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

=== 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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