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Equilibrium climate sensitivity refers to the ultimate change in global mean temperature in response to a change in external forcing. Despite decades of research attempting to narrow uncertainties, equilibrium climate sensitivity estimates from climate models still span roughly 1.5 to 5 degrees Celsius for a doubling of atmospheric carbon dioxide concentration, precluding accurate projections of future climate. The spread arises largely from differences in the feedback from low clouds, for reasons not yet understood. Here we show that differences in the simulated strength of convective mixing between the lower and middle tropical troposphere explain about half of the variance in climate sensitivity estimated by 43 climate models. The apparent mechanism is that such mixing dehydrates the low-cloud layer at a rate that increases as the climate warms, and this rate of increase depends on the initial mixing strength, linking the mixing to cloud feedback. The mixing inferred from observations appears to be sufficiently strong to imply a climate sensitivity of more than 3 degrees for a doubling of carbon dioxide. This is significantly higher than the currently accepted lower bound of 1.5 degrees, thereby constraining model projections towards relatively severe future warming.
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ARTICLE doi:10.1038/nature12829
Spread in model climate sensitivity
traced to atmospheric convective mixing
Steven C. Sherwood
1
, Sandrine Bony
2
& Jean-Louis Dufresne
2
Equilibrium climate sensitivity refers to the ultimate change in global mean temperature in response to a change in
external forcing. Despite decades of research attempting to narrow uncertainties, equilibrium climate sensitivity
estimates from climate models still span roughly 1.5 to 5 degrees Celsius for a doubling of atmospheric carbon dioxide
concentration, precluding accurate projections of future climate. The spread arises largely from differences in the
feedback from low clouds, for reasons not yet understood. Here we show that differences in the simulated strength of
convective mixing between the lower and middle tropical troposphere explain about half of the variance in climate
sensitivity estimated by 43 climate models. The apparent mechanism is that such mixing dehydrates the low-cloud layer
at a rate that increases as the climate warms, and this rate of increase depends on the initial mixing strength, linking the
mixing to cloud feedback. The mixing inferred from observations appears to be sufficiently strong to imply a climate
sensitivity of more than 3 degrees for a doubling of carbon dioxide. This is significantly higher than the currently
accepted lower bound of 1.5 degrees, thereby constraining model projectionstowardsrelatively severe future warming.
Ever since numerical global climate models (GCMs) were first developed
in the early 1970s, they have exhibited a wide range of equilibrium
climate sensitivities (roughly 1.5–4.5 uC warming per equivalent doub-
ling of CO
2
concentration)
1
and consequently a broad range of future
warming projections, with the uncertainty due mostly to the range of
simulated net cloud feedback
2,3
. This feedback strength varies from roughly
zero in the lowest-sensitivity models to about 1.2–1.4 W m
22
K
21
in the highest
4
. High clouds (above about 400hPa or 8km) contribute
about 0.3–0.4 W m
22
K
21
to this predicted feedback because the tem-
peratures at the tops of the clouds do not increase much in warmer
climates, which enhances their greenhouse effect. Mid-level cloud
changes also make a modest positive-feedback contribution in most
models
5
.
Another positive feedback in most models comes from low cloud,
occurring below about 750 hPa or 3 km, mostly over oceans in the
planetary boundary layer below about 2 km. Low cloud is capable of
particularly strong climate feedback because of its broad coverage and
because its reflection of incoming sunlight is not offset by a commen-
surate contribution to the greenhouse effect
6
. The change in low cloud
varies greatly depending on the model, causing most of the overall
spread in cloud feedbacks and climate sensitivities among GCMs
5,7
.
No compelling theory of low cloud amount has yet emerged.
A number of competing mechanisms have, however, been suggested
that might account for changes in either direction. On the one hand,
evaporation from the oceans increases at about 2% K
21
, which—all
other things being equal—may increase cloud amount
8
. On the other
hand, detailed simulations of non-precipitating cloudy marine bound-
ary layers show that if the layer deepens in a warmer climate, more dry
air can be drawn down towards the surface, desiccating the layer and
reducing cloud amount
8,9
.
The lower-tropospheric mixing mechanism
We consider that a mechanism similar to this one, which has so far
been considered only for a particular cloud regime, could apply more
generally to shallow upward moisture transports, such as by cumulus
congestus clouds or larger-scale shallow overturning found broadly
over global ocean regions. Air lifted out of the boundary layer can
continue ascending, rain out most of its water vapour, and then return
to a relatively low altitude—or it can exit the updraught directly at the
low altitude, retaining much more of its initial vapour content. The
latter process reduces the ‘‘bulk precipitation efficiency’’ of convection
10
,
allowing greater transport of moisture out of the boundary layer for a
given precipitation rate. Such a process can increase the relative humidity
above the boundary layer
11
and dry the boundary layer. Unlike the global
hydrological cycle and the deep precipitation-forming circulations
12
,
however, it is not strongly constrained by atmospheric energetics
11
.
We present measures of this lower-tropospheric mixing and the
amount of moisture it transports, and show that mixing varies sub-
stantially among GCMs and that its moisture transport increases in
warmer climates at a rate that appears to scale roughly with the initial
lower-tropospheric mixing.
Mixing-induced low cloud feedback
The resulting increase in the low-level drying caused by lower-tropospheric
mixing produces a mixing-induced low cloud (MILC) feedback ofvari-
able strength, which can explain why low-cloud feedback is typically
positive
5
and why it is so inconsistent among models.
In a GCM, vertical mixing in the lower troposphere occurs in two
ways (Extended Data Fig. 1). First, small-scale mixing of heat and water
vapour within a single grid-column of the model is implied by con-
vective and other parametrizations. Lower-tropospheric mixing and
associated moisture transport would depend on transport by shallow
cumulus clouds, but also on the downdrafts, local compensating sub-
sidence and evaporationof falling rain that are assumed to accompany
deeper cumulus. Second, large-scale mixing across isentropes occurs
via explicitly resolved circulations. Whether this contributes to lower-
tropospheric mixing will again depend on model parametrizations,
but in this case, on their ability to sustain the relatively shallow heating
that must accompany a shallow (lower-tropospheric) circulation. We
measure these two mixing phenomena independently, starting with
1
Climate Change Research Centre and ARC Centre of Excellence for Climate System Science, University of New South Wales, Sydney 2052, Australia.
2
Laboratoire de Me
´te
´orologie Dynamique and Institut
Pierre Simon Laplace (LMD/IPSL), CNRS, Universite
´Pierre et Marie Curie, Paris 75252, France.
2 JANUARY 2014 | VOL 505 | NATURE | 37
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©2014
the small-scale part, and show that both phenomena progressively dry
the boundary layer as climate warms.
The small-scale component of mixing
Lower-tropospheric mixing parametrized within a GCM grid cell
cannot be directly diagnosed from model output (although it contri-
butes to the convective terms in the water vapour budget; see below).
We assert, however, that an atmosphere’s propensity to generate such
mixing can be gauged by observing the thermal structure just above
the boundary layer in ascending, raining regions. As discussed above,
air there is either transported directly from the boundary layer with
minimal precipitation via lower-tropospheric mixing, or indirectly by
ascending in deeper, raining clouds and then descending. Theair would
arrive cool and humid in the former case, but warmer and drier in the
latter case owing to the extra condensation, allowing us to evaluate
which pathway dominates by observing mean-state air properties.
To do this we use an index S, proportional to the differences DT
700–850
and DR
700–850
of temperature and relative humidity between 700 hPa
and 850 hPa (Staken as a linear combination; see Methods Summary)
averaged within a broad ascending region which roughly coincides
with the region of highest Indo-Pacific ocean temperatures (the Indo-
Pacific Warm Pool; Fig. 1). Of the full set of 48 models used in this
study, those with a less negative DT
700–850
in this region consistently
show a more negative DR
700–850
there (Fig. 2a), and the variations in
each quantity are quite large. We interpret this as strong evidence that
both quantities are dominated by variations, evidently large, in the
amount of lower-tropospheric mixing in the ascent region, with higher
Sindicating stronger mixing.
Small-scale lower-tropospheric mixing of moisture is part of the
overall source of the water vapour that is associated with the para-
metrized convection, M
small
. This quantity is available from nine of
the models (see Methods Summary). It always exhibits strong drying
near the surface. Above about 850 hPa, it can either dry the atmo-
sphere on average or moisten it depending on the model (Extended Data
Fig. 2), reflecting the competition between drying from condensation
and moistening from lower-tropospheric mixing and from evaporat-
ing precipitation falling from higher altitudes.
Although M
small
does not reflect lower-tropospheric mixing alone,
we can test whether lower-tropospheric mixing (as diagnosed from S)
affects how M
small
responds as climate warms. The available data
confirm that, given a 14 K warming, convective drying of the plan-
etary boundary layer increases by 4–17 W m
22
(6–30%), compared to
a typical increase of 8% in global or tropical surface evaporation. The
drying increase is highly correlated (r520.79) with S(Fig. 2b). Thus,
convective dehydration of the planetary boundary layer outstrips the
increase in surface evaporation with warming, in all models except
those with the lowest S. Higher-sensitivity models also have higher S
(Fig. 1), suggesting that this process drives a positive feedback on climate.
The large-scale component of mixing
We next turn to the large-scale lower-tropospheric mixing, which we
associate with shallow ascent or flows of air upward through the top of
the boundary layer that diverge horizontally before reaching the
upper troposphere. Although air ascending on large scales over warm
tropical oceans typically passes through nearly the whole troposphere,
over cooler oceans its ascent often wanes with altitude, showing that
this type of mixing indeed occurs in the Earth’s atmosphere (Fig. 3).
The associated mid-level outflows are well documented for the central
a Low sensitivity
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
s (unitless)
b High sensitivity
Figure 1
|
Multimodel-mean local stratification parameter
s
.The index Sis
the mean of swithin the regions outlined in white. Multimodel averages of sare
shown separately for low-sensitivity (ECS ,3.0 uC) (a) and high-sensitivity
(ECS .3.5 uC) (b) models, amongcoupled models with known ECS. The white
dots inside the S-averaging region show the locations of radiosonde stations
used to help estimate Sobservationally. A few coastal regions that are off-scale
appear white.
–11 –10 –9 –8 –7 –6
ΔT700–850 (K)
–30
–20
–10
0
10
ΔR700–850 (%)
r = –0.76
a
S
0.30 0.35 0.40 0.45 0.50
S
–20
–15
–10
–5
0
+4 K change in planetary
boundary layer Msmall (W m–2)
b
r = –0.79
BCC
GCESS/BNU
CCC
NCAR
CMCC
CSIRO/QCCCE
LASG/IAP
GFDL
GISS
MOHC+ACCESS
INM
IPSL
MIROC
MPI+INGV
MRI
NCC
CNRM
CMIP3
CMIP5
Figure 2
|
Basis for the index
S
of small-scale lower-tropospheric mixing
and its relationship to the warming response. a,DT
700–850
versus DR
700–850
,
each averaged over a tropical region of mean ascent (see Fig. 1), from all 48
coupled models. For reference, a saturated-adiabatic value of DTis shown by
dotted line at 27.2 K, and a dry-adiabatic value (not shown) would be about
216 K. Error bars are 2sranges. b, Change in small-scale moisture source
M
small
below 850 hPa in the tropics upon 14 K ocean warming, versus S
computed from the control run, in eight atmosphere models and one CMIP3
model. Symbol colour indicates modelling centre or centre where atmosphere
model was originally developed and symbol shape indicates model generation.
RESEARCH ARTICLE
38|NATURE|VOL505|2JANUARY2014
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©2014
and eastern Pacific and Atlantic Intertropical Convergence Zone and
some monsoon circulations
13,14
. Although these are indeed the regions
where shallow ascent is steadiest, and hence clearest in monthly-mean
data (Fig. 3), in daily reanalysis data, shallow ascent is equally strong
outside the tropics owing largely to contributions from extratropical
storms. We also note that although we focus here on regions of
ascending air, that is because the ascending branches are where the
circulations are easiest to measure; they must, however, descend else-
where, exerting a net transport of water vapour that is upward and
towards the convective regions.
Figure 3 compares the observations with two example models. Neither
model shows as much shallow ascent (red colour) as the observation-
based estimates, but the Institut Pierre Simon Laplace (IPSL)-CM5A
model comes closer. Althoughconvective treatment in the newer IPSL-
CM5B model is more detailed and produces better results in important
respects
15
, here it is seen to produce strong deep ascent of air (white
spots) where it is weaker and shallower in observations (red zones),
showing that improvement in some aspects of a simulation does not
automatically improve others.
We quantify the large-scale lower-tropospheric mixing more thor-
oughly by calculating the ratio Dof shallow to deep overturning (see
Methods Summary) in a broad region encompassing most of the
persistent shallow ascent (see Fig. 3). This index Dvaries by a factor
of four across 43 GCMs (see below). Interestingly, however, Dand S
are uncorrelated (r50.01), confirming that the two scales of mixing
are controlled by different aspects of model design.
The effective source of moisture M
LT, large
due to this shallow over-
turning (that is, large-scale, lower-tropospheric convection) and its
change upon climate warming, can be directly calculated from model
wind and humidity fields. We approximate M
LT, large
using monthly-
mean data from the ten available atmospheric models (see Methods
Summary). M
LT, large
isolates only shallow mixing, whereas M
small
includes the effects of all parameterized convection; yet despite this,
the profiles M
LT, large
(Fig. 4) resemble those of M
small
, with strong
drying in the boundary layer and weak moistening above. Not unex-
pectedly, these effects are greater in the high-Dmodels than in the
low-Dones.
Crucially, the low-level drying also increases faster upon 14K
warming in the high-Dmodels (by about 30%, or 1.5 W m
22
K
21
when expressed as a latent heat flux) than in the low-Dmodels (25%,
or 0.9 W m
22
K
21
). Thus, the response of M
LT, large
grows with Das
M
small
grew with S; the relationship for Dis not as strong (r50.46 for
land 1ocean, r50.25 for ocean only), partly because the spread of D
happens to be somewhat narrow among the available atmosphere
models, but is still significant at 95% confidence.
Climate sensitivity
We now apply the indices Sand Dto the 43 GCMs for which an
equilibrium climate sensitivity (ECS) is available. Each index inde-
pendently explains about 25% of the variance in ECS (Fig. 5a, b).
Because the ranges of Dand Sare similar (each 0.3–0.4), as are
(approximately) those of their drying responses upon warming (see
below), we form an overall lower-tropospheric mixing index (the
LTMI) by simply adding the two: LTMI 5S1D. This LTMI explains
about 50% of the variance in total system feedback (r50.70) and ECS
(r50.68) (Fig. 5c). Thus, although our measure of lower-tropospheric
mixing does not explain all of the variations among GCMs, it does
explain a significant portion of the model spread.
This explanatory power derives primarily from low cloud feed-
backs. The correlation between LTMI and the 14 K change in short-
wave cloud radiative effect in the atmosphere models, which spans a
range of 1.8 W m
22
K
21
in the tropics, is 0.65 in the tropics and 0.57
in subsidence regions (equivalent values estimated from a subset of
the coupled models providing the needed output are 0.25 and 0.47
MERRAa
IPSL-CM5AbIPSL-CM5Bc
–140
0
140
ω500 (hPa day–1)
140 0 –140
ω850 (hPa day–1)
Figure 3
|
The structure of monthly-meantropospheric ascent reveals large-
scale lower-tropospheric mixing in observations and models. Upward
pressure velocity vin one month (September) from the MERRA reanalysis
(a), the IPSL-CM5A model (b) and the IPSL-CM5B model (c) with values at
850 hPa shown in red and those at 500 hPa shown in green plus blue. Bright
red implies ascent that is weighted toward the lower troposphere with
mid-tropospheric divergence (see colour scale), white implies deep ascent, and
dark colours imply descent. In a, black lines outline the region in which the
index Dof large-scale lower-tropospheric mixing is computed. The Pacific and
Atlantic Intertropical Convergence Zone regions are consistently red in the
reanalyses and models, whereas isolated red patches in other areas tend to vary
with time.
ARTICLE RESEARCH
2 JANUARY 2014 | VOL 505 | NATURE | 39
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respectively). These correlations suggest that the predictive skill of
LTMI arises from both subsidence and other regions; further work
is needed to better assess this. Cloud amount reduces more in high-
LTMI models both at low and mid-levels (Extended Data Fig. 3),
although the greater net radiative impact of low cloud makes its effect
dominant
16
. Previously reported water vapour and lapse-rate feed-
backs
17
are, in contrast, not correlated with the LTMI.
Is the imputed lower-tropospheric mixing impact on low clouds
strong enough to explain the approximately 1.5 W m
22
K
21
spread of
cloud feedbacks seen in GCMs?
4
One recent study
18
imposed increased
surface latent heat fluxes in a large region typified by shallow clouds,
finding an increase in cloud-related net cooling of about 1 W m
22
for a
2–3 W m
22
increase in the surface flux, other things held fixed. An
even larger sensitivity, nearly 1:1, has been reported in a different
model for advective changes in moisture input
19
. If a similar but opposite
cloud response occurred for moisture removal by lower-tropospheric
mixing, then to explain the feedback spread, the boundary-layer drying
responses would need to span a range across models of about 3 W m
22
per K of surface warming. This roughly matches the contributionto the
spread from M
small
alone (Fig. 2b). The additional drying response
from M
LT, large
was about 0.6 W m
22
K
21
greater in the high-Dmodels
(mean Dof 0.34) than in the low-Dones (mean 0.24), which, if rescaled
by the full spread of Din the full GCM ensemble, implies a further
source of spread in drying response of about 2 Wm
22
K
21
. We con-
clude that, even if not all low clouds are as sensitive as the ones exam-
ined in the cited studies, the lower-tropospheric mixing response is
strong enough to account for the cloud feedback spread and its typ-
ically positive sign
5
.
Why does moisture transport increase so strongly with warming?
The magnitude of these increases, typically 5%–7% per K of surface
warming, is roughly what would be expected if the circulations remained
similar against a Clausius–Clapeyron increase in moisture gradients
20
,
as indeed it does,at least for the large-scale part
21
(ExtendedData Fig. 4).
Further study is needed to understand why this is so, and to examine in
greater detail how clouds respond to changing moisture transports;
changes in low cloud amount may for example help the atmosphere
restore imbalances in boundary layer moist enthalpy such as those caused
by lower-tropospheric mixing
19
. Because LTMI ignores any information
on clouds, it is likely that additional measures of cloud characteristics
22
could explain some of the variations in low-cloud feedback not yet
explained here.
We end by considering observational estimates of Sand D(see
Fig. 5). These show an Snear the middle of the GCM range, but a
Dclose to the top end, as hinted already by Fig. 3. Dmay not be well
constrained because vmust be inferred from observational reana-
lyses, although available horizontal wind observations support the
existence of strong mid-level outflows
13
, and the result is consistent
across both reanalyses examined. The reanalysis estimates of Sare less
consistent but this quantity can be fairly well constrained by radio-
sonde observations.
Taking the available observations at face value implies a most likely
climate sensitivity of about 4 uC, with a lower limit of about 3 uC.
Indeed, all 15 of the GCMs with ECS below 3.0 uC have an LTMI
below the bottom of the observational range. Further work may be
needed to better constrain these indices, and to test whether their
relationship to ECS is robust to design factors common to all models.
For example, this should be tested in global cloud-resolving models.
–0.8 –0.6 –0.4 –0.2 0.0 0.2
Lar
g
e-scale source (
g
k
g
–1 day–1)
1,000
800
600
400
200
Pressure (hPa)
High D
Low D
High D, +4 K
Low D, +4 K
Figure 4
|
Estimated water vapour source M
LT, large
due to large-scale lower-
tropospheric mixing and its response to warming. See Methods for
calculation details. Data are from ten atmosphere models, averaged from 30uS
to 30uN over oceans, with the average of the four models having the largest D
shown in magenta and the average of the four models with the smallest D
shown in blue. Dashes show results in 14 K climate. Changes at 14 K are
nearly identical whether or not land areas are included.
0.2 0.3 0.4 0.5 0.6 0.7
S
1
2
3
4
5
Climate sensitivity
a
r = 0.50
0.1 0.2 0.3 0.4 0.5
D
1
2
3
4
5
Climate sensitivity
b
r = 0.46
0.4 0.5 0.6 0.7 0.8 0.9 1.0
LTMI, (S + D)
1
2
3
4
5
Climate sensitivity
c
r = 0.68/0.70
MERRA
ERAi
Figure 5
|
Relation of lower-tropospheric mixing indices to ECS. ECS versus
S(a), D(b) and LTMI 5S1D(c) from the 43 coupled models with known
ECS. Linear correlationcoefficients rare given in each panel (r50.70 in cis the
correlation to the total system feedback). Error bars shown near panel axes
indicate 2sranges of the direct radiosonde estimate (a) and the Svalue from
radiosondes added to the Dvalue from each of the two reanalyses(c). ERAi and
MERRA are the two monthly reanalysis products.
RESEARCH ARTICLE
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©2014
The possibility can never be ruled out that feedbacks could exist in
nature that are missing from all models, which would change the
climate sensitivity from that suggested by our result. Nonetheless,
on the basis of the available data, the new understanding presented
here pushes the likely long-term global warming towards the upper
end of model ranges.
Discussion
Although a few previous studies have already noted that higher-sensitivity
models simulate certain cloud-relevant phenomena better
23–25
, ours is
the first to demonstrate a causal physical mechanism, or to show
consistent predictive skill across so many models, or to point to pro-
cesses connecting low-cloud regions to the deep tropics. The MILC
mechanismis surprisingly straightforward. Lower-tropospheric mixing
dries the boundary layer, and the drying rate increases by 5–7% K
21
in
warmer climates owing to stronger vertical water vapour gradients.
The moisture source from surface evaporation increases at only about
2% K
21
. Thus as climate warms, any drying by lower-tropospheric
mixing becomes larger relative to the rest of the hydrological cycle,
tending to dry the boundary layer. How important this is depends on
how important the diagnosed lower-tropospheric mixing was in the
base state of the atmosphere. Lower-tropospheric mixing is unrealist-
ically weak in models that have low climate sensitivity.
Climate-sensitivity-related differences in lower-tropospheric mix-
ing, both at small (Fig. 1) and large scales (Fig. 3), are most detectable
in regions of tropical deep or mixed-level convection and mean upward
motion. This does not mean, however, thatthe greater low-level drying
in a warmer climate or the spread of drying among models will be
limited to these regions.
Large-scale lower-tropospheric mixing carries water vapour not only
upward but also horizontally away from subsidence regions; because both
directions of transport intensify in a warmer atmosphere
20
, subsidence
regions should bear the brunt of the overall boundary-layer drying.
Moreover, shallow ascent is equally strong (though more transient) in
mid-latitude storm tracks and in the tropics, suggesting that MILC
feedback may be just as important outside the tropics as within them.
As for small-scale lower-tropospheric mixing, even though there are
reasons to measure it in ascending regions (see Methods), its impact
upon warming is much more widespread and differs significantly among
models in subsiding regions (Extended Data Fig. 5). We hypothesise
that this is because models with more small-scale lower-tropospheric
mixing in ascending regions also have more in descending regions,
although we cannot confirm this directly. Overall, the behaviour is con-
sistent withpublished results showing that subsiding regions contribute
strongly to the spread of cloud feedbacks in models, with storm tracks
and tropical convective regions also playing a part
16,26,27
.
Lower-tropospheric mixing behaviour appears to result from a
competition between shallow and deep convection in situations where
either could occur. Such situations persist in many tropical regions,
notably the Intertropical Convergence Zone. Understanding and
properly representing this competition in climate models is undoubt-
edly necessary for more accurate future climate projections.
Although tested here on models used over the past decade or so, we
presume that this mechanism has been a leading source of spread in
sensitivity since the dawn of climate modelling. Finally to identify an
atmospheric process that drives variations in climate sensitivity offers an
unprecedented opportunity to focus research and model development
in ways that should lead to more reliable climate change assessments.
METHODS SUMMARY
Data for computing Sand Dcome from control runs of 48 models: 18 from the
Coupled Model Intercomparison Project version 3 (CMIP3)
28
and 30 from
CMIP5 (ref. 29) (see Extended Data Tables 1 and 2). ECS was reported for all
but one CMIP3 model by the Intergovernmental Panel on Climate Change
28
. For
CMIP5 we employ effective climate sensitivities calculated from abrupt 4 3CO
2
experiments, availablefor 26 models, following a standard regression procedure
30,31
.
Data for M
small
and M
LT, large
come from ten CMIP5 atmospheremodels providing
‘amip’ (specified ocean surface temperature) control and 14 K ocean warming
runs. Eight of these models providedM
small
; we also included data fromthe Parallel
Climate Model (CMIP3).
Observational estimates come from radiosondes and two monthly reanalysis
products (ERAi and MERRA). Reanalyses are produced from a model con-
strained to the fullest extent possible by a variety of observations
32,33
.
We calculate Swithin a region where convective effects are a leading term in
thermodynamic budgets, defined by the upper quartile of the annual-mean mid-
tropospheric ascent rate where it is upward, 2v
500
(vthe pressure velocity). We
define S;(DR
700–850
/100% 2DT
700–850
/9 K)/2, which normalizes DR
700–850
to
100% humidity, DT
700–850
to the approximately 9-K range between dry and
saturated adiabatic values, and averages these two pieces of information with
equal weight to reduce noise from other factors.
To calculate M
LT, large
we compute v
1
(the average of vat 850 hPa and 700 hPa)
and v
2
(the average of vat 600 hPa, 500 hPa and 400 hPa). D5v
2
2v
1
measures
the local horizontal outflow in the lower troposphere above the boundary layer.
Moisture is transported upward and outward wherever D.0 and v
1
,0. We
restrict measurement to tropical ocean regions from 160uWto30uE (see Fig. 3).
The moisture supplied to the environment is estimated as M
LT, large
52Æqdv/
dpH(D)H(2v
1
)æ, where pis the pressure, qis the specific humidity, Æ...æindicates
the mean over the restricted region, and His the step function. Finally,
D;ÆDH(D)H(2v
1
)æ/Æ2v
2
H(2v
2
)æ.
Online Content Any additional Methods, Extended Data display items and Source
Data are available in the online version of the paper; references unique to these
sections appear only in the online paper.
Received 16 May; accepted 5 November 2013.
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Acknowledgements This work was supported by the FP7-ENV-2009-1 European
project EUCLIPSE (number 244067). We acknowledge the World Climate Research
Programme’s Working Group on Coupled Modelling, which is responsible for CMIP,
and we thank the climate modelling groups for producing and making available their
model output, especially the participants contributing additional CFMIP2experiments
and diagnostics crucial to our study. The US Department of Energy’s Program for
Climate ModelDiagnosis and Intercomparison providescoordinating supportfor CMIP
and led the development of software infrastructure in partnership with the Global
Organisation for Earth System Science Portals. We also thank the National Center for
Atmospheric Research and the Earth System Grid Federation for providing access to
PCM output, the Australian National Computational Infrastructure, and the IPSL
Prodiguer-Ciclad facility for providing a convenient archive of CMIP data. Finally, we
thank B. Stevens, C. Bretherton and G. Schmidt for comments on early versions of the
manuscript.
Author Contributions S.C.S. led the study and the writing of the paper, and did the
calculations of LTMI and related diagnostics.S.B. computed cloud radiative effect and
assisted in interpreting results and writing the paper. J.-L.D. computed ECS and
assisted in interpreting results and writing the paper.
Author Information Reprints and permissions information is available at
www.nature.com/reprints. The authors declare no competing financial interests.
Readers are welcome to comment on the onlineversion of the paper. Correspondence
and requests for materials should be addressed to S.C.S. (s.sherwood@unsw.edu.au).
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METHODS
Data for computing Sand Dcome from 48 models: 18 from the CMIP3 (Coupled
Model Intercomparison Project version 3)
28
, the first two years of each ‘‘picntrl’’
run, and 30 models from theCMIP5 (ref. 29), the first two years of each ‘‘1pctCO2’’
run. Two years of datais sufficient to specify Sand Dto within 0.02 or betterof their
long-term values. CMIP3 data were obtained from the Australian National
Computational Infrastructure node, and CMIP5 data including the ‘amip’ and
‘amip14K’ runs were obtained on 14 September 2012 and 22 October 2012 from
the IPSL Ciclad repository. ECS values for CMIP3 were reported for all but one
model bythe Intergovernmental Panel on ClimateChange
28
. For CMIP5 we employ
effective climate sensitivities calculated from abrupt 4 3CO
2
experiments, avail-
able for 26 of the 30 CMIP5 models, followinga standard regression procedure
30,31
.
Data for M
small
and M
LT, large
come from ten CMIP5 atmosphere models pro-
viding ‘amip’ (specified ocean surface temperature) control and 14 K ocean
warming experiments. A key advantage of this experiment setup is that inter-
annual ocean variability is the same in the control and warming runs, and changes
in the sea surface temperature pattern—which could complicate interpretation,
especially for circulation changes—are avoided. Data are from 1989–98, except
for IPSL-CM5A, in which some of these years were corrupted and alternative
years were used. Results from individual years were similar to those for the ten-
year averages. Eight of these models provided M
small
; we also included data from
the PCM CMIP3 1%-per-year-to-quadrupling experiment, with changes rescaled
to the 14 K equivalent (actualchange 3.3 K). PCM M
small
data come from tenyears
near the beginning and ten years near the end of the 1%-per-year-to-quadrupling
experiment, obtainedfrom the National Center for AtmosphericResearch node of
the Earth System Grid.
The shortwave cloud radiative effect is obtained by differencing the all-sky and
clear-sky top-of-atmosphere shortwave fluxes for each model run. To calculate
cloud feedback we first composite the sensitivity of the shortwave cloud radiative
effect to sea surface temperature in dynamical regimes defined by vertical-mean
vertical velocity, and then we compute the sum (weighted by the probability
distribution function of v) over regimes (or only subsidence regimes defined
by v.0)
7
. For coupled models, the warming-induced change is obtained from
abrupt CO
2
-quadrupling experiments, after removing the instantaneous change
associated with rapidadjustment to higher CO
2
estimated from thefirst 12 months
after quadrupling. Only one realization is used per model. For atmosphere-only
models it is simply the difference between the 14K and the control simulations.
Observational estimates come from radiosondes and from two monthly reana-
lysis products (ERAi and MERRA), years 2009–10. The reanalyses are produced
from a model constrainedto the full extent possible by a variety of observations
32,33
.
MERRA reanalysisdata from 1 September 2009 were used to compare Dinside and
outside the tropics, but monthly data were used otherwise. Radiosonde data were
obtained from the Integrated Global Radiosonde Archive and subjected to simple
quality-controlchecks for outliers. The ten stations sited in the relevant region and
meeting the criteria describedby a previous study
34
were used, and the mean taken
over the 2 years. The radiosonde network sampling bias, as determined from
station-sampled reanalysis output, was relatively small compared to the overall
reanalysis biases.
We calculate Sin ascending regions, where convective effects are a leading term
in thermodynamic budgets; in subsidence regions humidity is sensitive to irrel-
evant non-local factors and even to numerical resolution
35
, perhaps explaining
why it is less informative for our purposes. The calculation region is defined by the
upper quartile of the annual-mean mid-tropospheric ascent rate in ascending
regions, 2v
500
(where vis the pressure velocity). We define S;(DR
700–850
/
100% 2DT
700–850
/9 K)/2, which normalizes DR
700–850
to 100% humidity and
DT
700–850
to the approximately 9 K range between the dry and saturated adiabatic
values, and then averages these two pieces of information with equal weight. Such
averaging should reduce the noise from other factors that influence one quantity
or the other. Varyingthe weighting of the two terms does notstrongly affect results.
To calculate M
LT, large
, we first compute v
1
(the average vat 850 hPa and
700 hPa) and v
2
(the average vat 600 hPa, 500 hPa and 400 hPa). The difference
D5v
2
2v
1
then measures the local horizontal outflow in the lower troposphere
above the boundary layer. Moisture is transported upward and outward at this
level wherever D.0 and v
1
,0. We restrict measurement to tropical ocean
regions from 160uWto30uE (see Fig. 3). The moisture supplied to the envir-
onment is then estimated as M
LT, large
52Æqdv/dpH(D)H(2v
1
)æ, where qis the
specific humidity, Æ...æindicates the mean over the restricted calculation region,
and His the step function. The index Dis computed as D;ÆDH(D)H(2v
1
)æ/
Æ2v
2
H(2v
2
)æ.
Values of Dand Sare similar over ten years of data or one year, and are similar
whether individual months or long-term means for each month of the year are
used. These indices capture over 25% of the ECS variance even if computed from
only a single month of data from each model. Thus, long records are unnecessary
for deducing the strength of lower-tropospheric mixing.
The reason for restricting calculation of Dto the cooler tropical longitudes is
that a few climate models erroneously place much of the shallow ascent over
warm oceans, where it does not seem to contribute as much to low-cloud feed-
back. In observations, and in most models, the restriction has little effect because
most of the shallow ascent persistent enough to appear in monthly-mean data is
already located in the specified region. We speculate that the location of the ascent
matters because the associated shallow descent is more relevant if it occurs over,
or upstream of, regions of radiatively important low cloud.
Both lower-tropospheric mixing indices retain statistically significant correla-
tions with ECS for all alterations to their definitions that we tried. Specifically, the
correlation of Swith ECS (r
S–ECS
) is similar with v
500
percentiles of 0.25 or 0.5,
but drops with looser thresholds, which begin to pick up parts of the resolved
lower-tropospheric mixing region. Tighter thresholds reduce the spread in S
between models, reducing r
S–ECS
. The correlation r
D–ECS
is somewhat weaker
(as low as 0.3) if the longitudinal restriction for Dis removed, or if other defini-
tions of v
1
and v
2
are used.
34. Sherwood, S. C., Meyer, M. L., Allen, R. J. & Titchner, H. A. Robust tropospheric
warming revealed by iteratively homogenized radiosonde data. J. Clim. 21,
5336–5352 (2008).
35. Sherwood, S. C., Roca, R., Weckwerth, T. M. & Andronova, N. G.
Tropospheric water vapor, convection and climate. Rev. Geophys. 48, RG2001
(2010).
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Extended Data Figure 1
|
Illustration of atmospheric overturning
circulations. Deep overturning strongly coupled to the hydrological cycle and
atmospheric energy budget isshown by solid lines; lower-tropospheric mixing
is shown by dashed lines. The MILC feedback results from the increasing
relative role of lower-tropospheric mixing in exporting humidity from the
boundary layer as the climate warms, thus depleting the layer of water vapour
needed to sustain low cloud cover.
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Extended Data Figure 2
|
Small-scale moisture source
M
small
.Vertical
profile averaged over all tropical oceans, for two selected climate models (see
legend) with very differentwarming responses, in present-day (solid) and 14K
(dashed) climates.
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Extended Data Figure 3
|
Response of cloud fraction to warming. Profile of
average change in model cloud fractional cover at 14 K in the four atmosphere
models with largest (magenta) and smallest (blue) estimated 14K increases in
planetary-boundary-layer drying, averaged from 30uSto30uN (dashed) or
60uSto60uN (solid). The drying estimate is obtained by adding the explicitly
computed change in M
LT, large
to the change in M
sm
estimated from Svia the
relationship shown inFig. 2a. The typical mean cloud fraction below 850 hPa is
about 10% to 20%, and the changes shown are absolute changes in this fraction,
so are of the order of 10% of the initial cloud cover.
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Extended Data Figure 4
|
Response of large-scale lower-tropospheric
mixing to warming. Profiles of mean vertical velocity in regions of shallow
ascent, in control and 14 K climates. The similarity of dashed and solid lines
indicates that mass overturning associated with these regions is roughly the
same in the warmer simulations, on average.
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Extended Data Figure 5
|
Response of small-scale, low-level drying to
warming. Change in convective moisture source M
small
below 850 hPa upon a
14 K warming in eight atmosphere models and one CMIP3 coupled model;
units are W m
22
, with negative values indicating stronger drying near the
surface. Zero contours are shown in white (a few off-scale regions also appear
white). The models used for calculating M
large
are the eight shown here plus two
for which M
small
data were unavailable: CNRM-CM5 and FGOALS-g2.
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Extended Data Table 1
|
List of CMIP5 coupled models used
Centre acronyms used to identify them in scatter plots are also shown. The derived forcing, total feedback, and equilibrium climate sensitivities are given for models with abrupt 4 3CO
2
simulations.
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Extended Data Table 2
|
List of CMIP3 coupled models used
Centre acronyms used to identify them in scatter plots are also shown, as are feedback values given by
ref. 28.
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