From IPCC, AR6, Working Group I, "The Physical Science Basis", Full Report, Pg 992
7.5 Estimates of ECS and TCR
Equilibrium climate sensitivity (ECS) and transient climate response (TCR) are metrics of the global surface air temperature (GSAT) response to forcing, as defined in Box 7.1. ECS is the magnitude of the long-term GSAT increase in response to a doubling of atmospheric CO2 concentration after the planetary energy budget is balanced, though leaving out feedbacks associated with ice sheets; whereas the TCR is the magnitude of GSAT increase at year 70 when CO2 concentration is doubled in a 1% yr –1 increase scenario. Both are idealized quantities, but can be inferred from paleoclimate or observational records or estimated directly using climate simulations, and are strongly correlated with the climate response in realistic future projections (Sections 4.3.4 and 7.5.7; Grose et al., 2018).
TCR is always smaller than ECS because ocean heat uptake acts to reduce the rate of surface warming. Yet, TCR is related to ECS across CMIP5 and CMIP6 models (Grose et al., 2018; Flynn and Mauritsen, 2020) as expected since TCR and ECS are inherently measures of climate response to forcing; both depend on effective radiative forcing (ERF) and the net feedback parameter, α. The relationship between TCR and ECS is, however, non-linear and becomes more so for higher ECS values (Hansen et al., 1985; Knutti et al., 2005; Millar et al., 2015; Flynn and Mauritsen, 2020; Tsutsui, 2020) owing to ocean heat uptake processes and surface temperature pattern effects temporarily reducing the rate of surface warming. When α is small in magnitude, and correspondingly ECS is large (recall that ECS is inversely proportional to α), these temporary effects are increasingly important in reducing the ratio of TCR to ECS.
Before AR6, the assessment of ECS relied on either CO2-doubling experiments using global atmospheric models coupled with mixed-layer ocean or standardized CO2-quadrupling (abrupt4xCO2) experiments using fully coupled ocean–atmosphere models or Earth system models (ESMs). The TCR has similarly been diagnosed from ESMs in which the CO2 concentration is increased at 1% yr –1 (1pctCO2, an approximately linear increase in ERF over time) and is in practice estimated as the average over a 20-year period centred at the time of atmospheric CO2 doubling, that is, year 70.
In AR6, the assessments of ECS and TCR are made based on multiple lines of evidence, with ESMs representing only one of several sources of information. The constraints on these climate metrics are based on radiative forcing and climate feedbacks assessed from process understanding (Section 7.5.1), climate change and variability seen within the instrumental record (Section 7.5.2), paleoclimate evidence (Section 7.5.3), emergent constraints (Section 7.5.4), and a synthesis of all lines of evidence (Section 7.5.5). [Emphasis mine --OP] In AR5, these lines of evidence were not explicitly combined in the assessment of climate sensitivity, but as demonstrated by Sherwood et al. (2020) their combination narrows the uncertainty ranges of ECS compared to that assessed in AR5. ECS values found in CMIP6 models, some of which exhibit values higher than 5°C (Meehl et al., 2020; Zelinka et al., 2020), are discussed in relation to the AR6 assessment in section 7.5.6.
7.5.1 Estimates of ECS and TCR Based on Process Understanding
This section assesses the estimates of ECS and TCR based on process understanding of the ERF due to a doubling of CO2 concentration and the net climate feedback (Sections 7.3.2 and 7.4.2). This process-based assessment is made in Section 7.5.1.1 and applied to TCR in Section 7.5.1.2.
7.5.1.1 ECS Estimated Using Process-based Assessments of Forcing and Feedbacks
The process-based assessment is based on the global energy budget equation (Box 7.1, Equation 7.1), where the ERF (ΔF) is set equal to the effective radiative forcing due to a doubling of CO2 concentration (denoted as ΔF2×CO2) and the climate state reaches a new equilibrium, that is, Earth’s energy imbalance averages to zero (ΔN = 0). ECS is calculated as the ratio between the ERF and the net feedback parameter: ECS = –ΔF2×CO2/α. Estimates of ΔF2×CO2 and α are obtained separately based on understanding of the key processes that determine each of these quantities. Specifically, ΔF2×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 (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 (Section 7.4.2).
The effective radiative forcing of CO2 doubling is assessed to be ΔF2×CO2 = 3.93 ± 0.47 W m–2 (Section 7.3.2.1), while the net feedback parameter is assessed to be α = –1.16 ± 0.40 W m–2 °C–1 (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 ΔF2×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 and Baker, 2007; Knutti and Hegerl, 2008). The wide range of the process-based ECS estimate is not due solely to uncertainty in the estimates of ΔF2×CO2 and α, but is partly explained by the assumption that ΔF2×CO2 and α are independent in this approach. In CMIP5 and CMIP6 ensembles, ΔF2×CO2 and α are negatively correlated when they are calculated using linear regression in abrupt4xCO2 simulations (r2 = 0.34; Andrews et al., 2012; Webb et al., 2013; 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 ΔF2×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 ΔF2×CO2 and α is not adopted, there is no change in the mean, but the wide range still applies.
A significant correlation between ΔF2×CO2 and α also occurs when the two parameters are estimated separately from atmospheric ESM f ixed-SST experiments (Section 7.3.1) or fixed CO2 concentration experiments (Section 7.4.1; Ringer et al., 2014; Chung and Soden, 2018). Hence the relationship is not expected to be an artefact of calculating the parameters using linear regression in abrupt4xCO2 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 et al., 2014; 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 and Fueglistaler, 2019) and for the low-cloud feedback (Watanabe et al., 2018), and therefore the responses of these clouds to the direct CO2 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 (Section 7.4.2.4). For these reasons, the co-dependency between ΔF2×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 ΔF2×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 ΔF2×CO2.
[This is far too much text and graphics to for a post here. So, from this point on, I will only show section titles: -OP]
7.5.1.2 Emulating Process-based ECS to TCR
7.5.2 Estimates of ECS and TCR Based on the Instrumental Record
7.5.2.1 Estimates of ECS and TCR Based on the Global Energy Budget
7.5.2.2 Estimates of ECS and TCR Based on Climate Model Emulators
7.5.2.3 Estimates of ECS Based on Variability in Earth’s Top-of-atmosphere Radiation Budget
7.5.2.4 Estimates of ECS Based on the Climate Response to Volcanic Eruptions
7.5.2.5 Assessment of ECS and TCR Based on the Instrumental Record
7.5.3 Estimates of ECS Based on Paleoclimate Data
7.5.3.1 Estimates of ECS from the Last Glacial Maximum
7.5.3.2 Estimates of ECS from Glacial–Interglacial Cycles
7.5.3.3 Estimates of ECS from Warm Periods of the Pre-Quaternary
7.5.3.4 Synthesis of ECS Based on Paleo Radiative Forcing and Temperature
Table 7.11 | Estimates of equilibrium climate sensitivity (ECS) derived from paleoclimates; from AR5 (above double lines) and from post-AR5 studies (below double lines).
7.5.4 Estimates of ECS and TCR Based on Emergent Constraints
7.5.4.1 Emergent Constraints Using Global or Near-global Surface Temperature Change
7.5.4.2 Emergent Constraints Focused on Cloud Feedbacks and Present-day Climate
7.5.4.3 Assessed ECS and TCR Based on Emergent Constraints
7.5.5 Combined Assessment of ECS and TCR
Table 7.12 | Emergent constraint studies used in the assessment of equilibrium climate sensitivity (ECS).