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

==== 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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