Editing IPCC:AR6/WGI/Chapter-7 (section)

== 7.5 Estimates of ECS and TCR ==

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Equilibrium climate sensitivity (ECS) and transient climate response (TCR) are metrics of the global surface air temperature (GSAT) response to forcing, as defined in Box 7.1. ECS is the magnitude of the long-term GSAT increase in response to a doubling of atmospheric CO <sub>2</sub> concentration after the planetary energy budget is balanced, though leaving out feedbacks associated with ice sheets; whereas the TCR is the magnitude of GSAT increase at year 70 when CO <sub>2</sub> concentration is doubled in a 1% yr <sup>–1</sup> increase scenario. Both are idealized quantities, but can be inferred from paleoclimate or observational records or estimated directly using climate simulations, and are strongly correlated with the climate response in realistic future projections (Sections 4.3.4 and 7.5.7; [[#Grose--2018|Grose et al., 2018]] ).

TCR is always smaller than ECS because ocean heat uptake acts to reduce the rate of surface warming. Yet, TCR is related to ECS across CMIP5 and CMIP6 models ( [[#Grose--2018|Grose et al., 2018]] ; [[#Flynn--2020|Flynn and Mauritsen, 2020]] ) as expected since TCR and ECS are inherently measures of climate response to forcing; both depend on effective radiative forcing (ERF) and the net feedback parameter, α . The relationship between TCR and ECS is, however, non-linear and becomes more so for higher ECS values ( [[#Hansen--1985|Hansen et al., 1985]] ; [[#Knutti--2005|Knutti et al., 2005]] ; [[#Millar--2015|Millar et al., 2015]] ; [[#Flynn--2020|Flynn and Mauritsen, 2020]] ; [[#Tsutsui--2020|Tsutsui, 2020]] ) owing to ocean heat uptake processes and surface temperature pattern effects temporarily reducing the rate of surface warming. When α is small in magnitude, and correspondingly ECS is large (recall that ECS is inversely proportional to α ), these temporary effects are increasingly important in reducing the ratio of TCR to ECS.

Before AR6, the assessment of ECS relied on either CO <sub>2</sub> -doubling experiments using global atmospheric models coupled with mixed-layer ocean or standardized CO <sub>2</sub> -quadrupling ( ''abrupt 4xCO2'' ) experiments using fully coupled ocean–atmosphere models or Earth system models (ESMs). The TCR has similarly been diagnosed from ESMs in which the CO <sub>2</sub> concentration is increased at 1% yr <sup>–1</sup> ( ''1pctCO'' 2 , an approximately linear increase in ERF over time) and is in practice estimated as the average over a 20-year period centred at the time of atmospheric CO <sub>2</sub> doubling, that is, year 70. In AR6, the assessments of ECS and TCR are made based on multiple lines of evidence, with ESMs representing only one of several sources of information. The constraints on these climate metrics are based on radiative forcing and climate feedbacks assessed from process understanding ( [[#7.5.1|Section 7.5.1]] ), climate change and variability seen within the instrumental record ( [[#7.5.2|Section 7.5.2]] ), paleoclimate evidence ( [[#7.5.3|Section 7.5.3]] ), emergent constraints ( [[#7.5.4|Section 7.5.4]] ), and a synthesis of all lines of evidence ( [[#7.5.5|Section 7.5.5]] ). In AR5, these lines of evidence were not explicitly combined in the assessment of climate sensitivity, but as demonstrated by [[#Sherwood--2020|Sherwood et al. (2020)]] their combination narrows the uncertainty ranges of ECS compared to that assessed in AR5. ECS values found in CMIP6 models, some of which exhibit values higher than 5°C ( [[#Meehl--2020|Meehl et al., 2020]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ), are discussed in relation to the AR6 assessment in section 7.5.6.

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=== 7.5.1 Estimates of ECS and TCR Based on Process Understanding ===

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This section assesses the estimates of ECS and TCR based on process understanding of the ERF due to a doubling of CO <sub>2</sub> concentration and the net climate feedback (Sections 7.3.2 and 7.4.2). This process-based assessment is made in [[#7.5.1.1|Section 7.5.1.1]] and applied to TCR in [[#7.5.1.2|Section 7.5.1.2]] .

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==== 7.5.1.1 ECS Estimated Using Process-based Assessments of Forcing and Feedbacks ====

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The process-based assessment is based on the global energy budget equation (Box 7.1, Equation 7.1), where the ERF (Δ ''F'' ) is set equal to the effective radiative forcing due to a doubling of CO <sub>2</sub> concentration (denoted as Δ ''F'' 2×CO2 ) and the climate state reaches a new equilibrium, that is, Earth’s energy imbalance averages to zero (Δ ''N'' = 0). ECS is calculated as the ratio between the ERF and the net feedback parameter: ECS = –Δ ''F'' 2×CO 2 / α . Estimates of Δ ''F'' 2×CO2 and α are obtained separately based on understanding of the key processes that determine each of these quantities. Specifically, Δ ''F'' 2×CO2 is estimated based on instantaneous radiative forcing that can be accurately obtained using line-by-line calculations, to which uncertainty due to adjustments are added ( [[#7.3.2|Section 7.3.2]] ). The range of α is derived by aggregating estimates of individual climate feedbacks based not only on ESMs but also on theory, observations, and high-resolution process modelling ( [[#7.4.2|Section 7.4.2]] ).

The effective radiative forcing of CO <sub>2</sub> doubling is assessed to be Δ ''F'' 2×CO2 = 3.93 ± 0.47 W m <sup>–2</sup> [[#7.3.2.1|Section 7.3.2.1]] ), while the net feedback parameter is assessed to be α = –1.16 ± 0.40 W m <sup>–2</sup> °C <sup>–1</sup> (Table 7.10), where the ranges indicate one standard deviation. These values are slightly different from those directly calculated from ESMs because more information is used to assess them, as explained above. Assuming Δ ''F'' 2×CO2 and α each follow an independent normal distribution, the uncertainty range of ECS can be obtained by substituting the respective probability density function into the expression of ECS (red curved bar in Figure 7.16). Since α is in the denominator, the normal distribution leads to a long tail in ECS towards high values, indicating the large effect of uncertainty in α in estimating the likelihood of a high ECS ( [[#Roe--2007|Roe and Baker, 2007]] ; [[#Knutti--2008|Knutti and Hegerl, 2008]] ).

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[[File:34ef9e3395525c41fd73cb7b95b4eb98 IPCC_AR6_WGI_Figure_7_16.png]]

'''Figure 7.16''' '''|''' '''Probability distributions of ERF to CO''' <sub>2</sub> '''doubling''' ( '''Δ''' ''F'' 2×CO2 ''';''' '''top) and the net climate feedback''' ( α ''';''' '''right), derived from process-based assessments in Sections 7.3.2 and 7.4.2.''' Central panel shows the joint probability density function calculated on a two-dimensional plane of ''Δ'' ''F'' 2×CO2 and ''α'' (red), on which the 90% range shown by an ellipse is imposed to the background theoretical values of ECS (colour shading). The white dot, and thick and thin curves inside the ellipse represent the mean, ''likely'' and ''very likely'' ranges of ECS. An alternative estimation of the ECS range (pink) is calculated by assuming that Δ ''F'' 2×CO2 and ''α'' have a covariance. The assumption about the co-dependence between Δ ''F'' 2×CO2 and ''α'' does not alter the mean estimate of ECS but affects its uncertainty. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

The wide range of the process-based ECS estimate is not due solely to uncertainty in the estimates of Δ ''F'' 2×CO2 and α , but is partly explained by the assumption that Δ ''F'' 2×CO2 and α are independent in this approach. In CMIP5 and CMIP6 ensembles, Δ ''F'' 2×CO2 and α are negatively correlated when they are calculated using linear regression in ''abrupt 4xCO2'' simulations ( ''r'' <sup>2</sup> = 0.34; [[#Andrews--2012|Andrews et al., 2012]] ; [[#Webb--2013|Webb et al., 2013]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ). The negative correlation leads to compensation between the inter-model spreads of these quantities, thereby reducing the ECS range estimated directly from the models. If the process-based ECS distribution is reconstructed from probability distributions of Δ ''F'' 2×CO2 and α assuming that they are correlated as in CMIP model ensembles, the range of ECS will be narrower by 14% (pink curved bar in Figure 7.16). If, however, the covariance between Δ ''F'' 2×CO2 and α is not adopted, there is no change in the mean, but the wide range still applies.

A significant correlation between Δ ''F'' 2×CO2 and α also occurs when the two parameters are estimated separately from atmospheric ESM fixed-SST experiments ( [[#7.3.1|Section 7.3.1]] ) or fixed CO <sub>2</sub> concentration experiments ( [[#7.4.1|Section 7.4.1]] ; [[#Ringer--2014|Ringer et al., 2014]] ; [[#Chung--2018|Chung and Soden, 2018]] ). Hence the relationship is not expected to be an artefact of calculating the parameters using linear regression in ''abrupt 4xCO2'' simulations. A possible physical cause of the correlation may be a compensation between the cloud adjustment and the cloud feedback over the tropical ocean ( [[#Ringer--2014|Ringer et al., 2014]] ; [[#Chung--2018|Chung and Soden, 2018]] ). It has been shown that the change in the hydrological cycle is a controlling factor for the low-cloud adjustment ( [[#Dinh--2019|Dinh and]] [[#Fueglistaler--2019|Fueglistaler, 2019]] ) and for the low-cloud feedback ( [[#Watanabe--2018|Watanabe et al., 2018]] ), and therefore the responses of these clouds to the direct CO <sub>2</sub> radiative forcing and to the surface warming may not be independent. However, robust physical mechanisms are not yet established, and furthermore, the process-based assessment of the tropical low-cloud feedback is only indirectly based on ESMs given that physical processes which control the low-clouds are not sufficiently well-simulated in models ( [[#7.4.2.4|Section 7.4.2.4]] ). For these reasons, the co-dependency between Δ ''F'' 2×CO2 and α is assessed to have ''low confidence'' and, therefore, the more conservative assumption that they are independent for the process-based assessment of ECS is retained.

In summary, the ECS based on the assessed values of Δ ''F'' 2×CO2 and α is assessed to have a median value of 3.4°C with a ''likely'' range of 2.5 to 5.1 °C and ''very likely'' range of 2.1 to 7.7 °C. To this assessed range of ECS, the contribution of uncertainty in α is approximately three times as large as the contribution of uncertainty in Δ ''F'' 2×CO2 .

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==== 7.5.1.2 Emulating Process-based ECS to TCR ====

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ECS estimated using the ERF due to a doubling of CO <sub>2</sub> concentration and the net feedback parameter (ECS = –Δ ''F'' 2×CO 2 / α ) can be translated into the TCR so that both climate sensitivity metrics provide consistent information about the climate response to forcing. Here a two-layer energy budget emulator is used to transfer the process-based assessment of forcing, feedback, efficacy and heat uptake to TCR (Supplementary Material 7.SM.2.1 and Cross-Chapter Box 7.1). The emulator can reproduce the transient surface temperature evolution in ESMs under ''1pctCO'' 2 simulations and other climate change scenarios, despite the very low number of degrees of freedom ( [[#Held--2010|Held et al., 2010]] ; [[#Geoffroy--2012|Geoffroy et al., 2012]] , 2013a; [[#Palmer--2018|Palmer et al., 2018]] ). Using this model with parameters given from assessments in Sections 7.2, 7.3, and 7.4, TCR is assessed based on the process-based understanding.

In the two-layer energy balance emulator, additional parameters are introduced: heat capacities of the upper and deep ocean, heat uptake efficiency ( γ ), and the so-called efficacy parameter ( ε ) that represents the dependence of radiative feedbacks and heat uptake on the evolving SST pattern under CO <sub>2</sub> forcing alone ( [[#7.4.4|Section 7.4.4]] ). In the real world, natural internal variability and aerosol radiative forcing also affect the efficacy parameter, but these effects are excluded for the current discussion.

The analytical solution of the energy balance emulator reveals that the global surface temperature change to abrupt increase of the atmospheric CO <sub>2</sub> concentration is expressed by a combination of a fast adjustment of the surface components of the climate system and a slow response of the deep ocean, with time scales of several years and several centuries, respectively (grey curve in Figure 7.17b). The equilibrium response of upper ocean temperature, approximating SST and the surface air temperature response, depends, by definition, only on the radiative forcing and the net feedback parameter. Uncertainty in α dominates (80–90%) the corresponding uncertainty range for ECS in CMIP5 models ( [[#Vial--2013|Vial et al., 2013]] ), and also an increase of ECS in CMIP6 models ( [[#7.5.5|Section 7.5.5]] ) is attributed by about 60–80% to a change in α ( [[#Zelinka--2020|Zelinka et al., 2020]] ). For the range of TCR, the contribution from uncertainty in α is reduced to 50–60% while uncertainty in Δ ''F'' 2×CO 2 becomes relatively more important ( [[#Geoffroy--2012|Geoffroy et al., 2012]] ; [[#Lutsko--2019|Lutsko and Popp, 2019]] ). TCR reflects the fast response occurring approximately during the first 20 years in the ''abrupt 4xCO2'' simulation ( [[#Held--2010|Held et al., 2010]] ), but the fast response is not independent of the slow response because there is a non-linear co-dependence between them ( [[#Andrews--2015|Andrews et al., 2015]] ). The non-linear relationship between ECS and TCR indicates that the probability of high TCR is not very sensitive to changes in the probability of high ECS ( [[#Meehl--2020|Meehl et al., 2020]] ).

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[[File:3cb90a4fd38c4fcd385d88e6c1ff05a1 IPCC_AR6_WGI_Figure_7_17.png]]

'''Figure 7.17''' '''|''' '''(a) Time evolution of the effective radiative forcing (ERF) to the CO''' <sub>2</sub> '''concentration increased by 1% per year until year 70 (equal to the time of doubling) and kept fixed afterwards (white line).''' The ''likely'' and ''very likely'' ranges of ERF indicated by light and dark orange have been assessed in ( [[#7.3.2.1|Section 7.3.2.1]] . '''(b)''' Surface temperature response to the CO <sub>2</sub> forcing calculated using the emulator with a given value of ECS, considering uncertainty in Δ F 2×CO2 , ''α'' , and κ associated with the ocean heat uptake and efficacy (white line). The ''likely'' and ''very likely'' ranges are indicated by cyan and blue, respectively. For comparison, the temperature response to abrupt doubling of the CO <sub>2</sub> concentration is displayed by a grey curve. The mean, ''likely'' and ''very likely'' ranges of ECS and TCR are shown at the right (the values of TCR also presented in the panel). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

Considering an idealized time evolution of ERF (1% increase per year until CO <sub>2</sub> doubling and held fixed afterwards, see Figure 7.17a), the TCR defined by the surface temperature response at year 70 is derived by substituting the process-based ECS into the analytical solution of the emulator (Figure 7.17b, see also Supplementary Material 7.SM.2.1). When additional parameters in the emulator are prescribed by using CMIP6 multi-model mean values of those estimates ( [[#Smith--2020b|Smith et al., 2020b]] ), this calculation translates the range of ECS in ( [[#7.5.2.1|Section 7.5.2.1]] to the range of TCR. The transient temperature response, in reality, varies with different estimates of the ocean heat uptake efficiency ( γ ) and efficacy ( ε ). When the emulator was calibrated to the transient responses in CMIP5 models, it shows that uncertainty in heat capacities is negligible and differences in γ and ε explain 10–20% of the inter-model spread of TCR among GCMs ( [[#Geoffroy--2012|Geoffroy et al., 2012]] ). Specifically, their product, κ = γε , appearing in a simplified form of the solution, that is, TCR ≅ –Δ ''F'' 2×CO 2 /( α – κ ), gives a single parameter quantifying the damping effects of heat uptake ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ). This parameter is positive and acts to slow down the temperature response in a similar manner to the ‘pattern effect’ (Sections 7.4.4.3 and 7.5.2.1). The ocean heat uptake in nature is controlled by multiple processes associated with advection and mixing ( [[#Exarchou--2014|Exarchou et al., 2014]] ; [[#Kostov--2014|Kostov et al., 2014]] ; [[#Kuhlbrodt--2015|Kuhlbrodt et al., 2015]] ) but is simplified to be represented by a single term of heat exchange between the upper and deep ocean in the emulator. Therefore, it is challenging to constrain γ and ε from process-based understanding ( [[#7.5.2|Section 7.5.2]] ). Because the estimated values are only weakly correlated across models, the mean value and one standard deviation of κ are calculated as κ = 0.84 ± 0.38 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation) by ignoring their covariance (the mean value is very similar to that used for Box 4.1, Figure 1; see Supplementary Material 7.SM.2.1). By incorporating this inter-model spread in κ , the range of TCR is widened by about 10% (blue bar in Figure 7.17b). Yet, the dominant contribution to the uncertainty range of TCR arises from the net feedback parameter α, consistent with analyses of CMIP6 models ( [[#Williams--2020|Williams et al., 2020]] ), and this assessment remains unchanged from AR5 stating that uncertainty in ocean heat uptake is of secondary importance.

In summary, the process-based estimate of TCR is assessed to have the central value of 2.0°C with the ''likely'' range from 1.6 to 2.7 °C and the ''very likely'' range from 1.3 to 3.1 °C ( ''high confidence'' ). The upper bound of the assessed range was slightly reduced from AR5 but can be further constrained using multiple lines of evidence ( [[#7.5.5|Section 7.5.5]] ).

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=== 7.5.2 Estimates of ECS and TCR Based on the Instrumental Record ===

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This section assesses the estimates of ECS and TCR based on the instrumental record of climate change and variability with an emphasis on new evidence since AR5. Several lines of evidence are assessed including the global energy budget ( [[#7.5.2.1|Section 7.5.2.1]] ), the use of simple climate models evaluated against the historical temperature record ( [[#7.5.2.2|Section 7.5.2.2]] ), and internal variability in global temperature and TOA radiation ( [[#7.5.2.3|Section 7.5.2.3]] ). [[#7.5.2.4|Section 7.5.2.4]] provides an overall assessment of TCR and ECS based on these lines of evidence from the instrumental record.

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==== 7.5.2.1 Estimates of ECS and TCR Based on the Global Energy Budget ====

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The GSAT change from 1850–1900 to 2006–2019 is estimated to be 1.03 [0.86 to 1.18] °C (Cross-chapter Box 2.3). Together with estimates of Earth’s energy imbalance ( [[#7.2.2|Section 7.2.2]] ) and the global ERF that has driven the observed warming ( [[#7.3|Section 7.3]] ), the instrumental temperature record enables global energy budget estimates of ECS and TCR. While energy budget estimates use instrumental data, they are not based purely on observations. A conceptual model typically based on the global mean forcing and response energy budget framework (Box 7.1) is needed to relate ECS and TCR to the estimates of global warming, ERF and Earth’s energy imbalance ( [[#Forster--2016|Forster, 2016]] ; [[#Knutti--2017|Knutti et al., 2017]] ). Moreover, ESM simulations partly inform estimates of the historical ERf ( [[#7.3|Section 7.3]] ) as well as Earth’s energy imbalance in the 1850–1900 climate (the period against which changes are measured; [[#Forster--2016|Forster, 2016]] ; [[#Lewis--2018|Lewis and Curry, 2018]] ). ESMs are also used to estimate uncertainty due the internal climate variability that may have contributed to observed changes in temperature and energy imbalance (e.g., [[#Palmer--2014|Palmer and McNeall, 2014]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ). Research since AR5 has shown that global energy budget estimates of ECS may be biased low when they do not take into account how radiative feedbacks depend on the spatial pattern of surface warming ( [[#7.4.4.3|Section 7.4.4.3]] ) or when they do not incorporate improvements in the estimation of global surface temperature trends which take better account of data-sparse regions and are more consistent in their treatment of surface temperature data ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ). Together with updated estimates of global ERF and Earth’s energy imbalance, these advances since AR5 have helped to reconcile energy budget estimates of ECS with estimates of ECS from other lines of evidence.

The traditional global mean forcing and response energy budget framework ( [[#7.4.1|Section 7.4.1]] and Box 7.1; [[#Gregory--2002|Gregory et al., 2002]] ) relates the difference between the ERF (Δ ''F'' ) and the radiative response to observed global warming ( α Δ ''T'' ) to the Earth’s energy imbalance (Δ ''N'' ): Δ ''N'' = α Δ ''T'' + Δ ''F'' . Given the relationship ECS = –Δ ''F'' 2×CO 2 / α , where Δ ''F'' 2×CO2 is the ERF from CO <sub>2</sub> doubling, ECS can be estimated from historical estimates of Δ ''T'' , Δ ''F'' , Δ ''N'' and Δ ''F'' 2×CO2 : ECS = Δ ''F'' 2×CO2 Δ ''T'' /(Δ ''F'' – Δ ''N'' ). Since TCR is defined as the temperature change at the time of CO <sub>2</sub> doubling under an idealized 1% yr <sup>–1</sup> CO <sub>2</sub> increase, it can be inferred from the historical record as: TCR = Δ ''F'' 2×CO2 <sub></sub> Δ ''T/'' Δ ''F'' , under the assumption that radiative forcing increases quickly compared to the adjustment time scales of the deep ocean, but slowly enough and over a sufficiently long time that the upper ocean is adjusted, so that Δ ''T'' and Δ ''N'' increases approximately in proportion to Δ ''F'' . Because Δ ''N'' is positive, TCR is always smaller than ECS, reflecting weaker transient warming than equilibrium warming. TCR is better constrained than ECS owing to the fact that the denominator of TCR, without the quantity Δ ''N'' , is more certain and further from zero than is the denominator of ECS. The upper bounds of both TCR and ECS estimated from historical warming are inherently less certain than their lower bounds because Δ ''F'' is uncertain and in the denominator.

The traditional energy budget framework lacks a representation of how radiative feedbacks depend on the spatial pattern of warming. Thus, studies employing this framework ( [[#Otto--2013|Otto et al., 2013]] ; [[#Lewis--2015|Lewis and Curry, 2015]] , 2018; [[#Forster--2016|Forster, 2016]] ) implicitly assume that the net radiative feedback has a constant magnitude, producing an estimate of the effective ECS (defined as the value of ECS that would occur if α does not change from its current value) rather than of the true ECS. As summarized in ( [[#7.4.4.3|Section 7.4.4.3]] , there are now multiple lines of evidence providing ''high confidence'' that the net radiative feedback will become less negative as the warming pattern evolves in the future (the pattern effect). This arises because historical warming has been relatively larger in key negative feedback regions (e.g., western tropical Pacific Ocean) and relatively smaller in key positive feedback regions (e.g., eastern tropical Pacific Ocean and Southern Ocean) than is projected in the near-equilibrium response to CO <sub>2</sub> forcing ( [[#7.4.4.3|Section 7.4.4.3]] ; [[#Held--2010|Held et al., 2010]] ; [[#Proistosescu--2017|Proistosescu and Huybers, 2017]] ; [[#Dong--2019|Dong et al., 2019]] ), implying that the true ECS will be larger than the effective ECS inferred from historical warming. This section first assesses energy budget constraints on TCR and the effective ECS based on updated estimates of historical warming, ERF, and Earth’s energy imbalance. It then assesses what these energy budget constraints imply for values of ECS once the pattern effect is accounted for.

Energy budget estimates of TCR and ECS have evolved in the literature over recent decades. Prior to AR4, the global energy budget provided relatively weak constraints, primarily due to large uncertainty in the tropospheric aerosol forcing, giving ranges of the effective ECS that typically included values above 10°C ( [[#Forster--2016|Forster, 2016]] ; [[#Knutti--2017|Knutti et al., 2017]] ). Revised estimates of aerosol forcing together with a larger greenhouse gas forcing by the time of AR5 led to an estimate of Δ ''F'' that was more positive and with reduced uncertainty relative to AR4. Using energy budget estimates and radiative forcing estimates updated to 2009, [[#Otto--2013|Otto et al. (2013)]] estimated that TCR was 1.3 [0.9 to 2.0] °C, and that the effective ECS was 2.0 [1.2 to 3.9] °C. This AR5-based energy budget estimate of ECS was lower than estimates based on other lines of evidence, leading AR5 to expand the assessed ''likely'' range of ECS to include lower values relative to AR4. Studies since AR5 using similar global energy budget methods have produced similar or slightly narrower ranges for TCR and effective ECS ( [[#Forster--2016|Forster, 2016]] ; [[#Knutti--2017|Knutti et al., 2017]] ).

Energy budget estimates of TCR and ECS assessed here are based on improved observations and understanding of global surface temperature trends extended to the year 2020 [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ), revised estimates of Earth’s energy imbalance ( [[#7.2|Section 7.2]] ), and revised estimates of ERf ( [[#7.3|Section 7.3]] ). Accurate, in situ-based estimates of Earth’s energy imbalance can be made from around 2006 based on near-global ocean temperature observations from the ARGO array of autonomous profiling floats (Sections 2.3 and 7.2). Over the period 2006–2018 the Earth’s energy imbalance is estimated to be 0.79 ± 0.27 W m <sup>–2</sup> [[#7.2|Section 7.2]] ) and it is assumed that this value is also representative for the period 2006–2019. Anomalies are taken with respect to the baseline period 1850–1900, although other baselines could be chosen to avoid major volcanic activity ( [[#Otto--2013|Otto et al., 2013]] ; [[#Lewis--2018|Lewis and Curry, 2018]] ). Several lines of evidence, including ESM simulations ( [[#Lewis--2015|Lewis and Curry, 2015]] ), energy balance modelling ( [[#Armour--2017|Armour, 2017]] ), inferred ocean warming given observed SSTs using ocean models ( [[#Gebbie--2019|Gebbie and Huybers, 2019]] ; [[#Zanna--2019|Zanna et al., 2019]] ), and ocean warming reconstructed from noble gas thermometry ( [[#Baggenstos--2019|Baggenstos et al., 2019]] ) suggest a 1850–1900 Earth energy imbalance of 0.2 ± 0.2 W m <sup>–2</sup> . Combined with estimates of internal variability in Earth’s energy imbalance, calculated using periods of equivalent lengths of years as used in unforced ESM simulations ( [[#Palmer--2014|Palmer and McNeall, 2014]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ), the anomalous energy imbalance between 1850–1900 and 2006–2019 is estimated to be Δ ''N'' = 0.59 ± 0.35 W m <sup>–2</sup> . GSAT change between 1850–1900 and 2006–2019 is estimated to be Δ ''T'' = 1.03°C ± 0.20 °C (Cross-Chapter Box 2.3 and Box 7.2) after accounting for internal temperature variability derived from unforced ESM simulations ( [[#Sherwood--2020|Sherwood et al., 2020]] ). The ERF change between 1850–1900 and 2006–2019 is estimated to be Δ ''F'' = 2.20 [1.53 to 2.91] W m <sup>–2</sup> [[#7.3.5|Section 7.3.5]] ) and the ERF for a doubling of CO <sub>2</sub> is estimated to be Δ ''F'' 2×CO2 = 3.93 ± 0.47 W m <sup>–2</sup> [[#7.3.2|Section 7.3.2]] ). Employing these values within the traditional global energy balance framework described above (following the methods of [[#Otto--2013|Otto et al. (2013)]] and accounting for correlated uncertainties between Δ ''F'' and Δ ''F'' 2×CO2 ) produces a TCR of 1.9 [1.3 to 2.7] °C and an effective ECS of 2.5 [1.6 to 4.8] °C. These TCR and effective ECS values are higher than those in the recent literature ( [[#Otto--2013|Otto et al., 2013]] ; [[#Lewis--2015|Lewis and Curry, 2015]] , 2018) but are comparable to those of [[#Sherwood--2020|Sherwood et al. (2020)]] who also used updated estimates of observed warming, Earth’s energy imbalance, and ERF.

The trend estimation method applied to global surface temperature affects derived values of ECS and TCR from the historical record. In this Report, the effective ECS is inferred from estimates that use global coverage of GSAT to estimate the surface temperature trends. The GSAT trend is assessed to have the same best estimate as the observed global mean surface temperature (GMST), although the GSAT trend is assessed to have larger uncertainty (see Cross-Chapter Box 2.3). Many previous studies have relied on HadCRUT4 GMST estimates that used the blended observations and did not interpolate over regions of incomplete observational coverage such as the Arctic. As a result, the ECS and TCR derived from these studies has smaller ECS and TCR values than those derived from model-inferred estimates (M. [[#Richardson--2016|Richardson et al., 2016]] , 2018). The energy budget studies assessing ECS in AR5 employed HadCRUT4 or similar measures of GMST trends. As other lines of evidence in that report used GSAT trends, this could partly explain why AR5-based energy budget estimates of ECS were lower than those estimated from other lines of evidence, adding to the overall disparity in M. [[#Collins--2013|]] [[#Collins--2013|Collins et al. (2013)]] . In this report, GSAT is chosen as the standard measure of global surface temperature to aid comparison with previous model- and process-based estimates of ECS, TCR and climate feedbacks (see Cross-Chapter Box 2.3).

The traditional energy budget framework has been evaluated within ESM simulations by comparing the effective ECS estimated under historical forcing with the ECS estimated using regression methods (Box 7.1) under ''abrupt 4xCO2'' ( [[#Andrews--2019|Andrews et al., 2019]] ; [[#Winton--2020|Winton et al., 2020]] ). For one CMIP6 model (GFDL-CM4.0), the value of effective ECS derived from historical energy budget constraints is 1.8°C while ECS is estimated to be 5.0°C ( [[#Winton--2020|Winton et al., 2020]] ). For another model (HadGEM3-GC3.1-LL) the effective ECS derived from historical energy budget constraints is 4.1°C (average of four ensemble members) while ECS is estimated to be 5.5°C ( [[#Andrews--2019|Andrews et al., 2019]] ). These modelling results suggest that the effective ECS under historical forcing could be lower than the true ECS owing to differences in radiative feedbacks induced by the distinct patterns of historical and equilibrium warming ( [[#7.4.4.3|Section 7.4.4.3]] ). Using GFDL-CM4, [[#Winton--2020|Winton et al. (2020)]] also find that the value of TCR estimated from energy budget constraints within a historical simulation (1.3°C) is substantially lower than the true value of TCR (2.1°C) diagnosed within a ''1pctCO'' 2 simulation owing to a combination of the pattern effect and differences in the efficiency of ocean heat uptake between historical and ''1pctCO'' 2 forcing ''.'' This section next considers how the true ECS can be estimated from the historical energy budget by accounting for the pattern effect. However, owing to '''limited evidence''' this section does not attempt to account for these effects in estimates of TCR.

Research since AR5 has introduced extensions to the traditional energy budget framework that account for the feedback dependence on temperature patterns by allowing for multiple radiative feedbacks operating on different time scales ( [[#Armour--2013|Armour et al., 2013]] ; [[#Geoffroy--2013a|Geoffroy et al., 2013a]] ; [[#Armour--2017|Armour, 2017]] ; [[#Proistosescu--2017|Proistosescu and Huybers, 2017]] ; [[#Goodwin--2018|Goodwin, 2018]] ; [[#Rohrschneider--2019|Rohrschneider et al., 2019]] ), by allowing feedbacks to vary with the spatial pattern or magnitude of ocean heat uptake ( [[#Winton--2010|Winton et al., 2010]] ; [[#Rose--2014|Rose et al., 2014]] ; [[#Rugenstein--2016a|Rugenstein et al., 2016a]] ), or by allowing feedbacks to vary with the type of radiative forcing agent ( [[#Kummer--2014|Kummer and Dessler, 2014]] ; [[#Shindell--2014|Shindell, 2014]] ; [[#Marvel--2016|Marvel et al., 2016]] ; [[#Winton--2020|Winton et al., 2020]] ). A direct way to account for the pattern effect is to use the relationship ECS = –Δ ''F'' 2×CO2 /( α + α ''’'' ), where α = (Δ ''N'' – Δ ''F'' )/Δ ''T'' is the effective feedback parameter (Box 7.1) estimated from historical global energy budget changes and α ''’'' represents the change in the feedback parameter between the historical period and the equilibrium response to CO <sub>2</sub> forcing, which can be estimated using ESMs ( [[#7.4.4.3|Section 7.4.4.3]] ; [[#Armour--2017|Armour, 2017]] ; [[#Andrews--2018|Andrews et al., 2018]] , 2019; [[#Lewis--2018|Lewis and Curry, 2018]] ; [[#Dong--2020|Dong et al., 2020]] ; [[#Winton--2020|Winton et al., 2020]] ).

The net radiative feedback change between the historical warming pattern and the projected equilibrium warming pattern in response to CO <sub>2</sub> forcing ( α ''’'' ) is estimated to be in the range 0.0 to 1.0 W m <sup>–2</sup> °C <sup>–1</sup> (Figure 7.15). Using the value α ''’'' = +0.5 ± 0.5 W m <sup>–2</sup> °C <sup>–1</sup> to represent this range illustrates the effect of changing radiative feedbacks on estimates of ECS. While the effective ECS inferred from historical warming is 2.5 [1.6 to 4.8] °C, ECS = –Δ ''F'' 2×CO 2 /( α + α ''’'' ) is 3.5 [1.7 to 13.8] °C. For comparison, values of α ''’'' derived from the response to historical and idealized CO <sub>2</sub> forcing within coupled climate models ( [[#Armour--2017|Armour, 2017]] ; [[#Lewis--2018|Lewis and Curry, 2018]] ; [[#Andrews--2019|Andrews et al., 2019]] ; [[#Dong--2020|Dong et al., 2020]] ; [[#Winton--2020|Winton et al., 2020]] ) can be approximated as α ''’'' = +0.1 ± 0.3 W m <sup>–2</sup> °C <sup>–1</sup> [[#7.4.4.3|Section 7.4.4.3]] ), corresponding to a value of ECS of 2.7 [1.7 to 5.9] °C. In both cases, the low end of the ECS range is similar to that of the effective ECS inferred using the traditional energy balance model framework that assumes α ''’'' = 0, reflecting a weak dependence on the value of α ''’'' when ECS is small ( [[#Armour--2017|Armour, 2017]] ; [[#Andrews--2018|Andrews et al., 2018]] ); the low end of the ECS range is robust even in the hypothetical case that α ''’'' is slightly negative. However, the high end of the ECS range is substantially larger than that of the effective ECS and strongly dependent on the value of α ''’'' .

The values of ECS obtained from the techniques outlined above are all higher than those estimated from both AR5 and recently published estimates (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; [[#Otto--2013|Otto et al., 2013]] ; [[#Lewis--2015|Lewis and Curry, 2015]] , 2018; [[#Forster--2016|Forster, 2016]] ). Four revisions made in this Report are responsible for this increase: (i) an upwards revision of historic global surface temperature trends from newly published trend estimates ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ); (ii) an 8% increase in the ERF for Δ ''F'' 2×CO2 [[#7.3.2|Section 7.3.2]] ); (iii) a more negative central estimate of aerosol ERF, which acts to reduce estimates of historical ERF trends; and (iv) accounting for the pattern effect in ECS estimates. Values of ECS provided here are similar to those based on the historical energy budget found in [[#Sherwood--2020|Sherwood et al. (2020)]] , with small differences owing to methodological differences and the use of different estimates of observed warming, Earth’s energy imbalance, and ERF.

Overall, there is ''high confidence'' that the true ECS is higher than the effective ECS as inferred from the historical global energy budget, but there is substantial uncertainty in how much higher because of ''limited evidence'' regarding how radiative feedbacks may change in the future. While several lines of evidence indicate that α ''’'' &gt; 0, the quantitative accuracy of feedback changes is not known at this time ( [[#7.4.4.3|Section 7.4.4.3]] ). Global energy budget constraints thus provide ''high confidence'' in the lower bound of ECS which is not sensitive to the value of α ''’'' : ECS is ''extremely unlikely'' to be less than 1.6°C. Estimates of α ''’'' that are informed by idealized CO <sub>2</sub> forcing simulations of coupled ESMs ( [[#Armour--2017|Armour, 2017]] ; [[#Lewis--2018|Lewis and Curry, 2018]] ; [[#Andrews--2019|Andrews et al., 2019]] ; [[#Dong--2020|Dong et al., 2020]] ; [[#Winton--2020|Winton et al., 2020]] ) indicate a median value of ECS of around 2.7°C while estimates of α ''’'' that are informed by observed historical sea surface temperature patterns ( [[#Andrews--2018|Andrews et al., 2018]] ) indicate a median value of ECS of around 3.5°C. Owing to large uncertainties in future feedback changes, the historical energy budget currently provides little information about the upper end of the ECS range.

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==== 7.5.2.2 Estimates of ECS and TCR Based on Climate Model Emulators ====

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Energy budget emulators are far less complex than comprehensive ESMs ( [[IPCC:Wg1:Chapter:Chapter-1#1.5.3|Section 1.5.3]] and Cross-Chapter Box 7.1). For example, an emulator could represent the atmosphere, ocean, and land using a small number of connected boxes (e.g., [[#Goodwin--2016|Goodwin, 2016]] ), or it could represent the global mean climate using two connected ocean layers (e.g., Cross-Chapter Box 7.1 and Supplementary Material 7.SM.2). The numerical efficiency of emulators means that they can be empirically constrained by observations: a large number of possible parameter values (e.g., feedback parameter, aerosol radiative forcing, and ocean diffusivity) are randomly drawn from prior distributions; forward integrations of the model are performed with these parameters and weighted against observations of surface or ocean warming, producing posterior estimates of quantities of interest such as TCR, ECS and aerosol forcing ( [[#7.3|Section 7.3]] ). Owing to their reduced complexity, emulators lack full representations of the spatial patterns of sea surface temperature and radiative responses to changes in those patterns (discussed in ( [[#7.4.4.3|Section 7.4.4.3]] ) and many represent the net feedback parameter using a constant value. The ranges of ECS reported by studies using emulators are thus interpreted here as representative of the effective ECS over the historical record rather than of the true ECS.

Improved estimates of ocean heat uptake over the past two decades ( [[#7.2|Section 7.2]] ) have diminished the role of ocean diffusivity in driving uncertainty in ECS estimates, leaving the main trade-off between posterior ranges in ECS and aerosol radiative forcing ( [[#Forest--2002|Forest, 2002]] ; [[#Knutti--2002|Knutti et al., 2002]] ; [[#Frame--2005|Frame et al., 2005]] ). The AR5 ( [[#Bindoff--2013|Bindoff et al., 2013]] ) assessed a variety of estimates of ECS based on emulators and found that they were sensitive to the choice of prior parameter distributions and temperature datasets used, particularly for the upper end of the ECS range, though priors can be chosen to minimize the effect on results (e.g., [[#Lewis--2013|Lewis, 2013]] ). Emulators generally produced estimates of effective ECS between 1°C and 5°C and ranges of TCR between 0.9°C and 2.6°C. [[#Padilla--2011|Padilla et al. (2011)]] use a simple global-average emulator with two time scales ( [[#7.5.1.2|Section 7.5.1.2]] ; Supplementary Material 7.SM.2) to estimate a TCR of 1.6 [1.3 to 2.6] °C. Using the same model, [[#Schwartz--2012|Schwartz (2012)]] finds TCR in the range 0.9°C–1.9°C while [[#Schwartz--2018|Schwartz (2018)]] finds that an effective ECS of 1.7°C provides the best fit to the historical global surface temperature record while also finding a median aerosol forcing that is smaller than that assessed in ( [[#7.3|Section 7.3]] . Using an eight-box representation of the atmosphere–ocean–terrestrial system constrained by historical warming, [[#Goodwin--2016|Goodwin (2016)]] found an effective ECS of 2.4 [1.4 to 4.4] °C while [[#Goodwin--2018|Goodwin (2018)]] found effective ECS to be in the range 2°C–4.3°C when using a prior for ECS based on paleoclimate constraints.

Using an emulator comprised of Northern and Southern hemispheres and an upwelling-diffusive ocean ( [[#Aldrin--2012|Aldrin et al., 2012]] ), with surface temperature and ocean heat content datasets updated to 2014, [[#Skeie--2018|Skeie et al. (2018)]] estimate a TCR of 1.4 [0.9 to 2.0] °C and a median effective ECS of 1.9 [1.2 to 3.1] °C. Using a similar emulator comprised of land and ocean regions and an upwelling-diffusive ocean, with global surface temperature and ocean heat content datasets up to 2011, [[#Johansson--2015|Johansson et al. (2015)]] find an effective ECS of 2.5 [2.0 to 3.2] °C. The estimate is found to be sensitive to the choice of dataset endpoint and the representation of internal variability meant to capture the El Niño–Southern Oscillation and Pacific Decadal Variability. Differences between these two studies arise, in part, from their different global surface temperature and ocean heat content datasets, different radiative forcing uncertainty ranges, different priors for model parameters, and different representations of internal variability. This leads to different estimates of effective ECS, with the median estimate of [[#Skeie--2018|Skeie et al. (2018)]] lying below the 5–95% range of effective ECS from [[#Johansson--2015|Johansson et al. (2015)]] . Moreover, while the [[#Skeie--2018|Skeie et al. (2018)]] emulator has a constant value of the net feedback parameter, the [[#Johansson--2015|Johansson et al. (2015)]] emulator allows distinct radiative feedbacks for land and ocean, contributing to the different results.

The median estimates of TCR and effective ECS inferred from emulator studies generally lie within the 5–95% ranges of those inferred from historical global energy budget constraints (1.3 to 2.7 °C for TCR and 1.6 to 4.8 °C for effective ECS). Their estimates would be consistent with still-higher values of ECS when accounting for changes in radiative feedbacks as the spatial pattern of global warming evolves in the future ( [[#7.5.2.1|Section 7.5.2.1]] ). Cross-Chapter Box 7.1 and references therein show that four very different physically based emulators can be calibrated to match the assessed ranges of historical GSAT change, ERF, ECS and TCR from across the report. Therefore, the fact that the emulator effective ECS values estimated from previous studies tend to lie at the lower end of the range inferred from historical global energy budget constraints may reflect that the energy budget constraints in ( [[#7.5.2.1|Section 7.5.2.1]] use updated estimates of Earth’s energy imbalance, GSAT trends and ERF, rather than any methodological differences between the lines of evidence. The ‘emergent constraints’ on ECS based on observations of climate variability used in conjunction with comprehensive ESMs are assessed in ( [[#7.5.4.1|Section 7.5.4.1]] .

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==== 7.5.2.3 Estimates of ECS Based on Variability in Earth’s Top-of-atmosphere Radiation Budget ====

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While continuous satellite measurements of top-of-atmosphere (TOA) radiative fluxes (Figure 7.3) do not have sufficient accuracy to determine the absolute magnitude of Earth’s energy imbalance ( [[#7.2.1|Section 7.2.1]] ), they provide accurate estimates of its variations and trends since the year 2002 that agree well with estimates based on observed changes in global ocean heat content ( [[#Loeb--2012|Loeb et al., 2012]] ; [[#Johnson--2016|Johnson et al., 2016]] ; [[#Palmer--2017|Palmer, 2017]] ). When combined with global surface temperature observations and simple models of global energy balance, satellite measurements of TOA radiation afford estimates of the net feedback parameter associated with recent climate variability ( [[#Tsushima--2013|Tsushima and Manabe, 2013]] ; [[#Donohoe--2014|Donohoe et al., 2014]] ; [[#Dessler--2018|Dessler and Forster, 2018]] ). These feedback estimates, derived from the regression of TOA radiation on surface temperature variability, imply values of ECS that are broadly consistent with those from other lines of evidence ( [[#Forster--2016|Forster, 2016]] ; [[#Knutti--2017|Knutti et al., 2017]] ). A history of regression-based feedbacks and their uncertainties is summarized in [[#Bindoff--2013|Bindoff et al. (2013)]] , [[#Forster--2016|Forster (2016)]] , and [[#Knutti--2017|Knutti et al. (2017)]] .

Research since AR5 has noted that regression-based feedback estimates depend on whether annual- or monthly-mean data are used and on the choice of lag employed in the regression, complicating their interpretation ( [[#Forster--2016|Forster, 2016]] ). The observed lead–lag relationship between global TOA radiation and global surface temperature, and its dependence on sampling period, is well replicated within unforced simulations of ESMs ( [[#Dessler--2011|Dessler, 2011]] ; [[#Proistosescu--2018|Proistosescu et al., 2018]] ). These features arise because the regression between global TOA radiation and global surface temperature reflects a blend of different radiative feedback processes associated with several distinct modes of variability acting on different time scales (Annex IV), such as monthly atmospheric variability and interannual El Niño–Southern Oscillation (ENSO) variability ( [[#Lutsko--2018|Lutsko and Takahashi, 2018]] ; [[#Proistosescu--2018|Proistosescu et al., 2018]] ). Regression-based feedbacks thus provide estimates of the radiative feedbacks that are associated with internal climate variability (e.g., [[#Brown--2014|Brown et al., 2014]] ), and do not provide a direct estimate of ECS ( ''high confidence'' ). Moreover, variations in global surface temperature that do not directly affect TOA radiation may lead to a positive bias in regression-based feedback, although this bias appears to be small, particularly when annual-mean data are used ( [[#Murphy--2010|Murphy and Forster, 2010]] ; [[#Spencer--2010|Spencer and Braswell, 2010]] , 2011; [[#Proistosescu--2018|Proistosescu et al., 2018]] ). When tested within ESMs, regression-based feedbacks have been found to be only weakly correlated with values of ECS ( [[#Chung--2010|Chung et al., 2010]] ), although cloudy-sky TOA radiation fluxes have been found to be moderately correlated with ECS at ENSO time scales within CMIP5 models ( [[#Lutsko--2018|Lutsko and Takahashi, 2018]] ).

Finding such correlations within models requires simulations that span multiple centuries, suggesting that the satellite record may not be of sufficient length to produce robust feedback estimates. However, correlations between regression-based feedbacks and long-term feedbacks have been found to be higher when focused on specific processes or regions, such as for the cloud- or water-vapour feedbacks ( [[#7.4.2|Section 7.4.2]] ; [[#Dessler--2013|Dessler, 2013]] ; [[#Zhou--2015|Zhou et al., 2015]] ). Assessing the global radiative feedback in terms of the more stable relationship between tropospheric temperature and TOA radiation offers another potential avenue for constraining ECS. The ‘emergent constraints’ on ECS based on variability in the TOA energy budget are assessed in ( [[#7.5.4.1|Section 7.5.4.1]] .

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==== 7.5.2.4 Estimates of ECS Based on the Climate Response to Volcanic Eruptions ====

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A number of studies consider the observed climate response to volcanic eruptions over the 20th century ( [[IPCC:Wg1:Chapter:Chapter-3#3.3.1|Section 3.3.1]] and Cross-Chapter Box 4.1; [[#Knutti--2017|Knutti et al., 2017]] ). However, the direct constraint on ECS is weak, particularly at the high end, because the temperature response to short-term forcing depends only weakly on radiative feedbacks and because it can take decades of a sustained forcing before the magnitude of temperature changes reflects differences in ECS across models ( [[#Geoffroy--2013b|Geoffroy et al., 2013b]] ; [[#Merlis--2014|Merlis et al., 2014]] ). It is also a challenge to separate the response to volcanic eruptions from internal climate variability in the years that follow them ( [[#Wigley--2005|Wigley et al., 2005]] ). Based on ESM simulations, radiative feedbacks governing the global surface temperature response to volcanic eruptions can be substantially different than those governing long-term global warming ( [[#Merlis--2014|Merlis et al., 2014]] ; [[#Marvel--2016|Marvel et al., 2016]] ; [[#Ceppi--2019|Ceppi and Gregory, 2019]] ). Estimates based on the response to volcanic eruptions agree with other lines of evidence ( [[#Knutti--2017|Knutti et al., 2017]] ), but they do not constitute a direct estimate of ECS ( ''high confidence'' ). The ‘emergent constraints’ on ECS based on climate variability, including volcanic eruptions, are summarized in ( [[#7.5.4.1|Section 7.5.4.1]] .

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==== 7.5.2.5 Assessment of ECS and TCR Based on the Instrumental Record ====

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Evidence from the instrumental temperature record, including estimates using global energy budget changes ( [[#7.5.2.1|Section 7.5.2.1]] ), climate emulators ( [[#7.5.2.2|Section 7.5.2.2]] ), variability in the TOA radiation budget ( [[#7.5.2.3|Section 7.5.2.3]] ), and the climate response to volcanic eruptions ( [[#7.5.2.4|Section 7.5.2.4]] ) produce median ECS estimates that range between 2.5°C and 3.5°C, but a best estimate value cannot be given owing to a strong dependence on assumptions about how radiative feedbacks will change in the future. However, there is ''robust evidence'' and ''high agreement'' across the lines of evidence that ECS is ''extremely likely'' greater than 1.6°C ( ''high confidence'' ). There is ''robust evidence'' and ''medium agreement'' across the lines of evidence that ECS is ''very likely'' greater than 1.8°C and ''likely'' greater than 2.2°C ( ''high confidence'' ). These ranges of ECS correspond to estimates based on historical global energy budget constraints ( [[#7.5.2.1|Section 7.5.2.1]] ) under the assumption of no feedback dependence on evolving SST patterns (i.e., α ’ = 0) and thus represent an underestimate of the true ECS ranges that can be inferred from this line of evidence ( ''high confidence'' ). Historical global energy budget changes do not provide constraints on the upper bound of ECS, while the studies assessed in ( [[#7.5.2.3|Section 7.5.2.3]] based on climate variability provide ''low confidence'' in its value owing to ''limited evidence'' .

Global energy budget constraints indicate a central estimate (median) TCR value of 1.9°C and that TCR is ''likely'' in the range 1.5 to 2.3 °C and ''very likely'' in the range 1.3 to 2.7 °C ( ''high confidence'' ). Studies that constrain TCR based on the instrumental temperature record used in conjunction with ESM simulations are summarized in ( [[#7.5.4.3|Section 7.5.4.3]] .

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=== 7.5.3 Estimates of ECS Based on Paleoclimate Data ===

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Estimates of ECS based on paleoclimate data are complementary to, and largely independent from, estimates based on process-based studies ( [[#7.5.1|Section 7.5.1]] ) and the instrumental record ( [[#7.5.2|Section 7.5.2]] ). The strengths of using paleoclimate data to estimate ECS include: (i) the estimates are based on observations of a real-world Earth system response to a forcing, in contrast to using estimates from process-based modelling studies or directly from models; (ii) the forcings are often relatively large (similar in magnitude to a CO <sub>2</sub> doubling or more), in contrast to data from the instrumental record; (iii) the forcing often changes relatively slowly so the system is close to equilibrium; as such, all individual feedback parameters, α x , are included, and complications associated with accounting for ocean heat uptake are reduced or eliminated, in contrast to the instrumental record. However, there can be relatively large uncertainties on estimates of both the paleo forcing and paleo global surface temperature response, and care must be taken to account for long-term feedbacks associated with ice sheets ( [[#7.4.2.6|Section 7.4.2.6]] ), which often play an important role in the paleoclimate response to forcing, but which are not included in the definition of ECS. Furthermore, the state-dependence of feedbacks ( [[#7.4.3|Section 7.4.3]] ) means that climate sensitivity during Earth’s past may not be the same as it is today, which should be accounted for when interpreting paleoclimate estimates of ECS.

AR5 stated that data and modelling of the Last Glacial Maximum (LGM; Cross-Chapter Box 2.1) indicated that it was ''very unlikely'' that ECS lay outside the range 1°C–6°C ( [[#Masson-Delmotte--2013|Masson-Delmotte et al., 2013]] ). Furthermore, AR5 reported that climate records of the last 65 million years indicated an ECS 95% confidence interval of 1.1 to 7.0 °C.

Compared with AR5, there are now improved constraints on estimates of ECS from paleoclimate evidence. The strengthened understanding and improved lines of evidence come in part from the use of high-resolution paleoclimate data across multiple glacial–interglacial cycles, taking into account state-dependence ( [[#7.4.3|Section 7.4.3]] ; [[#von%20der%20Heydt--2014|von der Heydt et al., 2014]] ; [[#Köhler--2015|Köhler et al., 2015]] , 2017, 2018; [[#Friedrich--2016|Friedrich et al., 2016]] ; [[#Snyder--2019|Snyder, 2019]] ; [[#Stap--2019|Stap et al., 2019]] ) and better constrained pre-ice-core estimates of atmospheric CO <sub>2</sub> concentrations ( [[#Martínez-Botí--2015|Martínez-Botí et al., 2015]] ; [[#Anagnostou--2016|Anagnostou et al., 2016]] , 2020; [[#de%20la%20Vega--2020|de la Vega et al., 2020]] ) and surface temperature ( [[#Hollis--2019|Hollis et al., 2019]] ; [[#Inglis--2020|Inglis et al., 2020]] ; [[#McClymont--2020|McClymont et al., 2020]] ).

Overall, the paleoclimate lines of evidence regarding climate sensitivity can be broadly categorized into two types: estimates of radiative forcing and temperature response from paleo proxy measurements, and emergent constraints on paleoclimate model simulations. This section focuses on the first type only; the second type (emergent constraints) are discussed in ( [[#7.5.4|Section 7.5.4]] .

In order to provide estimates of ECS, evidence from the paleoclimate record can be used to estimate forcing (Δ ''F'' ) and global surface temperature response (Δ ''T'' ) in Equation 7.1, Box 7.1, under the assumption that the system is in equilibrium (i.e., Δ ''N'' = 0). However, there are complicating factors when using the paleoclimate record in this way, and these challenges and uncertainties are somewhat specific to the time period being considered.

<div id="7.5.3.1" class="h3-container"></div>

<span id="estimates-of-ecs-from-the-last-glacial-maximum"></span>
==== 7.5.3.1 Estimates of ECS from the Last Glacial Maximum ====

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The LGM (Cross-Chapter Box 2.1) has been used to provide estimates of ECS (see Table 7.11 for estimates since AR5; [[#Sherwood--2020|Sherwood et al., 2020]] ; [[#Tierney--2020b|Tierney et al., 2020b]] ). The major forcings and feedback processes that led to the cold climate at that time (e.g., CO <sub>2</sub> , non-CO <sub>2</sub> greenhouse gases, and ice sheets) are relatively well-known ( [[IPCC:Wg1:Chapter:Chapter-5#5.1|Section 5.1]] ), orbital forcing relative to pre-industrial was negligible, and there are relatively high spatial resolution and well-dated paleoclimate temperature data available for this time period ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ). Uncertainties in deriving global surface temperature from the LGM proxy data arise partly from uncertainties in the calibration from the paleoclimate data to local annual mean surface temperature, and partly from uncertainties in the conversion of the local temperatures to an annual mean global surface temperature. Overall, the global mean LGM cooling relative to pre-industrial is assessed to be ''very likely'' from 5 to 7 °c ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ). The LGM climate is often assumed to be in full equilibrium with the forcing, such that Δ ''N'' in Equation 7.1, Box 7.1, is zero. A calculation of sensitivity using solely CO <sub>2</sub> forcing, and assuming that the LGM ice sheets were in equilibrium with that forcing, would give an Earth System Sensitivity (ESS) rather than an ECS (see Box 7.1). In order to calculate an ECS, which is defined here to include all feedback processes except ice sheets, the approach of [[#Rohling--2012|Rohling et al. (2012)]] can be used. This approach introduces an additional forcing term in Equation 7.1, Box 7.1, that quantifies the resulting forcing associated with the ice-sheet feedback (primarily an estimate of the radiative forcing associated with the change in surface albedo). However, differences between studies as to which processes are considered as forcings (for example, some studies also include vegetation and/or aerosols, such as dust, as forcings), means that published estimates are not always directly comparable. Additional uncertainty arises from the magnitude of the ice-sheet forcing itself ( [[#Stap--2019|Stap et al., 2019]] ; [[#Zhu--2021|Zhu and Poulsen, 2021]] ), which is often estimated using ESMs. Furthermore, the ECS at the LGM may differ from that of today due to state-dependence ( [[#7.4.3|Section 7.4.3]] ). Here, only studies that report values of ECS that have accounted for the long-term feedbacks associated with ice sheets, and therefore most closely estimate ECS as defined in this chapter, are assessed here (Table 7.11).

<div id="7.5.3.2" class="h3-container"></div>

<span id="estimates-of-ecs-from-glacialinterglacial-cycles"></span>
==== 7.5.3.2 Estimates of ECS from Glacial–Interglacial Cycles ====

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Since AR5, several studies have extended the [[#Rohling--2012|Rohling et al. (2012)]] approach (described above for the LGM) to the glacial–interglacial cycles of the last approximately 1 to 2 million years ( [[#von%20der%20Heydt--2014|von der Heydt et al., 2014]] ; [[#Köhler--2015|Köhler et al., 2015]] , 2017, 2018; [[#Friedrich--2016|Friedrich et al., 2016]] ; [[#Royer--2016|Royer, 2016]] ; [[#Snyder--2019|Snyder, 2019]] ; [[#Stap--2019|Stap et al., 2019]] ; [[#Friedrich--2020|Friedrich and Timmermann, 2020]] ; see Table 7.11). Compared to the LGM, uncertainties in the derived ECS from these periods are in general greater, due to greater uncertainty in global surface temperature (due to fewer individual sites with proxy temperature records), ice-sheet forcing (due to a lack of detailed ice-sheet reconstructions), and CO <sub>2</sub> forcing (for those studies that include the pre-ice-core period, where CO <sub>2</sub> reconstructions are substantially more uncertain). Furthermore, accounting for varying orbital forcing in the traditional global mean forcing and response energy budget framework (Box 7.1) is challenging ( [[#Schmidt--2017b|Schmidt et al., 2017b]] ), due to seasonal and latitudinal components of the forcing that, despite a close-to-zero orbital forcing in the global annual mean, can directly result in responses in annual mean global surface temperature ( [[#Liu--2014|Liu et al., 2014]] ), ice volume ( [[#Abe-Ouchi--2013|Abe-Ouchi et al., 2013]] ), and feedback processes such as those associated with methane ( [[#Singarayer--2011|Singarayer et al., 2011]] ). In addition, for time periods in which the forcing relative to the modern era is small (interglacials), the inferred ECS has relatively large uncertainties because the forcing and temperature response (Δ ''F'' and Δ ''T'' in Equation 7.1, Box 7.1) are both close to zero.

<div id="7.5.3.3" class="h3-container"></div>

<span id="estimates-of-ecs-from-warm-periods-of-the-pre-quaternary"></span>
==== 7.5.3.3 Estimates of ECS from Warm Periods of the Pre-Quaternary ====

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In the pre-Quaternary (prior to about 2.5 million years ago), the forcings and response are generally of the same sign and similar magnitude as future projections of climate change ( [[#Burke--2018|Burke et al., 2018]] ; [[#Tierney--2020a|Tierney et al., 2020a]] ). Similar uncertainties as for the LGM apply, but in this case a major uncertainty relates to the forcing, because prior to the ice-core record there are only indirect estimates of CO <sub>2</sub> concentration. However, advances in pre-ice-core CO <sub>2</sub> reconstruction (e.g., [[#Foster--2016|Foster and Rae, 2016]] ; [[#Super--2018|Super et al., 2018]] ; [[#Witkowski--2018|Witkowski et al., 2018]] ) mean that the estimates of pre-Quaternary CO <sub>2</sub> have less uncertainty than at the time of AR5, and these time periods can now contribute to an assessment of climate sensitivity (Table 7.11). The mid-Pliocene Warm Period (MPWP; Cross-Chapter Box 2.1 and Cross-Chapter Box 2.4) has been targeted for constraints on ECS ( [[#Martínez-Botí--2015|Martínez-Botí et al., 2015]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ), due to the fact that CO <sub>2</sub> concentrations were relatively high at this time (350–425 ppm) and because the MPWP is sufficiently recent that topography and continental configuration are similar to modern-day. As such, a comparison of the MPWP with the pre-industrial climate provides probably the closest natural geological analogue for the modern day that is useful for assessing constraints on ECS, despite the effects of different geographies not being negligible (global surface temperature patterns; ocean circulation). Furthermore, the global surface temperature of the MPWP was such that non-linearities in feedbacks ( [[#7.4.3|Section 7.4.3]] ) were relatively modest. Within the MPWP, the KM5c interglacial has been identified as a particularly useful time period for assessing ECS ( [[#Haywood--2013|Haywood et al., 2013]] , 2016b) because Earth’s orbit during that time was very similar to that of the modern day.

Further back in time, in the Early Eocene (Cross-Chapter Box 2.1), uncertainties in forcing and temperature change become larger, but the signals are generally larger too ( [[#Anagnostou--2016|Anagnostou et al., 2016]] , 2020; [[#Shaffer--2016|Shaffer et al., 2016]] ; [[#Inglis--2020|Inglis et al., 2020]] ). Caution must be applied when estimating ECS from these time periods, due to differing continental position and topography/bathymetry ( [[#Farnsworth--2019|Farnsworth et al., 2019]] ), and due to temperature-dependence of feedbacks ( [[#7.4.3|Section 7.4.3]] ). On even longer time scales of the last 500 million years ( [[#Royer--2016|Royer, 2016]] ) the temperature and CO <sub>2</sub> measurements are generally asynchronous, presenting challenges in using this information for assessments of ECS.

<div id="7.5.3.4" class="h3-container"></div>

<span id="synthesis-of-ecs-based-on-paleo-radiative-forcing-and-temperature"></span>
==== 7.5.3.4 Synthesis of ECS Based on Paleo Radiative Forcing and Temperature ====

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The lines of evidence directly constraining ECS from paleoclimates are summarized in Table 7.11. Although some of the estimates in Table 7.11 are not independent because they use similar proxy records to each other (e.g., [[#von%20der%20Heydt--2014|von der Heydt et al., 2014]] ; [[#Köhler--2015|Köhler et al., 2015]] , 2017; [[#Stap--2019|Stap et al., 2019]] ), there are still multiple independent lines of paleoclimate evidence regarding ECS, from differing past time periods: LGM ( [[#Sherwood--2020|Sherwood et al., 2020]] ; [[#Tierney--2020b|Tierney et al., 2020b]] ); glacial–interglacial ( [[#Royer--2016|Royer, 2016]] ; [[#Köhler--2017|Köhler et al., 2017]] ; [[#Snyder--2019|Snyder, 2019]] ; [[#Friedrich--2020|Friedrich and Timmermann, 2020]] ); Pliocene ( [[#Martínez-Botí--2015|Martínez-Botí et al., 2015]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ); and the Eocene ( [[#Anagnostou--2016|Anagnostou et al., 2016]] , 2020; [[#Shaffer--2016|Shaffer et al., 2016]] ; [[#Inglis--2020|Inglis et al., 2020]] ), with differing proxies for estimating forcing (e.g., CO <sub>2</sub> from ice cores or boron isotopes) and response (e.g., global surface temperature from δ <sup>18</sup> O, Mg/Ca or Antarctic δ D). Furthermore, although different studies have uncertainty estimates that account for differing sources of uncertainty, some studies ( [[#Snyder--2019|Snyder, 2019]] ; [[#Inglis--2020|Inglis et al., 2020]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ; [[#Tierney--2020b|Tierney et al., 2020b]] ) do consider many of the uncertainties discussed in Sections 7.5.3.1–7.5.3.3. All the studies based on glacial–interglacial cycles account for some aspects of the state-dependence of climate sensitivity ( [[#7.4.3|Section 7.4.3]] ) by considering only the warm phases of the Pleistocene, although what constitutes a warm phase is defined differently across the studies.

None of the post-AR5 studies in Table 7.11 have an estimated lower range for ECS below 1.6°C. As such, based solely on the paleoclimate record, it is assessed to be ''very likely'' that ECS is greater than 1.5°C ( ''high confidence'' ).

In general, it is the studies based on the warm periods of the glacial–interglacial cycles ( [[#7.5.3.2|Section 7.5.3.2]] ) that give the largest values of ECS. Given the large uncertainties associated with estimating the magnitude of the ice-sheet forcing during these intervals ( [[#Stap--2019|Stap et al., 2019]] ), and other uncertainties discussed in ( [[#7.5.3.2|Section 7.5.3.2]] , in particular the direct effect of orbital forcing on estimates of ECS, there is only ''low confidence'' in estimates from the studies based on glacial–interglacial periods. This ''low confidence'' also results from the temperature-dependence of the net feedback parameter, α , resulting from several of these studies (Figure 7.10), that is hard to reconcile with the other lines of evidence for α , including proxy estimates from warmer paleoclimates ( [[#7.4.3.2|Section 7.4.3.2]] ). A central estimate of ECS, derived from the LGm ( [[#7.5.3.1|Section 7.5.3.1]] ) and warm periods of the pre-Quaternary ( [[#7.5.3.3|Section 7.5.3.3]] ), that takes into account some of the interdependencies between the different studies, can be obtained by averaging across studies within each of these two time periods, and then averaging across the two time periods; this results in a central estimate of 3.4°C. This approach of focussing on the LGM and warm climates was also taken by [[#Sherwood--2020|Sherwood et al. (2020)]] in their assessment of ECS from paleoclimates. An alternative method is to average across all studies, from all periods, that have considered multiple sources of uncertainty (Table 7.11); this approach leads to a similar central estimate of 3.3°C. Overall, we assess ''medium confidence'' for a central estimate of 3.3°C to 3.4°C.

There is more variation in the upper bounds of ECS than in the lower bounds. Estimates of ECS from pre-Quaternary warm periods have an average upper range of 4.9°C, and from the LGM of 4.4°C; taking into account the independence of the estimates from these two time periods, and accounting for state-dependence ( [[#7.4.3|Section 7.4.3]] ) and other uncertainties discussed in ( [[#7.5.3|Section 7.5.3]] , the paleoclimate record on its own indicates that ECS is ''likely'' less than 4.5°C. Given the higher values from many glacial–interglacial studies, this value has only ''medium'' ''confidence'' . Despite the large variation in individual studies at the extreme upper end, all except two studies (both of which are from glacial–interglacial time periods associated with ''low confidence'' ) have central estimates that are below 6°C; overall we assess that it is ''extremely likely'' that ECS is below 8°C ( ''high confidence'' ).

<div id="_idContainer061" class="Basic-Text-Frame"></div>

'''Table 7.11''' '''|''' '''Estimates of equilibrium climate sensitivity (ECS) derived from paleoclimates; from AR5 (above double lines) and from post-AR5 studies (below double lines).''' Many studies provide an estimate of ECS that includes only CO <sub>2</sub> and the ice-sheet feedback as forcings, providing an estimate of S <sub>[CO2, LI]</sub> using the notation of [[#Rohling--2012|Rohling et al. (2012)]] , which is equivalent to our definition of ECS (Box 7.1). However, some studies provide estimates of other types of sensitivity (column 4). Different studies (column 1) focus on different time periods (column 2) and use a variety of different paleoclimate proxies and models (column 3) to give a best estimate (column 5) and/or a range (column 5). The published ranges given account for varying sources of uncertainty (column 6). See Cross-Chapter Box 2.1 for definition of time periods. All temperature values in column 5 are shown to a precision of 1 decimal place.

{| class="wikitable"
|-
| (1) Study

| (2) Time Period (kyr = thousand years; Myr = million years; Ma = million years ago)

| (3) Proxies/Models Used for CO <sub>2</sub> , Temperature (T) and Global Scaling (GS)

| (4) Climate Sensitivity Classification According to [[#Rohling--2012|Rohling et al. (2012)]]

| (5) Published Best Estimate of ECS [and/or Range]

| (6) Range Accounts For:

|-
| AR5 ( [[#Masson-Delmotte--2013|Masson-Delmotte et al., 2013]] )

| LGM (Last Glacial Maximum)

| Assessment of multiple lines of evidence

| S <sup>a</sup> = ECS a

| [ ''very likely'' &gt;1.0; ''very unlikely'' &gt;6.0°C]

| Multiple sources of uncertainty

|-
| AR5 ( [[#Masson-Delmotte--2013|Masson-Delmotte et al., 2013]] )

| Cenozoic (last 65 Myr)

| Assessment of multiple lines of evidence

| S <sub>[CO2,LI]</sub>

| [95% range: 1.1°C to 7.0°C]

| Multiple sources of uncertainty

|-
| [[#Tierney--2020b|Tierney et al. (2020b)]]

| LGM

| CO <sub>2</sub> : ice core

T: multi-proxy

| S <sub>[CO2,LI,CH4, N2O]</sub>

| 3.8°C

[68% range: 3.3°C to 4.3°C]

| Multiple sources of uncertainty

|-
| [[#Sherwood--2020|Sherwood et al. (2020)]]

| LGM

| CO <sub>2</sub> : ice core

T: multiple lines of evidence

| S <sub>[CO2, LI, CH4, N2O, dust, VG]</sub>

| maximum likelihood [likelihood of 1.0]: 2.6°C

[ ''likely'' range depends on chosen prior; likelihood of 0.6: 1.6°C to 4.4°C]

| Multiple sources of uncertainty

|-
| [[#von%20der%20Heydt--2014|von der Heydt et al. (2014)]]

| Warm states of glacial–interglacial cycles of last 800 kyr

| CO <sub>2</sub> : ice core

T: ice core δ D, benthic δ <sup>18</sup> O

GS: [[#Schneider%20von%20Deimling--2006|Schneider von Deimling et al. (2006)]] ; [[#Annan--2013|Annan and Hargreaves (2013)]]

| S <sub>[CO2,LI]</sub>

| 3.5°C

[range: 3.1°C to 5.4°C] <sup>b</sup>

| Varying LGM global mean temperatures used for scaling

|-
| [[#Köhler--2015|Köhler et al. (2015)]]

| Warm states of glacial–interglacial cycles of last 2 Myr

| CO <sub>2</sub> : ice core alkenones and boron isotopes

T: benthic δ <sup>18</sup> O

GS: PMIP LGM and PlioMIP MPWP

| S <sub>[CO2,LI]</sub>

| 5.7°C

[68% range: 3.7°C to 8.1°C] <sup>b</sup>

| Temporal variability in records

|-
| [[#Köhler--2017|Köhler et al. (2017)]]

| Warm states of glacial–interglacial cycles of last 2 Myr

| CO <sub>2</sub> : boron isotopes

T: benthic δ <sup>18</sup> O

GS: PMIP LGM and PlioMIP MPWP

| S <sub>[CO2,LI]</sub>

| 5.6°C

[16th to 84th percentile: 3.6°C to 8.1°C] <sup>b</sup>

| Temporal variability in records

|-
| [[#Köhler--2018|Köhler et al. (2018)]]

| Warm states of glacial–interglacial cycles of last 800 kyr, excluding those for which CO <sub>2</sub> and T diverge

| CO <sub>2</sub> : ice cores

T: benthic δ <sup>18</sup> O, alkenone, Mg/Ca, MAT, and faunal SST

GS: PMIP3 LGM

| S <sub>[CO2, LI]</sub>

| [range: 3.0°C to 5.9°C] <sup>b</sup>

| Varying temperature reconstructions

|-
| [[#Stap--2019|Stap et al. (2019)]]

| States of glacial–interglacial cycles of last 800 kyr for which forcing is zero compared with modern, excluding those for which CO <sub>2</sub> and T diverge

| CO <sub>2</sub> : ice cores

T: benthic δ <sup>18</sup> O

GS: PMIP LGM and PlioMIP MPWP

| S <sub>[CO2, LI]</sub>

| [range: 6.1°C to 11.0°C] <sup>b</sup>

| Varying efficacies of ice-sheet forcing

|-
| (1) Study

| (2) Time Period (kyr = thousand years; Myr = million years; Ma = million years ago)

| (3) Proxies/Models Used for CO <sub>2</sub> , Temperature (T) and Global Scaling (GS)

| (4) Climate Sensitivity Classification According to [[#Rohling--2012|Rohling et al. (2012)]]

| (5) Published Best Estimate of ECS [and/or Range]

| (6) Range Accounts For:

|-
| [[#Friedrich--2016|Friedrich et al. (2016)]]

| Warm states of glacial–interglacial cycles of last 780 kyr

| CO <sub>2</sub> : ice cores

T: alkenone, Mg/Ca, MAT, and faunal SST

GS: PMIP3 LGM

| S <sub>[GHG,LI,AE]</sub>

| 4.9°C

[ ''Likely'' range: 4.3°C to 5.4°C] <sup>b</sup>

| Varying LGM global mean temperatures, aerosol forcing

|-
| [[#Friedrich--2020|Friedrich and Timmermann (2020)]]

| Last glacial–interglacial cycle

| CO <sub>2</sub> : ice cores

T: alkenone, Mg/Ca, MAT

| S <sub>[GHG,LI,AE]</sub>

| 4.2°C

[range: 3.4°C to 6.2°C] <sup>b</sup>

| Varying aerosol forcings

|-
| [[#Snyder--2019|Snyder (2019)]]

| Interglacial periods and intermediateglacial climates of last 800 kyr

| CO <sub>2</sub> : ice cores

T: alkenone, Mg/Ca, species assemblages

GS: PMIP models

| S <sub>[GHG,LI,AE,VG]</sub>

| 3.1°C

[67% range: 2.6°C to 3.7°C] <sup>b</sup>

| Multiple sources of uncertainty

|-
| [[#Royer--2016|Royer (2016)]]

| Glacial–interglacial cycles of the Pliocene (3.4 to 2.9 Ma)

| CO <sub>2</sub> : boron isotopes

T: benthic δ <sup>18</sup> O

| S <sub>[CO2,LI]</sub>

| 10.2°C

[68% range: 8.1°C to 12.3°C]

| Temporal variability in records

|-
| [[#Martínez-Botí--2015|Martínez-Botí et al. (2015)]]

| Pliocene

| CO <sub>2</sub> : boron isotopes

T: benthic δ <sup>18</sup> O

| S <sub>[CO2,LI]</sub>

| 3.7°C

[68% range: 3.0°C to 4.4°C] <sup>b</sup>

| Pliocene sea level, temporal variability in records

|-
| [[#Sherwood--2020|Sherwood et al. (2020)]]

| Pliocene

| CO <sub>2</sub> : boron isotopes

T: multiple lines of evidence

| S <sub>[CO2, LI,N2O,CH4,VG]</sub>

| maximum likelihood [likelihood of 1.0]: 3.2°C

[ ''likely'' range depends on chosen prior; likelihood of 0.6: 1.8°C to 5.2°C]

| Multiple sources of uncertainty

|-
| [[#Anagnostou--2016|Anagnostou et al. (2016)]]

| Early Eocene

| CO <sub>2</sub> : boron isotopes

T: various terrestrial MAT, Mg/Ca, TEX, δ <sup>18</sup> O SST

| S <sub>[CO2,LI]</sub>

| 3.6°C

[66% range: 2.1°C to 4.6°C]

| Varying calibrations for temperature and CO <sub>2</sub>

|-
| [[#Anagnostou--2020|Anagnostou et al. (2020)]]

| Late Eocene (41.2 to 33.9 Ma)

| CO <sub>2</sub> : boron isotopes

T: one SST record

GS: CESM1

| S <sub>[CO2,LI]</sub>

| 3.0°C

[68% range: 1.9°C to 4.1°C]

| Temporal variability in records

|-
| [[#Shaffer--2016|Shaffer et al. (2016)]]

| Pre-PETM (Paleocene–Eocene Thermal Maximum)

| CO <sub>2</sub> : mineralogical, carbon cycling, and isotope constraints

T: various terrestrial MAT, Mg/Ca, TEX, δ <sup>18</sup> O SST

| S <sub>[GHG,AE,VG,LI]</sub>

| [range: 3.3°C to 5.6°C]

| Varying calibration of temperature and CO <sub>2</sub>

|-
| [[#Inglis--2020|Inglis et al. (2020)]]

| Mean of EECO (Early Eocene Climatic Optimum), PETM, and latest Paleocene

| CO <sub>2</sub> : boron isotopes

T: multiproxy SST and SAT

GS: EoMIP models

| S <sub>[CO2,LI, VG,AE]</sub>

| 3.7°C [ ''likely'' range: 2.2°C to 5.3°C]

| Multiple sources of uncertainty

|}

a S <sup>a</sup> in this table denotes a classification of climate sensitivity following [[#Rohling--2012|Rohling et al. (2012)]] .

<sup>b</sup> Although our assessed value of ERF due to CO <sub>2</sub> doubling is 3.93 W m <sup>–2</sup> [[#7.3.2.1|Section 7.3.2.1]] ), for these studies the best estimate and range of temperature is calculated from the published estimate of sensitivity in units of °C (W m <sup>–2</sup> ) <sup>–1</sup> using an ERF of 3.7 W m <sup>–2</sup> , for consistency with the typical value used in the studies to estimate the paleo CO <sub>2</sub> forcing.

<div id="7.5.4" class="h2-container"></div>

<span id="estimates-of-ecs-and-tcr-based-on-emergent-constraints"></span>
=== 7.5.4 Estimates of ECS and TCR Based on Emergent Constraints ===

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ESMs exhibit substantial spread in ECS and TCr ( [[#7.5.7|Section 7.5.7]] ). Numerous studies have leveraged this spread in order to narrow estimates of Earth’s climate sensitivity by employing methods known as ‘emergent constraints’ [[IPCC:Wg1:Chapter:Chapter-1#1.5.4|Section 1.5.4]] ). These methods establish a relationship between an observable and either ECS or TCR based on an ensemble of models, and combine this information with observations to constrain the probability distribution of ECS or TCR. Most studies of this kind have clearly benefitted from the international efforts to coordinate the CMIP and other multi-model ensembles.

A number of considerations must be taken into account when assessing the diverse literature on ECS and TCR emergent constraints. For instance, it is important to have physical and theoretical bases for the connection between the observable and modelled ECS or TCR since in model ensembles thousands of relationships that pass statistical significance can be found simply by chance ( [[#Caldwell--2014|Caldwell et al., 2014]] ). It is also important that the underlying model ensemble does not exhibit a shared bias that influences the simulation of the observable quantity on which the emergent constraint is based. Also, correctly accounting for uncertainties in both the observable (including measurement uncertainty and natural variability) and the emergent constraint statistical relationship can be challenging, in particular in cases where the latter is not expected to be linear ( [[#Annan--2020|Annan et al., 2020]] ). A number of proposed emergent constraints leverage variations in modelled ECS arising from tropical low-clouds, which was the dominant source of inter-model spread in the CMIP5 ensemble used in most emergent constraint studies. Since ECS is dependent on the sum of individual feedbacks ( [[#7.5.1|Section 7.5.1]] ) these studies implicitly assume that all other feedback processes in models are unbiased and should therefore rather be thought of as constraints on tropical low-cloud feedback ( [[#Klein--2015|Klein and Hall, 2015]] ; [[#Qu--2018|Qu et al., 2018]] ; [[#Schlund--2020|Schlund et al., 2020]] ). The following sections go through a range of emergent constraints and assess their strengths and limitations.

<div id="7.5.4.1" class="h3-container"></div>

<span id="emergent-constraints-using-global-or-near-global-surface-temperature-change"></span>
==== 7.5.4.1 Emergent Constraints Using Global or Near-global Surface Temperature Change ====

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Perhaps the simplest class of emergent constraints regress past equilibrium paleoclimate temperature change against modelled ECS to obtain a relationship that can be used to translate a past climate change to ECS. The advantage is that these are constraints on the sum of all feedbacks, and furthermore unlike constraints on the instrumental record they are based on climate states that are at, or close to, equilibrium. So far, these emergent constraints have been limited to the Last Glacial Maximum (LGM; Cross-Chapter Box 2.1) cooling ( [[#Hargreaves--2012|Hargreaves et al., 2012]] ; [[#Schmidt--2014|Schmidt et al., 2014]] ; [[#Renoult--2020|Renoult et al., 2020]] ) and warming in the mid-Pliocene Warm Period (MPWP; Cross-Chapter Box 2.1 and Cross-Chapter Box 2.4; [[#Hargreaves--2016|Hargreaves and Annan, 2016]] ; [[#Renoult--2020|Renoult et al., 2020]] ) due to the availability of sufficiently large multi-model ensembles for these two cases. The paleoclimate emergent constraints are limited by structural uncertainties in the proxy-based global surface temperature and forcing reconstructions ( [[#7.5.3|Section 7.5.3]] ), possible differences in equilibrium sea surface temperature patterns between models and the real world, and a small number of model simulations participating, which has led to divergent results. For example, [[#Hopcroft--2015|Hopcroft and Valdes (2015)]] repeated the study based on the LGM by [[#Hargreaves--2012|Hargreaves et al. (2012)]] using another model ensemble and found that the emergent constraint was not robust, whereas studies using multiple available ensembles retain useful constraints ( [[#Schmidt--2014|Schmidt et al., 2014]] ; [[#Renoult--2020|Renoult et al., 2020]] ). Also, the results are somewhat dependent on the applied statistical methods ( [[#Hargreaves--2016|Hargreaves and Annan, 2016]] ). However, [[#Renoult--2020|Renoult et al. (2020)]] explored this and found 95th percentiles of ECS below 6°C for LGM and Pliocene individually, regardless of statistical approach, and by combining the two estimates the 95th percentile dropped to 4.0°C. The consistency between the cold LGM and warm MPWP emergent constraint estimates increases confidence in these estimates, and further suggests that the dependence of feedback on climate mean state ( [[#7.4.3|Section 7.4.3]] ) as represented in PMIP models used in these studies is reasonable.

Various emergent constraint approaches using global warming over the instrumental record have been proposed. These benefit from more accurate data compared with paleoclimates, but suffer from the fact that the climate is not in equilibrium, thereby assuming that ESMs on average accurately depict the ratio of short-term to long-term global warming. Global warming in climate models over 1850 to the present day exhibits no correlation with ECS, which is partly due to a substantial number of models exhibiting compensation between a high climate sensitivity with strong historical aerosol cooling ( [[#Kiehl--2007|Kiehl, 2007]] ; [[#Forster--2013|Forster et al., 2013]] ; [[#Nijsse--2020|Nijsse et al., 2020]] ). However, the aerosol cooling increased up until the 1970s, when air quality regulations reduced the emissions from Europe and North America whereas other regions saw increases resulting in a subsequently reduced pace of global mean aerosol ERF increase ( [[IPCC:Wg1:Chapter:Chapter-2#2.2.8|Section 2.2.8]] and Figure 2.10). Energy balance considerations over the 1970–2010 period gave a best estimate ECS of 2.0°C ( [[#Bengtsson--2013|Bengtsson and Schwartz, 2013]] ), however this estimate did not account for pattern effects. To address this limitation an emergent constraint on 1970–2005 global warming was demonstrated to yield a best estimate ECS of 2.83 [1.72 to 4.12] °C ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ). The study was followed up using CMIP6 models yielding a best estimate ECS of 2.6 [1.5 to 4.0] °C based on 1975–2019 global warming ( [[#Nijsse--2020|Nijsse et al., 2020]] ), thereby confirming the emergent constraint. Internal variability and forced or unforced pattern effects may influence the results ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ; [[#Nijsse--2020|Nijsse et al., 2020]] ). For instance the Atlantic Multi-decadal Oscillation changed from negative to positive anomaly, while the Indo-Pacific Oscillation changed less over the 1970–2005 period, potentially leading to high-biased results ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ), whereas during the later period 1975–2019 these anomalies roughly cancel ( [[#Nijsse--2020|Nijsse et al., 2020]] ). Pattern effects may have been substantial over these periods ( [[#Andrews--2018|Andrews et al., 2018]] ), however the extent to which TOA radiation anomalies influenced surface temperature may have been dampened by the deep ocean ( [[#Hedemann--2017|Hedemann et al., 2017]] ; [[#Newsom--2020|Newsom et al., 2020]] ). It is therefore deemed ''more likely than not'' that these estimates based on post-1970s global warming are biased low by internal variability.

A study that developed an emergent constraint based on the response to the Mount Pinatubo 1991 eruption yielded a best estimate of 2.4 [ ''likely'' range 1.7 to 4.1] °C ( [[#Bender--2010|Bender et al., 2010]] ). When accounting for ENSO variations they found a somewhat higher best estimate of 2.7°C, which is in line with results of later studies that suggest ECS inferred from periods with substantial volcanic activity are low-biased due to strong pattern effects ( [[#Gregory--2020|Gregory et al., 2020]] ) and that the short-term nature of volcanic forcing could exacerbate possible underestimates of modelled pattern effects.

Lagged correlations present in short-term variations in the global surface temperature can be linked to ECS through the fluctuation–dissipation theorem, which is derived from a single heat-reservoir model ( [[#Einstein--1905|Einstein, 1905]] ; [[#Hasselmann--1976|Hasselmann, 1976]] ; [[#Schwartz--2007|Schwartz, 2007]] ; [[#Cox--2018a|Cox et al., 2018a]] ). From this it follows that the memory carried by the heat capacity of the ocean results in low-frequency global temperature variability (red noise) arising from high-frequency (white noise) fluctuations in the radiation balance, for example, caused by weather. Initial attempts to apply the theorem to observations yielded a fairly low median ECS estimate of 1.1°C ( [[#Schwartz--2007|Schwartz, 2007]] ), a result that was disputed ( [[#Foster--2008|Foster et al., 2008]] ; [[#Knutti--2008|Knutti et al., 2008]] ). Recently it was proposed by [[#Cox--2018a|Cox et al. (2018a)]] to use variations in the historical experiments of the CMIP5 climate models as an emergent constraint giving a median ECS estimate of 2.8 [1.6 to 4.0] °C. A particular challenge associated with these approaches is to separate short-term from long-term variability, and slightly arbitrary choices regarding the methodology of separating these in the global surface temperature from long-term signals in the historical record, omission of the more strongly forced period after 1962, as well as input data choices, can lead to median ECS estimates ranging from 2.5°C to 3.5°C ( [[#Brown--2018|Brown et al., 2018]] ; [[#Po-Chedley--2018a|Po-Chedley et al., 2018a]] ; [[#Rypdal--2018|Rypdal et al., 2018]] ). Calibrating the emergent constraint using CMIP5 modelled internal variability as measured in historical control simulations ( [[#Po-Chedley--2018a|Po-Chedley et al., 2018a]] ) will inevitably lead to an overestimated ECS due to externally forced short-term variability present in the historical record ( [[#Cox--2018b|Cox et al., 2018b]] ). Contrary to constraints based on paleoclimates or global warming since the 1970s, when based on CMIP6 models a higher, yet still well-bounded ECS estimate of 3.7 [2.6 to 4.8] °C is obtained ( [[#Schlund--2020|Schlund et al., 2020]] ). A more problematic issue is raised by [[#Annan--2020|Annan et al. (2020)]] who showed that the upper bound on ECS estimated this way is less certain when considering deep-ocean heat uptake. In conclusion, even if not inconsistent, these limitations prevent us from directly using this type of constraint in the assessment.

Short-term variations in the TOA energy budget, observable from satellites, arising from variations in the tropical tropospheric temperature have been linked to ECS through models, either as a range of models consistent with observations (those with ECS values between 2.0°C and 3.9°C; [[#Dessler--2018|Dessler et al., 2018]] ) or as a formal emergent constraint by deriving further model-based relationships to yield a median of 3.3 [2.4 to 4.5] °C ( [[#Dessler--2018|Dessler and Forster, 2018]] ). There are major challenges associated with short-term variability in the energy budget, in particular how it relates to the long-term forced response of clouds ( [[#Colman--2017|Colman and Hanson, 2017]] ; [[#Lutsko--2018|Lutsko and Takahashi, 2018]] ). Variations in the surface temperature that are not directly affecting the radiation balance lead to an overestimated ECS when using linear regression techniques where it appears as noise in the independent variable ( [[#Proistosescu--2018|Proistosescu et al., 2018]] ; [[#Gregory--2020|Gregory et al., 2020]] ). The latter issue is largely overcome when using the tropospheric mean or mid-tropospheric temperature ( [[#Trenberth--2015|Trenberth et al., 2015]] ; [[#Dessler--2018|Dessler et al., 2018]] ).

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==== 7.5.4.2 Emergent Constraints Focused on Cloud Feedbacks and Present-day Climate ====

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A substantial number of emergent constraint studies focus on observables that are related to tropical low-cloud feedback processes ( [[#Volodin--2008|Volodin, 2008]] ; [[#Sherwood--2014|Sherwood et al., 2014]] ; [[#Zhai--2015|Zhai et al., 2015]] ; [[#Brient--2016|Brient and Schneider, 2016]] ; [[#Brient--2016|Brient et al., 2016]] ). These studies yield median ECS estimates of 3.5°C–4°C and in many cases indicate low likelihoods of values below 3°C. The approach has attracted attention since most of the spread in climate sensitivity seen in CMIP5, and earlier climate model ensembles, arises from uncertainty in low-cloud feedbacks ( [[#Bony--2005|Bony and Dufresne, 2005]] ; [[#Wyant--2006|Wyant et al., 2006]] ; [[#Randall--2007|Randall et al., 2007]] ; [[#Vial--2013|Vial et al., 2013]] ). Nevertheless, this approach assumes that all other feedback processes are unbiased ( [[#Klein--2015|Klein and Hall, 2015]] ; [[#Qu--2018|Qu et al., 2018]] ; [[#Schlund--2020|Schlund et al., 2020]] ), for instance the possibly missing negative anvil area feedback or the possibly exaggerated mixed-phase cloud feedback ( [[#7.4.2.4|Section 7.4.2.4]] ). Thus, the subset of emergent constraints that focus on low-level tropical clouds are not necessarily inconsistent with other emergent constraints of ECS. Related emergent constraints that focus on aspects of the tropical circulation and ECS have led to conflicting results ( [[#Su--2014|Su et al., 2014]] ; [[#Tian--2015|Tian, 2015]] ; [[#Lipat--2017|Lipat et al., 2017]] ; [[#Webb--2020|Webb and Lock, 2020]] ), possibly because these processes are not the dominant factors in causing the inter-model spread ( [[#Caldwell--2018|Caldwell et al., 2018]] ).

The fidelity of models in reproducing aspects of temperature variability or the radiation budget has also been proposed as emergent constraints on ECS ( [[#Covey--2000|Covey et al., 2000]] ; [[#Knutti--2006|Knutti et al., 2006]] ; [[#Huber--2010|Huber et al., 2010]] ; [[#Bender--2012|Bender et al., 2012]] ; [[#Brown--2017|Brown and Caldeira, 2017]] ; [[#Siler--2018a|Siler et al., 2018a]] ). Here indices based on spatial or seasonal variability are linked to modelled ECS, and overall the group of emergent constraints yields best estimates of 3.3°C–3.7°C. Nevertheless, the physical relevance of present-day biases to the sum of long-term climate change feedbacks is unclear and therefore these constraints on ECS are not considered reliable.

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==== 7.5.4.3 Assessed ECS and TCR Based on Emergent Constraints ====

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The available emergent constraint studies have been divided into two classes: (i) those that are based on global or near-global indices, such as global surface temperature and the TOA energy budget; and (ii) those that are more focussed on physical processes, such as the fidelity of phenomena related to low-level cloud feedbacks or present-day climate biases. The former class is arguably superior in representing ECS, since it is a global surface temperature or energy budget change, whereas the latter class is perhaps best thought of as providing constraints on individual climate feedbacks, for example, the determination that low-level cloud feedbacks are positive. The latter result is consistent with and confirms process-based estimates of low-cloud feedbacks ( [[#7.4.2.4|Section 7.4.2.4]] ), but are potentially biased as a group by missing or biased feedbacks in ESMs and is accordingly not taken into account here. A limiting case here is [[#Dessler--2018|Dessler and Forster (2018)]] which is focused on monthly co-variability in the global TOA energy budget with mid-tropospheric temperature, at which time scale the surface-albedo feedback is unlikely to operate, thus implicitly assuming it is unbiased in the model ensemble.

In the first group of emergent constraints there is broad agreement on the best estimate of ECS ranging from 2.4°C–3.3°C. At the lower end, nearly all studies find lower bounds (5th percentiles) around 1.5°C, whereas several studies indicate 95th percentiles as low as 4°C. Considering both classes of studies, none of them yield upper ''very'' ''likely'' bounds above 5°C. Since several of the emergent constraints can be considered nearly independent one could assume that emergent constraints provide very strong evidence on ECS by combining them. Nevertheless, this is not done here because there are sufficient cross-dependencies, as for instance models are re-used in many of the derived emergent constraints, and furthermore the methodology has not yet reached a sufficient level of maturity since systematic biases may not have been accounted for. Uncertainty is therefore conservatively added to reflect these potential issues. This leads to the assessment that ECS inferred from emergent constraints is ''very likely'' 1.5 to 5 °C with ''medium confidence'' .

Emergent constraints on TCR with a focus on the instrumental temperature record, though less abundant, have also been proposed. These can be influenced by internal variability and pattern effects, as discussed in ( [[#7.5.4.1|Section 7.5.4.1]] , although the influence is smaller because uncertainty in forced pattern effects correlates between transient historical warming and TCR. In the simplest form [[#Gillett--2012|Gillett et al. (2012)]] regressed the response of one model to individual historical forcing components to obtain a tight range of 1.3°C–1.8°C, but later when an ensemble of models was used the range was widened to 0.9°C–2.3°C ( [[#Gillett--2013|Gillett et al., 2013]] ), and updated by [[#Schurer--2018|Schurer et al. (2018)]] . A related data-assimilation-based approach that accounted also for uncertainty in response patterns gave 1.33°C–2.36°C ( [[#Ribes--2021|Ribes et al., 2021]] ), but is dependent on the choice of prior ensemble distribution (CMIP5 or CMIP6). Another study used the response to the Pinatubo volcanic eruption to obtain a range of 0.8°C–2.3°C ( [[#Bender--2010|Bender et al., 2010]] ). A tighter range, notably at the lower end, was found in an emergent constraint focusing on the post-1970s warming exploiting the lower spread in aerosol forcing change over this period ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ). Their estimate was 1.67 [1.17 to 2.16] °C. Two studies tested this idea: [[#Tokarska--2020|Tokarska et al. (2020)]] estimates TCR was 1.60 [0.90 to 2.27] °C based on CMIP6 models, whereas [[#Nijsse--2020|Nijsse et al. (2020)]] found 1.68 [1.0 to 2.3] °C. In both cases there was a small sensitivity to choice of ensemble, with CMIP6 models yielding slightly lower values and ranges. Combining these studies gives a best estimate of 1.7°C and a ''very likely'' range of TCR of 1.1 to 2.3 °C with ''high confidence'' .

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<span id="combined-assessment-of-ecs-and-tcr"></span>
=== 7.5.5 Combined Assessment of ECS and TCR ===

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Substantial quantitative progress has been made in interpreting evidence of Earth’s climate sensitivity since AR5, through innovation, scrutiny, theoretical advances and a rapidly evolving data base from current, recent and paleo climates. It should be noted that, unlike AR5 and earlier reports, our assessment of ECS is not directly informed by ESM simulations ( [[#7.5.6|Section 7.5.6]] ). The assessments of ECS and TCR are focussed on the following lines of evidence: process-understanding; the instrumental record of warming; paleoclimate evidence; and emergent constraints. ESMs remain essential tools for establishing these lines of evidence, for instance, in estimating part of the feedback parameters and radiative forcings, and emergent constraints rely on substantial model spread in ECS and TCr ( [[#7.5.6|Section 7.5.6]] ).

A key advance over the AR5 assessment is the broad agreement across multiple lines of evidence. These support a central estimate of ECS close to, or at least not inconsistent with, 3°C. This advance is foremost following improvements in the understanding and quantification of Earth’s energy imbalance, the instrumental record of global temperature change, and the strength of anthropogenic radiative forcing. Further advances include increased understanding of how the pattern effect influences ECS inferred from historical global warming (Sections 7.4.4 and 7.5.3), improved quantification of paleo climatechange from proxy evidence and a deepened understanding of how feedback mechanisms increase ECS in warmer climate states (Sections 7.4.3, 7.4.4 and 7.5.4), and also an improved quantification of individual cloud feedbacks (Sections 7.4.2 and 7.5.4.2). The assessment findings for ECS and TCR are summarized in Table 7.13 and Table 7.14, respectively, and also visualized in Figure 7.18.

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'''Table 7.12''' '''|''' '''Emergent constraint studies used in the assessment of equilibrium climate sensitivity (ECS).''' These are studies that rely on global or near-global temperature change as the observable.

{| class="wikitable"
|-
| Study

| Emergent Constraint Description

| Published Best Estimate and Uncertainty (°C)

| Uncertainty Estimate

|-
| [[#Bender--2010|Bender et al. (2010)]]

| Pinatubo integrated forcing normalized by CMIP3 models’ own forcing versus temperature change regressed against ECS

| 2.4 [1.7 to 4.1]

| 5–95%

|-
| [[#Dessler--2018|Dessler and Forster (2018)]]

| Emergent constraint on TOA radiation variations linked to mid-tropospheric temperature in CMIP5 models

| 3.3 [2.4 to 4.5]

| 17–83%

|-
| [[#Hargreaves--2012|Hargreaves et al. (2012)]]

| Last Glacial Maximum tropical SSTs in PMIP2 models

| 2.5 [1.3 to 4.2]

| 5–95%

|-
| [[#Hargreaves--2016|Hargreaves and Annan (2016)]]

| Pliocene tropical SSTs in PlioMIP models

| [1.9 to 3.7]

| 5–95%

|-
| [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen (2019)]]

| Post-1970s global warming, 1995–2005 relative to 1970–1989, CMIP5 models

| 2.83 [1.72 to 4.12]

| 5–95%

|-
| [[#Nijsse--2020|Nijsse et al. (2020)]]

| Post-1970s global warming, 2009–2019 relative to 1975–1985, CMIP6 models

| 2.6 [1.5 to 4.0]

| 5–95%

|-
| [[#Renoult--2020|Renoult et al. (2020)]]

| Combined Last Glacial Maximum and Pliocene tropical SSTs in PMIP2, PMIP3, PMIP4, PlioMIP and PlioMIP2 models

| 2.5 [0.8 to 4.0]

| 5–95%

|}

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'''Table 7.13''' '''|''' '''Summary of equilibrium climate sensitivity (ECS) assessment.'''

{| class="wikitable"
|-
| Equilibrium Climate Sensitivity (ECS)

| Central Value

| Likely

| Very likely

| Extremely likely

|-
| Process understanding ( [[#7.5.1|Section 7.5.1]] )

| 3.4°C

| 2.5°C to 5.1°C

| 2.1°C to 7.7°C

| –

|-
| Warming over instrumental record ( [[#7.5.2|Section 7.5.2]] )

| 2.5°C to 3.5°C

| &gt;2.2°C

| &gt;1.8°C

| &gt;1.6°C

|-
| Paleoclimates ( [[#7.5.3|Section 7.5.3]] )

| 3.3°C to 3.4°C

| &lt;4.5°C

| &gt;1.5°C

| &lt;8°C

|-
| Emergent constraints ( [[#7.5.4|Section 7.5.4]] )

| 2.4°C to 3.3°C

| –

| 1.5°C to 5.0°C

| –

|-
| Combined assessment

| 3°C

| 2.5°C to 4.0°C

| 2.0°C to 5.0°C

| –

|}

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'''Table 7.14''' '''|''' '''Summary of TCR assessment.'''

{| class="wikitable"
|-
| Transient Climate Response (TCR)

| Central Value

| Likely Range

| Very likely Range

|-
| Process understanding ( [[#7.5.1|Section 7.5.1]] )

| 2.0°C

| 1.6°C to 2.7°C

| 1.3°C to 3.1°C

|-
| Warming over instrumental record ( [[#7.5.2|Section 7.5.2]] )

| 1.9°C

| 1.5°C to 2.3°C

| 1.3°C to 2.7°C

|-
| Emergent constraints ( [[#7.5.4|Section 7.5.4]] )

| 1.7°C

| –

| 1.1°C to 2.3°C

|-
| Combined assessment

| 1.8°C

| 1.4°C to 2.2°C

| 1.2°C to 2.4°C

|}

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[[File:79d3d92af99cc0b748591882f981bbc9 IPCC_AR6_WGI_Figure_7_18.png]]

'''Figure 7.18''' '''|''' '''Summary of the equilibrium climate sensitivity (ECS panel (a)) and transient climate response (TCR panel (b)) assessments using different lines of evidence.''' Assessed ranges are taken from Tables 7.13 and 7.14 for ECS and TCR respectively. Note that for the ECS assessment based on both the instrumental record and paleoclimates, limits (i.e., one-sided distributions) are given, which have twice the probability of being outside the maximum/minimum value at a given end, compared to ranges (i.e., two-tailed distributions) which are given for the other lines of evidence. For example, the ''extremely likely'' limit of greater than 95% probability corresponds to one side of the ''very likely'' (5–95%) range. Best estimates are given as either a single number or by a range represented by a grey box. CMIP6 model values are not directly used as a line of evidence but presented on the Figure for comparison. ECS values are taken from [[#Schlund--2020|Schlund et al. (2020)]] and TCR values from [[#Meehl--2020|Meehl et al. (2020)]] ; see Supplementary Material 7.SM.4. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

The AR5 assessed ECS to have a ''likely'' range from 1.5 to 4.5 °C (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ) based on the majority of studies and evidence available at the time. The broader evidence base presented in this Report and the general agreement among different lines of evidence means that they can be combined to yield a narrower range of ECS values. This can be done formally using Bayesian statistics, though such a process is complex and involves formulating likelihoods and priors ( [[#Annan--2006|Annan and Hargreaves, 2006]] ; [[#Stevens--2016|Stevens et al., 2016]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ). However, it can be understood that if two lines of independent evidence each give a low probability of an outcome being true, for example, that ECS is less than 2.0°C, then the combined probability that ECS is less than 2.0°C is lower than that of either line of evidence. On the contrary, if one line of evidence is unable to rule out an outcome, but another is able to assign a low probability, then there is a low probability that the outcome is true ( [[#Stevens--2016|Stevens et al., 2016]] ). This general principle applies even when there is some dependency between the lines of evidence ( [[#Sherwood--2020|Sherwood et al., 2020]] ), for instance between historical energy budget constraints ( [[#7.5.2.1|Section 7.5.2.1]] ) and those emergent constraints that use the historically observed global warming ( [[#7.5.4.1|Section 7.5.4.1]] ). Even in this case the combined constraint will be closer to the narrowest range associated with the individual lines of evidence.

In the process of providing a combined and self-consistent ECS assessment across all lines of evidence, the above principles were all considered. As in earlier reports, a 0.5°C precision is used. Starting with the ''very likely'' lower bound, there is broad support for a value of 2.0°C, including process understanding and the instrumental record (Table 7.13). For the ''very likely'' upper bound, emergent constraints give a value of 5.0°C whereas the three other lines of evidence are individually less tightly constrained. Nevertheless, emergent constraints are a relatively recent field of research, in part taken into account by adding uncertainty to the upper bound ( [[#7.5.4.3|Section 7.5.4.3]] ), and the underlying studies use, to a varying extent, information that is also used in the other three lines of evidence, causing statistical dependencies. However, omitting emergent constraints and statistically combining the remaining lines of evidence likewise yields 95th percentiles close to 5.0°C ( [[#Sherwood--2020|Sherwood et al., 2020]] ). Information for the ''likely'' range is partly missing or one-sided, however it must necessarily reside inside the ''very likely'' range and is therefore supported by evidence pertaining to both the ''likely'' and ''very likely'' ranges. Hence, the upper ''likely'' bound is assessed to be about halfway between the best estimate and the upper ''very likely'' bound while the lower ''likely'' bound is assessed to be about halfway between the best estimate and the lower ''very likely'' bound. In summary, based on multiple lines of evidence the best estimate of ECS is 3°C, it is ''likely'' within the range 2.5 to 4 °C and ''very likely'' within the range 2 to 5 °C. It is ''virtually certain'' that ECS is larger than 1.5°C. Whereas there is ''high confidence'' based on mounting evidence that supports the best estimate, ''likely'' range and ''very likely'' lower end, a higher ECS than 5°C cannot be ruled out, hence there is ''medium confidence'' in the upper end of the ''very likely'' range. Note that the best estimate of ECS made here corresponds to a feedback parameter of –1.3 W m <sup>–2</sup> °C <sup>–1</sup> which is slightly more negative than the feedback parameter from process-based evidence alone that is assessed in ( [[#7.4.2.7|Section 7.4.2.7]] .

There has long been a consensus ( [[#Charney--1979|Charney et al., 1979]] ) supporting an ECS estimate of 1.5°C–4.5°C. In this regard it is worth remembering the many debates challenging an ECS of this magnitude. These started as early as [[#Ångström--1900|Ångström (1900)]] criticizing the results of [[#Arrhenius--1896|Arrhenius (1896)]] arguing that the atmosphere was already saturated in infrared absorption such that adding more CO <sub>2</sub> would not lead to warming. The assertion of Ångström was understood half a century later to be incorrect. History has seen a multitude of studies (e.g., [[#Svensmark--1998|Svensmark, 1998]] ; [[#Lindzen--2001|Lindzen et al., 2001]] ; [[#Schwartz--2007|Schwartz, 2007]] ) mostly implying lower ECS than the range assessed as ''very likely'' here. However, there are also examples of the opposite, such as very large ECS estimates based on the Pleistocene records ( [[#Snyder--2016|Snyder, 2016]] ), which have been shown to be overestimated due to a lack of accounting for orbital forcing and long-term ice-sheet feedbacks ( [[#Schmidt--2017b|Schmidt et al., 2017b]] ), or suggestions that global climate instabilities may occur in the future ( [[#Steffen--2018|Steffen et al., 2018]] ; [[#Schneider--2019|Schneider et al., 2019]] ). There is, however, no evidence for unforced instabilities of such magnitude occurring in the paleo-record temperatures of the past 65 million years ( [[#Westerhold--2020|Westerhold et al., 2020]] ), possibly short of the Paleocene–Eocene Thermal Maximum (PETM) excursion ( [[IPCC:Wg1:Chapter:Chapter-5#5.3.1.1|Section 5.3.1.1]] ) that occurred at more than 10°C above present-day levels ( [[#Anagnostou--2020|Anagnostou et al., 2020]] ). Looking back, the resulting debates have led to a deeper understanding, strengthened the consensus, and have been scientifically valuable.

In the climate sciences, there are often good reasons to consider representing deep uncertainty, or what are sometimes referred to as ‘unknown unknowns’. This is natural in a field that considers a system that is both complex and at the same time challenging to observe. For instance, since emergent constraints represent a relatively new line of evidence, important feedback mechanisms may be biased in process-level understanding; pattern effects and aerosol cooling may be large; and paleo evidence inherently builds on indirect and incomplete evidence of past climate states, there certainly can be valid reasons to add uncertainty to the ranges assessed on individual lines of evidence. This has indeed been addressed throughout Sections 7.5.1–7.5.4. Since it is neither probable that all lines of evidence assessed here are collectively biased nor is the assessment sensitive to single lines of evidence, deep uncertainty is not considered as necessary to frame the combined assessment of ECS.

The evidence for TCR is less abundant than for ECS, and focuses on the instrumental temperature record (Sections 7.5.2 and 7.5.6), emergent constraints ( [[#7.5.4.3|Section 7.5.4.3]] ) and process understanding ( [[#7.5.1|Section 7.5.1]] ). The AR5 assessed a ''likely'' range for TCR of 1.0 to 2.5 °C. TCR and ECS are related, though, and in any case TCR is less than ECS (see the introduction to ( [[#7.5|Section 7.5]] ). Furthermore, estimates of TCR from the historical record are not as strongly influenced by externally forced surface temperature pattern effects as estimates of ECS are since both historical transient warming and TCR are affected by this phenomenon ( [[#7.4.4|Section 7.4.4]] ). A slightly higher weight is given to instrumental record warming and emergent constraints since these are based on observed transient warming, whereas the process-understanding estimate relies on pattern effects and ocean heat uptake efficiency from ESMs to represent the transient dampening effects of the ocean. If these effects are underestimated by ESMs then the resulting TCR would be lower. Given the interdependencies of the other two lines of evidence, a conservative approach to combining them as reflected in the assessment is adopted. Since uncertainty is substantially lower than in AR5 a 0.1°C precision is therefore used here. Otherwise the same methodology for combining the lines of evidence as applied to ECS is used for TCR. Based on process understanding, warming over the instrumental record and emergent constraints, the best estimate TCR is 1.8°C, it is ''likely'' 1.4 to 2.2 °C and ''very likely'' 1.2 to 2.4 °C. The assessed ranges are all assigned ''high confidence'' due to the high level of agreement among the lines of evidence.

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=== 7.5.6 Considerations on the ECS and TCR in Global Climate Models and Their Role in the Assessment ===

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Coupled climate models, such as those participating in CMIP, have long played a central role in assessments of ECS and TCR. In reports up to and including the IPCC Third Assessment Report (TAR), climate sensitivities derived directly from ESMs were the primary line of evidence. However, since AR4, historical warming and paleoclimate information provided useful additional evidence and it was noted that assessments based on models alone were problematic ( [[#Knutti--2010|Knutti, 2010]] ). As new lines of evidence have evolved, in AR6 various numerical models are used where they are considered accurate, or in some cases the only available source of information, and thereby support all four lines of evidence (Sections 7.5.1–7.5.4). However, AR6 differs from previous IPCC reports in excluding direct estimates of ECS and TCR from ESMs in the assessed ranges ( [[#7.5.5|Section 7.5.5]] ), following several recent studies ( [[#Annan--2006|Annan and Hargreaves, 2006]] ; [[#Stevens--2016|Stevens et al., 2016]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ). The purpose of this section is to explain why this approach has been taken and to provide a perspective on the interpretation of the climate sensitivities exhibited in CMIP6 models.

The primary consideration that led to excluding ECS and TCR directly derived from ESMs is that information from these models is incorporated in the lines of evidence used in the assessment: ESMs are partly used to estimate historical and paleoclimate ERFs (Sections 7.5.2 and 7.5.3); to convert from local to global mean paleo temperatures ( [[#7.5.3|Section 7.5.3]] ); to estimate how feedbacks change with SST patterns ( [[#7.4.4.3|Section 7.4.4.3]] ); and to establish emergent constraints on ECs ( [[#7.5.4|Section 7.5.4]] ). They are also used as important evidence in the process understanding estimates of the temperature, water vapour, albedo, biogeophysical, and non-CO <sub>2</sub> biogeochemical feedbacks, whereas other evidence is primarily used for cloud feedbacks where the climate model evidence is weak ( [[#7.4.2|Section 7.4.2]] ). One perspective on this is that the process understanding line of evidence builds on and replaces ESM estimates.

The ECS of a model is the net result of the model’s effective radiative forcing from a doubling of CO <sub>2</sub> and the sum of the individual feedbacks and their interactions. It is well known that most of the model spread in ECS arises from cloud feedbacks, and particularly the response of low-level clouds ( [[#Bony--2005|Bony and Dufresne, 2005]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ). Since these clouds are small-scale and shallow, their representation in climate models is mostly determined by sub-grid-scale parametrizations. It is sometimes assumed that parametrization improvements will eventually lead to convergence in model response and therefore a decrease in the model spread of ECS. However, despite decades of model development, increases in model resolution and advances in parametrization schemes, there has been no systematic convergence in model estimates of ECS. In fact, the overall inter-model spread in ECS for CMIP6 is larger than for CMIP5; ECS and TCR values are given for CMIP6 models in Supplementary Material 7.SM.4 based on [[#Schlund--2020|Schlund et al. (2020)]] for ECS and [[#Meehl--2020|Meehl et al. (2020)]] for TCR (see also Figure 7.18 and FAQ 7.3). The upward shift does not apply to all models traceable to specific modelling centres, but a substantial subset of models have seen an increase in ECS between the two model generations. The increased ECS values, as discussed in ( [[#7.4.2.8|Section 7.4.2.8]] , are partly due to shortwave cloud feedbacks ( [[#Flynn--2020|Flynn and Mauritsen, 2020]] ) and it appears that in some models extra-tropical clouds with mixed ice and liquid phases are central to the behaviour ( [[#Zelinka--2020|Zelinka et al., 2020]] ), probably borne out of a recent focus on biases in these types of clouds ( [[#McCoy--2016|McCoy et al., 2016]] ; [[#Tan--2016|Tan et al., 2016]] ). These biases have recently been reduced in many ESMs, guided by process understanding from laboratory experiments, field measurements and satellite observations ( [[#Lohmann--2018|Lohmann and Neubauer, 2018]] ; [[#Bodas-Salcedo--2019|Bodas-Salcedo et al., 2019]] ; [[#Gettelman--2019|Gettelman et al., 2019]] ). However, this and other known model biases are already factored into the process-level assessment of cloud feedback ( [[#7.4.2.4|Section 7.4.2.4]] ), and furthermore the emergent constraints used here focus on global surface temperature change and are therefore less susceptible to shared model biases in individual feedback parameters than emergent constraints that focus on specific physical processes ( [[#7.5.4|Section 7.5.4]] ). The high values of ECS and TCR in some CMIP6 models lead to higher levels of surface warming than CMIP5 simulations and also the AR6 projections based on the assessed ranges of ECS, TCR and ERF (Box 4.1 and FAQ 7.3; [[#Forster--2020|Forster et al., 2020]] ).

It is generally difficult to determine which information enters the formulation and development of parametrizations used in ESMs. Climate models frequently share code components, and in some cases entire sub-model systems are shared and slightly modified. Therefore, models cannot be considered independent developments, but rather families of models with interdependencies ( [[#Knutti--2013|Knutti et al., 2013]] ). It is therefore difficult to interpret the collection of models ( [[#Knutti--2010|Knutti, 2010]] ), and it cannot be ruled out that there are common limitations and therefore systematic biases to model ensembles that are reflected in the distribution of ECS as derived from them. Although ESMs are typically well-documented, in ways that increasingly include information on critical decisions regarding tuning ( [[#Mauritsen--2012|Mauritsen et al., 2012]] ; [[#Hourdin--2017|Hourdin et al., 2017]] ; [[#Schmidt--2017a|Schmidt et al., 2017a]] ; [[#Mauritsen--2020|Mauritsen and Roeckner, 2020]] ), the full history of development decisions could involve both process-understanding and sometimes also other information such as historical warming. As outlying or poorly performing models emerge from the development process, they can become re-tuned, reconfigured or discarded and so might not see publication ( [[#Hourdin--2017|Hourdin et al., 2017]] ; [[#Mauritsen--2020|Mauritsen and Roeckner, 2020]] ). In the process of addressing such issues, modelling groups may, whether intentionally or not, modify the modelled ECS.

It is problematic and not obviously constructive to provide weights for, or rule out, individual CMIP6 model ensemble members based solely on their ECS and TCR values. Rather these models must be tested in a like-with-like way against observational evidence. Based on the currently published CMIP6 models we provide such an analysis, marking models with ECS above and below the assessed ''very likely'' range (Figure 7.19). In the long-term historical warming (Figure 7.19a) both low- and high-ECS models are able to match the observed warming, presumably in part as a result of compensating aerosol cooling ( [[#Kiehl--2007|Kiehl, 2007]] ; [[#Forster--2013|Forster et al., 2013]] ; [[#Wang--2021|Wang et al., 2021]] ). In several cases of high ECS models that apply strong aerosol cooling it is found to result in surface warming and ocean heat uptake evolutions that are inconsistent with observations ( [[#Golaz--2019|Golaz et al., 2019]] ; [[#Andrews--2020|Andrews et al., 2020]] ; [[#Winton--2020|Winton et al., 2020]] ). Modelled warming since the 1970s is less influenced by compensation between climate sensitivity and aerosol cooling ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ; [[#Nijsse--2020|Nijsse et al., 2020]] ) resulting in the high-ECS models in general warming more than observed, whereas low-sensitivity models mostly perform better (Figure 7.19b); a result that may also have been influenced by temporary pattern effects (Sections 7.4.4 and 7.5.4). Paleoclimates are not influenced by such transient pattern effects, but are limited by structural uncertainties in the proxy-based temperature and forcing reconstructions as well as possible differences in equilibrium sea surface temperature patterns between models and the real world ( [[#7.5.4|Section 7.5.4]] ). Across the LGM, MPWP and EECO (Figure 7.19c–e), the few high-ECS models that simulated these cases were outside the observed ''very likely'' ranges (see also [[#Feng--2020|Feng et al., 2020]] ; [[#Renoult--2020|Renoult et al., 2020]] ; [[#Zhu--2020|Zhu et al., 2020]] ). Also the low-ECS model is either outside or on the edge of the observed ''very likely'' ranges.

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[[File:82b743adf7edf9bb6503d75269b423b1 IPCC_AR6_WGI_Figure_7_19.png]]

'''Figure 7.19''' '''|''' '''Global mean temperature anomaly in models and observations from five time periods. (a)''' Historical (CMIP6 models); '''(b)''' post-1975 (CMIP6 models); '''(c)''' Last Glacial Maximum (LGM; Cross-Chapter Box 2.1; PMIP4 models; [[#Kageyama--2021|Kageyama et al., 2021]] ; [[#Zhu--2021|Zhu et al., 2021]] ); '''(d)''' mid-Pliocene Warm Period (MPWP; Cross-Chapter Box 2.4; PlioMIP models; [[#Haywood--2020|Haywood et al., 2020]] ; [[#Zhang--2021|Zhang et al., 2021]] ); '''(e)''' Early Eocene Climatic Optimum (EECO; Cross-Chapter Box 2.1; DeepMIP models; [[#Zhu--2020|Zhu et al., 2020]] ; [[#Lunt--2021|Lunt et al., 2021]] ). Grey circles show models with ECS in the assessed ''very likely'' range; models in red have an ECS greater than the assessed ''very likely'' range (&gt;5°C); models in blue have an ECS lower than the assessed ''very likely'' range (&lt;2°C). Black ranges show the assessed temperature anomaly derived from observations ( [[IPCC:Wg1:Chapter:Chapter-2#2.3|Section 2.3]] ). The historical anomaly in models and observations is calculated as the difference between 2005–2014 and 1850–1900, and the post-1975 anomaly is calculated as the difference between 2005–2014 and 1975–1984. For the LGM, MPWP and EECO, temperature anomalies are compared with pre-industrial (equivalent to CMIP6 simulation ‘piControl’). All model simulations of the MPWP and LGM were carried out with atmospheric CO <sub>2</sub> concentrations of 400 and 190 ppm respectively. However, CO <sub>2</sub> during the EECO is relatively more uncertain, and model simulations were carried out at either 1120ppm or 1680 ppm (except for the one high-ECS EECO simulation which was carried out at 840 ppm; [[#Zhu--2020|Zhu et al., 2020]] ). The one low-ECS EECO simulation was carried out at 1680 ppm. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

As a result of the above considerations, in this Report projections of global surface temperature are produced using climate model emulators that are constrained by the assessments of ECS, TCR and ERF. In reports up to and including AR5, ESM values of ECS did not fully encompass the assessed ''very likely'' range of ECS, raising the possibility that past multi-model ensembles underestimated the uncertainty in climate change projections that existed at the times of those reports (e.g., [[#Knutti--2010|Knutti, 2010]] ). However, due to an increase in the modelled ECS spread and a decrease in the assessed ECS spread based on improved knowledge in multiple lines of evidence, the CMIP6 ensemble encompasses the ''very likely'' range of ECS [2 to 5] °C assessed in ( [[#7.5.5|Section 7.5.5]] . Models outside of this range are useful for establishing emergent constraints on ECS and TCR and provide useful examples of ‘tail risk’ ( [[#Sutton--2018|Sutton, 2018]] ), producing dynamically consistent realizations of future climate change to inform impact studies and risk assessments.

In summary, the distribution of CMIP6 models have higher average ECS and TCR values than the CMIP5 generation of models and the assessed values of ECS and TCR in ( [[#7.5.5|Section 7.5.5]] . The high ECS and TCR values can in some CMIP6 models be traced to improved representation of extratropical cloud feedbacks ( ''medium confidence'' ). The ranges of ECS and TCR from the CMIP6 models are not considered robust samples of possible values and the models are not considered a separate line of evidence for ECS and TCR. Solely based on its ECS or TCR values an individual ESM cannot be ruled out as implausible, though some models with high (greater than 5°C) and low (less than 2°C) ECS are less consistent with past climate change ( ''high confidence'' ). High climate sensitivity in models leads to generally higher projected warming in CMIP6 compared to both CMIP5 and that assessed based on multiple lines of evidence (Sections 4.3.1 and 4.3.4, and FAQ 7.3).

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=== 7.5.7 Processes Underlying Uncertainty in the Global Temperature Response to Forcing ===

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While the magnitude of global warming by the end of the 21st century is dominated by future GHG emissions, the uncertainty in warming for a given ERF change is dominated by the uncertainty in ECS and TCr ( [[IPCC:Wg1:Chapter:Chapter-4#4.3.4|Section 4.3.4]] ). The proportion of variation explained by ECS and TCR varies with scenario and the time period considered, but within CMIP5 models around 60–90% of the globally averaged projected surface warming range in 2100 can be explained by the model range of these metrics ( [[#Grose--2018|Grose et al., 2018]] ). Uncertainty in the long-term global surface temperature change can further be understood in terms of the processes affecting the global TOA energy budget, namely the ERF, the radiative feedbacks which govern the efficiency of radiative energy loss to space with surface warming, and the increase in the global energy inventory (dominated by ocean heat uptake) which reduces the transient surface warming. A variety of studies evaluate the effect of each of these processes on surface changes within coupled ESM simulations by diagnosing so-called ‘warming contributions’ ( [[#Dufresne--2008|Dufresne and Bony, 2008]] ; [[#Crook--2011|Crook et al., 2011]] ; [[#Feldl--2013|Feldl and Roe, 2013]] ; [[#Vial--2013|Vial et al., 2013]] ; [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Goosse--2018|Goosse et al., 2018]] ). By construction, the individual warming contributions sum to the total global surface warming (Figure 7.20b). For long-term warming in response to CO <sub>2</sub> forcing in CMIP5 models, the energy added to the climate system by radiative feedbacks is larger than the ERF of CO <sub>2</sub> (Figure 7.20a), implying that feedbacks more than double the magnitude of global warming (Figure 7.20b). Radiative kernel methods (see ( [[#7.4.1|Section 7.4.1]] ) can be used to decompose the net energy input from radiative feedbacks into its components. The water-vapour, cloud and surface-albedo feedbacks enhance global warming, while the lapse-rate feedback reduces global warming. Ocean heat uptake reduces the rate of global surface warming by sequestering heat at depth away from the ocean surface. [[#7.4.4.1|Section 7.4.4.1]] shows the warming contributions from these factors at the regional scale.

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[[File:0fab9a4e2c6b8d836649787302b6e33d IPCC_AR6_WGI_Figure_7_20.png]]

'''Figure 7.20''' '''|''' '''Contributions of effective radiative forcing, ocean heat uptake and radiative feedbacks to global atmospheric energy input and ne''' '''ar-su''' '''rface air temperature change at year 100 of''' ''abrupt 4xCO2'' '''simulations of CMIP6 models. (a)''' The energy flux to the global atmosphere associated with the effective CO <sub>2</sub> forcing, global ocean heat uptake, Planck response, and radiative feedbacks, which together sum to zero. The inset shows energy input from individual feedbacks, summing to the total feedback energy input. '''(b)''' Contributions to net global warming are calculated by dividing the energy inputs by the ''magnitude'' of the global Planck response (3.2 W m <sup>–2</sup> °C <sup>–1</sup> ), with the contributions from radiative forcing, ocean heat uptake, and radiative feedbacks (orange bars) summing to the value of net warming (grey bar). The inset shows warming contributions associated with individual feedbacks, summing to the total feedback contribution. Uncertainties show the interquartile range (25th and 75th percentiles) across models. Radiative kernel methods (see ( [[#7.4.1|Section 7.4.1]] ) were used to decompose the net energy input from radiative feedbacks into contributions from changes in atmospheric water vapour, lapse rate, clouds, and surface albedo ( [[#Zelinka--2020|Zelinka et al. (2020)]] using the [[#Huang--2017|Huang et al. (2017)]] radiative kernel). The CMIP6 models included are those analysed by [[#Zelinka--2020|Zelinka et al. (2020)]] and the warming contribution analysis is based on that of [[#Goosse--2018|Goosse et al. (2018)]] . Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

Differences in projected transient global warming across ESMs are dominated by differences in their radiative feedbacks, while differences in ocean heat uptake and radiative forcing play secondary roles (Figure 7.20b; [[#Vial--2013|Vial et al., 2013]] ). The uncertainty in projected global surface temperature change associated with inter-model differences in cloud feedbacks is the largest source of uncertainty in CMIP5 and CMIP6 models (Figure 7.20b), just as they were for CMIP3 models ( [[#Dufresne--2008|Dufresne and Bony, 2008]] ). Extending this energy budget analysis to equilibrium surface warming suggests that about 70% of the inter-model differences in ECS arises from uncertainty in cloud feedbacks, with the largest contribution to that spread coming from shortwave low-cloud feedbacks ( [[#Vial--2013|Vial et al., 2013]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ).

Interactions between different feedbacks within the coupled climate system pose a challenge to our ability to understand global warming and its uncertainty based on energy budget diagnostics ( [[#7.4.2|Section 7.4.2]] ). For example, water-vapour and lapse-rate feedbacks are correlated ( [[#Held--2006|Held and Soden, 2006]] ) owing to their joint dependence on the spatial pattern of warming ( [[#Po-Chedley--2018b|Po-Chedley et al., 2018b]] ). Moreover, feedbacks are not independent of ocean heat uptake because the uptake and transport of heat by the ocean influences the SST pattern on which global feedbacks depend ( [[#7.4.4.3|Section 7.4.4.3]] ). However, alternative decompositions of warming contributions that better account for correlations between feedbacks produce similar results ( [[#Caldwell--2016|Caldwell et al., 2016]] ). The key role of radiative feedbacks in governing the magnitude of global warming is also supported by the high correlation between radiative feedbacks (or ECS) and transient 21st-century warming within ESMs ( [[#Grose--2018|Grose et al., 2018]] ).

Another approach to evaluating the roles of forcing, feedbacks and ocean heat uptake in projected warming employs idealized energy balance models that emulate the response of ESMs, and which preserve the interactions between system components. One such emulator, used in ( [[#7.5.1.2|Section 7.5.1.2]] , resolves the heat capacity of both the surface components of the climate system and the deep ocean ( [[#Held--2010|Held et al., 2010]] ; [[#Geoffroy--2013a|Geoffroy et al., 2013a]] , b; [[#Kostov--2014|Kostov et al., 2014]] ; [[#Armour--2017|Armour, 2017]] ). Using this emulator, [[#Geoffroy--2012|Geoffroy et al. (2012)]] find that: under an idealized 1% per year increase in atmospheric CO <sub>2</sub> , radiative feedbacks constitute the greatest source of uncertainty (about 60% of variance) in transient warming beyond several decades; ERF uncertainty plays a secondary but important role in warming uncertainty (about 20% of variance) that diminishes beyond several decades; and ocean heat uptake processes play a minor role in warming uncertainty (less than 10% of variance) at all time scales.

More computationally intensive approaches evaluate how the climate response depends on perturbations to key parameter or structural choices within ESMs. Large ‘perturbed parameter ensembles’, wherein a range of parameter settings associated with cloud physics are explored within atmospheric ESMs, produce a wide range of ECS due to changes in cloud feedbacks, but often produce unrealistic climate states ( [[#Joshi--2010|Joshi et al., 2010]] ). [[#Rowlands--2012|Rowlands et al. (2012)]] generated an ESM perturbed-physics ensemble of several thousand members by perturbing model parameters associated with radiative forcing, cloud feedbacks and ocean vertical diffusivity (an important parameter for ocean heat uptake). After constraining the ensemble to have a reasonable climatology and to match the observed historical surface warming, they found a wide range of projected warming by the year 2050 under the SRES A1B scenario (1.4°C–3°C relative to the 1961–1990 average) that is dominated by differences in cloud feedbacks. The finding that cloud feedbacks are the largest source of spread in the net radiative feedback has since been confirmed in perturbed parameter ensemble studies using several different ESMs ( [[#Gettelman--2012|Gettelman et al., 2012]] ; [[#Tomassini--2015|Tomassini et al., 2015]] ; [[#Kamae--2016b|Kamae et al., 2016b]] ; [[#Rostron--2020|Rostron et al., 2020]] ; [[#Tsushima--2020|Tsushima et al., 2020]] ). By swapping out different versions of the atmospheric or oceanic components in a coupled ESM, [[#Winton--2013|Winton et al. (2013)]] found that TCR and ECS depend on which atmospheric component was used (using two versions with different atmospheric physics), but that only TCR is sensitive to which oceanic component of the model was used (using two versions with different vertical coordinate systems, among other differences); TCR and ECS changed by 0.4°C and 1.4°C, respectively, when the atmospheric model component was changed, while TCR and ECS changed by 0.3°C and less than 0.05°C, respectively, when the oceanic model component was changed. By perturbing ocean vertical diffusivities over a wide range, [[#Watanabe--2020|Watanabe et al. (2020)]] found that TCR changed by 0.16°C within the model MIROC5.2 while [[#Krasting--2018|Krasting et al. (2018)]] found that ECS changed by about 0.6°C within the model GFDL-ESM2G, with this difference linked to different radiative feedbacks associated with different spatial patterns of sea surface warming ( [[#7.4.4.3|Section 7.4.4.3]] ). By comparing simulations of CMIP6 models with and without the effects of CO <sub>2</sub> on vegetation, [[#Zarakas--2020|Zarakas et al. (2020)]] find a physiological contribution to TCR of 0.12°C (range 0.02°C–0.29°C across models) owing to physiological adjustments to the CO <sub>2</sub> eRf ( [[#7.3.2.1|Section 7.3.2.1]] ).

There is ''robust evidence'' and ''high agreement'' across a diverse range of modelling approaches and thus ''high confidence'' that radiative feedbacks are the largest source of uncertainty in projected global warming out to 2100 under increasing or stable emissions scenarios, and that cloud feedbacks in particular are the dominant source of that uncertainty. Uncertainty in radiative forcing plays an important but generally secondary role. Uncertainty in global ocean heat uptake plays a lesser role in global warming uncertainty, but ocean circulation could play an important role through its effect on sea surface warming patterns which in turn project onto radiative feedbacks through the pattern effect ( [[#7.4.4.3|Section 7.4.4.3]] ).

The spread in historical surface warming across CMIP5 ESMs shows a weak correlation with inter-model differences in radiative feedback or ocean heat uptake processes but a high correlation with inter-model differences in radiative forcing owing to large variations in aerosol forcing across models ( [[#Forster--2013|Forster et al., 2013]] ). Likewise, the spread in projected 21st-century warming across ESMs depends strongly on which emissions scenario is employed ( [[IPCC:Wg1:Chapter:Chapter-4#4.3.1|Section 4.3.1]] ; [[#Hawkins--2012|Hawkins and Sutton, 2012]] ). Strong emissions reductions would remove aerosol forcing (Section 6.7.2) and this could dominate the uncertainty in near-term warming projections ( [[#Armour--2011|Armour and Roe, 2011]] ; [[#Mauritsen--2017|Mauritsen and Pincus, 2017]] ; [[#Schwartz--2018|Schwartz, 2018]] ; [[#Smith--2019|Smith et al., 2019]] ). On post-2100 time scales carbon cycle uncertainty such as that related to permafrost thawing could become increasingly important, especially under high-emissions scenarios (Figure 5.30).

In summary, there is ''high confidence'' that cloud feedbacks are the dominant source of uncertainty for late 21st-century projections of transient global warming under increasing or stable emissions scenarios, whereas uncertainty is dominated by aerosol ERF in strong mitigation scenarios. Global ocean heat uptake is a smaller source of uncertainty in long-term surface warming ( ''high confidence'' ).

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