Clim Dyn (2014) 43:333–344
DOI 10.1007/s00382-013-1830-9

Atmospheric impacts of Arctic sea-ice loss, 1979–2009: separating
forced change from atmospheric internal variability
James A. Screen • Clara Deser • Ian Simmonds •Robert Tomas

Received: 5 March 2013 / Accepted: 4 June 2013 / Published online: 15 June 2013
Ó Springer-Verlag Berlin Heidelberg 2013

Abstract The ongoing loss of Arctic sea-ice cover has
implications for the wider climate system. The detection
and importance of the atmospheric impacts of sea-ice loss
depends, in part, on the relative magnitudes of the sea-ice
forced change compared to natural atmospheric internalvariability (AIV). This study analyses large ensembles of
two independent atmospheric general circulation models inorder to separate the forced response to historical Arctic
sea-ice loss (1979–2009) from AIV, and to quantify signalto-noise ratios. We also present results from a simulation
with the sea-ice forcing roughly doubled in magnitude. In
proximity to regions of sea-ice loss, we identify statisticallysignificant near-surface atmospheric warming and precipitation increases, in autumn and winter in both models. In
winter, both models exhibit a significant lowering of sea
level pressure and geopotential height over the Arctic. Allof these responses are broadly similar, but strengthened
and/or more geographically extensive, when the sea-ice
forcing is doubled in magnitude. Signal-to-noise ratios
differ considerably between variables and locations. The
temperature and precipitation responses are significantly
easier to detect (higher signal-to-noise ratio) than the sea
level pressure or geopotential height responses. Equally,
J. A. Screen (&)
College of Engineering, Mathematics and Physical Sciences,
University of Exeter, Harrison Building, Streatham Campus,
North Park Road, Exeter, Devon EX4 4QF, UK
e-mail: j.screen@exeter.ac.uk
J. A. Screen  I. Simmonds
School of Earth Sciences, University of Melbourne,
Melbourne, VIC, Australia
C. Deser  R. Tomas
Climate and Global Dynamics, National Center for AtmosphericResearch, Boulder, CO, USA

the local response (i.e., in the vicinity of sea-ice loss) iseasier to detect than the mid-latitude or upper-level
responses. Based on our estimates of signal-to-noise, we
conjecture that the local near-surface temperature andprecipitation responses to past Arctic sea-ice loss exceed
AIV and are detectable in observed records, but that thepotential atmospheric circulation, upper-level and remoteresponses may be partially or wholly masked by AIV.
Keywords Arctic sea ice  Atmospheric modelling 
Ensembles  Detection and attribution  Internal variability 
Signal-to-noise ratio

1 Introduction
One of the clearest manifestations of recent climate change
is the loss of summer and autumn sea-ice cover in the
Arctic (Stroeve et al. 2011). During the 2012 melt season,
the Arctic sea-ice extent shrunk to the lowest value in thesatellite record, which began in 1979 (Zhang et al. 2013;
Parkinson and Comiso 2013). Especially rapid sea-ice melt
occurred during August 2012 at the time of a ferocious
storm (Simmonds and Rudeva 2012), though model hindcasts suggest that a new sea-ice minimum would have beenrecorded even without this storm (Zhang et al. 2013). The
last 6 years (2007–2012) have witnessed the six lowest
September sea-ice extents on record, possibly suggesting a‘‘tipping point’’ has been passed (Livina and Lenton 2013).
Recent dramatic sea-ice reductions augment longer-term
trends, but statistically significant sea-ice extent reductions
are apparent in all calendar months even if the last 6 years
are excluded (Kay et al. 2011).
The ongoing retreat of Arctic sea-ice has implications
for the climate system. In order to better understand these,

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a number of studies have perturbed sea-ice conditions inatmospheric general circulation models (AGCMs) andexamined the atmospheric response (e.g., Singarayer et al.
2006; Seierstad and Bader 2009; Deser et al. 2010; Streyet al. 2010; Blüthgen et al. 2012; Orsolini et al. 2012;
Ghatak et al. 2012; Porter et al. 2012; Screen et al. 2012,2013). In a model setting, the sea-ice cover can be
manipulated in a controlled manner to reveal how and by
what processes it affects the wider climate system. Thesestudies have identified some robust and reasonably wellunderstood features of the local atmospheric response to
sea-ice loss (i.e., impacts proximate to regions of sea-iceloss). These include warming and moistening of the lower
troposphere and increases in cloud cover and precipitation.
The impacts of Arctic sea-ice loss may not be limited tothe high latitudes. Increasing attention is now turning to thepotential remote impacts of Arctic sea-ice loss, including
possible changes in mid-latitude weather (Honda et al.
2009; Petoukhov and Semenov 2010; Liu et al. 2012;
Francis and Vavrus 2012; Screen and Simmonds 2013a, b).
Progress in understanding the potential large-scale orremote impacts of Arctic sea-ice loss is hampered by large
uncertainties in the atmospheric circulation response to
sea-ice loss. Observational studies suggest links between
autumn sea-ice loss and circulation patterns in the following winter (Francis et al. 2009; Overland and Wang
2010; Wu and Zhang 2010: Strong et al. 2010; Jaiser et al.
2012), but the statistical significance of these linkages has
been questioned (Hopsch et al. 2012), causality is unclear
and the mechanisms are poorly understood. In model
simulations, the spatial pattern, strength, statistical significance and timing of the circulation response to sea-ice loss
differs considerably between studies, and can be hard todisentangle from atmospheric internal variability (AIV).
AIV, also known as ‘‘climate noise’’, arises from non-linear
dynamical processes intrinsic to the atmosphere (see, e.g.,
Deser et al. 2012 and references therein).
In an attempt to better separate, and quantify, thepotential forced response to Arctic sea-ice loss and AIV,
this manuscript presents results from large ensembles with
two independent models, in which the only prescribed
forcing was observed Arctic sea-ice loss. Both models havebeen run multiple times with identical surface boundary
conditions and external forcing, with each run beginningfrom a different atmospheric initial state. Therefore, thedifferences between the simulated atmospheric states ofeach of the ensemble members arise only due to AIV.
These ensembles are approximately a factor of ten larger
than those used in Screen et al. (2013), and appreciably
larger than in most of the studies mentioned above. In part,
we seek to answer the question: how many ensemble
members are required to detect a significant response (in aparticular variable) to Arctic sea-ice loss, if indeed it is123

J. A. Screen et al.

possible to detect a significant response at all? This ispertinent to assessing the strength of the forced change
compared to AIV and hence, whether it may be observablein the real world.

2 Data and methods
2.1 Simulations
We utilise two independent AGCMs: the UK–AustralianUnified Model (UM) version 7.3 and the US National
Center for Atmospheric Research (NCAR) Community
Atmosphere Model (CAM) version 3. The UM has beendeveloped by the UK Meteorological Office Hadley Centre
and is the atmospheric model used in their Global Environmental Model version 2 (HadGEM2) and in the Australian Community Climate and Earth System Simulator(ACCESS). Both HadGEM2 and ACCESS are participating models in the fifth Coupled Model Intercomparison
Project (CMIP). The configuration of the UM used here has
38 vertical levels with a horizontal resolution of 1.25
degrees of latitude by 1.875 degrees of longitude. CAM is
the atmospheric component of the NCAR Community
Climate System Model version 3 (CCSM3), which participated in the third CMIP. The version used here has 26
vertical levels and a spectral resolution of T42, roughly
equivalent to 2.8 degrees of latitude and longitude. For
further details the reader is directed to Martin et al. (2011)
and Bi et al. (2013) for the UM/ACCESS and Collins et al.
(2006) for the CAM.
We primarily analyse two distinct simulations, performed identically with each model, termed the control(CTRL) and perturbation (PERT) simulations. In CTRL,
the models were prescribed with an annually-repeating
monthly cycle of climatological (CLM) sea-ice concentration (SIC) and sea surface temperature (SST). Monthlymean SIC and SST were taken from the Hurrell et al. (2008)
data set, updated to 2009, which is derived from a combination of in situ and remotely-sensed observations. In
PERT, the linear trend (TRD) in SIC over 1979–2009 foreach month was added to the climatological monthly values and these CLM ? TRD values were prescribed in themodels. The prescription of SST in PERT was based on theapproach introduced by Screen et al. (2013) and was asfollows. In grid-boxes and months where the SIC TRD is
not zero, then the CLM ? TRD SST were prescribed.
Elsewhere, CLM SST was prescribed. This approach captures SST changes directly related to SIC changes, but does
not include SST changes outside the sea-ice zone (seeScreen et al. 2013 for further details and justification).
CTRL and PERT were run for 100 years in the UM and for
60 years in CAM. Since the prescribed surface forcing

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repeats annually, but the atmospheric initial conditions
vary, each year is considered to be an independent
ensemble member (atmospheric ‘‘memory’’ is negligible
from year-to-year).
A further simulation has been performed with the UM,
termed the PERT*2 simulation, in which the linear trends
in SIC were doubled before being added to climatologicalvalues and these CLIM ? (TRD*2) values were prescribedin the model. SST were prescribed as above, but this timewith CLM ? (TRD*2) values in place of CLM ? TRD
values. PERT*2 was run for 100 years in the UM only.
To isolate the atmospheric impacts of sea-ice loss, we
compare the ensemble-mean of a particular variable in
CTRL with the ensemble-mean in PERT or PERT*2. The
ensemble-mean difference, PERT-CTRL or PERT*2CTRL, is referred to as the ‘‘response’’ to Arctic sea-ice
loss in the single- or double-perturbation experiments. We
refer to ‘‘local’’ and ‘‘remote’’ responses, by which wemean responses that are in close proximity to sea-ice
changes and those that are geographically distant from seaice changes, respectively.
2.2 Statistical methods
To test the statistical significance of the ensemble-meandifferences we compute the Student’s t-statistic, t, using thedifference of means test (Von Storch and Zwiers 1999),
t¼

jx  yjqﬃﬃﬃ
sp  N2

ð1Þ

where x is the ensemble-mean from PERT (or PERT*2),
y is the ensemble-mean from CTRL, N is the ensemble sizeand sp is the pooled standard deviation, given by,sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Pn
2 Pm
2
i¼1 ðxi  xÞ þ
i¼1 ðyi  yÞ
ð2Þ
sp ¼
nþm2
where xi is an individual ensemble member from PERT (orPERT*2), yi is an individual ensemble member from CTRL
and n and m are the respective ensemble sizes (in our cases
N = n = m). The ensemble-mean difference is considered
statistically significant when t C tc where tc is the cutoff
value of the Student’s t-distribution for a two-tailed probability of 0.025 (i.e., 95 % confidence interval) andn ? m - 2 degrees of freedom.
To calculate the minimum ensemble-size required todetect a statistically significant ensemble-mean difference,
Nmin, we re-write (1) replacing t with tc and N with Nmin,tc ¼

jx  yj
qﬃﬃﬃﬃﬃﬃﬃ
2
sp  Nminand re-arrange to give,ð3Þ

Nmin ¼ 2tc2 



sp
xy

2
ð4Þ

It can be seen from combining (1) and (3) that whent C tc then Nmin B N. Nmin can be considered a measure of
the signal-to-noise ratio, with small values of Nmin
implying a large signal-to-noise ratio and large values ofNmin implying a small signal-to-noise ratio. A similar
approach for computing Nmin was used in Deser et al.
(2012) and Terray et al. (2012). Equation (4) assumes thatsp is insensitive to the ensemble size (i.e., sp for Nmin isequal to sp for N). This assumption is approximately valid,
except for small values of Nmin (when sp for Nmin is
generally lower than sp for N; not shown). When Nmin issmall however, the denominator in (4) is appreciably larger
than the numerator (sp  jx  yj) and thus, Nmin isrelatively insensitive to discrepancies in sp.
In this manuscript we focus on autumn (September–
November; SON) and winter (December–February; DJF) as
the atmospheric response to sea-ice loss is largest in these
two seasons (e.g., Deser et al. 2010; Porter et al. 2012;
Screen et al. 2013) and five key atmospheric variables: nearsurface (defined as 1.5 m in the UM and 2 m in CAM) air
temperature (Tref), air temperature on constant pressurelevels (T), precipitation (P), sea level pressure (SLP) andgeopotential height on constant pressure levels (Z).

3 Results
Figure 1a shows the SON SIC differences (PERT-CTRL)
in the single-perturbation experiment. SIC is reduced overmost of the Arctic marginal seas, with the greatest losses in
the Beaufort, Chukchi and East Siberian Seas. By design,
this pattern closely matches the SIC trends observed overthe period 1979–2009. In DJF, SIC reductions are mostpronounced over the Barents Sea, Sea of Okhotsk, Hudson
Bay and the Labrador Sea (Fig. 1b). Small SIC increases
are located along the east coast of Greenland and south of
the Bering Strait. The difference in sea-ice area between
CTRL and PERT is 1.73 and 0.98 million km2 in SON and
DJF, respectively, and between CTRL and PERT*2 is 2.53
and 1.48 million km2, respectively, in SON and DJF. Notethat the loss of sea-ice area in the double-perturbation
experiment is less than twice that in the single-perturbation
experiment because the SIC in any grid-box cannot belower than zero. Recall that the boundary conditions in
PERT are based on SIC trends from 1979 through to 2009,
which was the last full year of SIC data when the modelruns were initiated. The past 3 years (2010, 2011 and 2012)
have had low sea-ice coverage, with summer 2012 a newrecord minimum (Zhang et al. 2013; Parkinson and Comiso2013), enhancing the long-term trend. The observed sea-ice

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area loss from 1979 to 2012, based on the National Snowand Ice Data Center (NSIDC) sea-ice index (http://nsidc.org/data/G02135), is 2.40 and 1.34 million km2 in
SON and DJF, respectively. Thus, the single-forcing
experiment represents a smaller (by 28 and 27 % in SON
and DJF) loss of sea-ice than observed from 1979 to 2012
and the double-forcing experiment represents a slightly
larger (by 5 and 10 % in SON and DJF) loss of sea-ice thanobserved from 1979 to 2012. Figure 1c, d shows the corresponding differences in SST for SON and DJF, respectively. In general, the SST warms where SIC decreases, andvice versa. By design, SST is unchanged in regions ofconstant or zero SIC change. The SIC and SST differencesin the double-perturbation experiment have the same spatial patterns as in Fig. 1, but with differences that are larger
in magnitude (not shown).
Figure 2 shows the ensemble-mean Tref responses (a–c;g–i) and associated values of Nmin (d–f; j–l), with thepanels arranged as follows. The first (a–c) and second (d–f)
rows correspond to SON and the third (g–i) and fourth (j–l)
rows to DJF. The first (a, d, g, j) and second (b, e, h, k)columns are for the single-perturbation experiment in the
CAM and UM, respectively, and the third column (c, f, i, l)
is for the double-perturbation experiment.

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Fig. 2 Ensemble-mean differences in autumn near-surface air temperature (Tref) for a CAM PERT-CTRL, b UM PERT-CTRL andc UM PERT*2-CTRL. Statistically significant differences (at thep B 0.05 level) are enclosed by black contours. d–f Nmin for thedifferences shown in (a–c), respectively. Grey shading denotes aninsignificant ensemble-mean difference. g–l As (a–f), but for wintercd

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Sea surface temperature (oC)Fig. 1 Ensemble-mean differences (PERT-CTRL) in sea-ice concentration (SIC) for a autumn and b winter. (c–d) As (a–b), but forsea surface temperature (SST). Note the inverse scale for SIC

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In SON, both models show widespread and significant
warming over the Arctic Ocean and adjacent continents(Fig. 2a, b). Unsurprisingly, warming is largest over theregions of greatest ice loss (cf. Fig. 1a). The models are invery close agreement. The most obvious difference is thatthe warming extends further over Scandinavia and northeastern Russia in the CAM than UM. The DJF responses inboth models show four warming centres: the Barents Sea,
Hudson Bay, northern Bering Sea and the Sea of Okhotsk(Fig. 2g, h). These regions correspond to areas of wintersea-ice loss and associated SST warming (cf. Fig. 1b, d).
The atmospheric warming is largely confined to maritime
regions in the case of the Bering Sea and the Sea of
Okhotsk, but spreads to neighbouring land masses aroundthe Barents Sea and Hudson Bay. Farther away from theregions of sea-ice loss, there are very few areas of significant Tref response in either model. The UM depicts significant cooling over the Caspian Sea and CAM depicts
warming over central Asia.

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As might be expected, the local Tref response is larger inthe double-perturbation experiment than in the single-perturbation experiment (cf. Fig. 2b, c, h, i). Additionally, theTref response is larger over the high-northern continents
and significant Tref responses are detectable at lower latitudes. This suggests that if Arctic sea-ice loss continues
unabated, the geographical area affected by sea-ice loss
induced warming will increase. Under doubled forcing,
there is a weak cooling response over mid-latitude Eurasia
in DJF, but this is only significant over a limited areasurrounding the Caspian Sea (Fig. 2i).
In terms of Nmin, five or fewer ensemble members are
required to detect a statistically significant Tref response in
the proximity of sea-ice loss, irrespective of the model,
season or the magnitude of forcing. Away from the regionsof ice loss, approximately 30–50 ensemble members are
required to detect a significant response. The response overregions adjacent to ice loss is likely mediated by horizontal
advection due to synoptic systems (Deser et al. 2010), so it
follows that the non-local response will be weaker andsubject to larger AIV (i.e., lower signal-to-noise ratio,
higher Nmin) than the local response that is directly driven
by surface heat flux changes (e.g., Deser et al. 2010; Screen
et al. 2013). Under doubled forcing, the Tref response overthe high-northern continents is easier to detect (lower Nminthan with single forcing) and is detectable further south (cf.
Fig. 2e, f, k, l).
Figure 3 shows the latitudinal and vertical structure of
the zonal-mean T response. Consistent with earlier work
(Screen et al. 2012, 2013), Arctic warming due to observed
sea-ice loss is strongest in the lowermost atmosphere and isalmost entirely confined to below 700 hPa in both seasonsand models (Fig. 3a, b, g, h). In the double-perturbation
experiment, the T response is stronger in the near-surface
levels, but the response remains trapped in the lower troposphere (Fig. 3c, i). This implies that Arctic sea-ice loss
has no discernable influence on T aloft. Nmin generally
increases with altitude. At the few locations where there issignificant zonal-mean warming above 700 hPa, Nmin is 50
or more.
Figure 4 shows the ensemble-mean P responses, arranged as in Fig. 2. In SON, widespread P increases are foundover the Beaufort, Chukchi and East Siberia Seas in the
UM (Fig. 4b). In the CAM, P also increases in theseregions but with less spatial coherence (Fig. 4a). In bothmodels, the P increases are associated with significant
increases in cloud cover, principally low cloud, but thecloud responses are weaker in the CAM than UM (notshown). The weaker P and cloud cover responses in the
CAM versus UM were previously noted by Screen et al.
(2013) and appears to relate to problems with the cloud
cover scheme in CAM version 3. In the double-forcing
experiment, the P increases are stronger and are significant

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Fig. 3 Zonal-mean ensemble-mean differences in autumn air temperature (T) for a CAM PERT-CTRL, b UM PERT-CTRL and c UM
PERT*2-CTRL. Statistically significant differences are enclosed byblack contours. d–f Nmin for the differences shown in (a–c),respectively. Grey shading denotes an insignificant ensemble-meandifference. g–l As (a–f), but for winterover most of the Arctic Ocean (Fig. 4c). Away from the
Arctic Ocean there are isolated patches of significant
P response in both models, but no large-scale features evenin the double-perturbation experiment. In DJF, both models
show significant P increases over the regions of winter seaice loss: the Barents Sea, Sea of Okhotsk and Hudson Bay(Fig. 4g, h). Remote P decreases occur over the North
Atlantic and Pacific in CAM, but they are only significant
in small areas (Fig. 4g). In the double-forcing experiment,a similar spatial pattern is found, but with increased magnitude (Fig. 4i). Over regions of maximum sea-ice loss,
Nmin for P is less than 10 and over other regions of sea-ice
loss it is around 10–30 (Fig. 4d–f, j–l). The majority ofgrid-boxes with a significant P response have an associatedNmin of less than 40, with the main exceptions being the
sporadic remote P responses.
Figure 5 shows the SLP responses. In SON, SLP
decreases significantly over the Beaufort, Chukchi and East

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Fig. 4 As Fig. 2, but for precipitation (P). The P differences are
expressed as percentages relative to the ensemble-means in CTRL

Fig. 5 As Fig. 2, but for sea level pressure (SLP)

Siberian Seas in the UM (Fig. 5b). A second low SLP
centre is located over the Baltic countries. In CAM, tworegions of lowered SLP are identified in broadly similar,
but non-identical, locations (Fig. 5a). The first low isshifted to the southwest to be centred over Alaska and thesecond low is shifted westward to be located over Scandinavia. Away from these limited regions, the SLP
response is statistically insignificant in both models. The
spatial patterns of the SLP responses are largely consistent
between the single- and double-perturbation experiments,
but there are differences in the magnitudes and significanceof the responses (cf. Fig. 5b, c). In the double-perturbation
experiment, significantly lowered SLP is found over alarger area, including most of the Arctic Ocean, theCanadian Archipelago and Hudson Bay. The low-pressure
centre over the Baltic countries that is significant in the
single-perturbation is statistically insignificant in the double-perturbation experiment. Conversely, SLP increases
over Europe and East Asia become significant in the double-perturbation experiment.
In DJF, significant large-scale SLP decreases are foundover the Arctic Ocean, Hudson Bay and eastern Canada in

the UM (Fig. 5h). Isolated regions of significant SLP
reductions are also identified over the Sea of Okhotsk andcentral North America. SLP is increased over Europe, but
this feature is not statistically significant. In the CAM, SLP
decreases significantly over Hudson Bay, Greenland andthe Atlantic-side of the Arctic Ocean (Fig. 5g). SLP
increases significantly over the Bering Sea. Whilst the twomodels exhibit broadly similar SLP responses in the Arctic
and sub-Arctic Canada, the mid-latitude responses arerather different (cf. Fig. 5g, h). In particular, CAM depicts
larger SLP increases over the north Atlantic and northPacific than does the UM, and the responses over theUnited States are opposite in sign between the two models.
However, the mid-latitude responses are predominantly
statistically insignificant in both models, so these discrepancies can be explained by AIV. No regions show significant responses of opposite sign between the models. The
spatial patterns of the DJF SLP responses are similar in the
single- and double-perturbation experiments (cf. Fig. 5h, i).
The SLP decrease over the Arctic and Hudson Bay is larger
in magnitude in the latter, but the geographical extent of
the significant SLP response is not overly different. Three123

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small regions show significant responses in the doubleperturbation experiment that are not significant in the single-perturbation experiment. These are SLP increases overthe Bering Sea, Eastern Europe and eastern China. The
region of weak, but significant, SLP decrease over central
North America in the single-perturbation experiment is not
significant in the double-perturbation experiment.
Nmin for the SLP response is as low as 10 in the UM overregions of maximum ice loss, especially in the doubleperturbation case, but Nmin values this low are only foundin very limited geographical regions (Fig. 5d–f, j–l).
Generally, approximately 30–50 ensemble members are
required to detect a significant SLP response, and upwardsof 50 members are required to detect a significant response
in remote regions. It is notable that even with 100 ensemble
members in the UM, very few mid-latitude regions show asignificant SLP response in the single-perturbation experiment. Further, despite larger mid-latitude responses in
CAM, an ensemble size of 60 is insufficient for these toachieve statistical significance. This implies that the remote
SLP response to recent Arctic sea-ice loss is considerably
smaller than AIV.
Figure 6 shows the zonal-mean Z responses. In SON, thehigh-latitude response is baroclinic with Z decreases in thelowermost atmosphere and Z increases aloft. Significant
zonal-mean Z responses are only found at 1,000 hPa. The
vertical profile is fairly consistent across the models andexperiments. Taken together, the SLP and Z responses in
SON are suggestive of a shallow thermal (heat) low in
response to sea-ice loss. Thermal lows can occur when cold
air overlies warmer water, as is the case in regions of seaice loss (Higgins and Cassano 2009; Deser et al. 2010;
Strey et al. 2010; Orsolini et al. 2012). In DJF, the verticalprofile of the Z response is completely different. Bothmodels show a quasi-barotropic Z decrease over highnorthern latitudes. This high-latitude Z decrease is significant in the UM below 500 hPa, but only at 1,000 hPa in
CAM. Both models show Z increases over mid-latitudes. In
CAM, these extend throughout the troposphere, but are
only significant above 700 hPa. In the UM, Z increases arefound aloft but not at 1,000 hPa, and are shifted polewards
in comparison to those in CAM. They are insignificant in
the single-perturbation experiment, but significant above
850 hPa in the double-perturbation experiment. In all otherrespects, the Z responses in the single- and double-perturbation are very similar. Nmin for Z is high, typically 50 orabove in the single-perturbation experiment and only
slightly lower in the double-perturbation experiment.
In summary, the SLP and Z responses point to rather
different spatial and vertical structures to the circulation
responses in SON and DJF. In SON, the response isbaroclinic (restricted to the near-surface levels) and localised. Similar local circulation responses to sea-ice loss have

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Minimum ensemble size

Fig. 6 As Fig. 3, but for geopotential height (Z)been identified in other simulations (Higgins and Cassano
2009; Deser et al. 2010; Strey et al. 2010; Orsolini et al.
2012). By contrast in DJF, the circulation response is fairly
barotropic and more spatially extensive. This seasonaltransition from a local baroclinic response to a larger-scale
barotropic response was also noted by Deser et al. (2010),
although the horizontal structure of their winter responses
are rather different to that found here. In our CAM simulations, the DJF responses project onto the positive phaseof the Arctic Oscillation (AO). This is in contrast to thenegative-type AO responses found in February by Deseret al. (2010) and in DJF by Liu et al. (2012), both using
CAM but in response to projected future and past sea-ice
trends, respectively. Screen et al. (2013) reported a negative North Atlantic Oscillation (NAO) response in earlywinter (November–December) in the CAM and UM, but
cautioned that the response was weak and often exceeded
by AIV. The larger ensembles presented here do not support a shift towards to negative phase of the NAO in
response to observed sea-ice loss. Instead, in CAM the
response projects onto the positive NAO phase and in theUM the response is not NAO-like. Thus, the wintertime
circulation responses (and their interactions with the large-

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scale modes of atmospheric variability) are not robust
across simulations, even those using the same models.
So far we have considered a limited number of atmospheric variables. For a wider perspective, Table 1 provides the mean Nmin for a broad selection of atmosphericvariables. The values given in Table 1 are averages of Nmin
across all grid-points that exhibit a significant response inthat variable (recall Nmin is undefined where the response isinsignificant), all experiments, models (UM and CAM) andseasons (SON and DJF). For example, the mean Nmin for
Tref is the average of all the values in Fig. 2d–f, j–l. Table 1
also provides the mean percentage area of northern hemisphere extra tropics ([30°N) exhibiting a significant
response in each variable. Both the mean Nmin and area
metrics mask substantial spatial, seasonal and inter-model
variability, so the precise numbers must be interpreted withcaution. However, comparison of the mean Nmin between
variables is insightful as it clearly demonstrates that the
responses in certain variables are easier to detect thanothers. To aid interpretation, the variables in Table 1 arelisted in order of ascending mean Nmin. Recall, smaller

Table 1 Mean Nmin for a selection of atmospheric variables
Variable

Mean Nmin

Mean area

Surface sensible heat flux

21.9

19.1

Surface latent heat flux

24.5

19.7

Near-surface air temperature (Tref)
Low cloud cover

26.0
29.9

28.9
17.5

925 hPa air temperature (T925)

31.1

25.7

Net surface short-wave radiation

32.6

12.9

Net surface long-wave radiation

32.8

15.2

Total cloud cover

33.3

16.5

Precipitation

40.3

11.4

Sea level pressure (SLP)

50.3

11.9

10 m meridional wind speed

50.7

9.0

10 m zonal wind speed

50.8

9.4

500–1,000 hPa thickness

56.1

7.0

250 hPa zonal wind speed (U250)

65.4

5.5

250–1,000 hPa thickness

67.6

4.7

250 hPa meridional wind speed (V250)

68.0

3.2

500 hPa air temperature (T500)

70.0

4.3

500 hPa geopotential height (Z500)

71.9

5.0

250 hPa geopotential height (Z250)

73.3

4.8

For each variable, the value of Nmin given is the average over all gridboxes (with a significant response in that variable), all models andexperiments, and both autumn and winter. The right-hand column
shows the mean percentage area of northern hemisphere extra tropics([30°N) exhibiting a significant response in that variable (again
averaged across models, experiments and seasons). To aid interpretation, the variables are listed in order of ascending mean Nmin. Notethat low values imply a response that is easier to detect than highvalues123

values indicate that the response is easier to detect thanlarger values. The ranked variables can be split into four
categories of increasing mean Nmin. This ranking is largely
insensitive to whether or not the double-perturbation
experiment is included in the analysis (not shown). The
variables with smallest values (Nmin \ 30) are the surface
heat fluxes and Tref. The next group (30 \ Nmin \ 50)
includes variables related to clouds, precipitation andradiation. A third group (50 \ Nmin \ 60) contains variables related to surface atmospheric circulation, including
SLP and near-surface wind. The hardest responses to detect(Nmin [ 60) are in upper-level variables, for example, midtropospheric (500 hPa) temperature (T500) and geopotential
height (Z500) and jetstream-level (250 hPa) wind (U250,
V250). Although we have not considered stratosphericvariables here, Cai et al. (2012) found that the stratospheric
response to sea-ice loss is small compared to the tropospheric response.
Clearly, AIV is a key source of uncertainty in the simulated atmospheric response to Arctic sea-ice loss. Larger
ensembles can reduce this uncertainty by averaging out, tosome extent, the effects of AIV. Figure 7 quantifies the
reduction in uncertainty in the response to Arctic sea-ice
loss, due to AIV, as the ensemble size increases. To construct this figure, we have sub-sampled our large ensembles
into smaller sub-ensembles of varying size. For each subensemble size, a large number (100,000) of unique combinations are sampled to produce a large set of subensemble mean responses. For example, for a sub-ensemble size of 5 we sub-sampled 100,000 unique combinationsof 5 members from the full set. For each combination, weaveraged the selected members to produce a sub-ensemble
mean. This results in a set of 100,000 sub-ensemble mean
responses. The spread (difference between maximum andminimum values) of these sub-ensemble mean responses
provides a measure of the uncertainty in the response due
to AIV, for an ensemble of that size. Figure 7a, b shows
examples for the Arctic-mean ([70°N) SON Tref response
and DJF SLP response, respectively, but qualitatively
similar results are found for other seasons and variables.
Uncertainty due to AIV, as estimated by the spread ofsub-ensemble mean responses, can be seen to decrease
almost exponentially as the ensemble size increases. Thisimplies that to reduce uncertainty by one half, the ensemble
size has to be doubled. In absolute terms, uncertainty due to
AIV decreases rapidly as the ensemble-size increases from
5 (or fewer) to 20 members, and then continues to reduce
more slowly as further ensemble members are added. Thisbehaviour is very similar in the two models and in both thesingle- and double-perturbation experiments, however,
CAM has larger AIV than the UM for both Tref and SLP. In
the UM a point is reached, around 50–60 ensemble members, where adding further ensemble members has almostAtmospheric impacts of Arctic sea-ice loss

341

Uncertainty (oC)

a 1.5
1.0

0.5

0.0
20

40

60

80

Ensemble size

Uncertainty (hPa)

b 10
8
6
4
2
0
20

40

60

80

Ensemble size
Fig. 7 Uncertainty due to atmospheric internal variability [see text
for details] as a function of ensemble size for the Arctic-meana autumn near-surface air temperature (Tref) response and b winter sea
level pressure (SLP) response. Black and blue lines correspond to
PERT-CTRL in the UM and CAM respectively, and the red lines to
PERT*2-CTRL

no impact on the uncertainty due to AIV (spread of
responses). We assume a similar point would occur in the
CAM, but we have insufficient ensemble members to
confirm this.

4 Discussion and conclusions
Arguably one of the most surprising aspects of our results
is that over the Arctic we have identified a robust (in thesense that it is statistically significant in both models, andin both the single- and double-perturbation experiments)
lowering of SLP in response to Arctic sea-ice loss. This is
surprising because this high-latitude DJF SLP response is
opposite to that suggested in some empirical studies (e.g.,
Francis et al. 2009; Jaiser et al. 2012) and to that found inother modelling studies, for example, Deser et al. (2010)and Liu et al. (2012). It is of especial interest to draw
comparisons with Liu et al. because that study performed
very similar experiments to those presented here. It used
the same model (CAM version 3 at T42 resolution),experimental set-up and forcing based on observed sea-ice
trends. However, Liu et al. report a significant increase in
DJF SLP in response to Arctic sea-ice loss, in stark contrast

to the decrease shown here (cf. our Fig. 5g and theirFig. 4c). One notable difference between the two studies isthat Liu et al. used an ensemble of 20 CAM simulations
compared to our ensemble of 60 CAM simulations.
It is plausible that 20 ensemble members are insufficientto accurately separate the forced signal from AIV (Nmin for
DJF SLP is generally larger than 20). To test this hypothesis, we considered if it is possible to derive the Liu et al.
result from a subset of our larger CAM ensemble. Figure 8
shows probability distribution functions (PDFs) for theArctic-mean DJF sub-ensemble mean SLP responses (i.e.,the set of 100,000 sub-sampled responses). The PDFs
narrow as the ensemble size increases, implying that larger
ensembles yield more precise responses to Arctic sea-ice
loss. For a sub-ensemble size of 10, it is possible to obtain
both positive and negative sub-ensemble mean SLP
responses. This shows that AIV influences both the magnitude and sign of SLP responses in small ensembles.
However for a sub-ensemble size of 20, an Arctic-mean
increase in SLP is found in less than 0.1 % of cases. Thisimplies that the Liu et al. result cannot be derived from a
20-member subset of our larger ensemble. Thus, it is very
unlikely that the discrepancy between the Arctic winterSLP responses is this study and in Liu et al. is due to AIV
alone. A further difference between this study and Liu et al.
is the magnitude of the sea-ice forcing. Although the spatial pattern of the sea-ice forcing is highly similar between
the two studies, our forcing is approximately two-to-threetimes larger magnitude than that in Liu et al. (cf. ourFig. 1a, b and their Fig. 4a, b; note the different colour
scales). Whether or not this is the cause of the opposing
winter SLP responses is unclear, but the discrepancy
highlights that experimental differences between simulations, even with the same model, can lead to fundamentallydifferent responses.
We now return to the question posed earlier: how many
ensemble members are required to detect a significant
response to Arctic sea-ice loss? In reality, there is no
simple answer to this question as Nmin varies considerablyin space and by variable. As a general rule of thumb, wesuggest that detection of the thermo-dynamical (e.g., SLP,
wind) response requires an ensemble size approximately
twice as large as the thermal response (e.g., surface heat
fluxes, T). The hydrological response (e.g., cloud, P) lays
in-between, which likely reflects influences of both thermal
and thermo-dynamical factors on these variables. Deseret al. (2012) reported very similar findings in the context ofthe coupled climate response to greenhouse gas forcing, as
did Wehner (2000) and Taschetto and England (2008) bothin the context of the atmospheric response to global SST
and SIC trends. The upper-level response to Arctic sea-ice
loss (e.g., Z500, T500, U250, V250) is harder to detect than thenear-surface response as the signal-to-noise ratio decreases

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J. A. Screen et al.
12

Ensemble size

Frequency (%)

10

10
20
30
40
50

8

6

4

2

0
-6

-4

-2

0

2

4

Sea level pressure (hPa)Fig. 8 Probability distribution functions (PDF) for the winter Arcticmean sea level pressure (SLP) responses in sub-ensembles of varying
size. Each PDF is constructed from 100,000 unique combinations subsampled from the 60-member CAM ensemble. For example, the blueline represents sub-ensemble means for 100,000 unique combinationsof 20 CAM members sampled from the full set of 60 CAM members[see text for further details]

with altitude. Equally, the remote Tref or P responses (thatare mediated by thermo-dynamical processes) are harder todetect than the local Tref and P responses (that are primarily-driven by surface fluxes). Figure 7 suggests large
gains, in terms of reduced uncertainty, by increasing from asmall (less than 20 members) to moderate-sized (20–50
members) ensemble. Further increases in ensemble size
represent a case of ‘‘diminishing returns’’ with smaller
reductions in uncertainty per additional ensemble member.
On this basis, we argue that an ensemble size of around 50
members is desirable. This is considerably larger than the
typical ensemble size used in past studies of the atmospheric response to observed Arctic sea-ice loss (e.g., 5 in
Ghatak et al. (2012) and Orsolini et al. (2012), 5 or 8 in
Screen et al. (2013), 10 in Strey et al. (2010), 15 in Porter
et al. (2012), 20 in Liu et al. (2012)).
The values of Nmin have implications not only formodelling studies, but also for what aspects of the simulated Arctic sea-ice response may be observable in the realworld. Since each ensemble member is 1-year of simulation, Nmin can also be thought of as approximate measure of
the minimum number of years required to detect a significant response due to Arctic sea-ice loss, assuming the rateof loss is linear. The differences in prescribed boundary
conditions between CTRL and PERT have, in reality,
occurred over a 31-year period (1979–2009). Assumingthat the models are realistic in their depiction of the forced
response and AIV, a Nmin of 31 or less suggests that thesimulated response should be observable in nature over the123

period 1979–2009. Conversely, a Nmin of greater than 31
suggests that more than 31 years are required to separate
the forced response from AIV and therefore, the response
to past sea-ice loss would not be expected to be detectablein observed records. Accordingly, we argue that the simulated local Tref and P responses to Arctic sea-ice loss
should be detectable, but that the atmospheric circulation(e.g., SLP, 10 m wind), upper-level (e.g., Z500, T500, U250,
V250) and remote responses may be partially or whollymasked by AIV. In practise, the detection and importanceof the atmospheric impacts of sea-ice loss not only dependon the relative magnitudes of the sea-ice forced change
compared to AIV, but also on the relative magnitudes ofsea-ice forced response to other forced responses.
Figure 9a, d shows observed (from ERA-Interim; Deeet al. 2011) trends in Tref over the period 1979–2009 for
SON and DJF, respectively. These are highly similar to thesimulated Tref responses to Arctic sea-ice loss (Fig. 2),
suggesting that the Tref response is indeed detectable,consistent with previous studies (Screen and Simmonds
2010a, b; 2012). Figure 9b, e shows observed trends in
P for SON and DJF, respectively, taken from the Global
Precipitation Climatology Project (GPCP) data set (Adler
et al. 2003). These can be compared to the simulated
P responses in Fig. 4. Although the moderate values ofNmin in Fig. 4 suggested that the local P response may be
detectable, the observed trends are not in agreement withthe simulated P responses. We propose that there are two
likely reasons for this apparent disparity. One reason is that
detection of the atmospheric impacts of sea-ice loss not

a

b

c

d

e

f

-10 -8 -6 -4 -2 0 2 4 6 8 10

Temperature (oC) / SLP (hPa)-90 -60 -30

0

30

60

90

Precipitation (%)

Fig. 9 Observed trends in autumn a near-surface temperature (Tref),b precipitation (P) and c sea level pressure (SLP) for the period
1979–2009. Precipitation trends are expressed as percentages relative
to the climatological-means. d–f As (a–c), but for winter. Tref and SLP
data are from the ERA-Interim reanalysis and P data are from the
GPCP productAtmospheric impacts of Arctic sea-ice loss

only depend on the relative magnitudes of the sea-ice
forced change compared to AIV, but also on the relative
magnitudes of sea-ice forced response to other forced
responses. It is likely that the observed P trends are forced
by factors other than, or in addition to, sea-ice loss. Secondly, there is considerable uncertainty as to the sign andmagnitude of observed P trends over the poorly observed
Arctic region. P trends from alternative observationallyconstrained data sources—for example the CPC Merged
Analysis of Precipitation (CMAP; Xie and Arkin 1997) or
ERA-Interim–depict rather different patterns of P changeover the Arctic Ocean (not shown). It is possible therefore,that the simulated P response to sea-ice loss is undetectablein observations because of considerable observational
uncertainty. Observed (ERA-Interim) SON and DJF SLP
trends are shown in Fig. 9c, f. Neither resemble the simulated SLP responses in any of the models/experiments(Fig. 5), which is consistent with the conclusion that the
SLP response to Arctic sea-ice loss is masked by AIV, or
SLP trends due to other forcing factors. We note that theobserved trends are only one realisation (effectively one
ensemble member) and likely contain a sizeable component of natural (unforced) variability. Thus, the observed
trends would not be expected to match the ensemble-mean
simulated responses.
We close by emphasising two arguably obvious, butnonetheless important, considerations. Firstly, this study
has only considered the first-order ‘‘direct’’ atmospheric
response to Arctic sea-ice loss. The fully coupled climate
system response to Arctic sea-ice loss may be different tothat shown here. Secondly, Arctic sea-ice loss is only one
forcing factor that may be relevant to northern hemisphereclimate variability and change. Observed trends reflectchanges in multiple forcing factors and the complex
interactions between them.
Acknowledgments Laurent Terray is thanked for useful discussions
on the statistical methods. Two anonymous reviewers are thanked forthe constructive comments. Parts of this research were funded by theAustralian Research Council, the Merit Allocation Scheme on theAustralian National Computational Infrastructure, the US National
Science Foundation (NSF) Office of Polar Programs, and the UK
Natural Environment Research Council grant NE/J019585/1. NCARis sponsored by the NSF.

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