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Observational constraints on the effective climate sensitivityfrom the historical period

Citation for published version:Tokarska, KB, Hegerl, G, Schurer, A, Forster, PM & Marvel, K 2020, 'Observational constraints on theeffective climate sensitivity from the historical period', Environmental Research Letters.https://doi.org/10.1088/1748-9326/ab738f

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Environmental Research Letters

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Observational constraints on the effective climate sensitivity from thehistorical periodTo cite this article: Katarzyna B Tokarska et al 2020 Environ. Res. Lett. 15 034043

 

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Environ. Res. Lett. 15 (2020) 034043 https://doi.org/10.1088/1748-9326/ab738f

LETTER

Observational constraints on the effective climate sensitivity fromthe historical period

Katarzyna BTokarska1,5 , Gabriele CHegerl1 , AndrewPSchurer1 , PiersMForster2 andKateMarvel3,4

1 School of Geosciences, University of Edinburgh, UnitedKingdom2 University of Leeds, United Kingdom3 NASAGoddard Institute for Space Studies, NewYork,NY,United States of America4 Department of Applied Physics andAppliedMathematics, ColumbiaUniversity, NewYork, NY,United States of America5 Current affiliation: Institute for Atmospheric andClimate Science, ETHZurich, Zurich, Switzerland

E-mail: kasia.tokarska@ed.ac.uk

Keywords: climate sensitivity, detection and attribution, historical period, greenhouse gases

Supplementarymaterial for this article is available online

AbstractThe observedwarming in the atmosphere and ocean can be used to estimate the climate sensitivitylinked to present-day feedbacks, which is referred to as the effective climate sensitivity (Shist). However,such an estimate is affected by uncertainty in the radiative forcing, particularly aerosols, over thehistorical period.Here, wemake use of detection and attribution techniques to derive the surface airtemperature and oceanwarming that can be attributed directly to greenhouse gas increases. Theseserve as inputs to a simple energy budget to infer the likelihood of Shist in response to observedgreenhouse gases increases over two time periods (1862–2012 and 1955–2012). The benefit of usinggreenhouse gas attributable quantities is that they are not subject to uncertainties in the aerosol forcing(other than uncertainty in the attribution to greenhouse gas versus aerosol forcing not captured by themulti-model aerosol response pattern). The resulting effective climate sensitivity estimate, Shist, rangesfrom1.3 °C to 3.1 °C (5%–95% range) over the full instrumental period (1862–2012) for our bestestimate, and gets slightly wider when considering further uncertainties. This estimate increases to1.7 °C–4.6 °C if using the shorter period (1955–2012).We also evaluate the climatemodel simulatedsurface air temperature and ocean heat content increase in response to greenhouse gas forcing over thesame periods, and compare themwith the observationally-constrained values.Wefind that that theoceanwarming simulated in greenhouse gas only simulations inmodels considered here is consistentwith that attributed to greenhouse gas increases fromobservations, while onemodel simulatesmoregreenhouse gas-induced surface air warming than observed.However, othermodels with sensitivityoutside our range show greenhouse gas warming that is consistentwith that attributed in observations,emphasising that feedbacks during the historical periodmay differ from the feedbacks at CO2

doubling and from those at true equilibrium.

1.Motivation

The ultimate warming of the climate system inresponse to a doubling of atmospheric CO2 concentra-tion from preindustrial, and once the system reachesan equilibrium, is known as the equilibrium climatesensitivity (ECS), and is likely to range from 1.5 °C to4.5 °C (17%–83% probability), as assessed by the FifthAssessment Report of the Intergovernmental Panel on

Climate Change (IPCC AR5 2013). However, thehistorical and present-day state of the climate systemthat we can observe is not at equilibrium yet. Theglobal ocean stores more than 90% of the Earth’senergy imbalance, taking centuries to reach equili-brium (Hansen et al 2011, Church et al 2013).We referto the climate sensitivity inferred from the historicaland present-day conditions as the effective climatesensitivity (Shist), which may be different from climate

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sensitivity at equilibrium (Knutti et al 2017, Rugen-stein et al 2019), due to slow response additionalclimate feedbacks that come into play on longer time-scales and when the pattern of global warming is fullydeveloped (including, for example, sea ice retreat).(Note that the Earth system sensitivity that includesthe response to ice sheet melt and release of CO2 frompermafrost may be even higher; Knutti et al 2017.)Furthermore, the strength of some feedbacks, such asthe cloud feedback, may change over time and athigher levels of warming (Knutti et al 2017, Desslerand Forster 2018). Nevertheless, observations duringthe historical period (here defined as 1862–2012)provide us with useful information, allowing us toconstrain important aspects of the climate modelresponses (Forster 2016, Knutti et al 2017).

There are multitudes of estimates of climate sensi-tivity summarised in Knutti et al (2017), many ofwhich are based on estimates of feedbacks and analysisof climate models (summarised in Knutti et al 2017—figure 1 thereinwith red bars: e.g. Harris et al 2013, vanHateren 2013, Shindell 2014, Millar et al 2015). Otherestimates of climate sensitivity arise from observationsover the historical period (e.g. Gregory et al 2002,Frame et al 2005, Otto et al 2013, Johansson et al 2015,Forster 2016, Lewis 2016, Skeie et al 2018, see Knuttiet al 2017 for a comprehensive summary). Derivingobservational constraints on the effective climate sen-sitivity (Shist) from the historical period is challengingdue to the uncertainties in radiative forcing, oceanwarming, and the role of internal climate variability inlong-term change (Gregory et al 2002, Otto et al 2013,Forster 2016). The resulting Shist estimates are subjectto assumptions about radiative forcing, which arestrongly affected by uncertainty in the forcing byanthropogenic aerosols. Also, the observed warmingestimates are subject to incomplete coverage, which isespecially low in the earlier historical period (Cowtanand Way 2014). In addition, fitting simple climatemodels to observations as done in Aldrin et al (2012)and Johansson et al (2015), for example, is subject touncertainty in those simple models and can be quitesensitive to assumptions (see discussion in Sherwoodet al in review).

The uncertainty arising from the unknownmagni-tude of the aerosol forcing in the historical periodcould be avoided by focusing on the observed warm-ing that has been attributed to greenhouse gases only.Few previous studies (Frame et al 2005, Lewis 2016)followed that idea and derived constraints on theeffective climate sensitivity by making use of theanthropogenic or greenhouse gas attributable warm-ing, obtained in a detection and attribution analysis.However, these studies did not obtain greenhouse gasattributable ocean heat content in a detection andattribution analysis, using instead the observed oceanheat content estimates to all forcing.

Here, we make use of detection and attributiontechniques to quantify both the greenhouse gas

attributable change in surface temperature (usingblended surface air and sea surface temperature, for adirect comparison with the observed warming), andocean heat content. We then apply those results to theplanetary energy budget using the forcing-feedbackframework (Gregory et al 2004, Otto et al 2013) toderive observational constraints on the effective cli-mate sensitivity (ShistGHG

). These results are then com-pared with an alternative approach of applyingobservational constraints on futuremodel projections.

2.Methods

2.1. Greenhouse gas attributable warming andocean heat contentTo derive the greenhouse gas attributable contribu-tions to the ocean heat content (DNGHG) and totemperature (DTGHG) we make use of detection andattributionmethod of regularised optimal fingerprint-ing (ROF; Ribes and Terray 2013, Ribes et al 2013),which is based on a total least squares regression (Allenand Stott 2003). Under the assumption of linearadditivity of the forcings (e.g. Hegerl et al 1997, Tettet al 1999, Gillett et al 2004, Swart et al 2018), the trueobserved climate response (y*) can be expressed as asum of the models’ noise-free responses to individualforcings (x i* ), scaled by respective scaling factors (bi)(equation (1)). This method accounts for noise due tointernal variability in observations e ,y and noise ex i, inthe model response due to internal variability and afinite ensemble size for each noise-free modelledresponse (x i* ) (Ribes et al 2013):

å b==

y x 1i

l

i i1

* * ( )

The scaling factors (bGHG) for the oceanwarmingwerederived in the same way as in Tokarska et al (2019)(based on the period 1955–2012, due to availableobservational coverage), for the set of models consid-ered here (supplementary table S1, available online atstacks.iop.org/ERL/15/034043/mmedia). The scal-ing factors for surface warming were derived using themodels’ surface warming as a blended product ofsurface air temperature and the sea surface tempera-tures, for consistency with the observations (Had-CRUT4.5;Morice et al 2012), as in Schurer et al (2018),following Cowtan et al 2015, for the period1862–2012. In both cases (for ocean warming andsurface warming), the models’ responses were calcu-lated in the same way as observations, and maskedaccording to the observational coverage at each timestep, to allow for a like-to-like comparison of modelsand observations, prior to the detection and attribu-tion. Prior to masking, model output was re-griddedby bilinear interpolation onto the respective observa-tional grids, and on the common depth layers (in caseof ocean warming). In the energy budget analysis thatfollows in the results section (section 3.3), wemake useof full coverage of model simulated responses in

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Environ. Res. Lett. 15 (2020) 034043

Figure 1.Time-series ofmodel responses to greenhouse gas forcing: surface temperature (a), and ocean heat uptake at 0–2000 m (b).Panel (c) shows the relationship between the top two panels: surface air temperature as a function of ocean heat content (in response togreenhouse gas forcing alone).Note: All panels show responses to greenhouse gas only (GHG) forcing, based onCMIP5models (as labelled)in historical GHG-only simulations. Higher ECSmodels are indicated by red, while lower ECSmodels are indicated in blue (supplementarytable S1). Surface air temperature is shownwith respect to the 1862–1880 period.

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greenhouse gas only historical simulations in order toavoid low bias due to missing values (Benestad et al2019), multiplying the model simulated space-timepatterns by the range of the bGHG scaling factors thatare consistent with observed changes.

We carried on the detection and attribution (ROF)analysis on different sets of inputs, summarised insupplementary table S2. (The detection and attribu-tion analysis is described in detail in Tokarska et al(2019) and follows the Ribes et al (2013) approach.)We use also historical simulations driven by natural-only and greenhouse gas-only forcings that extend tothe year 2012. The historical all-forcing simulationswere obtained either using the extensions (until theyear 2012) or extended by the first few years from RCP4.5 simulations (for the period 2006–2012).

Internal variability is considered in detection andattribution, and its effect is included in the uncertaintyranges of the scaling factors. In order to estimate thesensitivity of results to uncertainty in estimates ofinternal variability we also use detection and attribu-tion results where the noise due to internal variabilitywas doubled by increasing the variance (in the noisefrom the control runs) by a factor of two (as inTokarska et al 2019).

2.2. Greenhouse gas attributable effective climatesensitivity (ShistGHG

)The ECS is determined by atmospheric feedbacks toincreases in greenhouse gases, (see definition above).In models, it is usually derived from simulations ofgreenhousewarming at equilibriumor in response to alarge abrupt forcing (i.e. high signal-to-noise ratio;Marvel et al 2018). It has been recognised that thefeedbacks to an early and increasing warming of theclimate system in response to increasing greenhousegases may not be identical to those to equilibratedgreenhouse warming. Also, feedbacks are influencedby spatial patterns of warming (Knutti et al 2017,Andrews et al 2018), which means that the effectiveclimate sensitivity during the historical period may bedifferent from that at equilibrium. Therefore, ifderived from the historical period, ECS is referred to asthe effective climate sensitivity (Gregory et al 2004,Otto et al 2013, Forster 2016), and can be expressed asShist in equation (2):

=D

D - D´S

F T

F N, 2hist

2 CO2 ( )

where ´F2 CO2is the radiative forcing to CO2 doubling

(quantified in a standard 1% per year CO2 increaseexperiment), DT is warming in the given historicalperiod, DF is the radiative forcing estimate, and DNis the net energy imbalance, dominated by the oceanheat uptake (Rhein et al 2013). Shist in equation (2) isequal to the ECS only if the feedbacks that determine it(often characterised by a parameter in an energybudget equation) are the same at present as atequilibrium.

This energy budget considers the total effectiveradiative forcing over the historical period, whose lar-gest uncertainty is due to the uncertainty of aerosolforcing: aerosols cause cooling, which may mask outsome of the warming caused by greenhouse gases.Here we aim to avoid aerosol uncertainty by makinguse of the atmospheric and ocean warming that hasbeen attributed to greenhouse gases alone (dominatedby CO2 radiative forcing). Hence, based onequation (2), we define the effective climate sensitivitydue to greenhouse gas-attributable response as S ,histGHG

expressed by equation (3):

=D

D - D´S

F T

F N, 3hist

GHG

GHG GHG

2 COGHG

2 ( )

where DFGHG is the greenhouse gas effective radiativeforcing for the analysis period. Both the greenhousegas attributable warming (DTGHG) and the greenhousegas attributable ocean heat content change (DN ,GHG

representing the net energy imbalance) and theirrespective uncertainties in the greenhouse gas attribu-table responses are obtained by scaling the modelresponses in surface air temperature and ocean heatcontent by the corresponding scaling factors bGHG

derived in a detection and attribution analysis (seesection 2.1 and supplementary tables S2 and S3).

In section 3.3, we compute probability density dis-tributions of ShistGHG

in two following ways. First, wecalculated ShistGHG

directly by drawing random samplesfrom Gaussian distributions (or joined half-Gaussian,if the 5%–95% attributed range was not symmetric;supplementary figure S1) of all the parameters on RHSof equation (3). (See Supplementary tables S1 to S4 fordetails, and supplementary figure S1 illustrating theinput distributions.) The spread for of DTGHG comesfrom the uncertainty range in the bGHG scaling factorstimes the model simulated change, replicating the fitto observations (figure 2). However, this directapproach of obtaining ShistGHG

is subject to an implicitprior on ShistGHG

which may be biasing the distributiontowards lower ShistGHG

values by under-sampling highShist values (Frame et al 2005).

To evaluate the implications of such an implicitprior on S ,histGHG

we also took an alternative approach(Sherwood et al in review), where we assume a flat uni-form prior on ShistGHG

and then calculated the expectedwarmingDTexpGHG

given the ranges ofDF ,GHG DN ,GHG

and ´F ,2 CO2by re-arranging equation (3) into a for-

ward model. For a putative value of S ,histGHGthe expec-

ted temperature is:

eD =D - D

+´

T SF N

F, 4exp hist

GHG GHG

2 COGHG GHG

2

( )

where e is the observational error (including observa-tional uncertainty and unforced climate variability(Sherwood et al in review). As before, the inputsDF ,GHG DN ,GHG and ´F2 CO2

are sampled fromcorresponding Gaussian or joined half-Gaussian (ifnot symmetric) distributions using the random sam-pling approach (i.e. drawing random samples from the

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Environ. Res. Lett. 15 (2020) 034043

input distributions), but DTexpGHGin equation (4) is

evaluated for ShistGHGvalues ranging from 0 to 10 K,

sampling a uniform prior. (We also performed sensi-tivity to the choice of a different range of the prior 0 °Cto 5 °C, and 0 °C to 20 °C, which does not influenceour results tofirst decimal place).

The resulting expected warming (DTexpGHG) can be

then evaluated against the observationally-con-strained greenhouse gas attributable warming(DTOBSGHG

), allowing us to derive the likelihood ofS ,histGHG

and its corresponding posterior probabilitydensity. The likelihood of ShistGHG

is calculated by eval-uating the distance for each of the random samples ofexpected warming (DTexpGHG

) to the greenhouse gas

attributable warming (DTOBSGHG). To avoid summing

extremely low density values, we considered only den-sity values which fall within s3 of the mean value ofDT ,expGHG

whichwere then aggregated for each corresp-onding ShistGHG

value, resulting in the likelihood dis-tribution for S .GHG

This likelihood DP T S N, ,OBS hist GHGGHG GHG( ∣

D D ´F F,GHG 2 CO2) quantifies how likely the observa-

tion-based greenhouse gas attributable warmingDTOBSGHG

would be, given the expected ranges ofDF ,GHG DN ,GHG and ´F2 CO2

and considering all plau-sible values of ShistGHG

(expressed by the flat prior) (as inSherwood et al in review). Since the prior ShistGHG

dis-tribution P ShistGHG

( ) is represented by a flat prior, theposterior distribution P(S T ,hist OBSGHG GHG

∣D D D ´N F F, ,GHG GHG 2 CO2

) is then the likelihood dis-tribution normalised to a unit area. Supplementarytable S3 contains the values of parameters used in thetwo different distributions discussed in section 3.3.

3. Results

3.1. Surface air temperature and ocean heat contentinGHG-only simulationsBoth surface air temperature and ocean heat contentcontinually increase in the historical period inresponse to greenhouse gas forcing in historical green-house gas only simulations (figures 1(a), (b)). As aresult, there is an approximately linear relationshipbetween the greenhouse gas attributable temperatureand ocean heat content, shown infigure 1(c).Wemakeuse of this emergent property of the climate system inresponse to greenhouse gases alone later in section 3.4to provide observational constraints on the historicalgreenhouse gas attributable responses. (Note thatmodels with high atmospheric warming do notnecessarily have larger increases in ocean heat content,for the periods considered here.)

3.2. Adjustments to greenhouse gas attributableresponsesTo derive the observationally-constrained greenhousegas attributable surface air temperature and oceanwarming, we performed a detection and attributionanalysis (Methods section 2.1). The resulting scalingfactors (figure 2) were derived separately for thesurface air warming (based on HadCRUT4.5 observa-tions) and ocean warming (based on the Levitus et al2012 dataset, and following the methodology inTokarska et al 2019), as specified in Supplementarytable S4. In the detection and attribution analysis(following Ribes et al 2013 and Tokarska et al 2019),the scaling factors were obtained by regressing the

Figure 2. Scaling factors for surface air temperature (a), and for oceanwarming (b); derived from individual detection and attributionanalyses for the time periods indicated in the title of each panel. The resulting scaling factors are for the anthropogenic-only signal(ANT), natural-only signal (NAT), greenhouse gas only signal (GHG), and other anthropogenic signal (OANT) such as aerosols (seesupplementary table S2 for details). For each pair of scaling factors, the second (right) scaling factor (in the same colour)with longeruncertainty bounds had double noise (i.e. inflated variance by a factor of two to account for additional uncertainties, as in Tokarskaet al 2019). SeeMethods section 2.1 and Supplementary table S2 for details of how the scaling factors were computed in both cases.Note: In the two-signal case for oceanwarming that derives GHGandOANT scaling factors, the natural-only signal (includingvolcanoes)was removed fromobservations by subtracting theNAT annualmean from the observed time-series prior to the detectionand attribution analysis (supplementary table S2).

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Environ. Res. Lett. 15 (2020) 034043

observations onto model response patterns (Methodssection 2.1; supplementary table S2). The scalingfactors and their uncertainty range resulting from theattribution analysis indicate how much the modelledresponse to each forcing needs to and can be adjustedto reconstruct the observations (Methods, section 2.1).

Our results show that for both, surface air warm-ing (in the 1861–2012 period) and ocean warming (inthe 1955–2012 period), the best estimate greenhousegas only response is well constrained and can be sepa-rated from natural and other anthropogenic responsesfor surface temperature (figure 2), and from otheranthropogenic factors for ocean warming, with nat-ural forcing estimated to have only a small influence(see Tokarska et al 2019). The greenhouse gas responseis found to be slightly smaller in the multi-modelmean than in observations, and thus is adjustedslightly downward (bGHG scaling factors less than 1;figure 2), but this adjustment is not significant (errorbars consistent with no adjustment, i.e. scaling factorconsistent with 1; figure 2). Next, we make use of thebGHG scaling factors, applied to the greenhouse gasonly time-series (figure 1), to calculate the observa-tionally-constrained greenhouse gas attributableresponses for the historical period (supplementarytables S2, S3), and the resulting effective climate sensi-tivity S ,histGHG

in section 3.3. Note that figure 2 showsfor comparison also scaling factors for anthropogeniccombined warming which are not used in this study,but they show that the attribution results are robustbetween signal combinations.

3.3. Energy budget approach to the greenhouse gasattributable effective climate sensitivityThe greenhouse gas-attributable responses (figure 1),scaled by the respective bGHG scaling factors to bettermatch the observations (figure 2;Methods section 2.1),allow us to derive a probability distribution for theobservationally-constrained, greenhouse gas attribu-table, effective climate sensitivity S .histGHG

Wemake useof the energy budget equation (equation (2)), using thefollowing two approaches: (1) a direct samplingapproach (Methods, equation (3)), and a ‘forwardmodel’ approach (Methods, equation (4); flat priorin ShistGHG

).We carried on analysis on two different periods:

1862–2012 (Case A) and for 1955–2012 (Case B), withinputs described in supplementary table S3. In thissection, case names with number ‘1’ (i.e. A1, B1) haveregular noise, and case names with number ‘2’ (i.e. A2,B2) have doubled the noise (by doubling the varianceobtained in the control-run simulations) prior todetection and attribution. Such inflating of the noiseresults in wider uncertainty ranges of the scaling fac-tors, and wider overall uncertainty ranges. This factorhas been estimated as approximately correcting for theuncertainty of using the multi-model mean response

instead of fully accounting for climate model responsepattern uncertainty (Schurer et al 2018).

We assume that the scaling factors b ,GHG whichdescribe the strength of the modelled response to for-cing, are constant through time. We calculate the scal-ing factors for surface temperature and ocean heatcontent using the longest period available (as infigure 2). We then apply those scaling factors to thetwo different time periods: 1862–2012 (case A), and1955–2012 (case B). Specifically, the scaling factorbGHG ocean heat content was derived for the period1955–2012 only, as earlier observations are not avail-able, and is applied to ocean heat content changes inclimatemodels across the full analysis period time per-iods in each case (case A that covers 1862–2012 period,and case B that covers 1955–2012 period). Similarly,the scaling factor bGHG for surface air temperature wasderived for the period with longest observational dataavailable (i.e. 1862–2012), and is applied in both casesA andB of the analysis here.

The resulting probability distributions from ran-dom sampling of the observationally-constrainedgreenhouse gas attributable responses (Methods,section 2.2), yield an estimate of the greenhouse gasattributable effective climate sensitivity ShistGHG

( ) forthe period 1862–2012 (case A) that ranges from 1.3 °Cto 3.1 °C (5%–95% interval with the most likely valueat 1.9 °C, and median of 2.0 °C ; figure 3; ‘Box model’case A1) using the direct sampling approach, and from1.3 to 3.1 °C (5%–95% interval with the most likelyvalue at 2.0 °C, and median 2.1 °C; figure 3(a); ‘For-ward model’ case A1). Using the ‘forward model’approach which is based on an explicit flat prior onECS hence shows only small sensitivity to the priorinformation used (supplementary table S4). However,using the a different period 1955–2012 (case B) resultsin higher values of S ,histGHG

with the median 2.8 °C,most likely value 2.6 °C, and the 5%–95% range of1.7 °C–4.6 °C (figure 3(b); case B1 Boxmodel, supple-mentary table S4). The uncertainty bounds are widerin case B, compared to case A, showing that the obser-vational constraint from the shorter period is weaker.Using the longer period also results in better con-strained greenhouse gas attributable warming. Usingdouble-noise in bGHG factors (figure 2), and samplingfrom the resulting inflated Gaussian distributionyields ShistGHG

that also have wider uncertainty bounds(Cases A2, B2, figure 3, supplementary table S3and S4).

Our estimate of ShistGHGis lower than the docu-

mented ECS of some climate models (e.g. CMIP5multi-model mean ECS of 3.22 °C; Forster et al 2013),including that of some used in the analysis (see supple-mentary table S1). However, it is well understood thattime-dependent feedbacks might render ShistGHG

lowerthan S at equilibrium (Knutti et al 2017, Andrews et al2018). Furthermore, different ways of calculating ECSin climate models results in different values, which are

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Figure 3.Probability distributions of the greenhouse gas attributable effective climate sensitivity (ShistGHG), using the direct samplingapproach and the forwardmodel approach. (a)Cases A: for the period 1862–2012; (b) cases B: for the period 1955–2012, with scalingfactors as in panel (a). Light blue and yellow lines (cases A2, B2)were derived in the sameway as the cases A1, B1 but include resultswith double noise (i.e. wider uncertainty in the input parameters due towider uncertainty on bGHG). Bars on the right panel indicatethemost likely andmedian values with the likely (17%–83%) and 5%–95% confidence intervals, for each distribution, as labelled. Fordescription of each case andmore detail, see supplementary tables S3 and S4. The energy budget (equation (2)) has been applied to theperiod 1862–2012 (panel (a)), and 1955–2012 in panel (b). bGHG to scale the ocean heat contentwas derived for the period 1955–2012in both cases, and bGHG to scale temperature derived for the period 1862–2012 in both cases (see section 3.2).

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often lower than the true ECS when using equilibratedsimulations (Rugenstein et al 2019).

Such lower values for ShistGHGthan S at equilibrium

can be explained by the effects of changing strength ofthe feedbacks at higher levels of warming (Knutti et al2017). The climate feedback parameter (defined as 1/Shist) has been shown to vary in the historical period(Gregory and Andrews 2016, Andrews et al 2018), anddepends on both time-variation and the forcing agent.Andrews et al 2018 show that the feedback parameter(1/Shist ) is decreasing, particularly after 1940sonwards (Andrews et al 2018; figure 2(f) therein). Thiswould suggest increase in Shist during that period.Potential changes in feedbacks are neglected if assum-ing that Shist is equal to S (at equilibrium), an assump-tion often made if inferring S using simple climatemodels with constant feedbacks. Our tighter andlower values for ShistGHG

may be affected by this effect,but may alternatively also reflect better constraintswith a longer time horizon, or be affected by uncer-tainties in the early record we can not fully quantify.For example, an uncertainty in the long period is that iteffectively uses extrapolation of the observational con-straint from the second half of the 20th century to thefull analysis period, which may introduce error parti-cularly if some model simulations are affected by driftin the ocean. Also, analysis periods can matter bothdue to effects of internal climate variability and possi-bly residuals from responses by other forcings thatmay have been not fully separated in the attributionanalysis.

The increased greenhouse gas scaling factors, andwith it the increase in estimated effective climate sensi-tivity calculated from the recent period (1955–2012)could reflect feedbacks associated with a rapid increasein greenhouse gas forcing. Gregory et al (2019) alsofind that the effective climate sensitivity is higher sincethe year 1975 when greenhouse gas forcing has rapidlyincreased. Alternative approaches have been also sug-gested to this simple energy balance model(equation (2)) that account for stratospheric adjust-ments, which are related to the changing feedbackparameters (Ceppi andGregory 2019).

3.4.Observational constraints on the climatemodelresponsesIn this section we use the attributed greenhousewarming in atmosphere and ocean to directly evaluatethe model simulated greenhouse gas response. This isto address the problem that time-dependent feedbacksmight render ShistGHG

lower than S at equilibrium, asdiscussed above section 3.3. The analysis presentedhere allows us also to evaluate if the rate of heatentering the ocean instead of warming the atmosphereis correct in models. There could be a trade-offbetween ocean warming and surface warming (forexample, some climate models may be very sensitiveand show too high ECS, yet mix heat rapidly into the

ocean over the historical period, resulting in surfacewarming that resembles observations). In order toevaluate if such a trade-off exists, we plotted thegreenhouse gas attributable surface temperaturechange (i.e. greenhouse gas only multi-model meanscaled by the bGHG scaling factor that results in anobservationally-constrained quantity) against thegreenhouse gas attributable ocean heat content (alsomulti-model mean scaled by the respective bGHG),which serve as an observational constraint. We thencompare these observationally-constrained rangeswith each ensemble member of the historical green-house gas only simulation for the models consideredhere. The observed attributable trend was arrived at byadjusting the multi-model mean from CMIP5 modelsconsidered here (figure 4; black empty diamond) bybGHG factors (for ocean and surface air temperature,respectively, as in figure 2), and is shown as the blackfull diamond. Grey rectangles indicate uncertaintyrange based on bGHG scaling factors given modelinternal variability noise (smaller square), and doublednoise in input parameters (larger square; Methodssection 2.1). For simplicity, we assume no dependencebetween ocean and atmospheric warming estimates(note that as the corners of the rectangles are notpopulated in our examples, this simplification is notimportant here).

If a model’s true forced signal (i.e. its well esti-mated ensemblemean) falls within the grey rectangles,such model’s greenhouse gas response in both oceanand atmosphere is considered to be consistent with theobserved greenhouse gas attributable surface air andocean warming individually. Based on this simpleselection, our results suggest that almost all climatemodels considered here are within the observation-ally-constrained greenhouse gas attributable oceanwarming. Figure 4 also shows that the models spreadin their simulated surface air and ocean warming inresponse to greenhouse gas forcing, but there is noindication of a correlation of points across the twoaxes, suggesting that the independent treatment ofboth constraints here is reasonable, and that there areno models that hide strong sensitivity through stron-ger ocean warming or that show weak warming com-pensated by lack of ocean heat uptake. Of the threemodels with ECS values outside our ShistGHG

values(3.4 °C as the 95th percentile in A2 forward modelcase, figure 3(a); for the longer analysis period1862–2012), indicated in red in figure 4(a) (see supple-mentary table S1 for climate sensitivity values), two areclearly consistent with the observed greenhouse gassignal in atmosphere and ocean in figure 4 (i.e. arewithin the grey rectangle), emphasising the impor-tance of changing feedbacks with time in thesemodels.In the case of one model with climate sensitivityexceeding 4 °C, however, all individual greenhouse gassimulations are outside even the narrower grey rec-tangle, suggesting that this model warms too much insurface temperature to be consistent with the

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Figure 4.Greenhouse gas-only surface temperature change as a function of greenhouse gas-only ocean heat content change. (a) Forthe period 1862–2012, as in case A; (b) for the period 1955–2012, as in case B (see supplementary table S3 for details). The empty blackdiamond indicates themulti-modelmean fromCMIP5models considered here, while the full black diamond indicates the adjustedmulti-model CMIP5mean, scaled by bGHG factors (i.e. observationally-constrained greenhouse gas attributable response for oceanheat content and surface air temperature, respectively, as infigure 2). The grey rectangles indicate the uncertainty range from thoseobservation-constrained scaling factors (figure 2)with regular noise (darker grey rectangle) and double noise (light grey rectangle).Symbols of the same colour indicate individual ensemblemembers of the samemodel. Higher ECSmodels are indicated by red, whilelower ECSmodels are indicated in blue (supplementary table S1). See supplementary tables S3 and S4 for details.

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attributed greenhouse gas warming. Figure 4 illus-trates that the multi-model-ensemble mean inresponse to greenhouse gas forcing is encompassed bythe observationally-constrained rectangles.

3.5. Sources of uncertaintyThe detection and attribution analysis used in thisstudy assumes linear additivity of the forcings, whichhas been shown to be a reasonable assumption bothfor surface warming (Hegerl et al 1997, Tett et al 1999,Gillett et al 2004), and ocean warming (Swart et al2018). Also, since we make use of the multi-modelmean in the inputs for the detection and attribution,our resulting scaling factors may be over-confident(Schurer et al 2018). We have addressed this, at least tosome extent, by doubling the noise due to internalvariability in preindustrial control simulations that areused for the noise estimate (prior to detection andattribution; as in Schurer et al 2018), which resulted inwider uncertainty ranges on the scaling factors(figure 2, see Tokarska et al 2019 for more detail) thattranslate to wider uncertainty ranges in the inputGaussian distributions (supplementary figures S1 andS2). Since fewermodels are used in this analysis than inTokarska et al 2019, the scaling factors bGHG for theocean have larger uncertainty bounds than if usingmoremodels.

Assumptions about the priors are crucial in prob-abilistic estimates of climate sensitivity (Frame et al2005), and our choice of parameters is indicated inSupplementary table S3. For simplicity, in the energybudget equation (equation (3)), we assume that all theheat storage occurs in the ocean (DNGHG component),as the ocean dominates the planetary heat storage(Rhein et al 2013), and is based only on the top 2000mof ocean depths. Taking these two assumptions intoaccount (land heat storage contribution and CO2 co-depended in radiative forcing terms) does not havemuch impact on the resulting ECS likelihood distribu-tion (Sherwood et al in review). Also, we did not sepa-rate the CO2 radiative forcing contributions in the

´F2 CO2and DFGHG components, thereby assuming

that they are independent, though CO2 is a comp-onent of the greenhouse gas forcing radiative for-cingDF .GHG

4.Discussion and conclusions

A simple zero-dimensional energy balance model(equation (2)) provides a straightforward way ofestimating the historical and present-day effectiveclimate sensitivity (Shist) by sampling observed quan-tities, such as surface air warming and ocean heatcontent, within their uncertainty range. By samplinggreenhouse gas attributable observed quantities, weprovide an observational constraint on climate sensi-tivity ShistGHG

as driven by feedbacks over the historicalperiod, which is not subject to uncertainties in the

aerosol forcing. This output distribution of ShistGHGis

only slightly sensitive to using a flat prior in S versusdirectly sampling from the input distributions (i.e.differences between the direct sampling approach‘Box model’ and the ‘Forward model’ approach), andalso widens only slightly if considering larger observa-tional uncertainties (i.e. doubling the noise due tointernal variability prior to detection and attributionanalysis; supplementary figures S1 and S2).

Recently, Tokarska et al (2020) found that therecent historical period can provide an observationalconstraint on simulated warming rates in the future,and that some models with high climate sensitivitiesare not consistent with the observed warming trendsfor the recent decades. The approach presented herefinds only a weak observational constraint, with onlyone model being outside the observationally-con-strained range, and a few models being close to theedge, suggesting that the greenhouse gas observation-ally-constrained response is not presently a strongconstraint for the future, despite suggesting a nar-rower range of ShistGHG

than supported by some mod-els. However, uncertainties considered here aredifferent in this approach, with more explicit con-sideration of uncertainty due to natural forcing anduncertainty in the aerosol forcing, at the cost of aweaker result (i.e. the observationally-constrainedrange here ends up being wider, thus screening-inmore models). Also, the time-period considered hereis different, and ends sooner than those considered byTokarska et al ( 2020).

Our results also suggest that the true ECS is likelyto be higher than the effective climate sensitivity infer-red from historical observations. We emphasise thatdimensions other than global mean temperature riseneed to be taken into account when discussing eitherpast or future climate change. Increases in greenhousegases also lead to changes in other components of theclimate system, such as hydrological cycle and carboncycle changes that may not necessarily scale linearlywith the globalmean temperature rise.

Acknowledgments

KBT and GCH were supported by the UK NERC-funded SMURPHs project (NE/N006143/1). GCHwas further funded by the Wolfson Foundation andthe Royal Society as a Royal Society Wolfson ResearchMerit Award (WM130060) holder. GCH and AS weresupported by the ERC funded project TITAN (EC-320691), and theUKNERCunder the Belmont forum,Grant PacMedy (NE/P006752/1).

We acknowledge the World Climate ResearchProgramme’sWorking Group on CoupledModelling,which is responsible for CMIP, and we thank the cli-mate modelling groups for producing and makingavailable their model output. For CMIP the USDepartment of Energy’s Program for Climate Model

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Diagnosis and Intercomparison provides coordinatingsupport and led development of software infra-structure in partnership with the Global Organizationfor Earth SystemScience Portals.

Data statement

Data used in this study is available from the followingsources:

CMIP model output is available at: http://pcmdi9.llnl.gov/.

Ocean warming data is available at: https://nodc.noaa.gov/OC5/3M_HEAT_CONTENT/.

Blended-masked HadCRUT4 time-series areavailable from the corresponding author uponrequest.

The Regularised Optimal Fingerprinting (ROF)detection and attribution package developed by Aur-élien Ribes is available at https://umr-cnrm.fr/spip.php?article23&lang=fr.

ORCID iDs

Katarzyna BTokarska https://orcid.org/0000-0001-8887-8798Gabriele CHegerl https://orcid.org/0000-0002-4159-1295AndrewP Schurer https://orcid.org/0000-0002-9176-3622

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