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

=== 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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