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

==== 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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