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Forced and Internal Components of Winter Air Temperature Trends over North
America during the past 50 Years: Mechanisms and Implications*
CLARA DESER
Climate and Global Dynamics Division, National Center for Atmospheric Research,1 Boulder, Colorado

LAURENT TERRAY
Sciences de L’Univers au CERFACS, URA-1875, CERFACS/CNRS, Toulouse, France

ADAM S. PHILLIPS
Climate and Global Dynamics Division, National Center for Atmospheric Research, Boulder, Colorado(Manuscript received 24 April 2015, in final form 29 December 2015)
ABSTRACTThis study elucidates the physical mechanisms underlying internal and forced components of winter surface airtemperature (SAT) trends over North America during the past 50 years (1963–2012) using a combined observational and modeling framework. The modeling framework consists of 30 simulations with the Community
Earth System Model (CESM) at 18 latitude–longitude resolution, each of which is subject to an identical scenario
of historical radiative forcing but starts from a slightly different atmospheric state. Hence, any spread within theensemble results from unpredictable internal variability superimposed upon the forced climate change signal.
Constructed atmospheric circulation analogs are used to estimate the dynamical contribution to forced andinternal components of SAT trends: thermodynamic contributions are obtained as a residual. Internal circulation
trends are estimated to account for approximately one-third of the observed wintertime warming trend over
North America and more than half locally over parts of Canada and the United States. Removing the effects ofinternal atmospheric circulation variability narrows the spread of SAT trends within the CESM ensemble andbrings the observed trends closer to the model’s radiatively forced response. In addition, removing internal
dynamics approximately doubles the signal-to-noise ratio of the simulated SAT trends and substantially advancesthe ‘‘time of emergence’’ of the forced component of SAT anomalies. The methodological framework proposed
here provides a general template for improving physical understanding and interpretation of observed andsimulated climate trends worldwide and may help to reconcile the diversity of SAT trends across the models fromphase 5 of the Coupled Model Intercomparison Project (CMIP5).

1. Introduction
With emerging public awareness of human-induced
climate change, a major challenge is to understand andcommunicate the causes of recent observed climate* Supplemental information related to this paper is available at the
Journals Online website: http://dx.doi.org/10.1175/JCLI-D-15-0304.s1.
1
The National Center for Atmospheric Research is sponsoredby the National Science Foundation.

Corresponding author address: Clara Deser, Climate and Global
Dynamics Division, NCAR, 1850 Table Mesa Drive, Boulder, CO
80307.
E-mail: cdeser@ucar.edu
DOI: 10.1175/JCLI-D-15-0304.1
Ó 2016 American Meteorological Society

trends, particularly at local and regional scales. Suchtrends are often interpreted in the context of risinganthropogenic emissions of greenhouse gases (GHGs)
and sulfate aerosols associated with the burning offossil fuels. However, internally generated variability
may also contribute to regional climate changes overperiods of several decades and longer (e.g., Van
Oldenborgh et al. 2009; Hoerling et al. 2010; Kelley et al.
2012; Ting et al. 2011; Meehl et al. 2013; Wallace et al. 2014;
Johnstone and Mantua 2014; Abatzoglou et al. 2014; Sriver
et al. 2015; Monier et al. 2015). Distinguishing between
anthropogenic and internal influences on time scalesof less than 50 years and spatial scales smaller thancontinental remains an outstanding issue (IPCC
2007, 2013).

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Global coupled climate model (GCM) simulations
provide estimates of the climatic impacts of anthropogenic(e.g., GHGs and sulfate aerosols) and natural (volcanicand solar) radiative forcings (IPCC 2013). However,comparison of observed and simulated trends is complicated by the fact that the chronologies of internal variability need not match (e.g., Van Oldenborgh et al. 2009;
Deser et al. 2012b; Wallace et al. 2014). Systematic model
biases, incomplete radiative forcing specifications, andobservational uncertainty further complicate direct comparison between models and observations (e.g., Räisänen
2007; Hegerl et al. 2007; Van Oldenborgh et al. 2009).
Isolating the effects of anthropogenic climate change
from those of internal multidecadal variability is relatively
straightforward in climate models, provided there areenough simulations to define the forced response (Deseret al. 2012a). That is, by averaging across ensemble
members from a particular model, the random sequencesof internally generated variability in the individual realizations can be sufficiently muted to reveal the model’s
response to external forcing. Once the externally forced
response is obtained, it can be subtracted from each run tofind the contribution from internal variability. Most
models however, including those participating in phases 3
and 5 of the Coupled Model Intercomparison Project(CMIP3 and CMIP5; Taylor et al. 2012), contain too few
realizations to adequately estimate the forced response on
local/regional scales (Deser et al. 2012b). Note that, while
it is common practice to average single runs from multiple
models to obtain a robust estimate of anthropogenic climate change [e.g., the multimodel mean (IPCC 2013)], thisapproach does not allow the forced and unforced components of the response to be isolated in any given model.
The use of large ‘‘initial condition’’ GCM ensembles
to identify the relative roles of forced and internal variability in determining future climate trends has led toimportant insights regarding uncertainty in climatechange projections at local/regional scales (e.g., Deseret al. 2012b; Hu and Deser 2013; Fischer et al. 2013;
Deser et al. 2014; Wettstein and Deser 2014; Wallace
et al. 2014; Hawkins et al. 2015; Thompson et al. 2015).
Such ensembles typically include 30–40 members, eachof which is subject to the identical scenario of radiative
forcing but starts from a slightly different atmosphericstate. The degree to which the different ensemble members diverge over time is indicative of the importance of
unpredictable, internal climate variability (Deser et al.
2012a). Such ensembles are designed to sample the rangeof possible trend outcomes resulting from the superposition of internal climate variability and anthropogenic
climate change. In addition, the large number of integrations allows for a robust determination of the forced
response at local/regional scales.

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Here we apply a new 30-member initial-condition ensemble covering the period 1920–2100 conducted with
the National Center for Atmospheric Research (NCAR)
Community Earth System Model, version 1 (CESM1;
Kay et al. 2015), to the understanding of observed climate
trends, particularly wintertime surface air temperature(SAT) over North America during the past 50 years.
Configured at a spatial resolution of 18 latitude/longitude(approximately 85 km at 40°N), this ensemble provides
important context for the interpretation of the one realization in nature: specifically, the relative importance ofinternal variability and external radiative forcing at local/
regional scales.
In addition to apportioning trends into forced and internal contributions, we assess the physical mechanisms
underlying these components: in particular, the roles ofdynamics (atmospheric circulation changes in the absence of radiatively induced changes in SAT) and thermodynamics (changes in SST, sea ice, and land surface
properties in the absence of atmospheric circulation
changes). Previous work has highlighted the importanceof dynamics to observed trends in Northern Hemisphere
winter SAT (e.g., Wallace et al. 1995; Hurrell 1996;
Thompson et al. 2009; Cattiaux et al. 2010; Smoliak et al.
2015). However, none distinguished between internal andforced dynamical components, a unique contribution of
our study enabled by the inclusion of the CESM1 Large
Ensemble. While the focus of this work is on winter SAT
trends over North America during the past 50 years, ourmethodology is generic and can be used to improvephysical understanding and interpretation of observed
and simulated climate variations, including trends of any
length, worldwide.
The remainder of this study is organized as follows.
Section 2 contains a description of the model experiments, observational datasets, and methods for determining dynamical and thermodynamic contributions
to forced and internal SAT trend components. Results
are presented in section 3 and discussed in section 4.
Implications for model evaluation and interpretation of
the CMIP5 archive are also included in section 4. A
summary is provided in section 5.

2. Data and methods
a. The CESM1 Large Ensemble
We make use of a new set of simulations conducted with
the Community Earth System Model, version 1 (Community Atmosphere Model, version 5) [CESM1(CAM5)], at
18 spatial resolution, referred to here as the CESM1 Large
Ensemble (CESM-LE). The CESM-LE consists of 30
simulations for the period 1920–2100, each subject to theidentical external radiative forcing but beginning from

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slightly different atmospheric initial conditions. Following the CMIP5 design protocol, historical naturaland anthropogenic radiative forcing was applied for
1920–2005 and representative concentration pathway
8.5 (RCP8.5) radiative forcing was used for 2006–2100(Taylor et al. 2012). The first ensemble member was
initialized with 1 January conditions taken from arandomly selected year of a 1700-yr preindustrial(1850) control integration (PiCTL) of the same model.
This first ensemble member was then integrated forward from 1850 to 2080. Ensemble members 2–30 were
all started on 1 January 1920 with initial conditions takenfrom the first ensemble member. A small [O(10214) K]
random round-off difference to the initial air temperaturefield was added to each ensemble member. This infinitesimal perturbation serves to create spread among
the ensemble members as internally generated modes ofclimate variability grow over time. A full description of
the CESM-LE is given in Kay et al. (2015).

b. The CMIP5 ensemble
We also make use of the CMIP5. Specifically, we use asingle run from each of the 38 models that submitted
both historical and RCP8.5 simulations to the CMIP5
archive [see Table 9.A.1 in IPCC (2013)]. If multiple
runs exist for a given model, we use the first one.

c. Observational datasets
We make use of three monthly mean SAT datasets: 1)
Merged Land–Ocean Surface Temperature analysis(MLOST), version 3.5, (Vose et al. 2012) on a 58
latitude 3 58 longitude grid; 2) GISS Surface Temperature Analysis (GISTEMP) on a 28 latitude 3 28 longitude grid and smoothed with a 250-km spatial filter(Hansen et al. 2010); and 3) Climatic Research Unit
Temperature, version 4, (CRUTEM4) on a 58 latitude 3 58
longitude grid (Osborn and Jones 2014). Unlike MLOST
and GISTEMP, CRUTEM4 is an uninterpolated, landonly dataset. We also make use of monthly mean sea levelpressure (SLP) from the Twentieth Century Reanalysis,
version 2, (Compo et al. 2011) on a 28 latitude 3 28 longitude grid. Similar results are obtained for the different
SAT datasets; for conciseness, we focus mainly on results
obtained with MLOST.

d. Methods
For each dataset and model simulation, we computemonthly anomalies by subtracting the long-term (1963–2012) monthly means from the corresponding month ofeach year. We then form 3-month winter [December–
February (DJF)] averages from the monthly anomalies.
Finally, we compute linear trends over the 50-yr period
1963–2012 using least squares regression analysis. This

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time period was chosen to match the length of record
used in Deser et al. (2014) in their study of projected
North American climate trends over the next 50 years(note that 2012 was the most recent year available for theobservational datasets at the time this study was carriedout). When computing pattern correlations and RMS
differences between model simulations and observations,
we regrid the model output to the observational grid.

e. Dynamical adjustment using the constructedcirculation analog approach
The objective of dynamical adjustment is to empiricallydetermine the component of SAT variability due solely toatmospheric circulation changes, all other factors being
equal (e.g., no changes in ocean or land surface conditions). Here we use a variation of the constructed circulation analog method (Van den Dool et al. 2003) to findthe dynamical contribution to SAT anomalies in both the
CESM-LE and observations. Circulation analogs were
pioneered by Lorenz (1969), Van den Dool (1994), andVan den Dool et al. (2003) as a statistical approach toweather prediction and have been applied more recently
to downscale climate projections from coarse-resolution
models (e.g., Zorita et al. 1995) as well as to infer thecontribution of dynamics to observed European SAT
trends (Cattiaux et al. 2010). A detailed description of our
methodology is provided in the appendix; a summary isgiven here.

1) APPLICATION TO THE CESM-LE
For each month and year of each of the 30 CESM-LE
simulations, we find a set of Na closest SLP analogs
within the 1700-yr CESM PiCTL, ranked according totheir Euclidean distance from the target CESM-LE SLP
field. For example, the SLP analogs for January 1920 ofrun 1 are found by searching all of the January SLP fields
in the PiCTL. The advantage of using the model’s control run to obtain the circulation analogs is twofold: one,
there is no effect of forced climate change on either the
analogs or the associated SAT anomalies; two, thenumber of samples from which to draw analogs is verylarge. We then randomly subsample Ns of the Na analogs and compute their optimal linear combination thatbest fits the target CESM-LE SLP field. The dynamicallyinduced SAT anomaly field is then defined as the corresponding optimal linear combination of PiCTL SAT
anomalies associated with the Ns SLP analogs. We thenrepeat this random sampling procedure Nr times. Finally, we average the Nr optimal sets of SLP analogs andassociated SAT anomalies to obtain a ‘‘best estimate’’ ofthe circulation-induced component of SAT anomalies in theabsence of climate change. The repeated subsampling of
optimal linear combinations of analogs ensures robustness

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JOURNAL OF CLIMATEof the results (see appendix). We use the domain 208–908N,
1808–3508E for the SLP analogs following Wallace et al.
(2012) and Deser et al. (2014), but there is little sensitivity
to the precise region used (e.g., within 6208of longitude
and 6108 of latitude; not shown). The results shown here
are based on the parameter values Na 5 150, Ns 5 100, andNr 5 50. However, there is little sensitivity to the precise
choice of these values as long as they lie within the parameter space that has converged (see the appendix).
Note that by using so many circulation analogs and by
weighting them according to their degree of resemblancewith the target CESM-LE SLP field, our technique can beviewed in some sense as a type of linear regression rather
than a strict circulation analog approach. An advantage
of our method compared to that of Wallace et al. (2012)
and Smoliak et al. (2015) is that the analog weights can beapplied to any field in order to estimate the dynamical
contribution, including the SLP field itself. In this way, we
are able to evaluate how much of the SLP anomaly fieldin question is reproduced by our optimal linear combination of circulation analogs. Finally, despite the different algorithms, our results are very similar to those ofWallace et al. (2012) and Smoliak et al. (2015), lending
confidence to both approaches (see Fig. S1 in the supplemental material).
To obtain the forced dynamical contribution, we average the dynamical contributions for all 30 ensemble
members. To obtain the internal dynamical contribution
for each ensemble member, we subtract the forced dynamical contribution from the total dynamical contribution. Thermodynamic contributions are obtained as
residuals (e.g., total minus dynamical) for both forced
and internal components.

2) APPLICATION TO OBSERVATIONS
To dynamically adjust the observed SAT, we use SLP
analogs from the Twentieth Century Reanalysis (20CR)
over the period 1899–2012, leaving out the targeted
month/year, and then construct their optimal linear set
following the procedures described above. For the results shown here, we use Na 5 80, Ns 5 50, and Nr 5
100. The results are not sensitive to the precise choices ofthese parameters (see the appendix). Since we do nothave an observational ‘‘control run’’ from which to draw
the SLP analogs and their associated effects on SAT, we
high-pass filter the SAT data before computing theirdynamically induced component to minimize any potential effects from forced, thermodynamically induced
SAT; a similar strategy was employed in Smoliak et al.
(2015). We use the framework of the CESM-LE to test
how well this approach works and to determine thesensitivity to our choice of high-pass filter. We find that
subtracting a quadratic trend or a spline trend over the

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full period 1920–2012 produces the closest estimates of
the true unforced dynamically induced SAT (on average,
within 3.7% of the true RMS amplitude using six ensemble members as test cases); 10- and 20-yr high-passfilters perform less well (within 16% and 23% of the true
RMS amplitude in a smaller sample of test cases). Further
information on the sensitivity to choice of high-pass filter
is provided in the appendix. For simplicity, the results
shown here are based on quadratic trend removal.
To obtain the internal dynamical contribution to theobserved SAT anomalies, we have performed a separate
dynamical adjustment based on the internal component of
the observed SLP anomalies, obtained by subtracting the
CESM-LE ensemble-mean SLP anomaly from the observed SLP anomaly at each time step. The forced dynamical contribution to observed SAT anomalies is thenobtained by subtracting the internal dynamical contribution from the total dynamical contribution. Thermodynamic contributions are obtained as residuals (e.g., total
minus dynamical) for both forced and internal components.

3. Results
This section is organized as follows. We begin byshowing the diversity of SAT and SLP trends simulated
across the 30 CESM-LE ensemble members and placing
the observed trends within this context (section 3a). We
then demonstrate the key role of internal dynamics inproducing much of the trend spread within the CESM-LE
and its influence on observed SAT trends (section 3b).
We show next that removing the influence of internal
dynamics brings the observed SAT trends into closeralignment with the radiatively forced component simulated by the CESM-LE (section 3c). Additional benefitsof removing internal dynamics from the SAT trends are
given in section 3d, including reduction of ensemble
spread, enhancement of signal to noise and advancement of time of emergence. We conclude with a complete decomposition of the simulated and observed SAT
trends into internal and forced dynamical and thermodynamic components, both for observations and an illustrative member of the CESM-LE (section 3e). In theremainder of this section, we use the term ‘‘dynamicallyadjusted SAT trends’’ to denote that the internal component of circulation-induced SAT trends has been removed, leaving the total (dynamic plus thermodynamic)
forced component plus the internal thermodynamic
component.

a. SAT and SLP trends in the CESM-LE andobservations
Figure 1 shows maps of 50-yr (1963–2012) winter SAT
and SLP trends over North America from each of the15 MARCH 2016

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FIG. 1. DJF SAT [color shading; 8C (50 yr)21] and SLP [contours; hPa (50 yr)21] trends (1963–2012) for each member of the CESM-LE(labeled 1–30), the CESM-LE ensemble-mean trend (labeled EM), and observations (labeled OBS). SLP contour interval is 1 hPa(50 yr)21 starting at 60.5 hPa (50 yr)21, with solid (dashed) contours for positive (negative) values. SAT and SLP observation are from
MLOST and 20CR, respectively.

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30 members of the CESM-LE (labeled 1–30), as well asfrom observations and the CESM-LE ensemble mean.
The SAT and SLP trends vary widely in pattern, polarity,and magnitude across the individual ensemble members,
despite the fact that each simulation was conducted withthe same model and subjected to the identical radiative
forcing. Focusing first on SAT, it is evident that mostensemble members show warming, consistent with physical expectation because of the increase in GHG concentrations. However, despite the increased radiative forcing,
it is also clear that large regions of North America canexperience cooling in any single realization. Further, thepattern of SAT trends can be nearly opposite between
individual runs. For example, run 28 exhibits cooling overnorthwestern North America and warming in the southeast, while run 19 shows opposite-signed trends. Manyother examples can be found where individual ensemble
members show SAT trends of opposite polarity or disparate amplitude at a given location.
The observed SAT trends (OBS) (Fig. 1, bottom-rightpanel) are positive everywhere, with the largest warming (.48C over 50 yr) over northwestern Canada andsmaller-amplitude warming (,18C over 50 yr) over thewestern United States and far eastern Canada. Some
members (e.g., runs 7, 12, and 24) resemble the observed
trend pattern while others are nearly orthogonal (e.g.,runs 14, 21, and 28). Viewed in the context of the
30-member CESM-LE, the observed SAT trend distribution lies within the range of simulated outcomes, eachof which is consistent with the response to radiative
forcing. As discussed further below, ensemble member 7
happens to provide a particularly close match to theobserved trends, both in terms of pattern and magnitude, because of the chance superposition of forced andinternal variability.
The degree of resemblance between the observed andsimulated trend maps can be quantified in terms of centered pattern correlation (e.g., the area-average SAT trend
is removed before computing the pattern correlation)
and RMS difference (Fig. 2, gray dots). Pattern correlations range from 20.7 to 10.7, and RMS differences
range from 0.68 to 1.88C (50 yr)21, with a close linear
relationship between the two (e.g., lowest RMS corresponding to highest pattern correlation and vice versa).
In other words, numerous SAT trend configurations are
possible because of the superposition of forced andinternally generated components, and no single CESMLE run need match the one realization in nature (although given enough ensemble members, one would
expect some to be realistic if the model is credible).
The externally forced component of the simulated SAT
trends can be obtained by averaging the trends from all 30
members together [the CESM-LE ensemble-mean trend

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FIG. 2. Pattern correlation (x axis) vs RMS difference [y axis; 8C(50 yr)21] of DJF SAT trends (1963–2012) over North America foreach member of the CESM-LE against observations (MLOST;
20CR). Gray dots are for total trends, and blue dots are for dynamically adjusted trends (internal dynamics removed). See text
for explanation.

(EM)] (Fig. 1, bottom panel). This component shows agenerally poleward-amplified warming pattern, withmaximum values ;28–3 8C (50 yr)21 along the Arctic
border compared to ;0.58–1.58C (50 yr)21 over most of
the United States. In addition to poleward amplification,
the forced warming trend in the CESM-LE exhibits zonal
contrasts across Canada, with smaller magnitudes in thewest compared to the east, and a local maximum over the
U.S. Rocky Mountains. Areas of amplified warming may
be due to local positive feedbacks associated with reductions in snow and sea ice.
It is instructive to compare the observed SAT trend
pattern with the CESM-LE forced response, noting thatagreement is not necessarily expected because of theadded contribution of internal variability in observations.
Like the model’s forced response, the observed trend
pattern shows some evidence for poleward amplification,
but the largest warming occurs over western Canada[.4 8C (50 yr)21] instead of the Canadian archipelago
and the Alaskan west coast (note, however, that thecomparison is hindered by sparse data coverage over the
Canadian archipelago). The pattern correlation between
SAT trends in observations and the CESM-LE ensemble
mean is only 0.12, with an RMS difference of 0.98C(50 yr)21 (recall that individual ensemble members exhibit much larger pattern correlations and smaller RMS
differences than the ensemble mean; Fig. 2).

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The diversity of SAT trends within the CESM-LE is
accompanied by a variety of atmospheric circulation(SLP) trend patterns and polarities (Fig. 1). Oppositesigned trends of similar magnitude are evident over the
North Pacific in individual ensemble members: for example, negative SLP trends in runs 7, 13, 17, 19, and 26
compared to positive trends in runs 8, 10, 14, 20, 21, and30, with maximum amplitudes approximately 4–8 hPa(50 yr)21. Notably, the ensemble-mean SLP trends
during 1963–2012 are near zero everywhere, indicatingthat SLP trends in any given realization are almost entirely due to internal variability. This point will become
especially important when we turn to the diagnosis ofdynamical versus thermodynamic contributions to theforced and internal components of the SAT trends.
The observed SLP trend pattern shows negativevalues over the northeast Pacific extending into western
Canada and weaker positive values to the south (Fig. 1,
bottom right). The observed SLP trend pattern bears
some resemblance to individual ensemble members,
notably runs 12 and 17, and a lack of resemblance toothers (e.g., runs 8, 10, 14, and 21). Consistent with thisvisual impression, the pattern correlations between thesimulated and observed SLP trend maps range from 20.6
to 10.8 (Fig. 3). Interestingly, there is a close relationshipbetween the pattern correlations of the simulated SLP
and SAT trends with observations (Fig. 3). That is, ensemble members that show large positive (negative) SLP
trend pattern correlations with observations also show
large positive (negative) SAT trend pattern correlations
with observations. This linear dependence of the SLP and
SAT trend pattern correlations suggests that the circulation plays an important role in the diversity of SAT
trends across the CESM-LE and, by extension, in theobserved SAT trends. Next, we quantify this role throughthe use of dynamical adjustment.

b. Dynamically adjusted SAT trends in the CESM-LE
and observations
Removing the effects of internal atmospheric circulation variability via the constructed analog techniquegreatly reduces the diversity of SAT trends across the
CESM-LE and essentially eliminates any SLP trends(Fig. 4). Not only are the patterns and magnitudes of the
SAT trends more similar between individual ensemble
members, their amplitudes are generally smaller thantheir unadjusted counterparts (recall Fig. 1). Notably,
regions of cooling are largely eliminated, and areas ofextreme warming [.48C (50 yr)21] are reduced. The
remaining spread across the dynamically adjusted SAT
trend maps is largely attributable to thermodynamic
processes (in particular, those associated with sea ice
and snow cover: see section 4), as the circulation analog

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FIG. 3. Pattern correlations between simulated and observed
1963–2012 DJF SAT (x axis) and SLP (y axis) trends. Each dot
represents a different CESM-LE run. Pattern correlations are
based on the Pacific-North American domain for SLP and North
America for SAT. SAT and SLP observation are from MLOST and
20CR, respectively.

technique removes more than 90% of the internal SLP
trend variance (Fig. S2 in the supplemental material).
Indeed, the SLP trend maps based on the PiCTL constructed analogs (Fig. S3 in the supplemental material)
are very similar to the raw SLP trend maps, with patterncorrelations . 0.96 and RMS differences , 0.11 hPa(50 yr)21 for all ensemble members.
In observations, the dynamically adjusted SAT trendmap (bottom-right panel of Fig. 4) shows less spatial
heterogeneity and a more dominant expression ofpoleward amplification compared to the raw SAT trend
map. In particular, the warming across western Canada
is considerably reduced, and the east–west contrast
across the United States is largely alleviated.
To highlight the importance of internal circulation
effects in observations, Fig. 5 compares maps of the totaland (internal) dynamically induced SAT trends, alongwith the contribution of internal dynamics expressed
as a fraction of the total SAT trend at each location.
Unforced circulation trends contribute 40%–60% of thetotal warming over much of western Canada and theeastern United States and up to 70% in some locations.
In other areas, such as the western United States, partsof Alaska, and far northeastern Canada, internal dynamics offset the warming trend by up to 20%–30%.
Dynamical adjustment improves the resemblance
between the observed SAT trend distribution and thoseof the individual CESM-LE ensemble members (Fig. 4).

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FIG. 4. As in Fig. 1, but internal circulation effects removed (see text).

In particular, the RMS differences are considerably
lower after applying dynamical adjustment to the internal
component of circulation trends, with values ranging from
0.328 to 0.718C (50 yr)21 and an average of 0.498C (50 yr)21(blue circles in Fig. 2) compared to 0.628–1.758C (50 yr)21

and an average of 1.158C (50 yr)21 for the raw trends (graycircles in Fig. 2). The pattern correlations are also improved
for the dynamically adjusted SAT trends, ranging from0.01 to 0.72 with a mean of 0.37 compared to a range
from 20.70 to 0.66 with a mean of 0.02 for the raw trends

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FIG. 5. Observed DJF SAT trends (1963–2012): (a) Total [8C (50 yr)21], (b) contribution from internal dynamics [8C (50 yr)21], and(c) fractional contribution from internal dynamics.

(Fig. 2; note that the spatial-mean trend is excluded when
computing pattern correlations).
Dynamical adjustment also improves the resemblance
between the observed SAT trend pattern and the forced
SAT trend pattern obtained from the average of the
CESM-LE members (Fig. 4, bottom-right panels labeled
OBS and EM, respectively). In particular, the patterncorrelation between the CESM-LE ensemble mean trend
and the observed trend increases from 0.12 to 0.54, andthe RMS difference decreases from 0.908 to 0.348C(50 yr)21, after applying dynamical adjustment. Thus,
dynamical adjustment provides an improved estimate of
the anthropogenic signal in observed 50-yr trends.

c. Probability distributions of raw and dynamicallyadjusted SAT trends
The raw and dynamically adjusted SAT trends for agiven location or region may be summarized in terms ofprobability distributions based on the set of 30 CESM-LE
simulations. These distributions also provide context forthe single estimate from observations. Figure 6 shows
results for three regions of contrasting spatial scale: North
America, western Canada (1408–908W), and the grid box
containing Fairbanks, Alaska. Compared to the raw trend
distributions (gray bars), the dynamically adjusted ones
(blue bars) are considerably narrower and more Gaussianin character. Not surprisingly, the relative degree of narrowing of the trend distributions depends on spatial scale,with the greatest reductions for Fairbanks and the smallest
for North America. For example, Fairbanks shows a broad
range of SAT trend values [from 21.88 to 16.18C (50 yr)21]
with 75% of the simulations in the range from 20.88
to 13.58C (50 yr)21. After removing the influence of internal atmospheric circulation variability, the distribution
narrows to a range from 10.18 to 12.58C (50 yr)21 andexhibits a more Gaussian character with ;75% of simulations within the range from 10.88 to 12.28C (50 yr)21.
For all three regions, the observed trends (raw anddynamically adjusted) lie within their respective model
distributions, with the raw values (dashed orange lines)

near the upper end of the model range and the dynamically adjusted values (solid orange lines) close to thecenter of the model range (e.g., the model’s forced response; Fig. 6). Recall from section 2e that the only model
information used in the calculation of the observed dynamically adjusted SAT trends is the CESM-LE ensemblemean SLP trends, which are nearly zero (recall Fig. 1).
For North America, the observed warming trend is reduced from 2.28 to 1.48C (50 yr)21 after dynamical adjustment, a decrease of 37%. Put another way, internal
circulation variability has augmented the warming trend
due to radiative forcing (plus a small contribution frominternal thermodynamics; see below) by 57%. The effects
are larger for western Canada, where dynamical adjustment reduces the warming trend by 48% [from 3.58 to
1.88C (50 yr)21]; that is, internal circulation variability has
nearly doubled the forced (plus internal thermodynamic)
warming trend. The effect of dynamical adjustment for
Fairbanks is smaller than that for North America andwestern Canada but still substantial, with a reduction in
warming of 34% [from 2.98 to 1.98C (50 yr)21].
The sensitivity of the observational results to the choiceof dataset is summarized in Table 1 and Fig. S4 in the
supplemental material. The contribution of internal dynamics to the total warming trend varies by 6%–7% acrossthe 3 SAT datasets (Table 1). In an absolute sense, thecontribution of internal dynamics ranges by 0.088C(50 yr)21 for North America, 0.178C (50 yr)21 for western
Canada, and 0.298C (50 yr)21 for Fairbanks, Alaska (Table 1):that is, not surprisingly, observational uncertainty increases as the spatial scale decreases, both for the total
SAT trend and the internal dynamically induced component (Table 1). However, the broad spatial patterns andmagnitudes of the SAT trends (total, internal dynamically induced, and residual components) across the threeobservational datasets are very similar (Fig. S4).

d. Additional consequences of dynamical adjustment
Here we quantify the utility of dynamical adjustment
in reducing ensemble spread, enhancing signal to noise,

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FIG. 6. Histograms of DJF SAT trends [1963–2012; 8C (50 yr)21]
for (a) North America, (b) western Canada, and (c) Fairbanks,
Alaska. Gray (blue) bars denote raw (dynamically adjusted) trends
from the CESM-LE. Dashed (solid) orange vertical lines denoteraw (dynamically adjusted: internal dynamics removed) trends
from observations. Note the different horizontal and vertical axis
ranges in each panel.

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and advancing the ‘‘time of emergence’’ of SAT trends
in the CESM-LE. Ensemble spread, defined here as thevariance of SAT trends across the individual ensemble
members, is reduced by more than 80% over much of
the western and southeastern portions of North America and by 50%–60% around Hudson Bay, the Great
Lakes, central Rockies, and Mexican highlands (Fig. 7c).
Averaged over the continent as a whole, removal ofinternal dynamical influences via our dynamical adjustment procedure reduces the variance of SAT trends(1963–2012) in the CESM-LE by 75%, more than in any
other season (not shown). The actual SAT trend variance in the raw data is largest over western Canada andAlaska extending southeastward along a narrow band to
the Great Lakes and over the U.S. Rocky Mountains,with maximum values ;3–5 [8C (50 yr)21]2 (Fig. 7a). In
contrast, the SAT trend variance in the dynamicallyadjusted data is nearly uniform across the continent,with values 0.5–1 [8C (50 yr)21]2 over Alaska and central
Canada and ,0.5 [8C (50 yr)21]2 elsewhere (Fig. 7b).
Related to the reduction in ensemble spread, dynamical adjustment increases the signal-to-noise ratio(SNR) of SAT trends, where the signal is defined as theforced (ensemble mean) SAT trend and the noise as thestandard deviation of SAT trends across the 30 ensemble members (Fig. 7f). Notably, dynamical adjustment
more than doubles the SAT trend SNR over the northwestern and southeastern portions of the continent andincreases it by at least 50% elsewhere (Fig. 7f). The raw
SAT trends show SNR values that are close to unity overmost of the continent (and ,1 in parts of the northwest):
only Mexico and a small area east of Hudson Bay exhibit
values .2 (Fig. 7d). On average, the raw SAT trend
SNR over North America is 1.3, indicating that theforced climate change signal and internal variability arecomparable for winter SAT trends over the past 50 yr. In
contrast, dynamically adjusted SAT trends show SNRvalues generally above two over most of the continent,with higher values (.3) along the Arctic border, Florida, the southwestern United States, and central Mexicoand lower values (1.5–2) over western Canada and thenorth-central United States (Fig. 7e). On average, thedynamically adjusted SAT trend SNR over North
America is 2.3, compared to 1.3 for the raw trends.
Many studies have examined the time of emergence(TOE) of the anthropogenic climate change signal, estimated by evaluating when the forced response firstexceeds a given amplitude of internal variability [typically, one or two standard deviations (e.g., Mahlstein
et al. 2011; Diffenbaugh and Scherer 2011; Deser et al.
2012a)]. Here we assess the effect of dynamical adjustment on TOE. We compute TOE from the CESM-LE
based on 10-yr running means of DJF SAT anomalies,15 MARCH 2016

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TABLE 1. Sensitivity of observed DJF SAT trends [1963–2012; 8C (50 yr)21] to choice of dataset for North America, western Canada,
and Fairbanks, Alaska (same regions used in Fig. 6). ‘‘Total’’ indicates the total trend; ‘‘internal dynamics’’ indicates the trend due tointernal dynamics; and ‘‘residual’’ indicates their difference (total minus internal dynamics). Percent change indicates the residual expressed as a fraction of the total (%). Datasets are MLOST, CRUTEM4 (CRUT), and GISTEMP (GIST). See text for details.
North America

Total
Internal dynamics
Residual% change

Western Canada

Fairbanks, Alaska

MLOST

CRUT

GIST

MLOST

CRU

GIST

MLOST

CRUT

GIST

2.19
0.82
1.37
237%

2.53
0.78
1.75
231%

2.44
0.86
1.58
235%

3.51
1.70
1.81
248%

3.95
1.61
2.34
241%

3.83
1.78
2.05
246%

2.93
0.99
1.94
234%

2.86
1.17
1.68
241%

3.16
1.30
1.86
241%

where anomalies are computed relative to the period
1920–49. Specifically, we find the year when the forced(ensemble mean) 10-yr running mean SAT anomaly firstexceeds and remains above one standard deviation of
the internal variability (computed across the 30 SAT
anomalies at each time step after applying a 10-yr running mean). We also compute TOE based on dynamically adjusted data (internal dynamics removed). This‘‘dynamically adjusted’’ TOE will generally be earlier

than the raw TOE because of the reduced amplitude ofinternal variability in the dynamically adjusted SAT
compared to the raw SAT.
The TOE map based on the raw 10-yr running mean
DJF SAT anomalies shows that the forced signal has not
yet emerged above the internal variability over a wideswath of the western portion of the continent (grayshading) and has only recently emerged (since 2005) overmuch of the intermountain west, the central portion of

FIG. 7. (Left) Variance of DJF SAT trends f1963–2012; [8C (50 yr)21]2g across the CESM-LE based on: (a) totaland (b) dynamically adjusted (internal dynamics removed) data. (c) The proportion of total trend variance (%)
accounted for by dynamical adjustment [e.g., (a) minus (b) divided by (a)]; red (blue) shading indicates that internal
dynamics contributes to a high (low) proportion of the total SAT trend variance. (right) SNR for DJF SAT trends(1963–2012) from the CESM-LE based on (d) total and (e) dynamically adjusted (internal dynamics removed) data.
(f) The ratios of the SNR values in (e) divided by those in (d). Signal is defined as the ensemble-mean trend, and noise
is defined as the standard deviation of the trends across the 30 members.

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FIG. 8. Maps of TOE of forced winter SAT anomalies based on
10-yr running means from the CESM-LE for (a) total and(b) dynamically adjusted (internal dynamics removed) data. See
text for details. Gray areas denote grid boxes where the forced
signal has not yet emerged by 2012.

North America, and far eastern Canada (Fig. 8a). The
earliest TOE values (1980s) occur along the Arctic
border and the southeastern United States (Fig. 8a).
Dynamical adjustment advances the TOE considerably
at all locations, and nearly all areas are now ‘‘emergent’’(Fig. 8b). Specifically, the dynamically adjusted TOE
values are in the 1970s over Alaska and northern Canada, the 1980s over much of the eastern half of thecontinent, the 1990s over the western United States, andafter 2005 over the midsection of the United States andalong the western portion of the Canadian–U.S. border(Fig. 8b). This advancement of TOE is entirely due tothe reduction of interannual variance in the dynamicallyadjusted data compared to the raw data, since the forced
signal is the same in both calculations.

e. Decomposition of forced and internal SAT trends
into dynamic and thermodynamic components in
the CESM-LE and observations
Having established the central role of internal atmospheric dynamics to the CESM-LE and observed SAT
trend patterns over North America, we conclude ouranalysis with a complete decomposition of the SAT trends
into forced and internal dynamical and thermodynamic

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components. This full decomposition is performed forobservations and for an illustrative member of the
CESM-LE (run 7 whose SAT trends happen to bear
the closest resemblance to observations; recall Fig. 1).
The results are shown in Fig. 9a for the CESM-LE andFig. 9b for observations. The model results are discussed
first. The top row shows the total SAT trends and theirconstituent internal and forced parts, the latter obtained
from the CESM-LE ensemble mean and the former
obtained by subtracting the forced component from thetotal. The middle row shows the contribution of dynamics to the total, internal, and forced components. As
mentioned earlier, the total dynamical contribution is
obtained directly by applying the constructed analog
technique to the total SLP trend field for that particular
run; the forced dynamical contribution is obtained byaveraging the total dynamical contributions for all 30
ensemble members; the internal dynamical contribution
is obtained by subtracting the forced dynamics contribution from the total dynamical contribution. Finally,
the bottom row shows the contribution of thermodynamics to the total, internal, and forced components,
obtained as residuals between the total and dynamical
contributions. Strictly speaking, the residuals also containdynamical contributions not accounted for in the circulation analog technique (as a result of both inadequate
sampling as well as methodological uncertainty). However, as discussed in the appendix, these errors are generally very small given the length of control run used to
identify the constructed analogs as well as the repeatedrandom sampling and averaging of the optimal linear
combinations of constructed analogs.
As already described, run 7 features strong warming
over the northern two-thirds of the continent, with maximum values exceeding 48C (50 yr)21 over large regionsof Canada and the northeast United States [Fig. 9a(i)].
Atmospheric circulation trends contribute much of thewarming over western Canada by virtue of anomalous
southerly flow associated with a deepened Aleutian low[recall Fig. 4; Fig. 9a(ii)]. Thermodynamic processes are
responsible for the enhanced warming in the vicinity of
Hudson Bay, the Canadian archipelago, and northern
Alaska [Fig. 9a(iii)], in association with diminished snow
cover and sea ice cover (not shown). The total dynamicalcomponent [Fig. 9a(ii)] is mainly a result of internal circulation trends [Fig. 9a(v)], with forced circulation trends
contributing mainly to warming along the Arctic border[Fig. 9a(viii)]. On the other hand, the total thermodynamic
contribution [Fig. 9a(iii)] is largely forced [Fig. 9a(ix)];
the internal thermodynamic component [Fig. 9a(vi)]augments the forced warming over eastern Canada, theGreat Lakes region, and Alaska and partially offsets theforced warming elsewhere. In summary, both dynamics

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FIG. 9. Decomposition of DJF SAT trends [1963–2012; 8C (50 yr)21] into internal, forced, dynamical, and thermodynamic components for(a) run 7 of the CESM-LE and (b) observations (MLOST). See text for details.

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JOURNAL OF CLIMATEand thermodynamics contribute to the total SAT trends;
further, the dynamical contribution is almost entirelyinternal, whereas the thermodynamic contribution isboth internal and forced.
The same decomposition is performed for the observed SAT trends in Fig. 9b. Strictly speaking, the only
partitioning that can be made based purely on observations is the separation of the raw trends into dynamical and thermodynamic components (left column).
Using the model’s forced SLP response in conjunction
with observed SLP–SAT relationships enables separation of the dynamical contribution into internal andforced components (middle row). Specifically, we have
performed a separate dynamical adjustment for observations based on the internal component of the SLP
anomalies at each time step, where the internal component is obtained by subtracting the ensemble-mean
SLP anomaly from the CESM-LE from the observed
SLP anomaly. The forced dynamical contribution in
observations is then obtained by subtracting the internal
dynamical contribution from the total dynamical contribution. The remaining components require use of themodel’s forced SAT and were determined as follows(note that, for this purpose, the model’s forced SAT was
regridded to the mesh of the observed SAT data). The
total forced component of the observed SAT is equatedto the model’s total forced SAT, and the total internal
component of the observed SAT is obtained by subtracting the forced SAT from the observed SAT. The
forced thermodynamic component of the observed SAT
is obtained by subtracting the forced dynamical component of the observed SAT from the total forced SAT.
Finally, the internal thermodynamic component of theobserved SAT is obtained by subtracting the internal
dynamic component from the total internal component.
Dynamics contributes to warming [28–38C (50 yr)21]
across western Canada and weak cooling over northeastern Canada, western Alaska and the northwestern
United States [Fig. 9b(ii)] while thermodynamics accounts for a broad pattern of warming over the entire
continent, with largest amplitudes over Canada [Fig. 9b(iii)].
These patterns are remarkably similar to those from
CESM-LE run 7 [Figs. 9a(ii), 9a(iii)], as are the patternsof the total trends [Fig. 9a(i)], although they are basedon completely independent datasets. This, in turn, lends
confidence to the robustness of the decomposition andinterpretation of the results in both the model and observations. The circulation-induced component of theobserved SAT trends [Fig. 9b(ii)] is almost entirely internal [Fig. 9b(v)], similar to that found for run 7 of the
CESM-LE except along the Arctic border, where themodel shows modest warming from forced circulation
changes [Fig. 9a(viii)]. It is difficult to assess whether the

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differences along the Arctic border are a result of model
shortcomings or observational data constraints, since thisis a region of limited data coverage. Further, this region
may be subject to thermodynamic influences from dynamically forced changes in sea ice cover that are implicitly included in the circulation analogs from themodel’s control run but may not be adequately sampled in
the short observational record. Finally, it is evident thatthe thermodynamic component of the observed SAT
trends [Fig. 9b(iii)] is mainly forced [Fig. 9b(ix)], withsecondary contributions from internal processes thataugment the warming over western Canada and Alaska
and cool much of the United States [Fig. 9b(vi)], in linewith the results from run 7. In summary, observed DJF
SAT trends over the past 50 years are largely the result ofinternal dynamics and forced thermodynamics, with secondary contributions from internal thermodynamics.
A complementary, temporal view of the relative contributions of internal and forced dynamics and thermodynamics to North American SAT anomalies during
1920–2012 in run 7 of the CESM-LE is shown in Fig. 10(observational results are shown in Fig. S5 of the supplemental material). The top pair of curves contrasts theraw (black) and dynamically adjusted (magenta) SAT
records. While the raw time series displays prominentinterannual fluctuations superimposed upon a long-termwarming trend beginning in the early 1960s, the dynamically adjusted record exhibits more muted variability
and a smaller but more monotonic rise in SAT starting in
the late 1970s (similar results are obtained when bothforced and internal dynamics are removed; not shown).
Thus, not only does dynamical adjustment alter the timing and amplitude of the long-term warming trend, it also
provides for a more stable estimate of these parameters
because of the reduction in interannual variance (noise inthis context). The second pair of curves contrasts theforced (red) and internal (blue) components of North
American SAT. The forced time series bears a close resemblance to the dynamically adjusted record, with evenless interannual variability, while the internal time series
is dominated by high-frequency fluctuations. The thirdpair of curves compares the thermodynamic (brown) anddynamical (orange) contributions to forced SAT. It isclear that thermodynamics dominates, with dynamics
making a small but nonnegligible contribution to theforced component of warming in recent decades. The final pair of curves compares the thermodynamic (green)and dynamical (cyan) contributions to the internal SAT
record. Both are primarily high frequency in character,with larger amplitudes for the dynamical component than
the thermodynamic one. In summary, dynamical adjustment leads to an improved estimate of the forced component of the North American SAT time series and15 MARCH 2016

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FIG. 10. Time series decomposition of DJF SAT anomalies (8C) averaged over North
America from run 7 of the CESM-LE into internal, forced, dynamical, and thermodynamic
components. (top) The total (black) and dynamically adjusted (magenta; internal dynamics
removed) components. (upper middle) The internal (blue) and forced (red) components.
(lower middle) The forced thermodynamics (brown) and forced dynamics (orange) components. (bottom) The internal thermodynamics (green) and internal dynamics (cyan) components. Note the different vertical scales for each set of curves. See text for explanation.

provides a more stable estimate (e.g., less subject tosampling fluctuations) of the timing and amplitude of
low-frequency trends.

4. Discussion
The utility of dynamical adjustment for attributing
SAT trends was demonstrated in the seminal studies ofWallace et al. (2012) and Smoliak et al. (2015) using avariety of techniques. These studies focused primarilyon the period 1965–2000, an interval characterized by aprominent trend in the northern annular mode withattendant effects on winter SAT over North America
and Eurasia. Similar to our results, both studies foundthat dynamics account for approximately 40% of thetotal cold season SAT trend over land poleward of 408N
during 1965–2000. As shown in Smoliak et al. (2015), thespatial pattern of the dynamical contribution to SAT
trends over North America during 1965–2000 resembles
that found in our study based on 1963–2012, except for
the lack of cooling over the western United States.
Neither Wallace et al. (2012) nor Smoliak et al. (2015)
distinguished between internal and forced contributions
to atmospheric circulation trends during 1965–2000.

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A key aspect of our study was to make use of the forced
SLP response as given by the ensemble mean of the
CESM-LE. This, in conjunction with the observed relationships between SLP and SAT anomalies, enabled us
to evaluate both the internal and forced dynamical contributions to observed SAT trends. In addition, by incorporating the model’s forced SAT response, we wereable to further decompose the remaining portion of theobserved SAT trends into internal and forced thermodynamic components. It is noteworthy that the forced component of winter SLP anomalies over the North Pacific andNorth America in any given year, and in trends over thelast 50 years, is small (nearly zero) compared to the internal
component, both according to the CESM-LE (Fig. 1, EM
panel) and the CMIP5 multimodel archive (Fig. S6 in the
supplemental material, EM panel). The extent to which
this result is model dependent remains to be assessed.
Although dynamical adjustment greatly reduces thediversity of SAT trends across the 30-member CESM-LE,
differences remain, especially in the vicinity of Hudson
Bay, the Great Lakes, and Alaska (recall Fig. 7b). For
example, dynamically adjusted warming trends over muchof Canada exceed 48C in run 4 but are ,1.58C in run 27(recall Fig. 4). What processes contribute to the remaining
spread in dynamically adjusted SAT trends? The patternof residual SAT trend variance (Fig. 11a) suggests thatsnow cover and sea ice changes may play a role. Indeed, asimilar pattern is obtained by regressing trends in dynamically adjusted SAT onto trends in sea ice concentration averaged over Hudson Bay (Fig. 11b). Our
physical interpretation of this regression pattern is thatinternal trends in Hudson Bay sea ice (possibly initiatedby atmospheric forcing) feed back onto SAT locally andover adjacent land areas via thermodynamic processes. In
addition, associated changes in snow cover west of theCanadian and U.S. Great Lakes may amplify these thermodynamic SAT feedbacks. We speculate that similar
physical mechanisms are at work over Alaska. Further
investigation of the processes contributing to the spread in
the thermodynamic component of internal SAT trends iswarranted.
As discussed in Hawkins and Sutton (2009) and otherstudies, the CMIP5 archive contains three sources of
uncertainty: model response uncertainty due to structural differences between models, radiative forcing uncertainty, and uncertainty due to internal variability.
How large is the contribution of structural model uncertainty versus internal variability uncertainty to the
spread of SAT trends within CMIP5 for a given radiative
forcing scenario, and does internal atmospheric circulation variability play a role? This question is difficult toaddress without a sufficient number of ensemble members to define the forced response in each model,

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FIG. 11. (a) Standard deviation of dynamically adjusted DJF
SAT trends [1963–2012; 8C (50 yr)21] across the CESM-LE.
(b) Regression map of dynamically adjusted SAT trends onto the
Hudson Bay sea ice trend index. See text for details.

although results based on a previous 40-member initialcondition ensemble with the Community Climate System Model, version 3 (CCSM3), suggested an importantrole for internal variability in the spread within CMIP3(Deser et al. 2012b).
We can gain some insight into these questions, however, by comparing the SLP and SAT trends simulatedby the CMIP5 models with those simulated by the
CESM-LE. Qualitatively, the diversity of SAT and SLP
trend patterns and magnitudes within the set of CMIP5
model runs is reminiscent of that within the CESM-LE,
although there appear to be fewer cases of strong negative SAT trends (Fig. S6). Particularly noteworthy is
the wide range of SLP trends whose multimodel mean
(panel labeled EM in Fig. S6) is near zero, just as in the
CESM-LE. A more quantitative comparison is provided
in Fig. 12a, which shows pattern correlations and RMS
differences between the SAT trends from each of the 38
CMIP5 models against observations (red dots). The setof CMIP5 model runs shows a similar range of pattern

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FIG. 12. (a) Pattern correlation vs RMS difference [(8C (50 yr)21] of DJF SAT trends (1963–2012) over North
America for each member of the CESM-LE (gray dots) and each member of the CMIP5 archive (red dots) against
observations (MLOST). (b) Pattern correlations between simulated and observed 1963–2012 winter SAT and SLP
trends. Dots are for the CESM-LE (gray) and CMIP5 (red) simulations. Pattern correlations are based on the PacificNorth American domain for SLP and North America for SAT.

correlations (albeit with fewer large negative values) and
RMS differences as the CESM-LE (gray dots in Fig. 12a),suggesting that internal variability may be an importantsource of SAT trend spread within the CMIP5 archive. The
range of pattern correlations between the observed andsimulated SLP trends is also comparable across the CMIP5
models (red dots) and the CESM-LE ensemble (gray dots),and importantly, the SLP and SAT pattern correlations
show a similar relationship in the two model ensembles(Fig. 12b). Taken together, these results are suggestive ofan important role for internal dynamics (as opposed tomodel response uncertainty) in the diversity of North
American SAT trends within the CMIP5 archive. Further
investigation of the role of internal variability versus model
uncertainty in the CMIP5 archive is clearly warranted.
Another important implication of our results pertains
to model evaluation. A common metric for climate
model assessment is the skill with which observed trends
during recent decades are simulated. However, as thisstudy highlights, a single simulation with a credible
model need not match the observed climate trajectory at
local/regional scales if the contribution from internalvariability is comparable or larger than that from external forcing. Conversely, a single integration with amodel that is lacking in realism may show fortuitous
agreement with the observed trends. The methodology
outlined in this paper, including the application of dynamical adjustment in conjunction with an estimate of
the forced circulation response, can be used to provide amore informative and reliable assessment of a model’sability to simulate observed climate trends.

Thompson et al. (2015) have recently argued thatclimate model evaluation would be well served to focus
on two simple statistical properties of the unforced interannual variability: standard deviation s and autocorrelation. These two parameters (especially s) dictate
the confidence intervals that can be placed on trends ofany length due to internal variability, provided the data
are normally distributed and stationary in time [seediscussion in Thompson et al. (2015)]. In this context, it
is worth noting that the CESM-LE simulates generally
realistic magnitudes (within 10%–20% of observations
in most regions) and spatial patterns of SAT and SLP
s for both unfiltered and 8-yr low-pass filtered data
(Fig. S7 in the supplemental material).
Our methodology, based on a combination of observations, a large initial-condition ensemble of historicalsimulations, and a technique for estimating the dynamical contribution, has general applicability beyond thespecific purpose of this study. In particular, it can beused to inform attribution of observed climate anomalies on a near-real-time basis, as well as improve thephysical understanding of differences in climate changes
simulated by different models. As with any empiricalmethod, inherent uncertainties due to limited samplingof circulation statistics in the short (;100 yr) observational record must be taken into account. This problem
is ameliorated to a great extent in models for which
lengthy control simulations exist. There is also the caveat
that, as models improve and resolve finer spatial andvertical scales, their forced SLP (and SAT) responses
may be altered, leading to new insights regarding the role

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5. Summary
By combining observations with a 30-member initialcondition ensemble of CESM1 coupled model simulations (the CESM-LE) and making use of ‘‘dynamical
adjustment,’’ we have provided insight into the mechanisms of internal and forced components of winter SAT
trends over North America during the past 50 years. Our
results show that, at local/regional scales, the simulated
SAT trends are strongly influenced by internal variability, with an average signal-to-noise ratio of only 1.3.
The importance of internal variability is evidenced by
the variety of spatial patterns, amplitudes, and polaritiesof trends among the 30 simulations, each of which is
subject to the identical scenario of historical radiative
forcing. The range of model solutions spans the single
realization of the real world, providing important context for the interpretation of observed long-term trends.
The internally generated component of SAT trends
within the CESM-LE is largely dynamically induced,
whereas the forced component is primarily thermodynamically controlled, either directly via radiative effects
from increased GHGs or indirectly via changes in SSTs,
sea ice, and snow cover. This follows from the fact thatthe simulated winter SLP trends in the CESM-LE overthe past 50 years are almost entirely a result of internal
climate variability, with a negligible forced component.
(It remains to be seen whether other climate models
with sufficient ensemble size also show negligible forced
SLP trends for the time period and region examined
here; however, we note that the CMIP5 multimodel
mean agrees with the CESM-LE in this respect.) For thereal world, we estimate that internal circulation trends
account for approximately one-third of the observed
wintertime warming over North America during thepast 50 years and more than half locally over parts ofCanada and the United States. In a few areas, such as thecentral Rocky Mountains, far western Alaska, andnortheastern Quebec province, internal dynamics has
offset the warming trend by 10%–30%. Removing theeffects of internal atmospheric circulation variability
via a constructed analog technique narrows the spreadwithin the CESM-LE, thereby enhancing the signal-tonoise ratio of the simulated SAT trends (by a factor of 2,
on average) and advancing the ‘‘time of emergence’’ ofthe forced SAT component (by approximately a decadein many locations). Dynamical adjustment also brings
the observed trends closer to the model’s forced response, both in terms of pattern and amplitude, facilitating their interpretation.

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The methodological framework proposed in this study
provides a general template for improving physical understanding and interpretation of observed and simulated climate trends worldwide. Application to otherseasons, regions, time periods, and parameters will be
pursued in future work.
Acknowledgments. We have benefited from useful
discussions with Drs. Julien Boé, Brian V. Smoliak,
David W. J. Thompson, and John M. Wallace during thecourse of this work. We thank the three reviewers fortheir constructive comments that helped to improve themanuscript. We also acknowledge the efforts of all those
who contributed to producing the CESM-LE and thankthe Climate and Global Dynamics Division at NCAR
for supporting L. Terray’s sabbatical visit. NCAR issponsored by the National Science Foundation.

APPENDIX
Constructed Analog Technique for Dynamical
Adjustment
Here we provide additional details on our constructedanalog methodology for dynamical adjustment. As described in the main text, we first determine the Na
closest analogs Xc from the PiCTL for each time step of aparticular CESM-LE run Xh, and then randomly draw
Ns of the Na analogs. We then estimate a constructed
SLP analog Xca as a linear combination of these Ns
analogs according to
Xh ’ X ca 5 Xc b ,(A1)where Xc is a matrix of column vectors comprising theselected Ns closest analogs of the column vector Xh, andb is a column vector of the fitted regression coefficientsthat are the linear proportions of the contributions ofeach column of Xc to the constructed analog Xca. The
dimensions of Xh are m 3 1, where m is the number ofgrid points contained in the SLP pattern. The dimensions of Xc are m 3 Ns and that of b are Ns 3 1. Theb coefficients can be estimated by using the Moore–
Penrose pseudoinverse of Xc :b 5 [(XTc Xc )21 XTc ]Xh .

(A2)

In practice, we calculate b using a singular value decomposition of Xc . The b coefficients are then applied to
the Ns SAT patterns from the PiCTL simulation corresponding to the selected SLP analogs to reconstruct the
dynamically induced component of SAT in the CESMLE run.

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FIG. A1. Total estimated dynamical contribution to SLP and SAT trends (1963–2012) as a function of the number of closest Ns analogs
used. (top) Observational results and (bottom) model results based on run 7 of the CESM–LE. (a),(d) The actual trends; (b),(c),(e),(f) the
constructed analog trend estimates [SAT in color shading, 8C (50 yr)21, and SLP in contours, contour interval 5 1 hPa (50 yr)21] based on
different choices of Ns, as stated in the panel titles.

For each month, we repeat the drawing of the Ns
analogs Nr times. We then end up with Nr different
samples of dynamically induced SAT. Note that thesediffer mainly because of thermodynamically induced
internal variability. We then take the mean of the Nrsamples as the final dynamically induced SAT. The
spread among the Nr samples gives a lower bound forthe spread because of thermodynamically induced internalvariability. We repeat all the steps for each month of the
CESM-LE simulation to obtain a complete reconstructionof dynamically induced SAT in that run. Finally, we repeat
the entire algorithm for each member of the CESM-LE.
Figure A1 shows the sensitivity of the results to the
choice of closest Ns analogs, for both observations andrun 7 of the CESM-LE. The SLP trends obtained fromthe constructed analog methodology closely match theactual SLP trends in both observations and CESM-LE
run 7 for a wide range of Ns values (5–50 for observations
and 10–100 for the model run; note that the observations
were only computed for Ns # 50). Similarly, only minor

FIG. A2. RMS error (RMSE) as a function of Nr for (a) SAT [8C (50 yr)21] and (b) SLP [hPa (50 yr)21] DJF trends(1963–2012) from the CESM-LE. Shading indicates the range across an ensemble of 200 averaging iteration steps that differ
by a random initial sequence of Nr SAT and SLP trends. The colored curve denotes the average over the ensemble.

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FIG. A3. Dynamical contribution to SAT trends [1963–2012; 8C (50 yr)21] in run 7 of the CESM-LE. Shown are(a) the ‘‘true’’ estimate and the estimates based on (b) quadratic trend removal, (c) spline trend removal, (d) 20-yr
high-pass filter, and (e) 10-yr high-pass filter. See text for explanation.

differences in the total estimated dynamical contribution to SAT trends are found between Ns 5 50 and Ns 5
5 for observations (Figs. A1b,c, respectively) and between
Ns 5 100 and Ns 5 10 for the model run (Figs. A1e,f,
respectively), although the dynamical contribution tosimulated SAT trends is slightly greater when more closest
analogs are used.
The sensitivity of the results to Nr, quantified in termsof RMS error, is shown in Fig. A2 for both SAT and
SLP. The shading indicates the range across all 30
CESM-LE simulations, and the colored curve denotes
the average over the ensemble. It is clear that the results
converge for Nr . 20 and that there is less spread for
SLP compared to SAT across all Nr.
As discussed in section 2e of the main text, we haveused the framework of the CESM-LE to determine
which high-pass filter to use for dynamically adjusting
the observations. Using a single run from the CESM-LE,

we can subtract the forced SLP and SAT responses(obtained from the CESM-LE ensemble mean) to obtain the unforced ‘‘residual’’ component of variability.
We can then find circulation analogs and associatedSAT anomalies from this residual record and apply ourdynamical adjustment procedure to obtain the ‘‘true’’unforced dynamically induced component in that run.
We can then compare this true dynamical estimate tothat obtained without knowledge of the forced response(as is the case when dealing with observations). The
latter is found by high-pass filtering the SAT record overthe period 1920–2012 and then applying our constructedcirculation analog protocol.
We have compared the true estimate of the dynamical
SAT trend contribution with those based on quadraticand spline trend removal for six of the CESM-LE ensemble members [these cases (runs 1, 7, 16, 21, 28, and 30)
were chosen to span a broad range of patterns; recall

15 MARCH 2016

DESER ET AL.

Fig. 1]. Both methods yield RMS amplitudes that differ
from the true RMS amplitude by 3.7% on average forthe six test cases. The 10-yr and 20-yr high-pass filters
perform less well (these were tested on only one
CESM-LE ensemble member, since their RMS errors
were found to be much larger than any of those basedon the quadratic and spline trend removals: 16% and23%, respectively). Figure A3 illustrates the results for
ensemble member 7 of the CESM-LE, comparing thetrue estimate of the dynamical SAT trend contribution(Fig. A3a) with those based on the four different
choices of high-pass filter: quadratic trend removal(Fig. A3b), spline trend removal (Fig. A3c), 20-yr highpass filter (Fig. A3d), and 10-yr high-pass filter(Fig. A3e). All four choices yield similar patterns ofdynamical contribution, but the quadratic and spline
trend removals are the closest to the true estimate.

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