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

==== 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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