight the improvements
in the quality of the time series of global-mean land
temperatures with the increase in the areal coverage of
the station network from 1951 onward; and 3) yield
a residual time series in which the signature of anthro-
pogenically induced global warming is more prominent.
The paper is organized as follows: In section 2 we
provide a brief review of the data used in the analysis. In
section 3 we describe the methodologies used to remove
from the global-mean temperature time series the im-
pacts of ENSO and dynamically induced variability. In
section 4 we examine the signal of volcanic eruptions in
the residual time series from which the effects of ENSO
and dynamically induced variability have been removed.
Section 5 describes the methodology used to remove the
impacts of volcanic eruptions from the global-mean
temperature time series, and section 6 discusses key
aspects of global-mean temperature variability high-
lighted by the residual time series. Section 7 provides
a summary of the key results.
2. Data and analysis details
The temperature data used in the study are version 3 of
the Climate Research Unit’s land surface air temperature
dataset (CRUTEM3; Brohan et al. 2006), version 2 of
the Hadley Centre’s Sea Surface Temperature data-
set (HadSST2; Rayner et al. 2006), and version 3 of
the Hadley Centre–Climate Research Unit’s combined
land surface temperature and SST dataset (HadCRUT3;
Brohan et al. 2006). All temperature datasets are avail-
able from the Climatic Research Unit at the University
of East Anglia in monthly mean form on a 58358
latitude–longitude mesh and are expressed as anomalies
with respect to the 1961–90 base period. The sea level
pressure (SLP) data are provided by the National Cen-
ter for Atmospheric Research’s Data Support Section
and are also formatted as monthly means on a 58358
latitude–longitude mesh, as described in Trenberth and
Paolino (1980). The seasonal cycle is removed from the
SLP data by subtra cting the long-term mean calculat ed
for the period 1950–2006 from the data as a function of
calendar m onth.
Time series are shown for the period January 1900–
March 2009. Unless otherwise noted, all analyses per-
formed in developing the filtering algorithms (including
correlations and regressions) are based on detrended
data limited to the period January 1950–December 2006
and are thus unaffected by the discontinuity in sea
15 NOVEMBER 2009 T H O M P S O N E T A L . 6121
surface temperatures in 1945 described by Thompson
et al. (2008). Detrending ensures that the algorithms are
not biased by the global warming of the past few de-
cades. The effective sample size used in significance
estimates is given by Eq. (31) in Bretherton et al. (1999).
The fitted and residual time series generated in the
analyses outlined here are available online (www.atmos.
colostate.edu/;davet/ThompsonWallaceJonesKennedy).
3. Removing the signatures of ENSO and
dynamically induced variability from
global-mean temperatures
a. Estimating the signal of ENSO in global-mean
temperatures
As noted in the introduction, previous studies have
defined the ENSO signal in the global-mean tempera-
ture record on the basis of lagged values of the east–west
SLP gradient in the tropical Pacific (e.g., the Southern
Oscillation index), or lagged values of SSTs averaged
over t he eastern tropical Pac ific cold-tongue region
(e.g., the ‘‘cold-tongue index’’ or Nin
˜
o-3.4). Here, we
define the ENSO signal as being linearly proportional
to the damped thermodynamic response of the global
atmospheric–oceanic mixed layer to the SST variability
and associated surface heat fluxes in the eastern equa-
torial Pacific cold-tongue region. We focus on the re-
sponse to variability only in the cold-tongue region for
the following reasons: 1) the ENSO signal in global-
mean temperature is derived primarily from the exchange
of heat between the subsurface ocean and the global
atmospheric–oceanic mixed layer, 2) ENSO primarily
perturbs the flux of heat between the subsurface ocean
and the global atmospheric–oceanic mixed layer in the
region of ocean upwelling in the eastern equatorial Pa-
cific, and 3) SST anomalies outside the cold-tongue re-
gion exhibit considerable decadal variability, much of
which is not linked to ENSO dynamics.
The approach is analogous to that exploited by
Hasselman (1976) to examine the ocean response to
stochastic atmospheric forcing, and by Yulaeva and
Wallace (1994) to examine the tropical-mean response
to ENSO. The global-mean surface temperature re-
sponse to variability in ENSO is modeled as
C
d
dt
T
ENSO
(t) 5 F(t)
T
ENSO
(t)
b
, (1)
where T
ENSO
denotes the simulated response of global-
mean surface temperatures to ENSO variability, F(t)is
the anomalous flux of sensible and latent heat in the
eastern tropical Pacific, b is a linear damping coeffi-
cient, and C is the effective heat capacity of the global
atmos pheric–oceanic mixed layer per unit area.
The anomalous heat fluxes given by F(t) are assumed
to be linearly congruent with variability in sea surface
temperatures in the dynamically active cold-tongue re-
gion. That is, the ocean dynamics force variability in sea
surface temperatures in the cold tongue, and this vari-
ability is communicated to the atmosphere via the
anomalous fluxes of heat at the ocean surface. The heat
fluxes are estimated by 1) subtracting monthly mean SST
anomalies averaged over the globe from SST anomalies
averaged over the dynamically active cold-tongue region
to form the difference cold-tongue index (CTI; the cold-
tongue region is defined as 58N–58S, 1808–908W) and
2) multiplying the difference CTI time series by (a) the
fractional area of the globe covered by the cold-tongue
region (assumed to be 2%) and (b) a coupling coef-
ficient of 10 W m
22
K
21
(cf. Fig. 17 from Barnett et al.
1991).
The linear damping coefficient b is a measure of the
climate sensitivity. Observationally and numerically de-
rived estimates of b range from ;0.4 to 1.2 K (W m
22
)
21
and the value of b depends on both the time scale and
nature of the forcing (e.g., Cess 1976; Hansen et al. 1985;
Forster and Gregory 2006; Knutti et al. 2008; Solomon
et al. 2007). Here, we set b to
2
/
3 K(Wm
22
)
21
.In
practice, the results are not sensitive to the choice of the
air–sea coupling coefficient or b provided that the values
fall within the range that is physically reasonable.
The effective heat capacity of the model was de-
termined empirically so that the correlation coefficient
between T
ENSO
and the time series of global-mean
surface temperature anomalies is maximized based on
detrended data from 1950 through 2006. The optimal
effective heat capacity (C;1.84 3 10
7
Jm
22
K
21
) im-
plies that the ENSO-related heat fluxes warm the entire
atmosphere plus an equivalent of ;2 m of the global
ocean. Note that the resulting heat capacity is a global
average and that, locally, ENSO perturbs the oceanic
mixed layer much deeper than ;2 m. The model was
initialized with anomalies in the cold-tongue region
starting in 1870 and the output T
ENSO
was retained for
the period January 1900–March 2009.
The difference cold-tongue index and the output of
Eq. (1) (T
ENSO
) are shown in the top panel of Fig. 1. The
simple thermodynamic model acts to low-pass filter the
input series and lag it by several months. The output
time series yields a substantially improved represen-
tation of the signal of ENSO in global-mean tempera-
tures: the global-mean temperature time series is more
strongly correlated with T
ENSO
than with the difference
cold-tongue index (r 5 0.41 versus r 5 0.31). We will
show the residual time series obtained by subtracting the
T
ENSO
time series from the global-mean temperature
time series later in this section.
6122 JOURNAL OF CLIMATE VOLUME 22
b. Estimating the signal of dynamically induced
variability in global-mean temperatures
Temporal variations in the atmospheric circulation
contribute to the variability of global-mean temperatures
because of the large differences between the heat ca-
pacities of the ocean and land areas. For example, winter
months when the surface westerlies are stronger than
normal over middle and subpolar latitudes of the North-
ern Hemisphere (NH) are marked by anomalously strong
warm advection over the NH continents and anomalously
strong cold advection over the oceans. Since the land
surface has a lower heat capacity than the oceanic mixed
layer, the resulting temperature anomalies tend to be
larger over the continents than over the ocean areas so
that the global-mean temperature tends to be anoma-
lously high, and vice versa. The impacts of dynamically
induced variability on surface temperatures are most
pronounced in the NH where the land areas account for
a substantial fraction of the hemisphere, and during the
winter season when the surface winds and the land–sea
contrast in surface temperatures are largest.
Previous studies have estimated the impacts of dy-
namically induced variability on area-averaged tem-
peratures using two somewhat different approaches.
The first approximates the dynamically induced contri-
bution to global-mean temperatures on the basis of
preferred patterns of internal atmospheric variability.
For example, the Northern Annular mode–North At-
lantic Oscillation (NAM–NAO) accounts for a compo-
nent of the dynamically induced variability in NH-mean
temperatures by virtue of its strong influence on tem-
perature over Eurasia and North America (e.g., Hurrell
1996; Thompson et al. 2000). The second method ap-
proximates the dynamically induced contribution to
variations in global-mean temperatures on the basis of
the cold-ocean–warm-land pattern (the COWL pattern;
Wallace et al. 1995). The COWL pattern is defined by
regressing the departure surface temperature field onto
the time series of NH mean temperature, where the
departure field is defined as the spatially varying tem-
perature minus the NH mean. By construction, the ex-
pansion coefficient time series of the COWL pattern
explains more variance of NH-mean temperatures than
the time series associated with any other surface tem-
perature pattern with a spatial mean of zero.
There are disadvantages to both of the above methods.
The NAM–NAO is an important pattern of internal at-
mospheric dynamics, but is not necessarily the most im-
portant structure in terms of driving dynamically induced
variability in hemispheric and global-mean temperatures.
The COWL pattern explains a substantial fraction of the
month-to-month variability in hemispheric and global-
mean temperatures (Wallace et al. 1995), but the COWL
pattern projects onto the predicted surface temperature
response to greenhouse-induced warming and hence in-
cludes a component of the radiative response to increasing
greenhouse gases (Broccoli et al. 1998).
FIG. 1. (a, top) Time series of SST anomalies in the eastern
tropical Pacific used to drive Eq. (1) (i.e., the CTI), and (a, bottom)
the output of Eq. (1) (T
ENSO
). Tick marks are 1 K for the CTI and
0.1 K for T
ENSO
. (b) Time series of the contribution of dynamically
induced variability to global-mean temperatures. (top) The T
dyn
time series found as the expansion coefficient time series of SLP
regressed on T
NHLand-NHSST
. (second from top) The linear sum
of the first 10 PCs of the NH SLP field, where the PCs are weighted
by the regression coefficient with T
NHLand-NHSST
. (second from
bottom) The expansion coefficient time series of SLP regressed
on high-pass values of T
NHLand-NHSST
. (bottom) The expansion
coefficient time series of surface temperature regressed on
T
NHLand-NHSST
. See text for details of the calculations. All sub-
sequent analyses are based on the top T
dyn
time series.
15 N
OVEMBER 2009 T H O M P S O N E T A L . 6123
Here, we estimate the contribution of dynamically in-
duced variability to variations in global-mean temperature
by adapting the COWL methodology to the SLP field.
The resulting SLP pattern is not restricted to patterns of
internal atmospheric variability, and it does not project
onto the radiative response to increased carbon diox-
ide. The corresponding estimate of dynamically induced
variability includes an anthropogenic component only to
the extent that anthropogenic forcing drives large-scale
changes in the Northern Hemisphere SLP field.
The analysis is performed as follows. First, we find
the pattern in NH sea level pressure anomalies most
strongly coupled to the difference between tempera-
tures averaged over the NH land and ocean areas
poleward of 308N. The pattern is found by regressing
SLP anomalies onto the land–ocean difference time
series (hereafter T
NHLand-NHSST
) rather than NH mean
temperature since we are interested in isolating the
pattern in SLP that contributes most to out-of-phase
variations between the land and ocean areas. The
T
NHLand-NHSST
basis index is detrended before calcu-
lating the regression coefficients and the analysis is re-
stricted to the NH since land accounts for a relatively
small fraction of the SH. The SLP maps are found for
3-month seasons centered on all calendar months so that
the resulting patterns can vary from one season to the
next (e.g., the SLP map for January is based on monthly
mean data for the months December–February, the map
for February on data for the months January–March,
etc). The analysis is based on the period 1950–2006.
The SLP loadings are found as
A(x, M) 5
SLP(x, t)
T
NHLand
-
NHSST
(t)
s
T(t)
, (2)
where A denotes the regression coefficients given as
a function of grid point x and calendar month M (e.g.,
February corresponds to M 5 2); SLP denotes the SLP
data; t corresponds to months M 2 1, M, and M 1 1 for
all years 1950–2006; T
NHLand-NHSST
(t)/s
T(t)
denotes the
detrended T
NHLand-NHSST
surface temperature time se-
ries for months t divided by its standard deviation; and
the overbar denotes the time mean.
The patterns derived from Eq. (2) are summarized in
the top panels in Fig. 2. The contours in the top panels in
Fig. 2 show the A(x, M) regression maps averaged over
the cold (left) and warm (right) season months. The
patterns are similar during the two seasons, but the cen-
ters of action are lower in amplitude and shifted pole-
ward during summer. The wintertime SLP pattern bears
resemblance to the signature of internal atmospheric
variability in the North Pacific sector (i.e., it resembles
the Pacific–North America pattern), but differs from the
pattern of the NAM–NAO over the Eurasian sector; that
is, whereas the center of action of the NAM–NAO is
focused over the Arctic and North Atlantic, the Eurasian
center of action in the top panels of Fig. 2 is located
farther to the east, along the Russian Arctic coast. The
peculiar shape of the SLP pattern can be understood by
superposing it on the climatological mean surface tem-
perature pattern, indicated by the shading in the top
panels of Fig. 2, which is derived from the National
Centers for Environmental Prediction–National Center
for Atmospheric Research (NCEP–NCAR) reanalysis
data. During both seasons, the SLP pattern is situated so
that the inferred geostrophic flow is oriented perpendic-
ular to the climatological-mean temperature gradients
over large areas of western North America and Russia.
The SLP patterns are thus situated to maximize the
anomalous temperature advection over the continents.
The expansion coefficient time series of the seasonally
varying SLP patterns found in Eq. (2) is found by pro-
jecting the SLP data for all months onto the respective
regression map (i.e., the time series for January is found
by projecting the January SLP data onto the January
regression map, etc.). Hence for calendar month M, the
expansion coefficient time series is found to be
T
dyn
(t) 5 SLP(x, t)
A(x)
s
A(x)
"#
, (3)
where SLP(x, t) denotes the anomalous SLP field for
calendar month M; A(x) is the SLP pattern for month M,
as found in Eq. (2); s
A(x)
denotes the (cosine weighted)
spatial standard deviation of A(x) for month M; and the
brackets denote the (cosine weighted) spatial average
over the NH poleward of 408N. The regression maps
A(x) are standardized by s
A(x)
separately for each cal-
endar month since the seasonally varying amplitude of
the SLP data is contained in SLP(x, t) [i.e., if A(x) were
not standardized as a function of calendar month, then
the seasonally varying amplitude in the SLP data would
be weighted twice in the projection]. The time series for
each month are concatenated to form a single expansion
coefficient time series.
By construction, the expansion coefficient time series
generated in Eq. (3) (hereafter labeled T
dyn
)ismore
strongly correlated with variations in T
NHLand-NHSST
than the expansion coefficient time series associated with
any other pattern in the SLP field. The correlation be-
tween T
dyn
and T
NHLand-NHSST
calculated for all months
in the detrended data between 1950 and 2006 is r 5 0.72.
We examined whether other patterns in the SLP field
contribute to T
NHLand-NHSST
by repeating the analy-
sis in Eqs. (2) and (3), but for the case where the T
dyn
index is linearly regressed from T
NHLand-NHSST
before
6124 JOURNAL OF CLIMATE VOLUME 22
calculating A(x). The resulting SLP pattern (not shown)
is more polar-centric than that shown in Fig. 2 and its
associated expansion coefficient is not correlated with
T
NHLand-NHSST
(r 5 0.02).
The efficiency of T
dyn
in capturing the covariability
between the SLP field and T
NHLand-NHSST
is exemplified
by Fig. 3. The solid horizontal line corresponds to the
correlation between T
NHLand-NHSST
and T
dyn
(r 5 0.72).
The circles show the cumulative correlations between
T
NHLand-NHSST
and the principal component (PC) time
series of the NH (308–908N) SLP field. The PCs are
calculated as a function of calendar month, and the
correlation associated with PC n denotes the cumulative
correlation between T
NHLand-NHSST
and principal com-
ponent time series 1/n (the total correlation is found
as the square root of the sum of the squares of the cor-
relations). As is evident in Fig. 3, T
dyn
explains as much
variance in T
NHLand-NHSST
as the first ;6 PC time series
of the SLP field, and higher-order PC time series con-
tribute little additional information to the correlation.
Figure 1b documents the T
dyn
index time series and
compares it with variants of the methodology outlined
FIG. 2. Patterns formed by regressing SLP and surface temperature onto the time series of the difference between NH mean land and
ocean temperatures (T
NHLand-NHSST
). (top) The regression coefficients for SLP (contours) superposed on the climatological mean iso-
therms (shading). (bottom) The regression coefficients for surface temperature. (left) The results averaged over the cold season months
(October–March). (right) The results averaged over the warm season months (April–September). Contour intervals are 0.5 and
0.2 hPa for the cold and warm seasons, respectively. Solid contours denote negative SLP anomalies; minima are labeled in hPa.
15 N
OVEMBER 2009 T H O M P S O N E T A L . 6125
above. The top time series shows the T
dyn
index extended
back to 1900 using the projection given by Eq. (3).
The extended T
dyn
index is dominated by variability on
month-to-month time scales but also exhibits weak de-
cadal variability consistent with trends toward falling
SLP over the Arctic through the mid-1990s (e.g., Hurrell
1995; Thompson et al. 2000). The decadal variability in
T
dyn
is contained entirely in the SLP field. Hence, while
T
dyn
may reflect the effects of increasing greenhouse
gases and/or decreasing stratospheric ozone, it does so
only to the extent that such forcing is manifested in the
variability of the atmospheric circulation.
The time series labeled variant 1 in Fig. 1b shows the
linear combination of the leading 10 PCs of the SLP field
(i.e., the PC time series used to generate the correlations
in Fig. 3). In the summation, the individual PCs are
weighted by their respective regression coefficients with
T
NHLand-NHSST
. The resulting combined PC time series
is largely indistinguishable from T
dyn
(cf. the top two
time series in Fig. 1b), and the correlation between the
time series for the period 1950–2006 is r 5 0.88.
The time series labeled variant 2 examines the impacts
of decadal variability in the temperature field on the
development of the T
dyn
index. In this case, the fifth-
order polynomial fit is removed from T
NHLand-NHSST
before calculating the SLP patterns in Eq. (2). The re-
sulting SLP patterns (not shown) are virtually identical
to those derived from the unfiltered T
NHLand-NHSST
time
series, and the associated expansion coefficient time
series (third from top time series in Fig. 1, bottom panel)
exhibits decadal variability comparable to that found in
T
dyn
. The correlation between T
dyn
and the third from
the top time series is r 5 0.99.
The time series labeled variant 3 shows results derived
by replacing the gridded SLP data in Eqs. (2) and (3)
with gridded surface temperature data. The corre-
sponding cold and warm season regression maps are
shown in the bottom panels of Fig. 2. The regression maps
are physically consistent with the patterns of temperature
advection inferred by the SLP patterns in the top panels
of Fig. 2; that is, temperatures are warmest in regions of
warm advection. Note that the cold season surface tem-
perature pattern in the bottom panels of Fig. 2 is analo-
gous to the COWL pattern found in Wallace et al. (1995),
but is based on regressions, not onto the hemispheric mean
temperature, but rather onto the difference time series
given by T
NHLand- NH SST
.
The expansion coefficient time series fo r t he
temperature-based results is found using the projection
in Eq. (3) (except that the SLP data are replaced
with the surface temperature data). The resulting time
series (variant 3 in Fig. 1b) is highly correlated with
T
NHLand-NHSST
(r 5 0.91) and exhibits a marked trend
over the past few decades, consistent with the enhanced
warming of the land areas relative to the ocean areas
since ;1980. The high correlation (r 5 0.91) between
T
NHLand-NHSST
and variant 3 reveals that the tempera-
ture field is more efficient than the SLP field in explaining
variability in T
NHLand-NHSST
, particularly on month-to-
month time scales. However, the low-frequency variabil-
ity in variant 3 is likely impacted by the thermodynamic
surface response to greenhouse gas forcing. For this
reason, we view the index based on the SLP field as being
a more reliable estimate of the impacts of atmospheric
dynamics on surface temperatures.
c. Removing the effects of ENSO and dynamically
induced variability from global-mean temperatures
The T
ENSO
and SLP-based T
dyn
index time series
derived in the previous sections are removed from three
global-mean temperature time series: the combined
global-mean land and ocean time series (hereafter T
g
),
the global-mean land time series (T
Land
), and the global-
mean ocean time series ( T
SST
).
The components of the global-mean time series that
are linearly congruent with T
ENSO
and T
dyn
are given by
x
fitted
(t) 5 a x(t) where a 5
x9(t) T9(t)
x9
2
(t)
, (4)
FIG. 3. Cumulative correlations (circles) between the leading PC
time series of the NH SLP field and the T
NHLand-NHSST
temperature
time series. For example, the correlation for PC 3 denotes the total
correlation between PCs 1–3 and T
NHLand-NHSST
. The horizontal
line denotes the correlation between T
dyn
and T
NHLand-NHSST
.
Results based on monthly mean data 1950–2006.
6126 JOURNAL OF CLIMATE VOLUME 22
in which the overbars denote the long-term mean,
primes denote departures from the long-term mean, T(t)
denotes the respective global-mean temperature time
series, x(t) denotes the T
ENSO
or T
dyn
index time series,
a corresponds to the regression of x(t) onto T(t), and
x
fitted
(t) corresponds to the component of T(t) that is
linearly congruent with variations in T
ENSO
or T
dyn
. The
regression coefficients (a) are calculated for detrended
monthly mean data for 1950–2006 and are calculated
separately for T
ENSO
and T
dyn
since the time series are
effectively uncorrelated (r 5 0.03). Note also that the
signal of dynamically induced variability is not filtered
from the ocean time series since T
dyn
and T
SST
are not
correlated (r 5 0.00). The results of the fitting are robust
with respect to changes in the periods of the analyses
and are not noticeably affected by the detrending.
Figures 4 and 5 show the effects of removing the T
ENSO
and T
dyn
time series from all three global-mean time se-
ries. The T
dyn
time series evidently accounts for a com-
ponent of the month-to-month variability in T
g
and T
Land
(Figs. 4 and 5b), whereas T
ENSO
accounts for much of the
interannual variability in all three time series (Figs. 4, 5a,
and 5b). The T
ENSO
and T
dyn
residual time series (bottom
time series in all panels) provide a comparatively smooth
rendition of the global-mean temperature variability,
and they also serve to highlight a number of sudden
drops in sur face temperatures over the past century. The
drop in late 1945, which is largely restricted to the T
g
and
T
SST
time series, is attributable to changes in SST
measurement methods, as discussed in Thompson et al.
(2008). Many of the other major drops are coincident
with large tropical volcanic eruptions (indicated by the
dashed vertical lines) and are considered in the follow-
ing section.
4. The volcanic signal in the T
ENSO
and T
dyn
residual data
In this section we document the volcanic signal in the
data formed by subtracting from global-mean temper-
atures the effects of ENSO and dynamically induced
variability. In section 5 we will outline a methodology
for removing the signal of volcanic eruptions from
global-mean surface temperature time series.
Large volcanic eruptions impact climate primarily via
the injection of sulfur-rich volatiles into the atmosphere
FIG. 4. (top) The time series of global-mean, monthly mean surface temperature anomalies
based on the HadCRUT3 combined SST and land surface air temperature data (T
g
). (second
from top) The component of T
g
that is linearly congruent with T
ENSO
. (second from bottom)
The component of T
g
that is linearly congruent with T
dyn
. (bottom) The residual global-mean
surface temperature time series found by removing the linear contributions of T
ENSO
and T
dyn
from T
g
. The vertical lines denote the month of August 1945 and volcano eruption dates (from
left to right) of Santa Marı
´
a, Mount Agung, El Chicho
´
n, and Mount Pinatubo. The horizontal
lines denote the mean for the period 1961–90 (i.e., the base period for the temperature data).
15 N
OVEMBER 2009 T H O M P S O N E T A L . 6127
[see the review by Robock (2000) and references
therein]. Within a few months of the eruption, the vol-
atiles condense to form sulfuric-acid aerosols, and the
resulting aerosol cloud scatters shortwave radiation
while absorbing longwave radiation. The scattering of
shortwave radiation acts to cool the surface whereas the
absorption of longwave radiation acts to warm the
stratosphere (e.g., Stenchikov et al. 1998). In the case of
large tropical eruptions, the meridional gradients in
stratospheric heating give rise to anomalously westerly
flow at middle latitudes not only in the lower strato-
sphere, but also at the earth’s surface (Robock and Mao
1992; see also the discussion in Robock 2000).
The impacts of volcanic eruptions on global climate
depend primarily on 1) the amounts of volatiles that reach
stratospheric levels and 2) the latitudes of the eruptions.
Volatiles that remain in the troposphere are scavenged
within a few months of the eruption and thus do not have
a long-lasting impact on global climate; volatiles ejected
by high-latitude eruptions are restricted primarily to the
eruption hemisphere by the predominantly poleward
meridional Brewer–Dobson circulation in the middle-
latitude stratosphere. On the basis of such criteria,
previous studies have identified the most climatically im-
portant volcanic events of the twentieth century to be the
eruptions of Mounts Pele
´
e–Soufrie
`
re–Santa Maria (in
Martinique, St. Vincent, and Guatemala, respectively)
between May and October 1902, Mount Agung (on the
Indonesian island of Bali) in March 1963; El Chicho
´
nin
April 1982 (in Mexico); and Mount Pinatubo in June 1991
(on the island of Luzon in the Philippines) (Robock 2000).
The surface cooling following the largest eruptions of
the twentieth century has been widely documented (e.g.,
see Jones et al. 2003 and references therein). However, the
amplitude and time scale of the cooling associated with
individual eruptions is difficult to ascertain for two rea-
sons: 1) the eruptions are superimposed upon temperature
variations due to nonvolcanic causes and 2) over the NH
continents, the radiatively driven cooling is opposed by
the dynamically induced warming associated with volcanic
eruptions (Robock and Mao 1992). Previous studies have
examined the volcanic signal in data adjusted for the ef-
fects of ENSO and trends in surface temperatures (e.g.,
Mass and Portman 1989; Santer et al. 2001). But to our
knowledge, no previous study has examined the signal of
volcanic cooling in temperature data after accounting for
the effects of dynamically induced variability.
The obfuscation of the volcanic cooling by dynam-
ically induced variability is exemplified in the response
of global-mean temperatures to the June 1991 eruption
of Mount Pinatubo. The left and middle panels in Fig. 6
are excerpts from the combined land and ocean global-
mean temperature time series (T
g
) and residual T
g
time
series from Fig. 4 but focused on the period surrounding
the June 1991 eruption of Mount Pinatubo. The right
panel in Fig. 6 shows the residual T
g
time series after the
30-yr trend centered on the June 1991 eruption date has
been removed from the data. The cooling following the
eruption of Mount Pinatubo is barely discernible in T
g
(Fig. 6, left) because it is masked by ENSO-related and
dynamically induced variability in the record. The vol-
canic signal is evidently much clearer in the residual
global-mean time series (Fig. 6, middle) but is distorted
by the pronounced global warming trend of the past few
decades. The volcanic signal is most clearly isolated
when the low-frequency global-scale warming of the
FIG. 5. As in Fig. 4, but for (a) global-mean SSTs from the
HadSST2 dataset and (b) the global-mean surface land data from
the CRUTEM3 dataset. Note that T
dyn
is not significantly corre-
lated with the global-mean SST time series and hence is not filtered
from the SST data.
6128 JOURNAL OF CLIMATE VOLUME 22
past decades has been removed from the residual time
series (Fig. 6, right). The results in the right panel in Fig. 6
suggest global-mean temperatures dropped by nearly
0.4 K after the eruption of Mount Pinatubo, an amplitude
that is comparable to the independently derived estimate
found in Santer et al. (2001).
The refinement of the Mount Pinatubo eruption signal
in Fig. 6 is also evidenced in association with the other
large volcanic eruptions of the twentieth century. Figure 7
shows temperatures averaged across the four largest
eruptions of the twentieth century for raw time series (left
column), residual time series (middle column), and de-
trended residual time series (right column; results for
individual eruptions are presented in appendix A). The
top panels in Fig. 7 show the results for T
g
, the middle
panels for T
Land
, and the bottom panels for T
SST
.The
composites are shown with respect to the climatology
for the 4-yr period prior to the eruptions, and are refer-
enced with respect to the first January following the
eruptions to account for the phase locking of the vol-
canic signal with the annual cycle (e.g., Robock and
Mao 1992). A s in Fig. 6, the results in the right column
of Fig. 7 are detrended by removing the 30-yr trend
centered on the eruption dates. Tick marks are shown
for Januarys, and the first January following the erup-
tions is denoted as lag 1. The 95% confidence levels
(horizontal dashed lines) are calculated separately for
each time series and denote values that are exceeded
only 5% of the time in 10
4
randomized sortings of the
composite dates.
The composites in the left column in Fig. 7 are remi-
niscent of similar analyses shown in previous studies (see
Jones et al. 2003 and references therein). The results re-
veal significant global-mean cooling following the erup-
tion date, but the cooling spans only ;2yr and is
matched by similarly large values ;6 yr prior to the
eruption date. The cooling over the land areas is slightly
larger than that over the ocean areas, but the temperature
response over land is noisy and only weakly significant.
The warming of the NH continents during the first winter
following the eruptions is apparent as weak warming at
lag1intheT
Land
composite [Fig. 7, middle panel of left
column; see also Robock and Mao (1992)], but this fea-
ture is not significant in the global mean.
The composites based on the data filtered for the
effects of ENSO and dynamically induced variability
(Fig. 7, middle column) give a clearer representation of
the radiatively driven surface cooling associated with
volcanic eruptions. The noise in the composite results is
greatly reduced, and the cooling following the eruption
date is both smoother and more statistically significant.
The emergence of the radiatively driven volcanic cooling
is particularly pronounced over land where the filtering
methodology accounts for not only random dynamically
induced variability but also the warming of the conti-
nents due to the dynamical impact of volcanic eruptions.
As in Fig. 6, the eruptions stand out even more clearly
when the 30-yr trends centered on the eruption dates are
removed from the data (Fig. 7, right column).
The results in the right column of Fig. 7 provide the
cleanest rendition of the radiative cooling due to vol-
canic eruptions that we are aware of in the existing lit-
erature based on the instrumental record. They are
similar in some respects to a composite of 50 volcanic
eruptions between 1400 and 1940 presented by Hegerl
et al. (2003) in which the timing of the eruptions is in-
ferred from records of ice-core aerosol optical depth and
year-to-year variations in Northern Hemisphere tem-
perature are inferred from tree-ring reconstructions.
The results presented in this study and Hegerl et al.
FIG. 6. (left and middle) The global-mean and residual time series from Fig. 4 but focused on the period surrounding the June 1991 eruption
of Mount Pinatubo. (right) As in the middle panel but the 30-yr trend centered on the eruption date has been removed from the data. The
vertical lines denote the June 1991 eruption date; the horizontal lines denote the mean for the 4-yr period preceding the eruption date.
15 N
OVEMBER 2009 T H O M P S O N E T A L . 6129
(2003) both suggest that the recovery time scale is on the
order of 7 yr: considerably longer than the ;2–3 yr
suggested in the composites in the left panel of Fig. 7.
The ;7 yr recovery time is evident not only over the
oceans but over land areas as well (Fig. 7, right column).
In the following section, we provide a methodology
for removing the volcanic signal from the global-mean
temperature data, and demonstrate that the ;7 yr time
scale is physically consistent with the damped thermo-
dynamic response of the oceanic mixed layer to com-
paratively short-lived volcanic radiative forcing.
5. Removing the volcanic signal from global-mean
temperatures
The methodology used to remove the volcanic signal
from global-mean temperatures is analogous to that used
in section 3 to remove ENSO. In the case of ENSO, we
drove the Hasselman climate model with the time series
of estimated anomalous heat fluxes in the eastern trop-
ical Pacific; in the case of volcanic eruptions, we drive the
same equation with the time series of estimated volcanic
radiative forcing. The response of the global ocean–
atmosphere system to volcanic forcing is thus modeled as
C
d
dt
T
Volcano
(t) 5 F(t)
T
Volcano
(t)
b
, (5)
where T
Volcano
denotes the simulated response of monthly
mean global-mean surface temperature anomalies to
the forcing associated with volcanic eruptions, F(t)is
the global-mean volcanic radiative forcing, b is the cli-
mate sensitivity used in Eq. (1), and C is the heat ca-
pacity of the global atmospheric–oceanic mixed layer
per unit area.
The global-mean volcanic forcing is shown as the top
time series of Fig. 8. The forcing is derived from optical
FIG. 7. Composite response to the eruptions of Santa Marı
´
a, Mount Agung, El Chicho
´
n, and Mount Pinatubo. (left) results calculated
for raw (i.e., unfiltered) global-mean surface temperature data from Figs. 4 and 5. (middle) Results calculated for the T
ENSO
and T
dyn
residual global-mean data from Figs. 4 and 5. (right) As in the middle column but for data detrended for the 30-yr period centered on the
eruption dates. Results are averaged as a function of calendar month and values of zero denote the mean for the 4 yr before the eruption
date. Lag 1 denotes the first January after the eruption date. Horizontal lines denote the 5% and 95% confidence levels for individual
months with respect to the mean for the 4 yr before the eruption date.
6130 JOURNAL OF CLIMATE VOLUME 22
depth measurements given by Sato et al. (1993), and the
optical depth data are multiplied by a factor of 24 W m
22
per unit optical depth to convert them to an equivalent
radiative forcing (Hansen et al. 2005). The volcanic
forcing data were obtained from the National Aero-
nautics and Space Administration’s Goddard Institute
for Space Studies (NASA GISS). The estimated forcing
is most reliable over the past few decades when satellite
measurements are widely available, but the general
characteristics of the forcing are broadly reproducible
over the last half of the twentieth century in other major
reconstructions (e.g., Ammann et al. 2003). The global-
mean forcing peaks at around 23Wm
22
during the
period immediately following the eruption of Mount
Pinatubo.
As was done for ENSO, the effective heat capacity in
Eq. (5) is determined empirically so that the correlation
coefficient is maximized between detrended values of
T
Volcano
and T
g
. In the case of volcanic eruptions the
correlation is maximized for the period surrounding
the eruption of Mount Pinatubo (1988–2000) since 1) the
forcing is well known for this eruption and 2) the period
immediately following the eruption is not complicated
by the superposition of a large ENSO event, as is the
case for the eruption of El Chicho
´
n. The resulting ef-
fective heat capacity (C ; 4.8 3 10
7
Jm
22
K
21
)is
equivalent to the global atmosphere plus ;9mofthe
global oc eanic mixed laye r. Note that the larger heat
capacity used to drive Eq. (5) relative t o Eq. (1) is
consistent with the longer time scale of the forcing
associated with volcanic eruptions than with in-
dividual ENSO events. The T
Volcano
time series was fi t
to the t hree residual global-mean time series in Figs. 4
and 5 using the regression methodology outlined in
Eq. (4).
The global-mean fit to T
Volcano
is shown as the bottom
time series in Fig. 8. Both the forcing and the global-
mean temperature response are dominated by the
eruptions of Mounts Pele
´
e–Soufrie
`
re–Santa Maria (be-
tween May and October 1902), Mount Agung (March
1963), El Chicho
´
n (April 1982), and Mount Pinatubo
(June 1991). But the Sato et al. (1993) time series also
reflects lesser loadings due to the smaller eruptions of, for
example, Mount Katmai (1912) in Alaska, Fernandina
Island (1968) in the Gala
´
pagos Islands of Ecuador, and
Mount Fuego (1974) in Guatemala. As is the case for
ENSO, the thermodynamic model acts to low-pass filter
and lag the input forcing time series.
The quality of the fit between the observed global-
mean temperatures and T
Volcano
is exemplified by Fig. 9.
The jagged lines in the top and bottom curves are re-
productions of the global-mean and detrended residual
global-mean time series from the left and right panels
of Fig. 6, respectively; the smooth curves show the esti-
mate of the response provided by T
Volcano
. As noted in
section 4, the eruption of Mount Pinatubo is difficult to
discern in the raw data (Fig. 9, top) but is readily ap-
parent in the ENSO and T
dyn
residual time series (Fig. 9,
bottom). As is evident in Fig. 9, the T
Volcano
time series
provides an excellent fit to the refined volcanic signal
provided by the residual data.
Figure 10 shows the eruption residual time series ob-
tained by subtracting T
Volcano
from the three global-
mean temperature time series considered in this study:
T
g
, T
Land
, and T
Ocean
. The methodology evidently ac-
counts for virtually all of the decreases in the global-mean
temperatures following the eruptions of El Chicho
´
nand
Mount Pinatubo, but not all of the decreases in temper-
atures following the 1902 eruptions of Mounts Pele
´
e–
Soufrie
`
re–Santa Maria and the 1963 eruption of Mount
Agung. The shortcomings of the fit in 1902 are not sur-
prising since both the temperature data and the forcing
are less reliable for that time. As noted in the following
section, the apparent signal of Mount Agung in the
eruption residual data may reflect changes in SST in-
strumentation or an underestimate of the forcing
FIG. 8. (top) Volcanic radiative forcing based on updated data
described in Sato et al. (1993) and obtained from NASA GISS.
(bottom) The response of global-mean temperatures to the radia-
tive forcing in the top curve, as estimated by Eq. (5).
FIG. 9. The jagged black lines show the (top) raw and (bottom)
detrended residual global-mean temperature time series repro-
duced from Fig. 6. The smooth curves show the response to vol-
canic radiative forcing reproduced from Fig. 8.
15 N
OVEMBER 2009 T H O M P S O N E T A L . 6131
FIG. 10. Subtracting the volcanic signal from the T
dyn
and T
ENSO
residual global-mean data.
In all panels, the top time series is a reproduction of the appropriate T
dyn
and T
ENSO
residual
time series from Figs. 4 and 5, the middle series is the volcanic fit, and the bottom is the resulting
T
dyn
, T
ENSO
, and volcanic residual time series. (a) The results for the combined global-mean
land and SST time series. (b) The results for global-mean SST data. (c) The results for global-
mean land temperature data. Note that T
dyn
is not filtered from the SST time series (see Fig. 5
caption and text).
6132 JOURNAL OF CLIMATE VOLUME 22
associated with the eruption. The implications of the
volcanic eruption residual time series for the in-
terpretation of twentieth-century climate variability are
discussed in the following section.
6. Discussion and implications
The results of the filtering methodology provide a re-
markably clean rendition of twentieth-century global-
mean temperature variability. When the ENSO and
dynamically induced variability are removed from the
global-mean temperature time series, the analyses
highlight the spurious drop in SSTs in 1945 and draw out
the signal of major volcanic eruptions in surface tem-
peratures (Figs. 4 and 5). When the signal of volcanic
eruptions is subsequently removed from the data, the
time series are dominated by century-long warming that
is punctuated primarily by 1) the step in global-mean
temperatures in ;1945 and 2) a brief cooling in the
1970s (Fig. 10). In this section we discuss three aspects of
twentieth-century temperature variability highlighted
by the residual data: the long-term trends, the coupling
between the ocean and land time series on the in-
terannual time scale, and a change in the properties of
the land time series around 1945–50.
a. Long-term tre nds
Figure 11a summarizes the implications of the meth-
odology outlined here for the interpretation of long-
term trends in global-mean temperature. The top panel
in Fig. 11 shows the raw and residual time series of
global-mean temperature T
g
repeated from Figs. 4 and
FIG. 11. (a, top series) The raw (unfiltered) combined land and ocean global-mean temperature time series (reproduced from Fig. 4).
(a, bottom series) The residual global-mean temperature time series formed by regressing T
dyn
, T
ENSO
, and the volcanic signal from the
global-mean data (reproduced from Fig. 10). (b) The residual temperature time series reproduced from the top panel alongside the
percentage of SST observations derived from U.S. ships.
15 N
OVEMBER 2009 T H O M P S O N E T A L . 6133
10a, respectively, where the residual time series is fil-
tered for the effects of ENSO, dynamically induced
variability, and volcanic eruptions. The residual time
series is dominated by variability on very long time
scales, namely the rise in temperatures during the first
half of the century, the sudden drop in global-mean
temperatures in late 1945, and the nearly monotonic rise
since ;1950. The drop in 1945 is consistent with changes
in SST measurement techniques as recorded in the ar-
chive of SST measurements (Thompson et al. 2008). But
a concurrent—albeit much weaker and shorter lived—
dip is also apparent in the residual land time series (Fig.
10c). The nearly monotonic warming from ;1900 to
1945 and from ;1950 to the current day is reflected in
both the residual land and ocean time series in Figs. 10b
and 10c.
The nearly monotonic warming in the residual time
series since ;1950 is punctuated most notably by 1) a
drop in temperatures in ;1963, 2) brief cooling in the
middle 1970s, and 3) a flattening since the late 1990s.
The drop in 1963 coincides with a decrease in the
number of SST measurements derived from U.S. ships
(Fig. 11b). As discussed in Thompson et al. (2008), U.S.
SST measurements were biased warm relative to SST
measurements from the United Kingdom in the middle
twentieth century, and might have been biased warm
relative to SST measurements from other countries in
the 1960s. Hence, the drop in 1963 may reflect changes
in the mix of SST measurements. However, the drop in
1963 also coincides with the eruption of Mount Agung
and is weakly apparent in the residual global-mean land
time series (Fig. 10c). Hence, it is also plausible that the
drop in 1963 reflects an underestimate of the amplitude
of the eruption by the Sato et al. (1993) volcanic forcing
used here. The slight decline in the residual time series
from 1970 to about 1977 i s not coincident with known
changes in measurement techni ques, nor is it clearly
tied to the only large eruption that occurred during the
1970s (Mount Fuego; Fig. 11b). As shown later, the
flatten ing of global-mean temperatures si nce the late
1990s is derived primarily from the SST data. To what
extent the flattening is affected by recent ch anges in SS T
measurements is currently under investiga tion (Worley
et al. 2005; Rayner et al. 2006; Forest and Reynolds
2008).
b. Coupled ocean–land temperature fluctuations
The residual data also highlight the existence of
temperature variations on the interannual time scale
that exhibit a high degree of coupling between the land
and ocean areas that is not attributable to ENSO and
volcanic eruptions. The top time series in Fig. 12 are
superposed values of the raw global-mean land and SST
time series transcribed from Figs. 5a and 5b; the bottom
pair are the corresponding superposed values of the
T
ENSO
/T
dyn
/volcano residual time series transcribed
from Figs. 10b and 10c. The raw time series are highly
correlated, in large part because ENSO and volcanic
eruptions affect both land and ocean temperatures
(Fig. 12, top). But surprisingly, the residual time series
are also strongly correlated, even after detrending. The
residual land and ocean time series in Fig. 12 track each
other remarkably well throughout much of the twentieth
century with two notable exceptions: the large drop in
SSTs in 1945 and the amplified warming of the land
areas since ;1980. The correlations between detrended
values of the global-mean land and SST time series
calculated for the period 1950–2006 are r 5 0.63 for the
raw data and r 5 0.49 for the residual data (both exceed
the one-tailed 99% confidence level).
Figure 13 illustrates the coupling between the raw and
residual global-mean time series in Fig. 12 in more de-
tail. The curves labeled ‘‘all timescales’’ in the top panels
of Fig. 13 represent lag correlations between detrended
values of the global-mean land and SST time series for
the raw (left) and residual (right) data. Negative lags
denote the land time series leading SSTs, and vice versa.
For both the raw and residual data, the correlations peak
near lag 0 but are not symmetric about their maximum
values. At a given lag they are larger when the SST field
leads. The amplitudes of the correlations are larger for
FIG. 12. The (top) raw and (bottom) residual land and SST time
series (gray and blue, respectively). The raw time series are re-
produced from Fig. 5; the residual time series are reproduced from
Fig. 10. The correlations for the period January 1950–December
2006 are r 5 0.84 (r 5 0.63 after detrending the data) for the top
time series and r 5 0.85 (r 5 0.49 after detrending the data) for the
bottom time series.
6134 JOURNAL OF CLIMATE VOLUME 22
the raw data, but the asymmetry of the correlations
about lag 0 is more striking for the residual data.
The asymmetry in the correlations is accentuated in
lag correlations calculated for 1–20-yr (i.e., 12–240
month) bandpass-filtered versions of the time series
(labeled ‘‘interannual’’ in the top panels in Fig. 13).
Similar results are obtained for high cutoff frequencies of
6, 12, and 24 months (not shown). For both the raw and
residual data, the correlations based on interannual data
have substantially higher amplitudes and peak when the
SST time series leads by ;2–3 months. However, the
asymmetry in the lag correlations is more pronounced in
the residual data. Both the significant covariability and
the ;2–3 month lag between the ocean and land time
series are visually apparent in the interannual versions of
the time series (Fig. 13, bottom panels).
As noted earlier, covariability between the raw
global-mean land and SST time series is to be expected
since ENSO projects onto both land and ocean areas.
But the coupling between the residual time series is
surprising since ENSO has been linearly removed from
both the land and SST time series. The observed cou-
pling documented in Fig. 13 provides observational
support for analogous coupling found in climate simu-
lations forced by prescribed SST anomalies (e.g., Zhang
et al. 2007; Compo and Sardeshmukh 2008; Hoerling
et al. 2008; Dommenget 2009).
Is the observed covariability between the residual
global-mean land and SST time series derived from any
particular region of the globe? Figure 14 shows the
correlation map formed by regressing gridded SST data
onto the residual interannual global-mean land time
series (i.e., the gray time series in Fig. 13, bottom right;
note that ENSO, volcanic eruptions, and dynamically
induced variability are removed from the global-mean
land time series but not from the gridded SST data since
the filtering methodology is only applicable to area av-
erages). The correlation map reveals scattered areas of
positive correlations over all three oceans, but in general
the correlations are most coherent over the tropical and
northern North Atlantic; that is, much of the covariance
between the residual land and ocean time series in Figs.
12 and 13 is derived from SST variability in the Atlantic
Ocean north of the equator. The correlations between
1–20-yr bandpass-filtered SST anomalies averaged over
the North Atlantic Ocean poleward of the equator and
the global-mean residual land time series are statistically
significant but are largest at zero lag (r 5 0.39; exceeds
FIG. 13. (a) Lag correlations between detrended values of the raw (i.e., unfiltered) land surface temperature and SST time series from
Fig. 12. Results are shown for interannual and all time scales (where interannual is defined as 1–20-yr bandpass filtered). (b) The in-
terannual versions of the raw land surface temperature and SST time series. (c),(d) As in (a),(b), but for analyses based on the residual land
and SST time series from Fig. 12.
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the 97.5% significance level), not when the SST field
leads (results not shown).
c. The drop in high-frequency variance in
global-mean land temperature data in the 1940s
Another aspect of global-mean temperature vari-
ability highlighted by the filtering technique is the
change in the mean value and month-to-month vari-
ability of the residual land temperature time series
around ;1945–50. The timing of the apparent change in
the statistical properties of the land data is of particular
interest since it coincides with the sudden drop in SSTs.
The top time series in Fig. 15 shows the residual land
time series transcribed from Fig. 10c. The decrease in
variance ;1945–50 is visually apparent in the residual
global-mean time series but is objectively verified by
plotting the derivative and the absolute value of the
derivative of the time series (Fig. 15, second and third
time series from the top). Taking the time derivative
amplifies the high-frequency sampling variability in the
record, much of which is attributable to the incomplete
spatial coverage of the station network, and taking the
absolute value of the derivative reveals its evolution
more clearly. The outstanding features are the decline in
sampling variability during the late 1940s and the
weaker increase after ;1990.
The curve at the bottom of Fig. 15 shows the fraction
of the globe covered by the gridded land data (defined as
the cosine-weighted global percentage of grid boxes
with at least one reporting station). The drop in variance
in the land time series in the late 1940s is broadly con-
sistent with the time history of the coverage of the land
surface temperature observing network. We test this
hypothesis by showing the same temperature time series
in Fig. 16, but calculated only from grid boxes with at
least 50% coverage between 1900 and 1940. Freezing
the spatial coverage to the pre-1940 era eliminates most,
albeit not all, of the decrease in the sampling variability
during the mid–twentieth century.
7. Concluding remarks
The purpose of this paper is to develop and apply
a robust, simple, and physically based methodology for
the removal from global-mean temperatures of the
FIG. 14. Correlations between the raw (i.e., unfiltered) SST data and the residual global-
mean land temperature time series. The residual land time series is the T
dyn
/T
ENSO
/volcanic
residual time series, and is filtered to retain only interannual variability between 1 and 20 yr
(i.e., it is the land time series from the bottom right of Fig. 13).
FIG. 15. (top) The residual global-mean surface land tem-
perature time series from Fig. 10. (second from top) The time de-
rivative of the top time series. (second from bottom) The absolute
value of the time derivative. (bottom) Time history of the per-
centage of station coverage used in the CRUTEM3 data (defined
as the cosine-weighted global percentage of grid boxes with at least
one reporting station).
6136 JOURNAL OF CLIMATE VOLUME 22
variability associated with known climate phenomena.
Previous studies have estimated the signals of ENSO,
volcanic eruptions, and internal atmospheric variability
in global-mean temperatures using various regression
methodologies. But as far as we know, this is the first
study to 1) represent the signals of ENSO and volcanic
eruptions using a simple thermodynamic model of the
climate system, 2) use the SLP pattern most strongly
coupled to the global-mean temperature time series to
represent the effe cts of dynamically induced variabil-
ity, and 3) explicitly remove (or filter out) the temporal
signatures of these three sources of natural variability
from global-mean t emperature time series. The filt er-
ing methodology does not degrade the time resolution
of the data. Hence, unlike filtering schemes based on
temporal smoothing, this new approach yields a residual
time series in which discrete changes in the time history
of global-mean temperatures, including changes in in-
strumentation and explosive volcanic eruptions, are fully
resolved.
The central findings highlighted by the filtering
methodology include the following:
1) Filtering global-mean temperature time series to re-
move the effects of known sources of natural vari-
ability enriches the signal of the anthropogenically
induced warming over the past century (Fig. 11a).
The trends in the raw and residual data for the period
January 1950–March 2009 are comparable (;0.12 K
decade
21
); but the standard deviation of the (de-
trended) residual data is only 2/3 as large as the
standard deviation of the raw data (;0.10 versus
;0.15 K). The residual time series shows more
clearly the enhanced warming of the land areas rel-
ative to the ocean areas over the past few decades
(Fig. 12). To what extent t he differences between
ocean and land warming reflect the cooling bias in
SSTs due to the recent transition from ship- to buoy-
derived SSTs remains to be determined (Worley
et al. 2005; Rayner et al. 2006; Forest and Reynolds
2008).
2) The residual time series show more clearly the signal
of volcanic eruptions in surface temperature. For ex-
ample, the signal of the eruption of Mount Pinatubo is
barely discernible in the raw global-mean tempera-
ture time series (Fig. 6, left), but is clearly visible in the
data filtered for the effects of ENSO and dynamically
induced variability (Fig. 6, middle and right). The
refined volcanic signal, with its longer decay time
scale, should be more suitable for estimating climate
sensitivity from observations of the climate system
responsetovolcanicforcing.
3) The analyses reveal the existence of observed coupling
between global-mean land and ocean temperatures on
the interannual time scale, even after the effects of
ENSO and volcanic eruptions are filtered out of the
temperature time series. The observed coupling is
largest when the SST field leads by ;2–3 months
(Fig. 13) and is most prominent in the sea surface
temperature variability in the North Atlantic Ocean
(Fig. 1 4).
4) The analyses highlight the spurious discontinuity in
global-mean temperatures in late 1945 (Fig. 11), and
they also reveal a marked decrease in variance in the
land temperature time series during the late 1940s
(Fig. 15). The discontinuity in 1945 is derived largely
from the SST field and appears to be related to the
difference in SST measurement techniques between
U.S. and U.K. ships in combination with an abrupt
transition in the mix of marine observations from
predominantly U.S. ships during World War II
(WWII) to predominantly U.K. ships in the postwar
years (Thompson et al. 2008). The drop in variance in
the land data is coincident with rapid increases in the
size of the observing network from ;1951 onward. It
is worth noting that the land data also exhibit a small
drop in the mean ;1945, although this decline is
much smaller than that found in the residual SST
time series (Fig. 10). The SST data corrected for in-
strument changes in the mid–twentieth century are
expected to become available in 2010, and it will be
interesting to see how the corrections affect the time
history of global-mean temperatures, particularly in
the middle part of the century.
The thermodynamic model used to estimate the signal
of ENSO and volcanic eruptions provides a framework
for deriving a ‘‘transfer function’ that yields the global-
mean temperature response to a prescribed forcing based
FIG. 16. As in the top three time series in Fig. 15, but for the
residual global-mean land surface temperature time series calcu-
lated for grid points with at least 50% coverage between 1900 and
1940.
15 N
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on a simple least squares best fit. In addition to the fitted
time series, the procedure yields an effective heat ca-
pacity, that is, the value of C that corresponds to the least
squares best fit. Given a climate sensitivity of b5
2
/
3 K(Wm
22
)
21
, the effective heat capacity was found to
be equivalent to the atmosphere plus a 2-m-deep ocean
in the case of ENSO, and a 9-m-deep ocean in the case
of volcanic eruptions. These estimates are only approxi-
mate in the sense that if they are doubled or halved, the
fit between the observations and the model is degraded
only slightly. Furthermore, t he estimates do not imply
that the signals of ENSO and volcanic eruptions are
limited everywhere to the top 2 and 9 m of ocean, re-
spectively; that is, the model is based on a globally av-
eraged heat capacity and neglects the flux of heat into
the deep ocean. In principle, the thermodynamic model
can be used in a diagnostic manner to derive information
about both the effective heat capacity and the climate
sensitivity, b. But we have not attempted to do that here
because C and b are both dependent on the time scale of
the forcing.
The filtering methodology should prove useful for
investigating variations in global-mean temperature
due to phenomena other than ENSO, variations in the
high-latitude NH winter circulation, and volcanic
eruptions (e.g., solar variability, variations in the oce-
anic thermohaline circulation, the e ffects of tropo-
spheric aerosols, etc.). It could also be extended to
include known sources o f variability other than those
considered here. For example, the pervasive negative
correlations between surface temperature and pre-
cipitation over low-latitude regions, where local con-
trol of temperature via the evaporation from the
underlying surface (Nicholls et al. 1996; Trenberth and
Shea 2005) might be exploited to filter out additional
variance of the temperature time series.
FIG. A1. As in Fig. 6, but for the raw, residual, and detrended residual SST time series focused on the period surrounding the four largest
eruptions of the twentieth century. Year 1 denotes the first January after the eruption date.
6138 JOURNAL OF CLIMATE VOLUME 22
Acknowledgments. We thank Kevin Trenberth and
Ben Santer for helpful commen ts on the manuscr ipt;
Susan Solomon, Dennis Hartmann, Jonathan Gregory,
and Piers Forster for helpful discussions of the results;
and Alan Robock and two anonymous referees for
insightful r eviews of the manuscript. The analyses of
the volcanic s ignal are an outgrowth of work that
DWJT did for his M.S. thesis at the University of
Washington during 1997–98. DWJT and JMW are
supported by the NSF’s Climate Dynamics Program
under budget numbers ATM-0132190 and A TM-
0613082 (DWJT) and ATM-0318675 and 0812802
(JMW). JJK was supported by the Joint DECC, Defra
and MoD Integrated Climate Programme–DECC/
Defra (GA01101), MoD (CBC/2B/0417_Annex C5).
PDJ is supported by the U.S. Department of Energy
(DE-FG02-98ER62601).
APPENDIX
Figures A1 and A2 document the volcanic signal in the
global-mean SST and land data, respectively, for the four
largest eruptions since 1900. The average of the results
shown in Figs. A1 and A2 corresponds to the ocean and
land composites in Fig. 7. As in Fig. 6, the left columns in
Figs. A1 and A2 show the results for the raw data, the
middle columns show the results for the residual data, and
the the right columns the results for the detrended re-
sidual data. The data are detrended by removing the
30-yr linear trend centered on each eruption date. As was
done for Fig. 6, the residual SST data are formed by re-
moving the ENSO signal from the data; the residual land
data are formed by removing the signatures of ENSO and
dynamically induced variability from the data. Year 1
denotes the first January after each eruption.
FIG. A2. As in Fig. A1, but for the raw, residual, and detrended residual land surface temperature time series focused on the period
surrounding the four largest eruptions of the twentieth century. Year 1 denotes the first January after the eruption date.
15 N
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... The Pinatubo event has several properties that make it attractive for our study: i) it is a "point forcing," which can be expected to have a temporally-localized response driven by a spatiallylocalized source; ii) it exhibits a large and immediately visible response, allowing us to focus on the fingerprinting problem without additional pre-or post-processing requirements; iii) it is well-characterized in the literature, having previously been studied by Thompson et al. (2009), Kremser et al. (2016), and Wagman et al. (2021, among many others, allowing for validation of our findings. Finally, while our analysis exclusively considers simulated data, we note that the Pinatubo eruption is, by climate standards, a recent event and that high-quality observational data or reanalysis products are available to validate simulated climate responses. ...
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