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

==== 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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