CHAPTER XXATTRIBUTION OF CLIMATE CHANGE IN THE PRESENCE OF INTERNAL VARIABILITY

John M. Wallace1, Clara Deser2, Brian V. Smoliak1, and Adam S. Phillips2
1

2

Department of Atmospheric Sciences, University of Washington,
Seattle, WA 98195, USA

Climate and Global Dynamics Division, National Center for Atmospheric Research,
Boulder, CO 80305, USA

Spontaneous, internally-generated variability of the climate system is pervasive. On the multidecadal time scale it dominates the variability of surface air temperature averaged over extratropicalland areas as large as the contiguous United States, and it modulates the rate of rise of global mean
temperature in response to the buildup of greenhouse gases. Unforced variability is one of the factors that imposes limitations on the degree of confidence that can be attached to assessments andpredictions of human-induced climate change. This chapter summarizes results of some recent
studies based on the analysis of large ensembles of numerical integrations run with a suite of different atmospheric initial conditions but with the same prescribed external forcing scenario. The
future trajectory of the real climate system is, in some sense, like the trajectory of an individual
member of such an ensemble. The diversity of the trends among the different ensemble members
is a part of the irreducible uncertainty inherent in projections of future climate change. It is shown
how statistical methods can be used to diagnose the causes of this diversity, most of which is in response to member-to-member diversity in the atmospheric circulation trends, as reflected in theassociated patterns of the sea-level pressure trends. Interactions between the atmosphere, oceans,
and land also contribute to the variability of surface air temperature trends on the multidecadal
time scale, as discussed in Chapters XX and XX. It is argued that in the face of such large uncertainties in the attribution of climate change in the extratropics, more attention should be focusedon climate change in the tropics, where the greenhouse warming signal stands out more clearly,
and on the broader suite of environmental issues that impact food security and the viability of ecosystems.

1. Introduction

turning Circulation was mainly responsible forthe mid-20th century hiatus and the recent
slowdown in the rate of global warming. Nor
is it clear why the Arctic has experienced rapid warming during the past decade while surface air temperatures over the Northern Hemisphere as a whole warmed less than in the twoprior decades, or why wintertime temperatures

Many questions concerning the nature andcauses of climate variability on the multidecadal time scale are still unresolved. For example, there is no consensus within the scientific community as to whether time-varying
forcing associated with aerosols or whether astrengthening of the Atlantic Meridional Over1

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Wallace, Deser, Smoliak, and Phillips

over the Northern Hemisphere continents
poleward of 40°N warmed three times as rapidly as global-mean (land plus ocean) annualmean surface air temperature during the late
20th century (e.g., see Trenberth et al. 2007).
These large spatial and temporal differences in
the rate of warming stem from the fact that theclimate system is varying on the multidecadal
time scale in response to its own internal variability as well as to a variety of natural andanthropogenic forcings. It is often difficult todistinguish between internally generated low
frequency climate variability and humaninduced climate change. In the words of theTechnical Summary of the IPCC’s Fourth Assessment Report, “Difficulties remain in attributing temperature changes at smaller thancontinental scales and over time scales lessthan 50 years.” (Solomon et al. 2007). Theseambiguities can be expected to persist until thesignature of human-induced climate change
becomes large enough to stand out clearly
above the natural “background variability”, asis projected to occur in the second half of thiscentury (Deser et al. 2012a).
The causes of surface air temperature(SAT) trends over the continents can be formally separated into the four categories listed
in Fig. 1, which are arranged in the form of a 2
x 2 matrix, the columns separating thermodynamically- versus dynamically-induced SAT
variability and the rows separating forced versus free variability. In this terminology, thermodynamically-induced refers to SAT changes
induced by time-varying radiative fluxes or bytime-varying fluxes of sensible and latent heatat the Earth’s surface, exclusive of any concomitant changes in the atmospheric circulation and dynamically-induced denotes SAT
changes attributable to changes in the atmospheric circulation, irrespective of their cause.

The term forced refers to responses to externally imposed changes in the Earth’s energybalance, including both anthropogenic influences and natural forcings such as volcanic
eruptions, solar variability and, on long timescales, orbital changes. Forced, thermodynamically-induced trends in global-mean temperature (the upper left box in Fig. 1) plays a central role in projections of human-induced climate change. However, for attribution of regional and perhaps even global climate trends
on the multidecadal time scale, the other three
categories need to be considered as well.
If the global atmospheric circulation
changes systematically in response to humaninduced global warming or due to naturalcauses it will result in further SAT changes
that can be said to be dynamically-induced(the upper right box in Fig. 1). Examples ofdynamically-induced climate change include a
circulation-induced poleward amplification of
the temperature trend at the Earth’s surface(Alekseev et al. 2005), a widening of the tropical Hadley cells (Lu et al. 2007), a poleward
shifting of the extratropical storm tracks (Yin
2005), and a systematic weakening of the tropical circulations (Vecchi and Soden 2007). It
has been proposed that the “robust response to
global warming” includes a suite of circula-

FIG. 1. A scheme for categorizing the factors that contribute to trends in regional surface air temperature. See
text for explanation.

Attribution of Climate Change in the Presence of Internal Variability

tion-related changes that can be inferred frombasic conservation laws (Held and Soden2006). Other examples of externally forced
dynamical responses include changes in thewintertime circulation over high northern latitudes induced by large volcanic eruptions(Robock and Mao 1994; Shindell et al. 2001)
and changes in the monsoon circulations in
response to the changing meridional profile ofinsolation induced by orbital changes(Kutzbach 1981).
Spontaneously occurring changes in theamplitude and polarity of preferred atmospheric circulation patterns such as the Northernand Southern Hemisphere annular modes(Wallace and Thompson 2002) or the patterns
observed in association with ENSO (Nitta and
Yamada 1989; Trenberth and Hurrell 1994;
Zhang et al. 1997), as represented by the lower
right box in Fig. 1, should induce regional
SAT trends on the multidecadal time scale.
The amplitude of the dynamically-induced
SAT changes tend to be much larger over land
than over sea, because of its lower heat capacity. Hence, if the dynamically-induced SAT
trends project strongly upon the land-sea distribution, they may contribute to the hemispherically or globally averaged temperature
trend; e.g., if they were to change in a mannerso as to cool the oceans and warm the land,that would constitute a positive contribution.
Dynamically-induced warming in response toatmospheric circulation changes has been invoked to account for the rapidity of the wintertime warming over Eurasia and North America poleward of 40°N during the late 20th Century (Hurrell 1996; Wallace et al. 1995, 1996;
Bracco et al. 2004).
In most of the existing literature on the impacts of the unforced (or internal) variabilityof the climate system it is assumed that the3associated regional or global temperature
trends over land are mediated by changes in
the atmospheric circulation. However, it isalso possible that a component of the SAT
trends could be thermodynamically-induced(the lower left box in Fig. 1). For example, it
has been suggested that the ENSO cycle affects SAT not only through planetary-scaleteleconnections (the lower right box), but also
by modulating the surface energy fluxes overthe equatorial Pacific cold tongue region(Yuleva et al. 1994; Chiang and Sobel 2002).
It has recently been proposed the sea surface
temperature variations over high latitudes of
the Atlantic Ocean and the Arctic Ocean that
occur in association with unforced variationsin the intensity of the meridional overturning
circulation on the multidecadal time scale
might be capable of causing even larger SAT
variations over Eurasia on the multidecadal
time scale (Semenov et al. 2010).
In the world of models, the distinctions between the four boxes are clear, at least in principle.
Anthropogenically-forced
climatechange can be distinguished from internallygenerated, free climate variability based on asuite of simulations, performed with a single
model in which each ensemble member isstarted from a different set of initial conditions
and run with the same prescribed, timevarying external forcings. In principle, thetrends in the ensemble-mean of the simulations can be identified with the externallyforced climate change “signal” and the departures of the trends in the individual realizations from the ensemble mean trends are attributable to the internal variability of the simulated climate system. This methodology isuseful when the number of individual realizations is large enough to ensure a high level ofstatistical significance. However, thus far, en-4Wallace, Deser, Smoliak, and Phillips

sembles sizes in the CMIP simulations havebeen so small that it has been necessary to use
multi-model ensemble means to obtain statistically significant results, in which case internal variability and model-to-model differences
both contribute to the departures of the trends
in the individual realizations from the ensemble-mean trend, rendering attribution problematical. In principle, thermodynamically versus
dynamically forced variability can likewise bedistinguished through experimentation withclimate models, but in practice the design ofexperiments that permit one kind of forcing
but not the other is not straightforward.
Just how applicable the results derived
from the model world are to the real world
depends upon how well the models run withand without various prescribed external forcings are able to simulate the internally generated low frequency variability of the climate
system. With only one observed climate trajectory that can be used as a basis for validating the models, this question can only be addressed in a probabilistic way. Validating climate models requires a robust characterizationof the low frequency variability in the historical climate record, including temporal means,variance and covariance statistics, and spectra.
To obtain robust estimates of these quantities(i.e., estimates with a sufficient number of statistical degrees of freedom) it is necessary to
restrict the analysis to frequencies at least anorder of magnitude higher than one cycle overthe length of the ~100-year-long historical
record, e.g., by applying a high pass filter. Attribution of variability with frequencies lower
than this cutoff frequency is inherently ambiguous. Multidecadal variability falls within this“twilight zone” in which attribution can be
performed only in a probabilistic way.

Another factor that limits our ability to diagnose the decadal-scale variability in the climate record is the fact that inherently stochastic variability on the interannual time scaleassociated, for example, with the ENSO cycle
or with large excursions of the Northern andSouthern Hemisphere annular modes is capable of inducing substantial sampling variability on the multidecadal time scale. For example, it has been questioned whether the socalled Pacific Decadal Oscillation (PDO:
Mantua et al. 1997), which is alleged to be amultidecadal phenomenon is merely a manifestation of such stochastic, sampling variability (Newman et al. 2003).
Regardless of the mechanisms that giverise to it, multidecadal climate variability mediates the rate of rise of global-mean temperature. Performing a “dynamical adjustment” toremove, or at least reduce the contribution ofthese circulation changes that contribute to or
detract from the rate of rise in global-meantemperature simplifies the space-time structureof the surface air temperature record and renders it more spatially and seasonally coherent(Wallace et al. 1995; Thompson et al. 2009).
The existence of internally generated sampling variability is well known and is discussed extensively in reviews of Barnett et al.
(2005) and Hegerl et al. (2007) and the references therein. Various approaches have beenused to estimate the uncertainty in past andprojected SAT trends that is attributable tosuch “climate noise,” but the emphasis in these studies has generally been on establishing
the statistical significance of historical or projected climate trends rather than on the characteristics of the noise itself. In many studies thenoise is represented as formless error bars
flanking the observed, reconstructed, or projected “signal.” In reality, climate noise exhib-

Attribution of Climate Change in the Presence of Internal Variability

its distinctive space-time structure that can
mimic that of human-induced climate change.
Later in this chapter we will recall two relatively recent instances in which apparent secular trends deemed as having been beyond therange of natural variability have subsequently
reversed, suggesting that they were, in fact,internally generated.
In this chapter we will summarize the stateof our knowledge of internally generated interdecadal variability of the climate system. In
the next section we will show how the interplay between free and forced climate variability complicates the attribution of global warming and regional climate impacts. In Section 3
we show examples of the dynamical contribution to SAT trends and we demonstrate how
performing a dynamical adjustment can simplify the representation of climate change inthe historical record. In Section 4 we offer a
few brief comments relating to the internallygenerated thermodynamically-induced variability. In the final section we summarize anddiscuss the implications of these results moregenerally.
2. On the role of internally-generated climate variability in climate change
In this section we will discuss the role ofinternally-generated climate variability in climate change on space scales ranging from regional to global. We will begin in Section 2.1
by considering the diversity and spatial patterns of surface air temperature (SAT), sealevel pressure (SLP) and precipitation trends
in a 40 member ensemble of simulations run

5with Version 3 of the Community Climate
System Model (CCSM3) forced with the A1B
greenhouse gas scenario initialized in 2000
and integrated forward in time through 2060.
Details of the model simulations may be foundin Deser et al. (2012a). Then in Section 2.2 wewill show and discuss observations and simulations of global warming during the 20th
Century. In interpreting these results it should
be noted that existing climate models exhibit
substantial diversity with respect to their mean
climates and the level of internally generated
climate variability. Hence, the results presented here, which are derived from only two ofthese models, should be regarded as illustrative, but not necessarily representative of the
behavior of the real climate system.
2.1. Insights derived from projections of future trends
As background for the discussion in thissubsection we show in Fig. 2a,c the ensemble
mean of the 56 year (2005–2060) DecemberFebruary (DJF) SLP and SAT trends in the 40
member CCSM3 ensemble in raw (hPa per 56
years; °C per 56 years) and standardized form
(Fig. 2b,d respectively). The SLP trends in theensemble mean map range up to several hPa(e.g., off the west coast of Canada) but withthe exception of a few patches in the tropics,
they are generally much less than one standard
deviation and therefore may be interpreted as
sampling fluctuations. In contrast, the ensemble mean SAT trend (Fig. 2d) exhibits a robust global warming signal, with an averagewarming of 2–3 standard deviations over the6

Wallace, Deser, Smoliak, and Phillips

Fig. 2. DJF sea level pressure (SLP) and surface air temperature (SAT) trends for 2005-2060 in a 40-member ensemble of simulations with the CCSM3 climate model. Left panels (a) Ensemble-mean SLP trend; (b) Ensemblemean SAT trend. Right panels (c) Standardized ensemble-mean SLP trend (SLP*) computed by dividing the ensemble mean trend at each grid point by the standard deviation of the 40-member ensemble trends at the same grid pointand (d) Standardized ensemble-mean SAT trend (SAT*). From Deser et al. (2012a).

FIG. 3. Partitioning of the 56-year temperature trends in Ensemble Members #4 and #22 into a component forced by
the buildup of greenhouse gases and a residual trend attributable to internally generated variability. Adapted from
Deser et al. (2013).

Attribution of Climate Change in the Presence of Internal Variability

Northern Hemisphere continents. In agreementwith observations, the “signal to noise ratio” of
the warming trend is larger in the tropics thanat higher latitudes (Mahlstein et al. 2011,2012).
The diversity of the patterns in SAT trends
in the 40 individual ensemble members is illustrated by contrasting the 2005–2060 trends
in Members #4 and #22, which correspond to
the weakest and strongest warming trends averaged over the contiguous United States. In
Fig. 3 the trends for these two ensemble mem-7

bers are partitioned into “Forced” and “Natural” components, the former defined by theensemble mean trend and the latter by the departure of the trends in these two ensemble
members from the ensemble mean trend. It isevident that the “Natural” component of thetrend, which is attributable to internally generated variability, is as large as the “Forced”
component.
Figure 4 shows selected time series of SAT
in Ensemble Members #4 and #22. The global-mean SAT trend (land areas only) is quite

FIG. 4. (Left panels) DJF temperature trends during 2005–2060 (°C per 56 years). Top panel shows the 40-member
ensemble mean; middle and bottom panels show the corresponding trends in Members #4 and #22. Right panels show
DJF time series for selected regions and specific locations as indicated by the labeling and marked by the open circles
in the left panels). The black segments of the curves show observed records from 1910–2008 (minus the long-termmean); the red and blue segments show model projections for 2005–2060 based on the ensemble members with thelargest and smallest projected trends, respectively, for each region or location. Dashed red and blue lines show the
best-fit linear trends in these same ensemble members. For visual clarity, time mean SAT in the model projections areadjusted to match to observations averaged over their common period of record 2005–2008. From Deser et al. (2012b).

8

Wallace, Deser, Smoliak, and Phillips

comparable in the two ensemble members but
the regional and local trends over the contiguous United States (CONUS) have a profoundly different character. In Member #22 averagewarming over the CONUS over the 56 year
period is ~3°C, whereas in Member #4 it is
only ~1°C and cooling occurs over parts of the
Pacific Northwest and the northern Rockies.
The patterns shown in Figs. 2–4 are for theboreal winter season December through February (DJF) when the internally generated variability is greatest. However, the spatial patterns in individual members of the CCSM3
40-member ensemble also exhibit substantial
diversity during the boreal summer JuneAugust (JJA), as shown in Fig. 5. The con-trasts between outliers are not as large as during winter but they are still appreciable.
In the summertime precipitation trends
based on the same 40-member ensemble, mostensemble members exhibit positive trends
over Canada and Alaska, but a wide memberto-member diversity of the rainfall trends overthe continental United States. The two examples shown in Fig. 6 portray sharply contrasting future rainfall trends over the Great
Plains and Midwest relative to the 2005–2008
rainfall climatology in that ensemble member.
Large ensembles are required to detect statistically significant precipitation trends in simulations with climate models and there is no
guarantee that nature will conform to the en-

Fig. 5. As in Fig. 4 but for Ensemble Members #3 and #31, the most contrasting runs in JJA. From Deser et al.,(2012b).

Attribution of Climate Change in the Presence of Internal Variability

semble-mean projection. It follows that unlessthe CCSM is seriously underestimating therole of soil moisture feedbacks, regional precipitation trends forced by the buildup of
greenhouse gases are not likely to become detectable above the internally generated background variability in the observations until
well beyond 2060.
2.2. Observed and simulated 20th Century
trendsHistorical reconstructions of the climate of
the 20th century provide an even more graphic
illustration of the inherent difficulties in comparing an individual realization (in this case,the historical record) with an ensemble of nu-

FIG. 6. As in Fig. 4 but for summer (JJA) precipitation.

9

merical simulations. Figure 7 shows 1970–2005 wintertime surface air temperature trends
for individual ensemble members of suites ofhistorical simulations conducted with the
CCSM4 and ECHAM5 models. These initialcondition historical ensembles follow a similar
experimental design as the 21st Century ensembles discussed above (Deser et al. 2013).
CCSM4, introduced in 2010, is more advanced than CCSM3 in several important respects (Gent et al. 2011). The patterns for thehistorical reconstructions are even more diverse than the ones shown in Figs. 4-6 because
the interval over which the trend is computed
is 36, rather than 56 years, and is thus subject
to smaller anthropogenic forcing and larger
sampling variability.

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Wallace, Deser, Smoliak, and Phillips

FIG. 7. DJF surface air temperature trends for the reference interval 1970–2005 in a 30-member ensemble of
the CCSM4 (C1–C30) and 17-member ensemble performed with the ECHAM model (E1–E17). Trends are
expressed in °C per 36 years. The ensemble-mean trend
and the observed trend for this period are shown at theend of the sequence of maps.

In the context of these simulations, the observational record is just one of the many possible outcomes of the time dependent forcingthat the climate system has been subject toover the past century. Let us now consider theobserved trends in greater detail. Figure 8
shows time series of observed and simulated
trends in (a) global mean surface temperatureincluding both land and ocean, (b) globalmean surface air temperature over land and (c)cold season surface air temperature poleward
of 40°N. The simulations in this case are basedon the reference interval 1965–2000 (5 years
earlier than the one used in the simulations
described in Fig. 7, but 30 out of the 36 yearsof the two records are overlapping. Both intervals 1965–2000 and 1970–2005 were marked

Fig. 8. Observed (solid) and multi-model ensemble mean
(MMEM) (dotted) temperature anomaly time series withrespect to the 1965–2000 reference period (indicated bylight gray shading) for (a) annual-mean, global-meansurface temperature (GST), (b) annual-mean, global
mean land temperature (GSAT), and (c) boreal cold season-mean (Nov.–Apr.) land temperature poleward of
40°N. Tick marks on the abscissa denote intervals of
0.5°C. Observations from NOAA merged ocean land
surface temperature dataset. Model output based on AR4(CMIP3) historical simulations in which ozone depletionand volcanic aerosols are included as part of the forcing(1900–1999) and SRES A1B simulations (2000–2012).
Adapted from Wallace et al. (2012).

by pronounced warming that was more rapid
over land than over the oceans, as shown in
Fig. 8a,b and the high latitude Northern Hemisphere continents warmed about three times asmuch as annual mean GST during the boreal
cold season (Fig. 8c).
The GST time series based on the multimember ensemble mean of the CMIP simulations closely tracks the observations during thereference period 1965–2000 but it fails to cap-

Attribution of Climate Change in the Presence of Internal Variability

ture the flattening of the curve in the past decade. As of the end of 2012 the projections
were ~0.4°C higher than the observed GST.
Figure 9 shows the spatial distribution of
the observed 1965–2000 SAT trends during
the boreal cold and warm seasons (a,c) together with multi-model ensemble means of numerical simulations that were used as a basis
for the Fourth Assessment Report of the IPCC
(b,d; Randall et al. 2007; Meehl et al. 2007):the simulations include nine different models
with ensemble sizes ranging from 1 to 5. Consistent with the modeling results presented in
the previous subsection, the multi-model ensemble-mean trends are much more spatiallyhomogeneous than the observed trends, particularly over high northern latitudes during
the boreal cold season. The observed warming
trends over Siberia and Canada during thisinterval, which ranged up to ~3°C per 36
years, were an order of magnitude larger thanthe mean rate of global (GST) warming during
the 20th Century (~0.08°C per decade). They11

are also larger and extend farther southward
than the corresponding multi-model ensemble
mean trends shown in the right hand columnof Fig. 9. Hence, it seems quite likely that theenhancement of the warming was either thermodynamically- or dynamically-induced by
the free (internally generated) variability of
the climate system; i.e., the categories listed in
the bottom row of Fig. 1.
Over the 92-year-long reference interval
1920–2011 the regional SAT trends shown in
Fig. 10, expressed in °C per 92 years, aresmaller than those for the shorter reference
interval shown in the previous figure, but they
still range up to nearly 3°C per century, about
three times the GST trend. The heterogeneityof the trends during the boreal winter shown in
Fig. 10a, and the fact that they are so muchlarger than the corresponding warm season
trends shown in Fig. 10b suggest that even on
this extended time scale, the internal variability of the climate system makes an important
contribution to the observed trends.

Fig. 9. Maps and zonally averaged meridional profiles showing rates of warming (i.e., the linear trend) over the historical reference interval 1965–2000 expressed in units of °C per 36 years: (a,b) boreal cold season; (c,d) boreal warm
season. Left column (a,c) based on observations and right column (b,d) the multi-model ensemble mean (MMEM) of
the AR4 simulations. From Wallace et al. (2012).

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Wallace, Deser, Smoliak, and Phillips

FIG. 10. Observed rates of warming in SAT over thehistorical reference interval 1920–2011 (i.e., the linear
trend) expressed in units of °C per 92 years: (a) boreal
cold season; (b) boreal warm season. Based on the
NCDC MLOST dataset.

3. Assessing the dynamically-induced
variability
As noted in the Introduction, dynamicallyinduced variability of SAT and rainfall (i.e.,variability attributable to the time-varying atmospheric circulation) is not identical to theinternally generated variability for two reasons: (1) anthropogenic forcing can inducechanges in the atmospheric general circulationand (2) internal variability of the climate system would be capable of inducing changes in
SAT, even in the absence of circulation
changes. These distinctions are reflected in the
categories of causal mechanisms in Fig. 1. But
despite these caveats, it appears that much of
the internally generated variability in the SAT
field is mediated by changes in the atmospheric circulation. To illustrate this point, we reexamine Ensemble Members #4 and #22 fromthe CCSM3 40-member ensemble, whose
SAT fields were depicted in Figs. 4, 5, and 6,
but here in Fig. 11a,b we show them together
superimposed on the corresponding trends inthe sea level pressure (SLP) field. The SLP
trend in Member #4 is in the sense as to favor
offshore flow along the west coast from British Columbia to California, reducing the moderating influence of the influx of marine air
masses upon winter temperatures over most of
North America. In contrast, the trend in Member #22 (Fig. 11b) is in the sense as to increase
the onshore flow over western Canada. Thatthe strength of the onshore flow along the Pacific seaboard exerts a strong influence on
wintertime SAT over the continental US isborne out in the Member #22 minus Member#4 SLP difference map shown in Fig, 11c, andthe regression map based an all the other ensemble members shown in Fig. 11d. It is notable that the SLP trends in these “outlier”
members of the 40-member ensemble aremuch larger than the ensemble-mean SLP
trend shown in Fig. 2a. The same must be trueof randomly selected members because at
most grid points the ensemble-mean 56-year
trend is less than 0.5 standard deviation of thetrends in the individual ensemble members, as
shown in Fig. 2b. In agreement with this conclusion, based on an analysis of simulations
performed with CMIP3 models, Oshima et al.
(2012) reported that the contribution of internal climate variability the diversity of centurylong SLP trends over the North Pacific in theensemble members is as large as the ensemble
mean trend itself and that internal variability
accounts for virtually all of the diversity of the
50-year SLP trends in the individual ensemble
members during the first half of the 20th century.	
  Is it merely chance coincidence that the
SLP trends in Ensemble Members #4 and #22
are dynamically consistent with the contrasting SAT trends over the continental United States? To address this question we show inAttribution of Climate Change in the Presence of Internal Variability

Fig. 11d the pattern of DJF SLP trends regressed on the standardized SAT trends averaged over the continental United States in theother individual ensemble members. That the13

SLP patterns in Figs. 11c,d are broadly similar
confirms the inference that the differences in
the SAT trends in the individual ensemble
members are at least to some degree dynami-

FIG. 11 (a,b) 2005-2060 DJF SAT trends in Ensemble Members 4 and 22 of the CCSM3 40-member ensemble, (c)The difference between (a) and (b). (d) Trends in the individual ensemble members (exclusive of #4 and #22) regressed on the 38 corresponding raw SAT trends averaged over the continental US. SAT trends are indicated by colored shading and SLP trends by contours. Contour interval 1 hPa per 56 years. The zero contour is bold and dashedcontours indicate SLP falls.

FIG. 12. As in Fig. 11 but for SAT and SLP in JJA, contrasting the two ensemble members that exhibit the weakest(#3) and strongest (#31) SAT trends averaged over the contiguous US.

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Wallace, Deser, Smoliak, and Phillips

FIG. 13. (a) Pattern of SLP anomalies (contoured) and SAT anomalies (shaded) during the US Great Plains Dust Bowl
summers, the average of JJA 1934, 1935, and 1936. The reference period for the anomalies is 1900-2010. (b) SLP and
SAT regressed on the detrended time series of JJA SAT averaged over the continental US. The regression coefficientsare based on the period of record 1900-2010, exclusive of JJA 1934, 1935, and 1936. Contour interval 0.5 hPa. Basedon the 20th Century Reanalyses (Compo et al. 2011).

cally induced.
Analogous results for ensemble memberswith contrasting summertime 2005–2060 SAT
trends are shown in Fig. 12. These runs exhibit
contrasting patterns of SLP trends over the
North Pacific and over the Canadian Arctic,
but distinctions between the warm and cold
patterns are not as clearly discernible over thecontiguous US. That the JJA SLP trends in theother 38 ensemble members regressed upon
the respective SAT trends averaged over thecontinental United States yields (Fig. 12d)yields a pattern similar to the difference map(Fig. 12c) is suggestive of a dynamical influence upon the SAT trends in the individual
ensemble members in summer as well as inwinter.	
  Patterns of SLP and SAT anomalies observed during anomalously hot summers overthe contiguous US the so-called “Dust Bowl)
and, more generally during hot summers over
CONUS are shown in Fig. 13. The anomalous
upstream anticyclone over the North Pacificand the anomalously low SLP along the Arctic
coast are not as prominent in the historical
data as they are in the simulated SLP patterns
shown in the previous figure. Apart from theanomalies over the regions of elevated terrain
over the southwestern US, which is mainly a
SAT signature, the SLP anomalies are quite
small. It is difficult to understand how the lowlevel circulation anomalies associated withsuch weak features could have been responsible for the large SAT anomalies either in thesimulations (Fig. 12) or in extreme years in thehistorical record (Fig. 13). Feedbacks involving soil moisture could greatly increase theamplitude of the internal variability of SAT, atleast in the model. The land surface tends tobecome drier as it warms and, conversely,
summer SAT tends to be warmer over dry
land surfaces. Both relationships contribute toa negative correlation between temperatureand precipitation. In the CCSM3 ensemble
members with strong summertime warming
trends over the continental US tend to bemarked by negative precipitation trends andvice versa: the correlation coefficient between
JJA SAT trends and precipitation trends averaged over the continental US among the 40
individual ensemble members is –0.82. Drymonths also tend to be warmer than normal in
the observations (Madden and Williams 1978;
Trenberth and Shea 2005) but the negative

Attribution of Climate Change in the Presence of Internal Variability

correlation between precipitation and SAT is
not as strong. A drying tendency favors a tendency toward reduced latent heat fluxes andenhanced sensible heat fluxes at the Earth’s
surface, which favors warming. Such land surface feedbacks can serve to amplify and prolong dynamically-induced heat waves (e.g.,
see Black et al. 2004 or Dole et al. 2012), rendering internally generated dynamically- andthermodynamically-induced diversity in thetemperature trends difficult to separate, evenin large ensembles of simulations.
3.1. Further insights derived from projectionsof future SAT trends
The 40-member ensemble of CCSM3 simulations in Deser et al. (2012a) has been subjected to a more formal analysis of the dynam-

15

ical contribution to the diversity of the wintertime SAT trends. The left hand columns ofFig. 14 show the leading Northern and Southern Hemisphere empirical orthogonal functions (EOFs) derived from the extratropical
DJF and JJA 2005-2060 SLP trends. In the
climate literature EOF analysis is usually performed in the space / time domain and the“modes” obtained from it consist of an ordered
set of spatial patterns (EOFs) whose timevarying amplitudes and polarities are described by their respective principal component (PC) time series. In Deser et al. (2012a)
the analysis is performed in the domain of
space / ensemble number: the EOFs are spatial
patterns but in their analysis the PCs refer tothe amplitude and polarity of various 20052060 trend EOFs as expressed in the individual ensemble members. Despite the differences

FIG. 14 The leading EOFs of extratropical SLP trends from the 40-member CCSM3 ensemble (a) DJF and (c) JJA; andin the CAM3 ensemble (b) DJF and (d) JJA. Trends are computed over the period 2005–2060 for CCSM3 and for 56year non-overlapping segments for CAM3. EOF analysis is performed for each hemisphere separately but plotted on asingle map. The percent variance explained by each EOF is given in the upper right corner of each panel, with the firstnumber denoting the NH and the second number the SH (for example, for CCSM3 in DJF, NH EOF1 accounts for 36%
of the NH variance and SH EOF1 accounts for 60% of the SH variance). From Deser et al. (2012a).

16

Wallace, Deser, Smoliak, and Phillips

in which that data are analyzed, the DJF SLP
patterns and the Northern Hemisphere JJA
pattern shown in Fig. 14 closely resemble theleading EOFs of the month-to-month variability in historical time series (Thompson andWallace 2000; not shown), which are commonly referred to as the “Northern and Southern Hemisphere annular modes” (NAM and
SAM, respectively; we will refer to them by
those names). They correspond to preferredmodes of variability in the historical record
and in extended control runs of the CCSM3
and other climate models (Miller et al. 2006).
The CCSM is a coupled model in which
ENSO and longer term climate variations resulting from large-scale atmosphere-oceaninteractions come into play. In order to distinguish between the internally generated variability that is attributable to changes in the atmospheric circulation alone and variability
that is a consequence of atmosphere-oceaninteractions, the SAT trends in the 40-member
ensemble of CCSM3 runs are compared withtrends in non-overlapping 56 year segments of
a 10,000 year control integration of the Community Atmospheric Model (CAM3), thesame atmospheric model that is used in the
coupled CCSM3 integrations. In the control
integration greenhouse gas and aerosol concentrations are held constant and SST is prescribed in accordance with the seasonally varying climatology but the treatment of land sur-

FIG. 15. Histograms of the SLP 2005–2060 trend projections onto EOF1 from the CAM3 control integration broken down by hemisphere and season as indicated. The red open bars show results from the 40-member CCSM3 andthe gray filled bars from the 178-member Community Atmospheric Model (CAM3), which is used as a control. The
x axis is in units of standard deviations of the CAM3 control integration, and the y axis is frequency (number ofensemble members divided by the total number of ensemble members). From Deser et al. (2012a).

Attribution of Climate Change in the Presence of Internal Variability

face feedbacks is the same as in CCSM3. Results are shown in the right hand panels of Fig.
14. If the atmosphere-ocean coupled variability were making an important contribution to
the diversity of the trends among the CCSM3
ensemble members, one would expect the amplitude of the annular modes and other preferred patterns of variability in the SLP field
to be larger in the CCSM3 ensemble members
than in the 56-year segments of the CAM simulations. That the EOFs obtained from the
CCSM3 and CAM3 runs are similar in shape,
comparable in amplitude, and explain comparable fractions of the total SLP variance suggests that the diversity of the SLP trends in the
CCSM3 ensemble members is mainly due tothe internal variability of the atmospheric circulation in the absence of any coupling to theocean.
The ensemble mean of the trends in the
56-year segments of the CAM3 control run is
indistinguishable from zero. However, the projections of the patterns of SLP trends in the 40
CCSM3 simulations onto EOF1 of the control
run shown in Fig. 15 exhibit a statistically significant positive bias indicative of falling SLP
in both polar cap regions and rising SLP overmuch of middle latitudes. SLP changes in thissense are commonly referred to as a trend toward the “high index polarity” of the NAM
and the SAM. Nearly all the climate models
used in the IPCC projections exhibit a trend in
this sense (Meehl et al. 2007). This shift toward the high index polarity of the annularmodes is evidently a robust feature of the ensemble-mean response to the buildup of
greenhouse gases in the CCSM3 (i.e., the upper right box in Fig. 1), but it is expressedwith different strengths in different ensemble
members and in some members the trend is in
the opposite sense. The diversity of the SLP

17trends in the individual members of the ensemble, as reflected in the width of the frequency distributions in Fig. 15, is a measure ofa kind of structural uncertainty inherent in the
projected SLP trends for 2005–2060.
The low level circulation pattern implied
by EOF1 of the SLP trend induces a spatiallyvarying SAT trend of the form shown in Fig.
16, which is obtained by averaging the SAT
trends over all ensemble members, weighting
each in accordance with the projection of its
pattern of SLP trend upon EOF1 (i.e., by its
value of PC1). The patterns of induced SAT
trend in the two hemispheres are dynamicallyconsistent with EOF1 of the SLP trend andthey resemble the SAT patterns obtained byregressing the SAT field upon time varying(SLP) indices of the annular modes (Thompson and Wallace 2000). The regression patterns in Fig. 16, in effect, define the anomaly
in the trend of SAT in each member of theensemble (i.e., the departure from the ensemble-mean SAT trend) that can be attributed to

FIG. 16. Surface temperature regressed upon the scoresof EOF1 of extratropical SLP trends from the 40member CCSM3 ensemble in DJF, shown in Fig. 15.
Contours show the SLP trend EOF (contour interval 0.6
hPa per 56 years; negative values are dashed). Trends arecomputed over the period 2005–2060. EOF and regression analyses are performed for each hemisphere separately but plotted on a single map. From Deser et al.
(2012a).

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Wallace, Deser, Smoliak, and Phillips

the anomalous trend in the NAM/SAM in eachensemble member (again, anomalous withreference to the ensemble mean trend). Subtracting out that portion of the SAT trend ateach grid point in each ensemble member thatis attributable to the anomalous trend in the
NAM/SAM in that ensemble member constitutes a dynamical adjustment that serves toreduce the diversity of the trends among theensemble members. A dynamically adjusted
global or hemispheric SAT trend field can becreated by subtracting the dynamical contribution from the raw SAT trend field for eachmember. In principle, a complete dynamical
adjustment of the SAT trends in the individual
members of the ensemble can be obtained by
the applying dynamical adjustments not only
for the NAM/SAM, but for all the significant
EOFs of the SLP trends. In practice, applying
this procedure to an ensemble with a finite
number of members will inevitably tend tooverestimate the dynamical contribution. The
challenge is to limit the degree of “overfitting.”
3.2. Estimating the dynamical adjustment
for individual ensemble members
In order to avoid serious overfitting of thediversity (or variance) of the trends in the individual ensemble members it is necessary toapply analysis techniques that are parsimonious i.e., that involve regression equations containing very few SLP predictors. Deciding
how best to perform the analysis is an area ofactive research. Here we will briefly describe
some of the linear analysis tools that might beused in performing such an analysis.
Consider the set of SAT trends T(n), (n =1, N) at a specified grid point, one belonging
to each of the N ensemble members. A simple, conservative approach is to apply leastsquares regression (LSR), using the SLP trend
field in a prescribed spatial domain to define asingle “predictor” T*(n) of T(n). The first stepis to regress the standardized SLP trend fieldupon T(n) to obtain a single predictor pattern
P(x). Here the standardization is performed in“ensemble-space”; i.e., the standard deviationof SLP trend at each grid point is based on thesample consisting of the N ensemble members.
The second step is to project the standardized
SLP trend field in each ensemble member upon P(x) to obtain a “score” S(n) that provides a
relative measure of the polarity and thestrength with which the predictor pattern P(x)is expressed in that ensemble member. The
final step is to scale the scores S(n) by fitting
them to T(n) using the method of least squares.
The rescaled scores are the predictors T*(n),which constitute the dynamical adjustment.
Spatial averaging and the steps in LSR are
commutative, so this procedure can equallywell be applied directly to an ensemble of spatially averaged SAT trends such as GST(n).
For each specified grid point or area average time series, LSR yields a single correlation coefficient or “predictor” T*(n) of the
SAT trend in the nth ensemble member and isthus as parsimonious as any method can be.
The LSR approach can be extended to multiple predictors by the method of partial leastsquares regression (PLSR). In PLSR, the firstpredictor T1*(n) is obtained by LSR, as described above. A residual data set is then created by regressing T1*(n) out of both the SLP
trend field in each of the individual ensemble
members (i.e., the field from which the “predictor patterns” are chosen) and the ensembleof grid point or area-average SAT trends T(n)(the “predictand”). Then LSR is applied tothese residuals to obtain a second predictor
T2*(n) that is orthogonal to T1*(n) by con-

Attribution of Climate Change in the Presence of Internal Variability

struction and a second set of residuals. The
procedure can be repeated as many times as
desired. PLSR is widely used in other fields
such as econometrics, chemometrics, neuroscience, and computer science, and is beginning to be more widely used in geophysics(Smoliak et al. 2010). It has been used byWallace et al. (2012) to estimate the dynamical contribution to the wintertime SAT trends
over the Northern Hemisphere continents, as
discussed in the next subsection.
The above procedure can be computationally intensive when it is applied pointwise(i.e., to every grid point in the SAT field) because of the high degree of redundancy inherent in the calculations, especially when thegrid is fine. Under some circumstances it may

FIG. 17. Examples of raw and dynamically adjusted
2005-2060 SAT trends for ensemble members 4 (left)
and 22 (right) of the 40-member CCSM3 ensemble, themembers that exhibited the smallest and largest SAT
trends averaged over the contiguous US. The top row ofpanels show the raw patterns, the second shows the adjusted patterns with one pass of PLSR, the third row withtwo passes, and the bottom row after three passes.

19

be preferable to expand the SAT trend field interms of EOFs and to perform LSR or PLSR
on a subset of the resulting PC time series.
The same considerations that apply topointwise or area-wise LSR/PLSR are also
applicable when these forms of analysis are
performed in PC space.
Figure 17 shows raw and dynamically adjusted wintertime SAT trends for Members #4
and #22 of the 40-member ensemble conducted with CCSM3, the ensemble members withthe smallest and largest SAT trends over CONUS. In this example the dynamical adjustment was computed by performing pointwise
PLSR on the SAT field over North America.
The patterns P(x) in the SLP field are for thedomain 10° to 90°N and from the Date Line to
the Greenwich Meridian. The dynamical adjustment has the strongest influence on outlier
ensemble members such as these. With each

FIG. 18. As in Fig. 7 but dynamically adjusted with twopasses of PLSR using the SLP field in the domain 10° to
90°N and from the Date Line to the Greenwich Meridianas the predictor field.

20

Wallace, Deser, Smoliak, and Phillips

pass the contrast between the two ensemble
members becomes less pronounced.
Figure 18 shows dynamically adjusted
trends for the individual members of the
CCSM4 and ECHAM ensembles, whose raw
trends were shown in Fig. 7. Application of
the dynamical adjustment substantially reduces the diversity of the SAT trend patterns in
the ensemble members, bringing them more
into line with the ensemble-mean trends. Averaged over the North American domain, applying this dynamical adjustment with twopasses accounts for 75% of the variance of the
SST trends in the 30-member CCSM4 ensemble. That it leaves 25% of the variance unexplained suggests that our dynamical adjustment scheme, which relies exclusively on the
SLP field, might not be capturing all the dynamically-induced variance.
When applied to regions the size of the
CONUS, the dynamical adjustment based on
SLP appears to be even more effective in reducing the diversity of the SAT trends insummer than in winter, accounting for 81% of
the variance of the SST trends in the 30member CCSM4 ensemble with only twopasses.
3.3. Dynamically adjusting SAT trends in thehistorical record
To adapt the methods described in the previous subsection to estimating the dynamical
contribution to the observed SAT trends it isnecessary to use temporal variability within
the historical record as a surrogate for the diversity of the individual ensemble members inthe simulations. In this case the goal is to explain the multidecadal variability of the trends
observed within a single time series using SLP
patterns derived from the analysis of that sametime series. The strong late 20th Century

warming trend during the boreal cold season
over the continental interiors documented in
Section 2.2 is arguably the most dramatic feature in the historical record. Was it dynamically induced? If so, is the adjustment large
enough to affect estimates of the rise in annual
mean GST during this period?
As background for addressing this question, Fig. 19 shows the global pattern of November-April SLP trends from 1965 to 2000.
Compared to other sampling intervals of comparable length, the trends during this interval
are particularly strong and spatially coherent,with pressure falls in both polar regions andpressure rises in midlatitudes, indicative of ashift toward the high index polarity of theNAM and the SAM. The trend in the PNA
pattern was associated with a spontaneous,
abrupt shift toward a more El Niño-like stateof the sea surface temperature distribution andrelated atmospheric circulation patterns equatorial Pacific in 1976-77 (Nitta and Yamada
1989; Trenberth and Hurrell 1994; Zhang etal. 1997).
Shindell et al. (2001) investigated thecause of the strong NAM-related trends during
this interval and they concluded, on the basisof numerical simulations with an array of external forcings, that the observed trend in the
NAM during this interval was beyond therange of internal variability and was likely
forced by a change in the meridional heating
gradient in the stratosphere induced by thebuildup of greenhouse gases. This explanation
would account for the prominence of theNAM signature in the 1965-2000 SLP trend
but does not explain the reversal in the trend in
the NAM that began in the mid- 1990s andbecame more clearly apparent after the turn ofthe millennium (see NCAR’s Climate Data
Guide, http://climatedataguide.ucar.edu, for aAttribution of Climate Change in the Presence of Internal Variability

21

FIG. 19. Observed 1965–2000 SLP trends for the boreal
cold season (Nov.–Apr.), based on the 20th Century
Reanalyses. The contour interval is 1 hPa per 36 years.
Negative values are dashed. Zero contour bold. From
Wallace et al. (2012).

NAM index from 1899 to present). Subsequent numerical experiments by Bracco et al.
(2004) and Deser and Phillips (2009) based on
ensembles of integrations with two atmospheric GCMs forced with the observed evolutionof SSTs, greenhouse gases, ozone and aerosols
suggest that the prominent NAM signature in
Fig. 19 is likely a manifestation of atmospheric internal variability that happened to be particularly strong during this 36-year interval.
In a similar manner, Trenberth and Hoar
(1996, 1997) investigated the cause of the late
20th Century trend toward the positive polarity of the PNA pattern; i.e., the prevalence ofan El Niño-like state of the tropical Pacificafter the mid-1970s. On the basis of a statistical analysis of the historical record of theSouthern Oscillation Index (SOI) they concluded in their second paper that the behaviorof the SOI during the post 1976 period had
been “highly unusual and very unlikely tohave been caused by natural variability”. With
the benefit of 15-years of hindsight it is evident that the role of natural (i.e., unforced)
variability of the climate system was underestimated in this case as well: the prevalence of
the El Niño-like state of the equatorial PacificFig. 20. 1965–2000 SAT trends for the boreal cold season (Nov.–Apr.): (a) the raw trend pattern, (b) the dynamical contribution, estimated by partial least squares
regression (PLSR) with two predictors for each grid
point, and (c) the dynamically adjusted trend pattern,
calculated by subtracting the dynamical contribution in(b) from the raw trend pattern in (a).

has not persisted into the 21st Century (Hu etal. 2013).
In contrast to the trends in the NAM and
the PNA pattern, the late 20th Century trend in
the SAM is widely regarded as having been atleast partially forced by a decrease in concentrations of stratospheric ozone due to thebuildup of CFCs during this period— the socalled “Antarctic ozone hole” (Thompson andSolomon 2002; Gillett and Thompson 2003;
Polvani et al. 2011). It has been suggested thatthe more subtle ozone losses that occurred
over the Arctic during this period might haveinduced an analogous trend in forcing theNAM, but the case is less clear (Hartmann etal., 2000).
The NAM- and PNA/ENSO-related SLP
trends have obviously contributed to the win-

22

Wallace, Deser, Smoliak, and Phillips

tertime warming of Eurasia and North America poleward of 40°N from 1965 to 2000. Results obtained by dynamically adjusting thetime series of SAT averaged over all the
Northern Hemisphere land grid points poleward of 40°N, using two PLSR Northern
Hemisphere SLP predictors, are shown in Fig.
20. The dynamical contribution to the SAT
trend resembles the SAT signature of theNAM. The residual SAT trend is weaker than
the raw trend and more closely resembles thecorresponding warm season trend shown in
Fig. 9c. Yet it is clear that the dynamical adjustment shown in Fig. 20 does not account for
all of the enhanced warming over the interiorsof the continents during the boreal cold season
relative to the model simulations shown in
Fig. 9b. Either the methodology described in
the previous subsection is failing to capture all
the dynamically-induced variability or there isa contribution from the thermodynamicallyinduced internal variability discussed in thenext subsection and in Chapter XX.
To place the dynamical adjustment for
1965–2000 in a global context, Table 1 showsa summary of how it affects the trends inglobal mean SAT over land (GSAT) and overthe entire globe (GST). Applying the dynam-

ical adjustment reduces the warming over thehigh latitude Northern Hemisphere land masses during the boreal cold season from 1.72°C
to 1.02°C over this 36-year interval, eliminating most of the excess warming relative to thewarm season and relative to the land lying
south of 40°N. The magnitude of the adjustment (0.70°C) is diluted by averaging over allland (to 0.28°C) and over the year (to 0.14°C)
and by combining land and ocean data (to0.04°C in GST). Hence, changing extratropical circulation patterns during the boreal winter accounted for less than 10% of the global
warming signal during this interval. Comparedto the accelerated warming; i.e., the rate ofrise of annual mean GST during this interval
minus the mean rate of rise of GST during thepast century of 0.08°C per decade or 0.29°C
per 36 years, it amounts to about 15%. Hence,
though appreciable and of first order importance for the attribution of high latitude
Northern Hemisphere wintertime temperature
trends over land, the dynamical contribution
explains only a small fraction of the accelerated global warming during the late 20th Century and even after it is removed, land (GSAT)
warmed twice as rapidly as ocean (GSST) during this period.

Table 1. Observed 1965-2000 SAT trends over land for boreal cold and warm seasons November-April and MayOctober expressed in °C per 36 years. The italicized numbers refer to dynamically adjusted trends as explained in
Section 4. GSAT refers to global-mean SAT, GSST to global-mean SST and GST refers to global mean surface
temperature including both land and sea. Data based on the National Climatic Data Center historical merged landocean land surface temperature analysis (MLOST), with its land component, GHCNv3, and ocean component,
ERSSTv3b. Adapted from Wallace et al. (2012).

N: 40°N–90°N
S: 60°S–40°N
GSAT (Land)
GSST (Ocean)
GST

Cold
1.72 (1.02)
0.70
1.03 (0.80)
0.35
0.57 (0.49)

Warm
0.79
0.69
0.72
0.37
0.48

Annual Mean
1.26 (0.91)
0.70
0.88 (0.76)
0.36
0.52 (0.49)

Attribution of Climate Change in the Presence of Internal Variability

FIG. 21. SAT trend patterns for the reference interval
1920–2011: (a) dynamically adjusted trend for the boreal
cold season estimated by PLSR as in Fig. 20, (b) raw
trend for the warm season, and (c) annual mean trend
estimated by averaging the dynamically adjusted coldseason trend and the raw warm season trend.

The importance of the dynamical adjustment tends to decline with the length of theinterval over which the trends are computed,
but even for the longer interval 1920–2011, it
remains quite important during the boreal coldseason, as seen in Fig. 21. Applying the dynamical adjustment to the cold season trends
and averaging them with the warm season
trends is seen to yield a relatively simple spatial pattern suggestive of reduced warming
over China and the southeastern United States
possibly in response to the buildup of aerosols.
Applying the dynamical adjustment to thecold season trends substantially improves thecoherence between cold and warm season
SAT time series both for the global mean andfor regional means, as illustrated in Fig. 22. In
particular, it accounts for most of the excess

23

FIG. 22. Time series of (red) warm season and (blue)
cold season SAT spatially averaged as indicated. The top
pair of curves in each set shows raw time series and thebottom pair shows the dynamically adjusted cold season
series and raw warm season series. Adapted from Wallace et al. (2012).

warming during the boreal cold season relative
to the warm season over the course of the 20th
Century. The positive correlation between thewarm and cold season time series on a year-toyear basis is indicative of a season-to-season
memory that transcends the very short thermal
adjustment time of the land surface. Features
such as the cooling following the 1991 eruption of Mt. Pinatubo are more clearly evident
in the adjusted data.
4. Does thermodynamically-induced variability play a role?
Of the four categories of processes listed inFig. 1 that contribute to climate trends, ther-

24

Wallace, Deser, Smoliak, and Phillips

modynamically-induced internal variability is
the most difficult to quantify because it requires an understanding of variations in theoceanic global overturning circulation and theland biosphere and hydrosphere, and in thecryosphere, all of which are on the frontiers ofclimate science. It is not clear how well themodels used in IPCC assessments, including
the ones referred to in this chapter, simulate
the relevant processes on the multidecadal
time scale. For example, it is quite possiblethat the diversity of the trends in Fig. 7, large
though it is, could be underestimated for failure of the models to realistically represent thevariability of the ocean circulation for lack ofadequate treatment of the physics or proper
initialization. In a similar manner, changes invegetation and ground hydrology that are ignored or not accurately represented in themodels could conceivably render the summertime trends more diverse than the examples
included in this chapter.
Multidecadal variations in the strength ofthe meridional overturning circulation in the
North Atlantic (MOC) affect the poleward
heat transport by the Gulf Stream and its extension to subpolar latitudes and they regulate
the rate of exchange of heat between the oceanic mixed layer and the layers below. The
temperature of the oceanic mixed layer responds rapidly to changes in the surface energy balance, through which the global warming
signal is transmitted together with regionalsignals associated with atmospheric circulation anomalies. When the MOC is anomalously strong, enhanced poleward heat transports
warm the surface waters of the subpolar North
Atlantic and parts of the Arctic, which in turn,transfer heat to the atmospheric boundary layer, where it may be advected downstream by
the winds. The MOC strength also modulates

the rate at which heat that accumulates in theocean mixed later is transferred into the deeper
ocean (Meehl et al. 2013). Hence, variations inthe strength of the MOC could act as a timevarying thermodynamic forcing of SAT that is
likely to be strongest over the higher latitudes
during the boreal cold season, when the sea to
air fluxes of sensible and latent heat arestrongest.
In the absence of reliable direct measurements of variations in the strength the MOC,
much of what is known about its role in multidecadal climate variability is inferred fromnumerical simulations of the oceanic response
to prescribed surface forcing as in AlvarezGarcia et al. (2008). The induced MOCrelated variations in the oceanic circulation
can feed back on the surface fluxes and thereby force the atmosphere on the interdecadal
time scale. Numerical experiments by Semenov et al. (2010) with a coupled model withinteractive MOC-related variability suggestthat the modulations in the fluxes may havebeen strong enough to force significant SAT
anomalies over the high latitude continents,
irrespective of any related circulation changes.
If so, the resulting thermodynamic contribution to the high latitude warming would appear
in the residual SAT trend field in Fig. 20c.
A prominent feature of the multidecadal
variability in the strength of the MOC is theso-called Atlantic Multidecadal Oscillation(AMO), which exhibits a period on the orderof 70 years, as discussed in Chapter XX.
There and in Chapter XX it is argued that the
AMO is a manifestation of internal variabilityof the coupled atmosphere-ocean climate system that would exist even in the absence of
external forcing. It has further been argued
that AMO-related variations in the strength of
the MOC during the 20th century are respon-Attribution of Climate Change in the Presence of Internal Variability

sible for much of the multidecadal variability
in the rate of rise of GST; i.e., the relatively
rapid rise in the 1920s and 30s, the midcentury hiatus, the resumption of the rapid
warming toward the end of the century andperhaps even the recent second hiatus (DelSole et al. 2011; Wu et al. 2011; Gulev et al.
2013). For further discussion, the reader isreferred to Chapter XX by K. K. Tung).
Another way in which the exchange of water between the mixed layer and the deep
ocean on a decadal time scales could exert athermodynamic influence global surface temperature is through the wind-driven zonal
overturning circulation in the equatorial Pacific, which pumps cold water from below thethermocline into the warm ocean mixed layer.
The stronger the equatorial trade winds, thestronger the zonal overturning circulation andthe sea surface temperature (SST) contrast
between the cooler eastern Pacific and the socalled Indo-Pacific warm pool” in the west.
Conversely, the stronger the east-west SST
contrast, the stronger the trade winds. The existence of this strong positive feedback gives
rise to pronounced variability of SST and windon time scales ranging from seasons to decades. It plays an essential role in the ENSO
cycle, but it would exist even in a hypotheticalatmosphere coupled to a passive ocean mixed
layer (Kitoh et al. 1999; Dommenget 2010;
Clement et al. 2011). Based on experimentswith numerical models, Meehl et al. (2011)
and Kosaka and Xie (2013) have shown evidence that an intensification of this zonal overturning circulation and the resulting cooling of
the tropical eastern Pacific contributed to the
pronounced slowdown in the rate of global
warming that occurred around the beginningof the current millennium.

25

Despite the array of statistical and modeling evidence that has been presented in support of the role of the ocean in thermodynamic
forcing, many climate scientists remain convinced that the irregularities in the rate ofwarming in the historical record are attributable to variations in the time-varying anthropogenic forcing by aerosols. For example, on thebasis of numerical experiments with a state-ofthe-art climate system model, Booth et al.
(2012) conclude that aerosol emissions andperiods of volcanic activity explain 76 per centof the simulated multidecadal variance indetrended 1860–2005 North Atlantic sea surface temperatures and that after 1950, theirsimulated variability is within observational
estimates. Numerical experiments reported in
the attribution chapter of the IPCC’s Fourth
Assessment Report (Hegerl et al. 2007) andhighlighted in the Technical Summary also
portray the late 20th Century warming in GST
as being entirely in response to anthropogenic
forcing. For further discussion of these issues
see Zhang et al. (2013) and Chapters XX, XX,
XX, and XX of this book.
Another arena in which thermodynamically forced internal variability of the climate
system might come into play is through the
feedbacks associated with the fluxes of latentand sensible heat by soil moisture and vegetation during the warm season (or in the tropics,
during the growing season). Although land
surface processes act on rather short timescales, the existence of positive feedbacks canserve to amplify the variability on all timescales. Another aspect of this problem on aregional scale is the existence of humaninduced external forcings not directly related
to global warming; e.g., cultivation, irrigation,
deforestation and afforestation, and inadvertent desertification.

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Wallace, Deser, Smoliak, and Phillips

5. Summary and Discussion
In this chapter we have categorized SAT
trends as being externally forced versus internally generated (i.e., forced versus free) and as
being dynamically versus thermodynamicallyinduced, as elaborated in Fig. 1. The distinction between forced and free is illuminated byanalysis of numerical simulations in which asingle model is run with a single set of timedependent external forcings but starting from asuite of different atmospheric initial conditions, yielding an ensemble of time-dependentclimate scenarios. The dynamically induced
component of the SAT trend is isolated bylinear regression using the SLP field as a“predictor” and the individual ensemble members as samples. When ensembles of climate
scenarios are not available, the regression canbe performed in the time domain. In principle,
this methodology can be applied to variables
other than SAT and variables other than SLP
can be used as “predictors” of the dynamically-induced trends.
The relative importance of the forced andfree components of the trends depends upon
the interval τ over which the trends are computed. If the forced component can be viewed
as increasing linearly with τ and the dynamically-induced variability can be modeled as
white noise whose contribution to the varianceof the trend is inversely proportional to τ, thenthe prominence of the forced component (i.e.,
the ratio of the trend to the standard deviationof the variability about the trend) should varyas τ 3/2. The “signal” in the SAT trends is also
latitude dependent (i.e., much more prominent
in the tropics than in the extratropics) and dependent upon the spatial averaging. Here wehave focused mainly on SAT trends over thecontinental US within 36 and 56 year intervals. The individual ensemble members inlarge ensembles of simulations are shown to
exhibit a remarkable amount of diversity, mostof which is dynamically induced. That thisdynamical contribution to the variability is aslarge in an atmospheric model run with SST
prescribed in accordance with its seasonallyvarying climatology as in the coupled runssuggests that the dynamically induced component of the trends is mainly attributable to atmosphere’s own internal variability rather thanto coupled atmosphere-ocean interactions.
Whether the real climate system exhibits asmuch dynamically-induced variability as theclimate models examined in this study remains
to be determined. There are indications thatthe temporal variance of the atmospheric circulation in the CAM3 is somewhat overestimated (Deser et al. 2012a) and this may also
be true of CCSM4. If this is the case, one
might expect the dynamically-induced variability to be overestimated as well. On the other
hand, it is possible that the coupled atmosphere-ocean system exhibits multidecadal variability that is not fully captured by the models(Deser et al. 2012c; Danabasoglu et al. 2012),
in which case, the uncertainty inherent in projections of 56-year SAT trends might be underestimated.
Dynamically-induced atmospheric variability accounts for ~0.7 of the 1.7°C the warming of the Northern Hemisphere continents
from 1965 to 2000, but this has had only asmall effect on the globally averaged warming. A potentially more important contributor
to multidecadal variations in the rate of rise of
GST is the variability in the strength of the
MOC, which modulates the fluxes of sensible
and latent heat at the air-sea interface over the
subpolar North Atlantic and parts of the Arctic. Just how much of the spatial and temporalvariability in the rate of warming over the con-

Attribution of Climate Change in the Presence of Internal Variability

tinents is MOC-related how much of it is induced by spatial and temporal inhomogeneities in the forcing by greenhouse gases andaerosols has important implications for estimates of climate sensitivity. If the enhanced
late 20th century warming was, indeed, a reflection of the internal variability of the climate system, the climate models purported toreplicate it in ensemble-mean simulations may
be getting the right answer for the wrong reason; i.e., they may be overly sensitive to theradiative forcing.
We have shown that sampling variability
constitutes a large part of the uncertainty inherent in projections of regional climatechange over the next 50 years, even in averages over areas as large as the continental US.
The uncertainty in estimates of the forced response can be narrowed by performing ensembles of simulations and/or by applying
dynamical adjustments to the individual ensemble members. However, even if the forced
variability were known exactly, the inherently
unpredictable, internally generated sampling
variability in the future trajectory of the climate system would still remain because it is
only one member of an ensemble of possible
time-dependent scenarios that could result
from a single prescribed external forcing. During the summer season the internally generated SLP variability is smaller than during winter but the thermodynamic consequences ofchanging atmospheric circulation patterns
could be amplified by hydrologic and terrestrial biosphere feedbacks. Deterministic, multidecadal, MOC-related variability is an additional source of uncertainty that could modulate or even temporarily reverse the sign ofshort term GST trends, as discussed in Chapter
XX.

27

The large sampling variability inherent inlocal or regional interdecadal and multidecadaltemperature trends has implications for theattribution of record high temperature eventsand heat waves, whose frequency of occurrence is closely tied to the mean temperature(Wergen and Krug 2010; Lau and Nath 2012,
Coumou et al. 2013). To the extent that inherently stochastic trends in atmospheric circulation patterns modulate local seasonal mean
temperatures, they also raise or lower the frequency of occurrence of extreme events, resulting in clusters of extreme events in particular geographical “hot spots” while extreme
event statistics other regions may appear to beunaffected by climate change.
Opponents of environmental protection
exploit the uncertainties inherent in projections of future climate change to cast doubt on
the immediacy, seriousness, and policy relevance of human-induced environmental degradation and to portray the scientific community as “crying wolf.” The sampling issues
discussed in this chapter afford the so-called“climate skeptics” some degree of aid andcomfort, but not nearly as much as they derivefrom misstatements about attribution of extreme events and exaggerated projections ofregional, near term climate change. Until thesignal of human-induced climate change
emerges more clearly above background variability, a more compelling case for environmental protection, including reductions theemissions of greenhouse gases, can be madeby focusing on the impacts of human-induced
warming in the tropics, where the “signal tonoise ratio” is much stronger (Mahlstein et al.
2011, 2012) and on the combined impacts ofclimate change, looming shortages of fresh
water (Pearce 2007; Brown 2010) and loss of
topsoil (Montgomery 2009) on food security.

28

Wallace, Deser, Smoliak, and Phillips

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