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

=== 7.5.4 Estimates of ECS and TCR Based on Emergent Constraints ===

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ESMs exhibit substantial spread in ECS and TCr ( [[#7.5.7|Section 7.5.7]] ). Numerous studies have leveraged this spread in order to narrow estimates of Earth’s climate sensitivity by employing methods known as ‘emergent constraints’ [[IPCC:Wg1:Chapter:Chapter-1#1.5.4|Section 1.5.4]] ). These methods establish a relationship between an observable and either ECS or TCR based on an ensemble of models, and combine this information with observations to constrain the probability distribution of ECS or TCR. Most studies of this kind have clearly benefitted from the international efforts to coordinate the CMIP and other multi-model ensembles.

A number of considerations must be taken into account when assessing the diverse literature on ECS and TCR emergent constraints. For instance, it is important to have physical and theoretical bases for the connection between the observable and modelled ECS or TCR since in model ensembles thousands of relationships that pass statistical significance can be found simply by chance ( [[#Caldwell--2014|Caldwell et al., 2014]] ). It is also important that the underlying model ensemble does not exhibit a shared bias that influences the simulation of the observable quantity on which the emergent constraint is based. Also, correctly accounting for uncertainties in both the observable (including measurement uncertainty and natural variability) and the emergent constraint statistical relationship can be challenging, in particular in cases where the latter is not expected to be linear ( [[#Annan--2020|Annan et al., 2020]] ). A number of proposed emergent constraints leverage variations in modelled ECS arising from tropical low-clouds, which was the dominant source of inter-model spread in the CMIP5 ensemble used in most emergent constraint studies. Since ECS is dependent on the sum of individual feedbacks ( [[#7.5.1|Section 7.5.1]] ) these studies implicitly assume that all other feedback processes in models are unbiased and should therefore rather be thought of as constraints on tropical low-cloud feedback ( [[#Klein--2015|Klein and Hall, 2015]] ; [[#Qu--2018|Qu et al., 2018]] ; [[#Schlund--2020|Schlund et al., 2020]] ). The following sections go through a range of emergent constraints and assess their strengths and limitations.

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==== 7.5.4.1 Emergent Constraints Using Global or Near-global Surface Temperature Change ====

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Perhaps the simplest class of emergent constraints regress past equilibrium paleoclimate temperature change against modelled ECS to obtain a relationship that can be used to translate a past climate change to ECS. The advantage is that these are constraints on the sum of all feedbacks, and furthermore unlike constraints on the instrumental record they are based on climate states that are at, or close to, equilibrium. So far, these emergent constraints have been limited to the Last Glacial Maximum (LGM; Cross-Chapter Box 2.1) cooling ( [[#Hargreaves--2012|Hargreaves et al., 2012]] ; [[#Schmidt--2014|Schmidt et al., 2014]] ; [[#Renoult--2020|Renoult et al., 2020]] ) and warming in the mid-Pliocene Warm Period (MPWP; Cross-Chapter Box 2.1 and Cross-Chapter Box 2.4; [[#Hargreaves--2016|Hargreaves and Annan, 2016]] ; [[#Renoult--2020|Renoult et al., 2020]] ) due to the availability of sufficiently large multi-model ensembles for these two cases. The paleoclimate emergent constraints are limited by structural uncertainties in the proxy-based global surface temperature and forcing reconstructions ( [[#7.5.3|Section 7.5.3]] ), possible differences in equilibrium sea surface temperature patterns between models and the real world, and a small number of model simulations participating, which has led to divergent results. For example, [[#Hopcroft--2015|Hopcroft and Valdes (2015)]] repeated the study based on the LGM by [[#Hargreaves--2012|Hargreaves et al. (2012)]] using another model ensemble and found that the emergent constraint was not robust, whereas studies using multiple available ensembles retain useful constraints ( [[#Schmidt--2014|Schmidt et al., 2014]] ; [[#Renoult--2020|Renoult et al., 2020]] ). Also, the results are somewhat dependent on the applied statistical methods ( [[#Hargreaves--2016|Hargreaves and Annan, 2016]] ). However, [[#Renoult--2020|Renoult et al. (2020)]] explored this and found 95th percentiles of ECS below 6°C for LGM and Pliocene individually, regardless of statistical approach, and by combining the two estimates the 95th percentile dropped to 4.0°C. The consistency between the cold LGM and warm MPWP emergent constraint estimates increases confidence in these estimates, and further suggests that the dependence of feedback on climate mean state ( [[#7.4.3|Section 7.4.3]] ) as represented in PMIP models used in these studies is reasonable.

Various emergent constraint approaches using global warming over the instrumental record have been proposed. These benefit from more accurate data compared with paleoclimates, but suffer from the fact that the climate is not in equilibrium, thereby assuming that ESMs on average accurately depict the ratio of short-term to long-term global warming. Global warming in climate models over 1850 to the present day exhibits no correlation with ECS, which is partly due to a substantial number of models exhibiting compensation between a high climate sensitivity with strong historical aerosol cooling ( [[#Kiehl--2007|Kiehl, 2007]] ; [[#Forster--2013|Forster et al., 2013]] ; [[#Nijsse--2020|Nijsse et al., 2020]] ). However, the aerosol cooling increased up until the 1970s, when air quality regulations reduced the emissions from Europe and North America whereas other regions saw increases resulting in a subsequently reduced pace of global mean aerosol ERF increase ( [[IPCC:Wg1:Chapter:Chapter-2#2.2.8|Section 2.2.8]] and Figure 2.10). Energy balance considerations over the 1970–2010 period gave a best estimate ECS of 2.0°C ( [[#Bengtsson--2013|Bengtsson and Schwartz, 2013]] ), however this estimate did not account for pattern effects. To address this limitation an emergent constraint on 1970–2005 global warming was demonstrated to yield a best estimate ECS of 2.83 [1.72 to 4.12] °C ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ). The study was followed up using CMIP6 models yielding a best estimate ECS of 2.6 [1.5 to 4.0] °C based on 1975–2019 global warming ( [[#Nijsse--2020|Nijsse et al., 2020]] ), thereby confirming the emergent constraint. Internal variability and forced or unforced pattern effects may influence the results ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ; [[#Nijsse--2020|Nijsse et al., 2020]] ). For instance the Atlantic Multi-decadal Oscillation changed from negative to positive anomaly, while the Indo-Pacific Oscillation changed less over the 1970–2005 period, potentially leading to high-biased results ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ), whereas during the later period 1975–2019 these anomalies roughly cancel ( [[#Nijsse--2020|Nijsse et al., 2020]] ). Pattern effects may have been substantial over these periods ( [[#Andrews--2018|Andrews et al., 2018]] ), however the extent to which TOA radiation anomalies influenced surface temperature may have been dampened by the deep ocean ( [[#Hedemann--2017|Hedemann et al., 2017]] ; [[#Newsom--2020|Newsom et al., 2020]] ). It is therefore deemed ''more likely than not'' that these estimates based on post-1970s global warming are biased low by internal variability.

A study that developed an emergent constraint based on the response to the Mount Pinatubo 1991 eruption yielded a best estimate of 2.4 [ ''likely'' range 1.7 to 4.1] °C ( [[#Bender--2010|Bender et al., 2010]] ). When accounting for ENSO variations they found a somewhat higher best estimate of 2.7°C, which is in line with results of later studies that suggest ECS inferred from periods with substantial volcanic activity are low-biased due to strong pattern effects ( [[#Gregory--2020|Gregory et al., 2020]] ) and that the short-term nature of volcanic forcing could exacerbate possible underestimates of modelled pattern effects.

Lagged correlations present in short-term variations in the global surface temperature can be linked to ECS through the fluctuation–dissipation theorem, which is derived from a single heat-reservoir model ( [[#Einstein--1905|Einstein, 1905]] ; [[#Hasselmann--1976|Hasselmann, 1976]] ; [[#Schwartz--2007|Schwartz, 2007]] ; [[#Cox--2018a|Cox et al., 2018a]] ). From this it follows that the memory carried by the heat capacity of the ocean results in low-frequency global temperature variability (red noise) arising from high-frequency (white noise) fluctuations in the radiation balance, for example, caused by weather. Initial attempts to apply the theorem to observations yielded a fairly low median ECS estimate of 1.1°C ( [[#Schwartz--2007|Schwartz, 2007]] ), a result that was disputed ( [[#Foster--2008|Foster et al., 2008]] ; [[#Knutti--2008|Knutti et al., 2008]] ). Recently it was proposed by [[#Cox--2018a|Cox et al. (2018a)]] to use variations in the historical experiments of the CMIP5 climate models as an emergent constraint giving a median ECS estimate of 2.8 [1.6 to 4.0] °C. A particular challenge associated with these approaches is to separate short-term from long-term variability, and slightly arbitrary choices regarding the methodology of separating these in the global surface temperature from long-term signals in the historical record, omission of the more strongly forced period after 1962, as well as input data choices, can lead to median ECS estimates ranging from 2.5°C to 3.5°C ( [[#Brown--2018|Brown et al., 2018]] ; [[#Po-Chedley--2018a|Po-Chedley et al., 2018a]] ; [[#Rypdal--2018|Rypdal et al., 2018]] ). Calibrating the emergent constraint using CMIP5 modelled internal variability as measured in historical control simulations ( [[#Po-Chedley--2018a|Po-Chedley et al., 2018a]] ) will inevitably lead to an overestimated ECS due to externally forced short-term variability present in the historical record ( [[#Cox--2018b|Cox et al., 2018b]] ). Contrary to constraints based on paleoclimates or global warming since the 1970s, when based on CMIP6 models a higher, yet still well-bounded ECS estimate of 3.7 [2.6 to 4.8] °C is obtained ( [[#Schlund--2020|Schlund et al., 2020]] ). A more problematic issue is raised by [[#Annan--2020|Annan et al. (2020)]] who showed that the upper bound on ECS estimated this way is less certain when considering deep-ocean heat uptake. In conclusion, even if not inconsistent, these limitations prevent us from directly using this type of constraint in the assessment.

Short-term variations in the TOA energy budget, observable from satellites, arising from variations in the tropical tropospheric temperature have been linked to ECS through models, either as a range of models consistent with observations (those with ECS values between 2.0°C and 3.9°C; [[#Dessler--2018|Dessler et al., 2018]] ) or as a formal emergent constraint by deriving further model-based relationships to yield a median of 3.3 [2.4 to 4.5] °C ( [[#Dessler--2018|Dessler and Forster, 2018]] ). There are major challenges associated with short-term variability in the energy budget, in particular how it relates to the long-term forced response of clouds ( [[#Colman--2017|Colman and Hanson, 2017]] ; [[#Lutsko--2018|Lutsko and Takahashi, 2018]] ). Variations in the surface temperature that are not directly affecting the radiation balance lead to an overestimated ECS when using linear regression techniques where it appears as noise in the independent variable ( [[#Proistosescu--2018|Proistosescu et al., 2018]] ; [[#Gregory--2020|Gregory et al., 2020]] ). The latter issue is largely overcome when using the tropospheric mean or mid-tropospheric temperature ( [[#Trenberth--2015|Trenberth et al., 2015]] ; [[#Dessler--2018|Dessler et al., 2018]] ).

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==== 7.5.4.2 Emergent Constraints Focused on Cloud Feedbacks and Present-day Climate ====

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A substantial number of emergent constraint studies focus on observables that are related to tropical low-cloud feedback processes ( [[#Volodin--2008|Volodin, 2008]] ; [[#Sherwood--2014|Sherwood et al., 2014]] ; [[#Zhai--2015|Zhai et al., 2015]] ; [[#Brient--2016|Brient and Schneider, 2016]] ; [[#Brient--2016|Brient et al., 2016]] ). These studies yield median ECS estimates of 3.5°C–4°C and in many cases indicate low likelihoods of values below 3°C. The approach has attracted attention since most of the spread in climate sensitivity seen in CMIP5, and earlier climate model ensembles, arises from uncertainty in low-cloud feedbacks ( [[#Bony--2005|Bony and Dufresne, 2005]] ; [[#Wyant--2006|Wyant et al., 2006]] ; [[#Randall--2007|Randall et al., 2007]] ; [[#Vial--2013|Vial et al., 2013]] ). Nevertheless, this approach assumes that all other feedback processes are unbiased ( [[#Klein--2015|Klein and Hall, 2015]] ; [[#Qu--2018|Qu et al., 2018]] ; [[#Schlund--2020|Schlund et al., 2020]] ), for instance the possibly missing negative anvil area feedback or the possibly exaggerated mixed-phase cloud feedback ( [[#7.4.2.4|Section 7.4.2.4]] ). Thus, the subset of emergent constraints that focus on low-level tropical clouds are not necessarily inconsistent with other emergent constraints of ECS. Related emergent constraints that focus on aspects of the tropical circulation and ECS have led to conflicting results ( [[#Su--2014|Su et al., 2014]] ; [[#Tian--2015|Tian, 2015]] ; [[#Lipat--2017|Lipat et al., 2017]] ; [[#Webb--2020|Webb and Lock, 2020]] ), possibly because these processes are not the dominant factors in causing the inter-model spread ( [[#Caldwell--2018|Caldwell et al., 2018]] ).

The fidelity of models in reproducing aspects of temperature variability or the radiation budget has also been proposed as emergent constraints on ECS ( [[#Covey--2000|Covey et al., 2000]] ; [[#Knutti--2006|Knutti et al., 2006]] ; [[#Huber--2010|Huber et al., 2010]] ; [[#Bender--2012|Bender et al., 2012]] ; [[#Brown--2017|Brown and Caldeira, 2017]] ; [[#Siler--2018a|Siler et al., 2018a]] ). Here indices based on spatial or seasonal variability are linked to modelled ECS, and overall the group of emergent constraints yields best estimates of 3.3°C–3.7°C. Nevertheless, the physical relevance of present-day biases to the sum of long-term climate change feedbacks is unclear and therefore these constraints on ECS are not considered reliable.

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==== 7.5.4.3 Assessed ECS and TCR Based on Emergent Constraints ====

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The available emergent constraint studies have been divided into two classes: (i) those that are based on global or near-global indices, such as global surface temperature and the TOA energy budget; and (ii) those that are more focussed on physical processes, such as the fidelity of phenomena related to low-level cloud feedbacks or present-day climate biases. The former class is arguably superior in representing ECS, since it is a global surface temperature or energy budget change, whereas the latter class is perhaps best thought of as providing constraints on individual climate feedbacks, for example, the determination that low-level cloud feedbacks are positive. The latter result is consistent with and confirms process-based estimates of low-cloud feedbacks ( [[#7.4.2.4|Section 7.4.2.4]] ), but are potentially biased as a group by missing or biased feedbacks in ESMs and is accordingly not taken into account here. A limiting case here is [[#Dessler--2018|Dessler and Forster (2018)]] which is focused on monthly co-variability in the global TOA energy budget with mid-tropospheric temperature, at which time scale the surface-albedo feedback is unlikely to operate, thus implicitly assuming it is unbiased in the model ensemble.

In the first group of emergent constraints there is broad agreement on the best estimate of ECS ranging from 2.4°C–3.3°C. At the lower end, nearly all studies find lower bounds (5th percentiles) around 1.5°C, whereas several studies indicate 95th percentiles as low as 4°C. Considering both classes of studies, none of them yield upper ''very'' ''likely'' bounds above 5°C. Since several of the emergent constraints can be considered nearly independent one could assume that emergent constraints provide very strong evidence on ECS by combining them. Nevertheless, this is not done here because there are sufficient cross-dependencies, as for instance models are re-used in many of the derived emergent constraints, and furthermore the methodology has not yet reached a sufficient level of maturity since systematic biases may not have been accounted for. Uncertainty is therefore conservatively added to reflect these potential issues. This leads to the assessment that ECS inferred from emergent constraints is ''very likely'' 1.5 to 5 °C with ''medium confidence'' .

Emergent constraints on TCR with a focus on the instrumental temperature record, though less abundant, have also been proposed. These can be influenced by internal variability and pattern effects, as discussed in ( [[#7.5.4.1|Section 7.5.4.1]] , although the influence is smaller because uncertainty in forced pattern effects correlates between transient historical warming and TCR. In the simplest form [[#Gillett--2012|Gillett et al. (2012)]] regressed the response of one model to individual historical forcing components to obtain a tight range of 1.3°C–1.8°C, but later when an ensemble of models was used the range was widened to 0.9°C–2.3°C ( [[#Gillett--2013|Gillett et al., 2013]] ), and updated by [[#Schurer--2018|Schurer et al. (2018)]] . A related data-assimilation-based approach that accounted also for uncertainty in response patterns gave 1.33°C–2.36°C ( [[#Ribes--2021|Ribes et al., 2021]] ), but is dependent on the choice of prior ensemble distribution (CMIP5 or CMIP6). Another study used the response to the Pinatubo volcanic eruption to obtain a range of 0.8°C–2.3°C ( [[#Bender--2010|Bender et al., 2010]] ). A tighter range, notably at the lower end, was found in an emergent constraint focusing on the post-1970s warming exploiting the lower spread in aerosol forcing change over this period ( [[#Jiménez-de-la-Cuesta--2019|Jiménez-de-la-Cuesta and Mauritsen, 2019]] ). Their estimate was 1.67 [1.17 to 2.16] °C. Two studies tested this idea: [[#Tokarska--2020|Tokarska et al. (2020)]] estimates TCR was 1.60 [0.90 to 2.27] °C based on CMIP6 models, whereas [[#Nijsse--2020|Nijsse et al. (2020)]] found 1.68 [1.0 to 2.3] °C. In both cases there was a small sensitivity to choice of ensemble, with CMIP6 models yielding slightly lower values and ranges. Combining these studies gives a best estimate of 1.7°C and a ''very likely'' range of TCR of 1.1 to 2.3 °C with ''high confidence'' .

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