Page 1
Time of emergence of climate signals
Article
Accepted Version
Hawkins, E. ORCID: https://orcid.org/0000-0001-9477-3677
and Sutton, R. ORCID: https://orcid.org/0000-0001-8345-8583
(2012) Time of emergence of climate signals. Geophysical
Research Letters, 39 (1). L01702. ISSN 0094-8276 doi:
10.1029/2011GL050087 Available at
https://centaur.reading.ac.uk/25489/
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GEOPHYSICAL RESEARCH LETTERS, IN PRESS, 2011, DOI: 10.1029/2011GL050087
Time of emergence of climate signals
E. Hawkins
1
and R. Sutton
1
The time at which the signal of climate change emerges from
the noise of natural climate variability (Time of Emergence,
ToE) is a key variable for climate predictions and risk assess-
ments. Here we present a methodology for estimating ToE
for individual climate models, and use it to make maps of
ToE for surface air temperature (SAT) based on the CMIP3
global climate models. Consistent with previous studies we
show that the median ToE occurs several decades sooner in
low latitudes, particularly in boreal summer, than in mid-
latitudes. We also show that the median ToE in the Arctic
occurs sooner in boreal winter than in boreal summer. A key
new aspect of our study is that we quantify the uncertainty
in ToE that arises not only from inter-model differences in
the magnitude of the climate change signal, but also from
large differences in the simulation of natural climate vari-
ability. The uncertainty in ToE is at least 30 years in the
regions examined, and as much as 60 years in some regions.
Alternative emissions scenarios lead to changes in the both
the median ToE (by a decade or more) and its uncertainty.
The SRES B1 scenario is associated with a very large uncer-
tainty in ToE in some regions. Our findings have important
implications for climate modelling and climate policy which
we discuss.
NOTE: This is the author’s version of the paper
accepted for publication in GRL. Copyright 2011
American Geophysical Union. Further reproduction
or electronic distribution is not permitted.
1. Introduction
The signal of anthropogenic climate change is emerging
against the background of natural climate variability. Only
when the signal of change is of sufficient magnitude relative
to this background variability can we be confident that a sig-
nificant change has been detected. Such detection is a neces-
sary step in the process of attributing a particular change to
a specific cause, such as the observed rise in greenhouse gas
concentrations [
Hegerl et al.
, 2007]. A headline conclusion
from the IPCC AR4 was that “most of the observed increase
in global average temperatures since the mid-20th century
is very likely due to the observed increase in anthropogenic
greenhouse gas concentrations”. Of greater importance for
adaptation to climate change are changes on the regional
and local scales that affect people, economies and ecosys-
tems. However, on these smaller scales natural variability is
larger, making detection more difficult. Some detection and
attribution studies that have addressed these scales have
obtained positive results [
Hegerl et al.
, 2007;
Stott et al.
,
2010], but for many regions and variables the signal of an-
thropogenic change has yet to clearly emerge from the ‘noise’
of natural climate variability.
1
NCAS-Climate, University of Reading, UK.
Copyright 2011 by the American Geophysical Union.
0094-8276/11/$5.00
So when will the signal emerge? And where and how?
These are key questions for adaptation policy and planning
in particular. Much attention has focused on the absolute
magnitude of future climate change, and uncertainties in
this magnitude [e.g.
Randall et al.
, 2007]. But in many situ-
ations it is not the absolute magnitude that matters so much
as the magnitude of change relative to the background levels
of variability. The reason is that many natural and human
systems are inherently adapted to the local background level
of variability. It is when changes move outside this range
that major impacts are most likely to arise. For example,
Lobell and Burke
[2008] demonstrate that uncertainty in fu-
ture crop yields is often dominated by uncertainty in pro-
jections of temperature, rather than precipitation, because
the changes in temperature are far further outside the range
of natural variability to which the crop is adapted.
The question of when a significant climate change signal
will emerge in different regions was discussed and presented
in tabular form in the IPCC AR4 [Table 11.1 of
Christensen
et al.
, 2007]. The general pattern of results is that the Time
of Emergence (ToE) is soonest (
∼
10 years) for low lati-
tude regions, longest (20-40 years) for mid-latitude regions
and of intermediate duration (15-20 years) for polar regions.
These findings were recently confirmed by
Mahlstein et al.
[2011], who additionally provided results at country scale,
and demonstrated that the earliest emergence of significant
warming occurs in the summer season in low latitude coun-
tries.
The results presented in AR4 and
Mahlstein et al.
[2011],
whilst valuable, leave many open questions about ToE. Ba-
sic but important questions concern the choices involved in
defining both signal and noise. In some studies the defini-
tion of noise has been broadened to include the uncertainty
in the climate response to anthropogenic forcing and the un-
certainty in future anthropogenic emissions [
Giorgi and Bi
,
2009;
Hawkins and Sutton
, 2009, 2011]. In this study we
focus on the natural internal variability of climate as the
key source of noise relevant for ToE. A major motivation for
our study is to address the question,
what is the uncertainty
in estimates of ToE?
This is a key question for adaptation
policy, as it is fundamental to the risk assessments on which
such policy must rely. To address it we develop a method-
ology for estimating ToE from individual climate models,
rather than relying on a multi-model mean. Our approach
recognises that current climate models show substantial dif-
ferences not only in their simulation of the climate change
signal (e.g. in their climate sensitivity), but also in their
simulation of the natural internal variability of climate. We
demonstrate that both these dimensions of uncertainty di-
rectly influence the uncertainty in ToE. We also consider
the question
how is ToE sensitive to alternative scenarios
for anthropogenic emissions?
This question has obvious rel-
evance to mitigation policy.
In Section 2 we describe the methods and data used. Sec-
tion 3 explores the natural variability across the models and
observations, and in Section 4 we show our ToE estimates
and discuss the sensitivity to various choices in the analysis.
We summarise in Section 5.
2. Methods and Data
Estimating the Time of Emergence (ToE) of any climate
signal requires estimates for the climate change signal (
S
)
1
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HAWKINS AND SUTTON: TIME OF EMERGENCE OF CLIMATE SIGNALS
MEDIAN MODEL
ICOSAHEDRAL GRID
LAT−LONG 5
o
×
5
o
GRID
HadCRUT3
ERA−40
OBSERVATIONS
RATIO
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
INTER−ANNUAL TEMPERATURE VARIABILITY
Figure 1.
The median model interannual variability using annual means on different spatial grids: an icosahedral grid
with roughly equal areas (top) and a regular 5
◦
×
5
◦
grid (bottom). The observations are shown in the middle column for
ERA-40 (top) and HadCRUT3 (bottom, with missing values in white). These four panels have units of [
K
]. The ratio of
the median model to the observations shows the GCMs tend to overestimate the variability in the northern extra-tropical
regions (right), with units of [
K/K
]. The two observational estimates also agree well where data exists for HadCRUT3.
and for the variability (or ‘noise’ -
N
). We define the ToE as
the first year in which the signal-to-noise ratio,
S/N
, crosses
particular threshold values (such as 1 and 2), but for certain
impacts other values may be more appropriate.
To estimate the signal for surface air temperature (SAT)
we use data from 1950-2099 from single ensemble members
from a set of 15 GCMs which have run all three SRES sce-
narios (A2, A1B, B1). We define
S
by first regressing SAT
from a single ensemble member for each model in each grid
box (
T
local
) onto a smoothed version of the global mean SAT
projection (
e
T
global
), making the assumption that the local
changes scale with global temperature. This assumption
works well in the past [e.g.
van Oldenborgh et al.
, 2009], but
may break down in the future if the aerosol and greenhouse
gas signals become decoupled. We estimate the regression
coefficients (
α, β
) between
T
local
and
e
T
global
, and define
S
(
t
) =
α
e
T
global
(
t
) +
β
(1)
for each grid point. The smoothing for
T
global
is a fourth
order polynomial, fitted over the period 1950-2099 [
Hawkins
and Sutton
, 2009]. All estimates are made relative to the ref-
erence period 1986-2005 - we choose the recent past as being
of greatest relevance for adaptation. We test this method
using an ensemble of 10 simulations with a single model,
producing an ensemble standard deviation in ToE for each
of the three regions considered later in Section 4 of less than
3 years (not shown).
To estimate the noise in SAT we utilise each GCM’s pre-
industrial control simulations. We define
N
as the interan-
nual standard deviation of seasonal (or annual) means. Note
that our choice contrasts with previous studies, which have
used the variability of 20-year averages [
Christensen et al.
,
2007;
Giorgi and Bi
, 2009]. Because variance decreases with
averaging our choice results in later estimates for ToE, but
we argue that it has greater relevance to adaptation policy.
As noted in the Introduction our definition of ToE differs
further from that of
Giorgi and Bi
[2009] in that their defi-
nition of
N
combines an estimate of the intermodel variance
in the signal strength with an estimate of the internal vari-
ability. Our view is that these two sources of variance are
very different in origin - in particular the latter is a funda-
mental property of the climate system, whilst the former is
not - and therefore it is helpful to keep them separate. Fur-
thermore, we suggest that ToE - as we define it - is also a
fundamental property of the climate system. The true val-
ues of ToE are unknown, but we can use climate models to
estimate it.
For observational comparisons of the variability we use
the HadCRUT3 dataset [
Brohan et al.
, 2006] from 1900-
2010 and ERA-40 [
Uppala et al.
, 2005] from 1958-2001. For
HadCRUT3, the interannual variability is derived by requir-
ing all 12 months of data to be present in a year at each
grid point to create an annual average, and at least 80 years
present since 1900 to estimate the interannual variability.
The variability is the standard deviation of the detrended
annual means, where HadCRUT3 is detrended as above by
regressing out the signal due to increases in the global mean
temperature fitted with a 4th order polynomial. We use
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HAWKINS AND SUTTON: TIME OF EMERGENCE OF CLIMATE SIGNALS
X - 3
SIGNAL 2040
MEDIAN
MODEL NOISE
10%
90%
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
Figure 2.
Inter-annual variability (top) and signal in 2040 (bottom) using annual means from the GCMs. The estimates
include the 10th, 50th and 90th percentiles for each gridpoint (columns). Note the non-linear colour scale at high values.
a linear detrending at each grid point for ERA-40, which
is spatially and temporally complete. Note that these es-
timates are likely to be slightly too large as there will be
residual variability due to non-linearities in the forced trend.
Cleanly separating the trend from the variability is non-
trivial, and we do not consider it further here.
3. Surface air temperature variability
Different GCMs show a very wide range of interannnual
variability [e.g.
Randall et al.
, 2007]. These differences in
variability characteristics across GCMs raises a key issue:
what estimate for the variability should be used to estimate
ToE? One option is to use the historical observations, but
this is complicated by the trends in temperature, and short
time-series for many regions. We later test the sensitivity
to other options which include using each GCM’s own esti-
mate of internal variability, or using a multi-model median
estimate.
3.1. Sensitivity to spatial grid used
Before considering the differences in variability, another
question arises concerning the spatial grid for analysis. On
a regular latitude-longitude grid, the grid cells in the polar
regions have a far smaller spatial area than in the tropics.
This could distort the analysis as smaller areas are likely to
have larger variability solely due to their size and would ar-
tificially inflate ToE at the poles, relative to tropical regions
for instance.
To examine this sensitivity we compare the interannual
variability for the high northern latitudes using the native
GCM data remapped on two different grids before analysis
(Fig. 1). The median standard deviation of annual mean
temperature on an icosahedral grid, with roughly equal areas
in each grid cell (top left), and a regular latitude-longitude
5
◦
×
5
◦
grid (bottom left) show very similar patterns, but
there are two key points to note. First, there is a local min-
imum in SAT variability in the vicinity of the North pole,
which is perhaps not widely appreciated [e.g.
Christensen
et al.
, 2007;
Mahlstein et al.
, 2011]. Secondly, there are
small differences between the results for the different grids,
with the icosahedral grid showing generally smaller variabil-
ity in some high latitude regions as would be expected if
the grid size is having an effect. However, the differences
are small and for the ToE analysis we focus on the regular
latitude-longitude 5
◦
×
5
◦
grid. Fig. S2 shows maps of ToE
on the icosahedral grid for comparison.
3.2. Comparing models and observations
Our observational estimates of the interannual variabil-
ity of annual mean SAT are shown in Fig. 1. When com-
paring the observations to the median model estimate, it
is seen that the GCMs tend to have too much variability
in the northern extra-tropical region, by up to 20% [also
see
Mahlstein et al.
, 2011]. Considering that the observa-
tions are likely to be an over-estimate of the true internal
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HAWKINS AND SUTTON: TIME OF EMERGENCE OF CLIMATE SIGNALS
ONDJFM
MEDIAN ToE S/N > 1
MEDIAN ToE S/N > 2
AMJJAS
1
2
3
2010
2015
2020
2025
2030
2035
2040
2045
2050
2055
2060
2065
Figure 3.
Median Time of Emergence for surface air temperatures for October-March (top) and April-September (bot-
tom). First year when temperature has expected
S/N >
1 (left) and
S/N >
2 (right). The regions indicated by the white
boxes are used in Figs. 4, 5.
variability (see Section 2), this finding would appear to be
robust. This bias will affect estimates of the ToE by making
it later than it would be if an observational estimate was
used. In other regions it appears the GCMs have too little
variability, although this may be an artefact of imperfectly
detrending the observations. In all examples, the variability
in SAT is generally greater at higher latitudes (excepting the
local minimum over the pole), and over land (Fig. 2). Ex-
ceptions are the ENSO region, and the region of the Barents
Sea, both of which show unusually high variability.
4. The Time of Emergence for regional
temperatures
The signal of SAT change in 2040 shows a wide range
across the GCMs (Fig. 2), with a range (10-90% quantiles)
of up to 4
◦
C at high latitudes and typically 1
◦
C at lower
latitudes. In addition, the range (10-90% quantiles) of the
GCM estimates of the interannual variability can be up to a
factor of 3 in standard deviation. Much previous work has
focussed on the large range of climate sensitivity, but the
ranges in variability are arguably as important across the
GCMs considered, contributing to uncertainty in
S/N
.
As noted in Section 2, we define the Time of Emergence
(ToE) as the first year when the
S/N
is larger than a partic-
ular threshold. ToE is estimated for each model separately,
and maps of the median ToE for SAT under SRES A1B,
for two half-years, are shown in Fig. 3, using two different
S/N
thresholds. Fig. S1 shows maps of ToE for individual
GCMs.
For many tropical regions, the median ToE for
S/N >
1
is within the next decade, and before 2030 for
S/N >
2. The
early emergence in these regions, and the tendency for earlier
emergence in boreal spring/summer (April-September) than
in boreal autumn/winter (October-March), is consistent
with the results of
Mahlstein et al.
[2011]. For extra-tropical
regions the ToE times are delayed by several decades, with
ToE for
S/N >
2 later than 2060 for many locations. In the
northern extratropics, ToE is again generally later for au-
tumn/winter than spring/summer. However, an interesting
contrast to this seasonal variation is seen over the central
Arctic, where the median ToE occurs 5-10 years
earlier
in
autumn/winter than in spring/summer (Fig. S2), primarily
because the signal is stronger.
Histograms of ToE for
S/N >
2 for three equal area land
regions (as indicated in Fig. 3) are shown in Fig. 4, for half-
years, using the SRES A1B scenario. Note that because the
noise variance decreases with averaging, the ToE for an area
mean is not the same, and will generally be earlier, than
the mean ToE for that area. The blue bars show the ToE
using each GCM’s own estimate of the variability, and the
green bars show the ToE using the median estimate of the
variability as
N
. The red bars show the projected ToE us-
ing the median signal
and
median noise. Fig. S3 shows the
histograms using the median signal and each GCM’s vari-
ability.
The blue bars demonstrate the large uncertainty in es-
timates of ToE from different climate models. This uncer-
tainty is at least 30 years in all three regions, and as much 60
years in some regions. Also evident in Fig. 4 is the seasonal
variation, with all three regions showing a shift to earlier
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HAWKINS AND SUTTON: TIME OF EMERGENCE OF CLIMATE SIGNALS
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2020
2040
2060
2080
0
2
4
6
8
10
Region 1
ONDJFM
2020
2040
2060
2080
0
2
4
6
8
10
Region 2
2020
2040
2060
2080
0
2
4
6
8
10
Region 3
2020
2040
2060
2080
0
2
4
6
8
10
AMJJAS
2020
2040
2060
2080
0
2
4
6
8
10
Time of Emergence − number of models per decade
2020
2040
2060
2080
0
2
4
6
8
10
Figure 4.
Time of emergence for surface air temperatures for three equal area regions as indicated in Fig. 3. October-
March (top) and April-September (bottom). Histograms representing the number of models which cross the
S/N >
2
temperature threshold in each decade, using each GCM’s own variability (blue) and median variability (green). The red
bars indicate the decade of ToE when using both the median signal and median noise.
ToE in boreal spring/summer (even though region 3 is in
the Southern hemisphere). The distributions of ToE show a
clear central peak for some regions and seasons (e.g. region
1 for boreal autumn/winter), but in other cases are rather
flat or even bimodal (e.g. region 3 in boreal autumn/winter
and region 1 in boreal spring/summer).
The differences between the blue and green bars indi-
cate the change in uncertainty in ToE when using a single
(median) estimate for the noise,
N
. Whilst the distribu-
tions change there is no consistent reduction, or increase,
in spread. The same is true when using the median signal
together with estimates of the noise from individual models
(see Fig. S3). These results demonstrate that the inter-
model spread in both signal and noise contribute signifi-
cantly to the spread in ToE.
The final sensitivity on ToE we consider is the dependence
on emissions scenario (Fig. 5). Overall, SRES A1B shows
a slightly earlier ToE for the various regions, because it is
actually the warmest scenario in the near-term [e.g.
Meehl
et al.
, 2007], whereas A2 is warmer at the end of the 21st
century. The B1 scenario shows a shift towards later ToE;
more striking, however, is a large increase in the uncertainty
in ToE under this scenario. This is because the lower levels
of emissions result in a more gradual rise in temperatures,
producing a wider range of threshold crossing times [also see
Joshi et al.
, 2011].
Lastly we consider the ‘Global Temperature for Regional
Emergence’ (GTRE), where the emergence is expressed as
the change in global mean temperature (from 1986-2005) re-
quired to produce a regional threshold crossing in
S/N
[in a
similar way to
Mahlstein et al.
, 2011]. Fig. S4 demonstrates
that this metric, which may be more useful for mitigation
decisions, effectively reduces the emissions uncertainty, but
still produces wide ranges in GTRE for different models and
regions.
5. Discussion and Conclusions
We have developed a new methodology for estimating
Time of Emergence (ToE) for individual climate models,
which has enabled us to estimate the uncertainty in ToE
that arises from intermodel differences in their simulations
of natural variability (noise) as well as differences in their
simulations of the signal of climate change. We applied our
methods to simulations of surface air temperature in the
CMIP3 ensemble of climate models. Our major findings
are:
1. Consistent with many other studies there is a large
spread in the magnitude of the climate change signal sim-
ulated by the models when forced by the same forcing sce-
nario. In some higher latitude regions the magnitude of the
signal in 2040 differs by more than 3
◦
C.
2. Less widely recognised, there is also a very large spread
in the amplitude of natural variability simulated by the mod-
els. In some regions the amplitude of variability differs by a
factor of 3 or 1.5
◦
C.
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HAWKINS AND SUTTON: TIME OF EMERGENCE OF CLIMATE SIGNALS
2020 2040 2060 2080 2100
0
2
4
6
8
10
Region 1
ONDJFM
A2
A1B
B1
2020 2040 2060 2080 2100
0
2
4
6
8
10
Region 2
2020 2040 2060 2080 2100
0
2
4
6
8
10
Region 3
2020 2040 2060 2080 2100
0
2
4
6
8
10
AMJJAS
2020 2040 2060 2080 2100
0
2
4
6
8
10
Time of Emergence − number of models per decade
2020 2040 2060 2080 2100
0
2
4
6
8
10
Figure 5.
Time of emergence for surface air temperatures for three equal area regions as indicated in Fig. 3. October-March
(top) and April-September (bottom). Histograms representing the number of models which cross the
S/N >
2 temperature
threshold in each decade, using each GCM’s own variability and different scenarios (blue - B1, green - A1B, red - A2).
3. The median ToE occurs several decades sooner in low
latitudes, particularly in boreal spring/summer, than in
mid-latitudes.
The median ToE in the Arctic occurs 5-
10 years sooner in boreal autumn/winter than in boreal
spring/summer.
4. There is a very large uncertainty in ToE arising from
the inter-model differences in simulating both signal and
noise. This uncertainty is at least 30 years in all regions
and as much 60 years in some regions.
5. Alternative emissions scenarios lead to changes in the
both the median ToE (by a decade or more) and its uncer-
tainty. The SRES B1 scenario is associated with a very large
uncertainty in ToE in some regions.
Our findings, especially the large uncertainty in ToE, have
important implications for climate policy. We have argued
that in many cases major impacts (e.g. widespread crop
failure) are likely to be associated with crossing thresholds
in signal-to-noise. To develop robust adaptation strategies,
policy makers and planners must take into account the large
uncertainty in
when
these events may take place [also see
Joshi et al.
, 2011].
A limitation of our study is that it is based on the anal-
ysis of a particular climate model ensemble of opportunity:
CMIP3. This ensemble is unlikely to span the full range
of uncertainty in ToE, particularly in light of recent stud-
ies which demonstrate that different climate models are not
independent [e.g.
Knutti et al.
, 2010;
Pennell and Reichler
,
2010]. These points highlight the importance of improv-
ing model simulations of natural climate variability, and
of exploring the potential for identifying observational con-
straints on ToE. There is also need to estimate ToE for a
wider range of climate and climate-related variables. In view
of the importance of ToE for climate adaptation and miti-
gation policy, we suggest that this research, and the related
development work to improve climate models, should be ac-
corded high priority.
Acknowledgments.
EH and RS are supported by NCAS-
Climate. We thank Hilary Weller for technical help with the
icosahedral grid and Jonathan Gregory for useful suggestions. We
also acknowledge Irina Mahlstein and an anonymous reviewer for
their constructive comments which helped improve the paper.
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E. Hawkins and R. Sutton, Department of Meteorology, Uni-
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RG6 6BB, UK. (e.hawkins@reading.ac.uk)
Page 9
Time of emergence of climate signals
Ed Hawkins
1,*
and Rowan Sutton
1
1
NCAS-Climate, Department of Meteorology, University of Reading, UK.
Supplementary Information
Time of Emergence for each GCM
Fig. S1 shows the Time of Emergence (ToE) for
S/N >
2 for each of the GCMs considered,
vividly demonstrating the broad range in this quantity.
Sensitivity to analysis grid
Fig. S2 shows the ToE for the northern hemisphere on different spatial grids for two half-year
means. The differences between the grids is small, but the short emergence times for the
pole are clear in this projection, especially in boreal winter.
The spatial regridding was performed from the native model grids before analysis using
the
remapcon
routine from the
cdo
library.
Sensitivity to choice of signal and noise
The distributions of ToE for the three regions discussed in the main paper are shown in
Fig. S3. The blue bars are using each GCM’s own estimate of both signal and variability,
whereas the green bars use the median estimate of the signal. This is the companion figure to
Fig. 4 of the main paper, which used the median estimate of the noise instead of the signal.
These results demonstrate that the intermodel spread in both signal and noise contribute
signficantly to the spread in ToE.
Temperature of Emergence
In Fig. S4 we show histograms of the global temperature change at which the
S/N >
2
threshold is expected to be crossed for the three regions, as a direct comparison with Fig.
5. The emissions uncertainty is reduced in this metric, which may be more relevant for
mitigation purposes.
∗
To whom correspondence should be addressed. Email: e.hawkins@reading.ac.uk
1
Page 10
BCCR BCM2.0
CCCMA CGCM3−T47
CNRM CM3
CSIRO MK3.0
GFDL CM2.0
GFDL CM2.1
GISS−ER
INMCM3.0
IPSL CM4
MIROC3.2−MED
MIUB−ECHO−G
MPI−ECHAM5
MRI−CGCM2.3.2
NCAR CCSM3
UKMO HADCM3
2010
2015
2020
2025
2030
2035
2040
2045
2050
2055
2060
2065
Figure S1: Time of emergence for surface air temperatures. First year when temperature
has
S/N >
2 for an annual mean for each GCM.
2
Page 11
ICOSAHEDRAL GRID
ONDJFM
LAT−LONG 5
o
×
5
o
GRID
AMJJAS
2010 2013 2016 2019 2022 2025 2028 2031 2034 2037 2040 2043 2046
ToE GRID COMPARISON
Figure S2: The sensitivity of the median ToE for surface air temperatures to the style of
grid used for analysis, focussing on the Arctic, using
S/N >
1. Note the different colour
scale from the main paper to highlight the nearer term in more detail.
3
Page 12
2020
2040
2060
2080
0
2
4
6
8
10
Region 1
ONDJFM
2020
2040
2060
2080
0
2
4
6
8
10
Region 2
2020
2040
2060
2080
0
2
4
6
8
10
Region 3
2020
2040
2060
2080
0
2
4
6
8
10
AMJJAS
2020
2040
2060
2080
0
2
4
6
8
10
Time of Emergence − number of models per decade
2020
2040
2060
2080
0
2
4
6
8
10
Figure S3: Time of emergence for surface air temperatures for three equal area regions
as indicated in Fig. 4. October-March (top) and April-September (bottom). Histograms
representing the number of models of when the first year temperature has expected
S/N >
2,
using each GCM’s own variability (blue) and median signal (green).
4
Page 13
0
0.5
1
1.5
2
0
2
4
6
8
10
Region 1
ONDJFM
A2
A1B
B1
0
0.5
1
1.5
2
0
2
4
6
8
10
Region 2
0
0.5
1
1.5
2
0
2
4
6
8
10
Region 3
0
0.5
1
1.5
2
0
2
4
6
8
10
AMJJAS
0
0.5
1
1.5
2
0
2
4
6
8
10
Global mean surface air temperature change [K]
Global Temperature for Regional Emergence − number of models
0
0.5
1
1.5
2
0
2
4
6
8
10
Figure S4: As Fig. 5, but for the global temperature for regional emergence (GTRE).
Histograms represent the number of models for each global temperature which have an
expected
S/N >
2. Note that models which cross the threshold after 2100 are not included.
5