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

== 7.4 Climate Feedbacks ==

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The magnitude of global surface temperature change primarily depends on the strength of the radiative forcings and feedbacks, the latter defined as the changes of the net energy budget at the top-of-atmosphere (TOA) in response to a change in the GSAT (Box 7.1, Equation 7.1). Feedbacks in the Earth system are numerous, and it can be helpful to categorize them into three groups: (i) physical feedbacks; (ii) biogeophysical and biogeochemical feedbacks; and (iii) long-term feedbacks associated with ice sheets. The physical feedbacks (e.g., those associated with changes in lapse rate, water vapour, surface albedo, or clouds; (Sections 7.4.2.1–7.4.2.4) and biogeophysical/biogeochemical feedbacks (e.g., those associated with changes in methane, aerosols, ozone, or vegetation; [[#7.4.2.5|Section 7.4.2.5]] ) act both on time scales that are used to estimate the equilibrium climate sensitivity (ECS) in models (typically 150 years, see Box 7.1) and on longer time scales required to reach equilibrium. Long-term feedbacks associated with ice sheets ( [[#7.4.2.6|Section 7.4.2.6]] ) are relevant primarily after several centuries or more. The feedbacks associated with biogeophysical/biogeochemical processes and ice sheets, often collectively referred to as Earth system feedbacks, had not been included in conventional estimates of the climate feedback (e.g., [[#Hansen--1984|Hansen et al., 1984]] ), but the former can now be quantified and included in the assessment of the total (net) climate feedback. Feedback analysis represents a formal framework for the quantification of the coupled interactions occurring within a complex Earth system in which everything influences everything else (e.g., [[#Roe--2009|Roe, 2009]] ). As used here (as presented in [[#7.4.1|Section 7.4.1]] ), the primary objective of feedback analysis is to identify and understand the key processes that determine the magnitude of the surface temperature response to an external forcing. For each feedback, the basic underlying mechanisms and their assessments are presented in [[#7.4.2|Section 7.4.2]] .

Up until AR5, process understanding and quantification of feedback mechanisms were based primarily on global climate models. Since AR5, the scientific community has undertaken a wealth of alternative approaches, including observational and fine-scale modelling approaches. This has in some cases led to more constrained feedbacks and, on the other hand, uncovered shortcomings in global climate models, which are starting to be corrected. Consequently, AR6 achieves a more robust assessment of feedbacks in the climate system that is less reliant on global climate models than in earlier assessment reports.

It has long been recognized that the magnitude of climate feedbacks can change as the climate state evolves over time ( [[#Manabe--1985|Manabe and Bryan, 1985]] ; [[#Murphy--1995|Murphy, 1995]] ), but the implications for projected future warming have been investigated only recently. Since AR5, progress has been made in understanding the key mechanisms behind this time- and state-dependence. Specifically, the state-dependence is assessed by comparing climate feedbacks between warmer and colder climate states inferred from paleoclimate proxies and model simulations ( [[#7.4.3|Section 7.4.3]] ). The time-dependence of the feedbacks is evident between the historical period and future projections and is assessed to arise from the evolution of the surface warming pattern related to changes in zonal and meridional temperature gradients ( [[#7.4.4|Section 7.4.4]] ).

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=== 7.4.1 Methodology of the Feedback Assessment ===

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The global surface temperature changes of the climate system are generally analysed with the classical forcing–feedback framework as described in Box 7.1 (Equation 7.1). In this equation α is the net feedback parameter (W m <sup>–2</sup> °C <sup>–1</sup> ). As surface temperature changes in response to the TOA energy imbalance, many other climate variables also change, thus affecting the radiative flux at the TOA. The aggregate feedback parameter can then be decomposed into an approximate sum of terms α = Σ x α x , where ''x'' is a vector representing variables that have a direct effect on the net TOA radiative flux ''N'' and

[[File:8727c6a608304637be8da3a8b6bac28f IPCC_AR6_WGI_Formula_Chapter_7_41_1.jpg]]
Following the conventional definition, the physical climate feedbacks are here decomposed into terms associated with a vertically uniform temperature change (Planck response, P), changes in the water-vapour plus temperature lapse-rate (WV+LR), surface albedo (A) and clouds (C). The water-vapour plus temperature lapse rate feedback is further decomposed using two different approaches, one based on changes in specific humidity, the other on changes in relative humidity. Biogeochemical feedbacks arise due to changes in aerosols and atmospheric chemical composition in response to changes in surface temperature, and [[#Gregory--2009|Gregory et al. (2009)]] and [[#Raes--2010|Raes et al. (2010)]] show that they can be analysed using the same framework as for the physical climate feedbacks (Sections 5.4 and 6.4.5). Similarly, feedbacks associated with biogeophysical and ice-sheet changes can also be incorporated.

In global climate models, the feedback parameters α x in global warming conditions are often estimated as the mean differences in the radiative fluxes between atmosphere-only simulations in which the change in SST is prescribed ( [[#Cess--1990|Cess et al., 1990]] ), or as the regression slope of change in radiation flux against change in GSAT using atmosphere–ocean coupled simulations with abrupt CO <sub>2</sub> changes ( ''abrupt 4xCO2'' ) for 150 years (Box 7.1; [[#Gregory--2004|Gregory et al., 2004]] ; [[#Andrews--2012|Andrews et al., 2012]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ). Neither method is perfect, but both are useful and yield consistent results ( [[#Ringer--2014|Ringer et al., 2014]] ). In the regression method, the radiative effects of land warming are excluded from the ERF due to doubling of CO <sub>2</sub> [[#7.3.2|Section 7.3.2]] ), which may overestimate feedback values by about 15%. At the same time, the feedback calculated using the regression over years 1–150 ignores its state-dependence on multi-centennial time scales ( [[#7.4.3|Section 7.4.3]] ), probably giving an underestimate of α by about 10% ( [[#Rugenstein--2019|Rugenstein et al., 2019]] ). These effects are both small and approximately cancel each other in the ensemble mean, justifying the use of regression over 150 years as an approximation to feedbacks in ESMs.

The change of the TOA radiative flux ''n'' as a function of the change of a climate variable ''x'' (such as water vapour) is commonly computed using the ‘radiative kernel’ method ( [[#Soden--2008|Soden et al., 2008]] ). In this method, the kernel ∂ ''N'' ''/'' ∂ ''x'' is evaluated by perturbing ''x'' within a radiation code. Then multiplying the kernel by d ''x/'' d ''T'' inferred from observations, meteorological analysis or GCMs produces a value of α x ''.''

Feedback parameters from lines of evidence other than global models are estimated in various ways. For example, observational data combined with GCM simulations could produce an emergent constraint on a particular feedback ( [[#Hall--2006|Hall and Qu, 2006]] ; [[#Klein--2015|Klein and Hall, 2015]] ), or the observed interannual fluctuations in the global mean TOA radiation and the surface air temperature, to which the linear regression analysis is applied, could generate a direct estimate of the climate feedback, assuming that the feedback associated with internal climate variability at short time scales can be a surrogate of the feedback to CO <sub>2</sub> -induced warming ( [[#Dessler--2013|Dessler, 2013]] ; [[#Loeb--2016|Loeb et al., 2016]] ). The assumption is not trivial, but can be justified given that the climate feedbacks are fast enough to occur at the interannual time scale. Indeed, a broad agreement has been obtained in estimates of individual physical climate feedbacks based on interannual variability and longer climate change time scales in GCMs ( [[#Zhou--2015|Zhou et al., 2015]] ; [[#Colman--2017|Colman and Hanson, 2017]] ). This means that the climate feedbacks estimated from the observed interannual fluctuations are representative of the longer-term feedbacks (decades to centuries). Care must be taken for these observational estimates because they can be sensitive to details of the calculation such as data sets and periods used ( [[#Dessler--2013|Dessler, 2013]] ; [[#Proistosescu--2018|Proistosescu et al., 2018]] ). In particular, there would be a dependence of physical feedbacks on the surface warming pattern at the interannual time scale due, for example, to El Niño–Southern Oscillation. However, this effect both amplifies and suppresses the feedback when data include the positive and negative phases of the interannual fluctuation, and therefore the net bias will be small.

In summary, the classical forcing–feedback framework has been extended to include biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks in addition to the physical feedbacks. It has also been used to analyse seasonal and interannual-to-decadal climate variations in observations and ESMs, in addition to long-term climate changes as seen in ''abrupt 4xCO2'' experiments. These developments allow an assessment of the feedbacks based on a larger variety of lines of evidence compared to AR5.

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=== 7.4.2 Assessing Climate Feedbacks ===

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This section provides an overall assessment of individual feedback parameters, α x , by combining different lines of evidence from observations, theory, process models and ESMs. To achieve this, we review the understanding of the key processes governing the feedbacks, why the feedback estimates differ among models, studies or approaches, and the extent to which these approaches yield consistent results. The individual terms assessed are the Planck response ( [[#7.4.2.1|Section 7.4.2.1]] ) and feedbacks associated with changes in water vapour and lapse rate ( [[#7.4.2.2|Section 7.4.2.2]] ), surface albedo ( [[#7.4.2.3|Section 7.4.2.3]] ), clouds ( [[#7.4.2.4|Section 7.4.2.4]] ), biogeophysical and non-CO <sub>2</sub> biogeochemical processes ( [[#7.4.2.5|Section 7.4.2.5]] ), and ice sheets ( [[#7.4.2.6|Section 7.4.2.6]] ). A synthesis is provided in ( [[#7.4.2.7|Section 7.4.2.7]] . Climate feedbacks in CMIP6 models are then evaluated in ( [[#7.4.2.8|Section 7.4.2.8]] , with an explanation of how they have been incorporated into the assessment.

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==== 7.4.2.1 Planck Response ====

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The Planck response represents the additional thermal or longwave (LW) emission to space arising from vertically uniform warming of the surface and the atmosphere. The Planck response α P , often called the Planck feedback, plays a fundamental stabilizing role in Earth’s climate and has a value that is strongly negative: a warmer planet radiates more energy to space. A crude estimate of α P can be made using the normalized greenhouse effect g̃ , defined as the ratio between the greenhouse effect ''G'' and the upwelling LW flux at the surface ( [[#Raval--1989|Raval and Ramanathan, 1989]] ). Current estimates ( [[#7.2|Section 7.2]] , Figure 7.2) give ''G'' = 159 W m <sup>–2</sup> and g̃ ≈ 0.4. Assuming g̃ is constant, one obtains for a surface temperature ''T'' s = 288 K, α P = ( g – 1) 4 σ ''T'' <sup>3</sup> s ≈ –3.3 W m <sup>–2</sup> °C <sup>–1</sup> , where σ is the Stefan–Boltzmann constant. This parameter α P is estimated more accurately using kernels obtained from meteorological reanalysis or climate simulations ( [[#Soden--2006|Soden and Held, 2006]] ; [[#Dessler--2013|Dessler, 2013]] ; [[#Vial--2013|Vial et al., 2013]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ; [[#Colman--2017|Colman and Hanson, 2017]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ). Discrepancies among estimates primarily arise because differences in cloud distributions make the radiative kernels differ ( [[#Kramer--2019|Kramer et al., 2019]] ). Using six different kernels, [[#Zelinka--2020|Zelinka et al. (2020)]] obtained a spread of ±0.1 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation). Discrepancies among estimates secondarily arise from differences in the pattern of equilibrium surface temperature changes among ESMs. For the CMIP5 and CMIP6 models this introduces a spread of ±0.04 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation). The multi-kernel and multi-model mean of α P is equal to –3.20 W m <sup>–2</sup> °C <sup>–1</sup> for the CMIP5 and –3.22 W m <sup>–2</sup> °C <sup>–1</sup> for the CMIP6 models (Supplementary Material, Table 7.SM.5). Overall, there is ''high confidence'' in the estimate of the Planck response, which is assessed to be α P = –3.22 W m <sup>–2</sup> °C <sup>–1</sup> with a ''very likely'' range of –3.4 to –3.0 W m <sup>–2</sup> °C <sup>–1</sup> and a ''likely range'' of –3.3 to –3.1 W m <sup>–2</sup> °C <sup>–1</sup> .

The Planck temperature response Δ ''T'' P is the equilibrium temperature change in response to a forcing Δ ''F'' when the net feedback parameter is equal to the Planck response parameter: Δ ''T'' P ''= –'' Δ ''F /'' α P .

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==== 7.4.2.2 Water-vapour and Temperature Lapse-rate Feedbacks ====

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Two decompositions are generally used to analyse the feedbacks associated with a change in the water-vapour and temperature lapse-rate in the troposphere. As in any system, many feedback decompositions are possible, each of them highlighting a particular property or aspect of the system ( [[#Ingram--2010|Ingram, 2010]] ; [[#Held--2012|Held and Shell, 2012]] ; [[#Dufresne--2016|Dufresne and Saint-Lu, 2016]] ). The first decomposition considers separately the changes (and therefore feedbacks) in the lapse rate (LR) and specific humidity (WV). The second decomposition considers changes in the lapse rate assuming constant relative humidity (LR*) separately from changes in relative humidity (RH).

The specific humidity (WV) feedback, also known as the water-vapour feedback, quantifies the change in radiative flux at the TOA due to changes in atmospheric water vapour concentration associated with a change in global mean surface air temperature. According to theory, observations and models, the water vapour increase approximately follows the Clausius–Clapeyron relationship at the global scale with regional differences dominated by dynamical processes ( [[IPCC:Wg1:Chapter:Chapter-8#8.2.1|Section 8.2.1]] ; [[#Sherwood--2010a|Sherwood et al., 2010a]] ; [[#Chung--2014|Chung et al., 2014]] ; [[#Romps--2014|Romps, 2014]] ; R. [[#Liu--2018|]] [[#Liu--2018|Liu et al., 2018]] ; [[#Schröder--2019|Schröder et al., 2019]] ). Greater atmospheric water vapour content, particularly in the upper troposphere, results in enhanced absorption of LW and SW radiation and reduced outgoing radiation. This is a positive feedback. Atmospheric moistening has been detected in satellite records ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1.3.3|Section 2.3.1.3.3]] ), it is simulated by climate models ( [[IPCC:Wg1:Chapter:Chapter-3#3.3.2.2|Section 3.3.2.2]] ), and the estimates agree within model and observational uncertainty ( [[#Soden--2005|Soden et al., 2005]] ; [[#Dessler--2013|Dessler, 2013]] ; [[#Gordon--2013|Gordon et al., 2013]] ; [[#Chung--2014|Chung et al., 2014]] ). The estimate of this feedback inferred from satellite observations is α WV <sub></sub> = 1.85 ± 0.32 W m <sup>–2</sup> °C <sup>–1</sup> (R. [[#Liu--2018|]] [[#Liu--2018|Liu et al., 2018]] ). This is consistent with the value α WV <sub></sub> = 1.77 ± 0.20 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation) obtained with CMIP5 and CMIP6 models ( [[#Zelinka--2020|Zelinka et al., 2020]] ).

The lapse-rate (LR) feedback quantifies the change in radiative flux at the TOA due to a nonuniform change in the vertical temperature profile. In the tropics, the vertical temperature profile is mainly driven by moist convection and is close to a moist adiabat. The warming is larger in the upper troposphere than in the lower troposphere ( [[#Manabe--1975|Manabe and Wetherald, 1975]] ; [[#Santer--2005|Santer et al., 2005]] ; [[#Bony--2006|Bony et al., 2006]] ), leading to a larger radiative emission to space and therefore a negative feedback. This larger warming in the upper troposphere than at the surface has been observed over the last 20 years thanks to the availability of sufficiently accurate observations ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1.2.2|Section 2.3.1.2.2]] ). In the extratropics, the vertical temperature profile is mainly driven by a balance between radiation, meridional heat transport and ocean heat uptake ( [[#Rose--2014|Rose et al., 2014]] ). Strong winter temperature inversions lead to warming that is larger in the lower troposphere ( [[#Payne--2015|Payne et al., 2015]] ; [[#Feldl--2017a|Feldl et al., 2017a]] ) and a positive LR feedback in polar regions ( [[#7.4.4.1|Section 7.4.4.1]] ; [[#Manabe--1975|Manabe and Wetherald, 1975]] ; [[#Bintanja--2012|Bintanja et al., 2012]] ; [[#Pithan--2014|Pithan and Mauritsen, 2014]] ). However, the tropical contribution dominates, leading to a negative global mean LR feedback ( [[#Soden--2006|Soden and Held, 2006]] ; [[#Dessler--2013|Dessler, 2013]] ; [[#Vial--2013|Vial et al., 2013]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ). The LR feedback has been estimated at interannual time scales using meteorological reanalysis and satellite measurements of TOA fluxes ( [[#Dessler--2013|Dessler, 2013]] ). These estimates from climate variability are consistent between observations and ESMs ( [[#Dessler--2013|Dessler, 2013]] ; [[#Colman--2017|Colman and Hanson, 2017]] ). The mean and standard deviation of this feedback under global warming based on the cited studies are α LR <sub></sub> = –0.50 ± 0.20 W m <sup>–2</sup> °C <sup>–1</sup> ( [[#Dessler--2013|Dessler, 2013]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ; [[#Colman--2017|Colman and Hanson, 2017]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ).

The second decomposition was proposed by [[#Held--2012|Held and Shell (2012)]] to separate the response that would occur under the assumption that relative humidity remains constant from that due to the change in relative humidity. The feedback is decomposed into three: (i) change in water vapour due to an identical temperature increase at the surface and throughout the troposphere assuming constant relative humidity, which will be called the Clausius–Clapeyron (CC) feedback here; (ii) change in LR assuming constant relative humidity (LR*); (iii) change in relative humidity (RH). Since AR5 it has been clarified that by construction, the sum of the temperature lapse rate and specific humidity (LR + WV) feedbacks is equal to the sum of the Clausius–Clapeyron feedback, the lapse rate feedback assuming constant relative humidity, and the feedback from changes in relative humidity (that is, CC + LR* + RH). Therefore, each of these two sums may simply be referred to as the ‘water-vapour plus lapse-rate’ feedback.

The CC feedback has a large positive value due to well understood thermodynamic and radiative processes: α CC <sub></sub> = 1.36 ± 0.04 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation; [[#Held--2012|Held and Shell, 2012]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ). The lapse-rate feedback assuming a constant relative humidity (LR*) in CMIP6 models has small absolute values ( α LR <sub>*</sub> = –0.10 ± 0.07 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation)), as expected from theoretical arguments ( [[#Ingram--2010|Ingram, 2010]] , 2013). It includes the pattern effect of surface warming that modulates the lapse rate and associated specific humidity changes ( [[#Po-Chedley--2018b|Po-Chedley et al., 2018b]] ). The relative humidity feedback is close to zero ( α RH = 0.00 ± 0.06 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation)) and the spread among models is confined to the tropics ( [[#Sherwood--2010b|Sherwood et al., 2010b]] ; [[#Vial--2013|Vial et al., 2013]] ; [[#Takahashi--2016|Takahashi et al., 2016]] ; [[#Po-Chedley--2018b|Po-Chedley et al., 2018b]] ). The change in upper tropospheric RH is closely related to model representation of current climate ( [[#Sherwood--2010b|Sherwood et al., 2010b]] ; [[#Po-Chedley--2019|Po-Chedley et al., 2019]] ), and a reduction in model RH biases is expected to reduce the uncertainty of the RH feedback. At interannual time scales, it has been shown that the change in RH in the tropics is related to the change of the spatial organization of deep convection ( [[#Holloway--2017|Holloway et al., 2017]] ; [[#Bony--2020|Bony et al., 2020]] ).

Both decompositions allow estimates of the sum of the lapse-rate and specific humidity feedbacks α LR+WV . The multi-kernel and multi-model mean of α LR+WV <sub></sub> is equal to 1.24 and 1.26 W m <sup>–2</sup> °C <sup>–1</sup> respectively for CMIP5 and CMIP6 models, with a standard deviation of 0.10 W m <sup>–2</sup> °C <sup>–1</sup> ( [[#Zelinka--2020|Zelinka et al., 2020]] ). These values are larger than the recently assessed value of 1.15 W m <sup>–2</sup> °C <sup>–1</sup> by [[#Sherwood--2020|Sherwood et al. (2020)]] as a larger set of kernels, including those obtained from meteorological reanalysis, are used here.

Since AR5, the effect of the water vapour increase in the stratosphere as a result of global warming has been investigated by different studies. This increase produces a positive feedback between 0.1 and 0.3 W m <sup>–2</sup> °C <sup>–1</sup> if the stratospheric radiative response is computed assuming temperatures that are adjusted with fixed dynamical heating ( [[#Dessler--2013|Dessler et al., 2013]] ; [[#Banerjee--2019|Banerjee et al., 2019]] ). However, various feedbacks reduce this temperature adjustment and the overall physical (water vapour, temperature and dynamical) stratospheric feedback becomes much smaller (0.0 to 0.1 W m <sup>–2</sup> °C <sup>–1</sup> ; [[#Huang--2016|Huang et al., 2016]] , 2020; [[#Li--2020|Li and Newman, 2020]] ), with uncertainty arising from limitations of current ESMs in simulating stratospheric processes. The total stratospheric feedback is assessed at 0.05 ± 0.1 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation).

The combined ‘water-vapour plus lapse-rate’ feedback is positive. The main physical processes that drive this feedback are well understood and supported by multiple lines of evidence including models, theory and observations. The combined ‘water-vapour plus lapse-rate’ feedback parameter is assessed to be α LR+WV <sub></sub> = 1.30 W m <sup>–2</sup> °C <sup>–1</sup> , with a ''very likely'' range of 1.1 to 1.5 W m <sup>–2</sup> °C <sup>–1</sup> and a ''likely'' range of 1.2 to 1.4 W m <sup>–2</sup> °C <sup>–1</sup> with ''high confidence.''

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==== 7.4.2.3 Surface-albedo Feedback ====

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Surface albedo is determined primarily by reflectance at Earth’s surface, but also by the spectral and angular distribution of incident solar radiation. Changes in surface albedo result in changes in planetary albedo that are roughly reduced by two-thirds, owing to atmospheric absorption and scattering, with variability and uncertainty arising primarily from clouds ( [[#Bender--2011|Bender, 2011]] ; [[#Donohoe--2011|Donohoe and Battisti, 2011]] ; [[#Block--2013|Block and Mauritsen, 2013]] ). Temperature change induces surface-albedo change through several direct and indirect means. In the present climate and at multi-decadal time scales, the largest contributions by far are changes in the extent of sea ice and seasonal snow cover, as these media are highly reflective and are located in regions that are close to the melting temperature (Sections 2.3.2.1 and 2.3.2.2). Reduced snow cover on sea ice may contribute as much to albedo feedback as reduced extent of sea ice ( [[#Zhang--2019|Zhang et al., 2019]] ). Changes in the snow metamorphic rate, which generally reduces snow albedo with warmer temperature, and warming-induced consolidation of light-absorbing impurities near the surface, also contribute secondarily to the albedo feedback ( [[#Flanner--2006|Flanner and Zender, 2006]] ; [[#Qu--2007|Qu and Hall, 2007]] ; [[#Doherty--2013|Doherty et al., 2013]] ; [[#Tuzet--2017|Tuzet et al., 2017]] ). Other contributors to albedo change include vegetation state (assessed separately in ( [[#7.4.2.5|Section 7.4.2.5]] ), soil wetness and ocean roughness.

Several studies have attempted to derive surface-albedo feedback from observations of multi-decadal changes in climate, but only over limited spatial and inconsistent temporal domains, inhibiting a purely observational synthesis of global surface-albedo feedback ( α A ). [[#Flanner--2011|Flanner et al. (2011)]] applied satellite observations to determine that the northern hemisphere (NH) cryosphere contribution to global α A over the period 1979–2008 was 0.48 [ ''likely'' range 0.29 to 0.78] W m <sup>–2</sup> °C <sup>–1</sup> , with roughly equal contributions from changes in land snow cover and sea ice. Since AR5, and over similar periods of observation, [[#Crook--2014|Crook and Forster (2014)]] found an estimate of 0.8 ± 0.3 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation) for the total NH extratropical surface-albedo feedback, when averaged over global surface area. For Arctic sea ice alone, [[#Pistone--2014|Pistone et al. (2014)]] and [[#Cao--2015|Cao et al. (2015)]] estimated the contribution to global α A to be 0.31 ± 0.04 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation) and 0.31 ± 0.08 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation), respectively, whereas [[#Donohoe--2020|Donohoe et al. (2020)]] estimated it to be only 0.16 ± 0.04 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation). Much of this discrepancy can be traced to different techniques and data used for assessing the attenuation of surface-albedo change by Arctic clouds. For the NH land snow, [[#Chen--2016|Chen et al. (2016)]] estimated that observed changes during 1982–2013 contributed (after converting from NH temperature change to global mean temperature change) by 0.1 W m <sup>–2</sup> °C <sup>–1</sup> to global α A , smaller than the estimate of 0.24 W m <sup>–2</sup> °C <sup>–1</sup> from [[#Flanner--2011|Flanner et al. (2011)]] . The contribution of the Southern Hemisphere (SH) to global α A is expected to be small because seasonal snow cover extent in the SH is limited, and trends in SH sea ice extent are relatively flat over much of the satellite record ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.2|Section 2.3.2]] ).

CMIP5 and CMIP6 models show moderate spread in global α A , determined from century time scale changes <sub></sub> ( [[#Qu--2014|Qu and Hall, 2014]] ; [[#Schneider--2018|Schneider et al., 2018]] ; [[#Thackeray--2019|Thackeray and Hall, 2019]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ), owing to variations in modelled sea ice loss and snow cover response in boreal forest regions. The multi-model mean global-scale α A (from all contributions) over the 21st century in CMIP5 models under the RCP8.5 scenario was derived by [[#Schneider--2018|Schneider et al. (2018)]] to be 0.40 ± 0.10 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation). Moreover, they found that modelled α A does not decline over the 21st century, despite large losses of snow and sea ice, though a weakened feedback is apparent after 2100. Using the idealized ''abrupt 4xCO2'' , as for the other feedbacks, the estimate of the global-scale albedo feedback in the CMIP5 models is 0.35 ± 0.08 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation; [[#Vial--2013|Vial et al., 2013]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ). The CMIP6 multi-model mean varies from 0.3 to 0.5 W m <sup>–2</sup> °C <sup>–1</sup> depending on the kernel used ( [[#Zelinka--2020|Zelinka et al., 2020]] ). [[#Donohoe--2020|Donohoe et al. (2020)]] derived a multi-model mean α A and its inter-model spread of 0.37 ± 0.19 W m <sup>–2</sup> °C <sup>–1</sup> from the CMIP5 ''abrupt 4xCO2'' ensemble, employing model-specific estimates of atmospheric attenuation and thereby avoiding bias associated with use of a single radiative kernel.

The surface-albedo feedback estimates using centennial changes have been shown to be highly correlated to those using seasonal regional changes for NH land snow ( [[#Qu--2014|Qu and Hall, 2014]] ) and Arctic sea ice ( [[#Thackeray--2019|Thackeray and Hall, 2019]] ). For the NH land snow, because the physics underpinning this relationship are credible, this opens the possibility to use it as an emergent constraint ( [[#Qu--2014|Qu and Hall, 2014]] ). Considering only the eight models whose seasonal cycle of albedo feedback falls within the observational range does not change the multi-model mean contribution to global α A (0.08 W m <sup>–2</sup> °C <sup>–1</sup> ) but decreases the inter-model spread by a factor of two (from ±0.03 to ±0.015 W m <sup>–2</sup> °C <sup>–1</sup> ; [[#Qu--2014|Qu and Hall, 2014]] ). For Arctic sea ice, [[#Thackeray--2019|Thackeray and Hall (2019)]] show that the seasonal cycle also provides an emergent constraint, at least until mid-century when the relationship degrades. They find that the CMIP5 multi-model mean of the Arctic sea ice contribution to α A <sub></sub> is 0.13 W m <sup>–2</sup> °C <sup>–1</sup> and that the inter-model spread is reduced by a factor of two (from ±0.04 to ±0.02 W m <sup>–2</sup> °C <sup>–1</sup> ) when the emergent constraint is used. This model estimate is smaller than observational estimates ( [[#Pistone--2014|Pistone et al., 2014]] ; [[#Cao--2015|Cao et al., 2015]] ) except those of [[#Donohoe--2020|Donohoe et al. (2020)]] . This can be traced to CMIP5 models generally underestimating the rate of Arctic sea ice loss during recent decades ( [[IPCC:Wg1:Chapter:Chapter-9#9.3.1|Section 9.3.1]] ; [[#Stroeve--2012|Stroeve et al., 2012]] ; [[#Flato--2013|Flato et al., 2013]] ), though this may also be an expression of internal variability, since the observed behaviour is captured within large ensemble simulations ( [[#Notz--2015|Notz, 2015]] ). CMIP6 models better capture the observed Arctic sea ice decline ( [[IPCC:Wg1:Chapter:Chapter-3#3.4.1|Section 3.4.1]] ). In the SH the opposite situation is observed. Observations show relatively flat trends in SH sea ice over the satellite era ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.2.1|Section 2.3.2.1]] ) whereas CMIP5 models simulate a small decrease ( [[IPCC:Wg1:Chapter:Chapter-3#3.4.1|Section 3.4.1]] ). SH α A is presumably larger in models than observations but only contributes about one quarter of the global α A . Thus, we assess that α A estimates are consistent, at global scale, in CMIP5 and CMIP6 models and satellite observations, though hemispheric differences and the role of internal variability need to be further explored.

Based on the multiple lines of evidence presented above that include observations, CMIP5 and CMIP6 models and theory, the global surface-albedo feedback is assessed to be positive with ''high confidence'' . The basic phenomena that drive this feedback are well understood and the different studies cover a large variety of hypotheses or behaviours, including how the evolution of clouds affects this feedback. The value of the global surface-albedo feedback is assessed to be α A <sub></sub> = 0.35 W m <sup>–2</sup> °C <sup>–1</sup> , with a ''very likely'' range from 0.10 to 0.60 W m <sup>–2</sup> °C <sup>–1</sup> and a ''likely'' range from 0.25 to 0.45 W m <sup>–2</sup> °C <sup>–1</sup> with ''high confidence'' .

<div id="7.4.2.4" class="h3-container"></div>

<span id="cloud-feedbacks"></span>
==== 7.4.2.4 Cloud Feedbacks ====

<div id="h3-27-siblings" class="h3-siblings"></div>

<div id="7.4.2.4.1" class="h4-container"></div>

<span id="decomposition-of-clouds-into-regimes"></span>
===== 7.4.2.4.1 Decomposition of clouds into regimes =====

<div id="h4-7-siblings" class="h4-siblings"></div>

Clouds can be formed almost anywhere in the atmosphere when moist air parcels rise and cool, enabling the water vapour to condense. Clouds consist of liquid water droplets and/or ice crystals, and these droplets and crystals can grow into larger particles of rain, snow or drizzle. These microphysical processes interact with aerosols, radiation and atmospheric circulation, resulting in a highly complex set of processes governing cloud formation and life cycles that operate across a wide range of spatial and temporal scales.

Clouds have various types, from optically thick convective clouds to thin stratus and cirrus clouds, depending upon thermodynamic conditions and large-scale circulation (Figure 7.9). Over the equatorial warm pool and inter-tropical convergence zone (ITCZ) regions, high SSTs stimulate the development of deep convective cloud systems, which are accompanied by anvil and cirrus clouds near the tropopause where the convective air outflows. The large-scale circulation associated with these convective clouds leads to subsidence over the subtropical cool ocean, where deep convection is suppressed by a lower tropospheric inversion layer maintained by the subsidence and promoting the formation of shallow cumulus and stratocumulus clouds. In the extratropics, mid-latitude storm tracks control cloud formation, which occurs primarily in the frontal bands of extratropical cyclones. Since liquid droplets do not freeze spontaneously at temperatures warmer than approximately –40°C and ice nucleating particles that can aid freezing at warmer temperatures are scarce (see ( [[#7.3.3|Section 7.3.3]] ), extratropical clouds often consist both of super-cooled liquid and ice crystals, resulting in mixed-phase clouds.

<div id="_idContainer040" class="Basic-Text-Frame"></div>

[[File:5aee661d7dc43dcdeffa6cfb9e858230 IPCC_AR6_WGI_Figure_7_9.png]]

'''Figure 7.9''' '''|''' '''Schematic cross section of diverse cloud responses to surface warming from the tropics to polar regions.''' Thick solid and dashed curves indicate the tropopause and the subtropical inversion layer in the current climate, respectively. Thin grey text and arrows represent robust responses in the thermodynamic structure to greenhouse warming, of relevance to cloud changes. Text and arrows in red, orange and green show the major cloud responses assessed with ''high'' , ''medium'' and ''low confidence'' , respectively, and the sign of their feedbacks to the surface warming is indicated in the parenthesis. Major advances since AR5 are listed in the box. Figure adapted from [[#Boucher--2013|Boucher et al. (2013)]] .

In the global energy budget at TOA, clouds affect shortwave (SW) radiation by reflecting sunlight due to their high albedo (cooling the climate system) and also longwave (LW) radiation by absorbing the energy from the surface and emitting at a lower temperature to space, that is, contributing to the greenhouse effect, warming the climate system. In general, the greenhouse effect of clouds strengthens with height whereas the SW reflection depends on the cloud optical properties. The effects of clouds on Earth’s energy budget are measured by the cloud radiative effect (CRE), which is the difference in the TOA radiation between clear and all skies (see ( [[#7.2.1|Section 7.2.1]] ). In the present climate, the SW CRE tends to be compensated by the LW CRE over the equatorial warm pool, leading to the net CRE pattern showing large negative values over the eastern part of the subtropical ocean and the extratropical ocean due to the dominant influence of highly reflective marine low-clouds.

In a first attempt to systematically evaluate equilibrium climate sensitivity (ECS) based on fully coupled general circulation models (GCMs) in AR4, diverging cloud feedbacks were recognized as a dominant source of uncertainty. An advance in understanding the cloud feedback was to assess feedbacks separately for different cloud regimes ( [[#Gettelman--2016|Gettelman and Sherwood, 2016]] ). A thorough assessment of cloud feedbacks in different cloud regimes was carried out in AR5 ( [[#Boucher--2013|Boucher et al., 2013]] ), which assigned ''high'' or ''medium confidence'' for some cloud feedbacks but ''low'' or ''no'' ''confidence'' for others (Table 7.9). Many studies that estimate the net cloud feedback using CMIP5 simulations ( [[#Vial--2013|Vial et al., 2013]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ; [[#Zelinka--2016|Zelinka et al., 2016]] ; [[#Colman--2017|Colman and Hanson, 2017]] ) show different values depending on the methodology and the set of models used, but often report a large inter-model spread of the feedback, with the 90% confidence interval spanning both weak negative and strong positive net feedbacks. Part of this diversity arises from the dependence of the model cloud feedbacks on the parametrization of clouds and their coupling to other sub-grid-scale processes ( [[#Zhao--2015|Zhao et al., 2015]] ).

Since AR5, community efforts have been undertaken to understand and quantify the cloud feedbacks in various cloud regimes coupled with large-scale atmospheric circulation ( [[#Bony--2015|Bony et al., 2015]] ). For some cloud regimes, alternative tools to ESMs, such as observations, theory, high-resolution cloud resolving models (CRMs), and large eddy simulations (LES), help quantify the feedbacks. Consequently, the net cloud feedback derived from ESMs has been revised by assessing the regional cloud feedbacks separately and summing them with weighting by the ratio of fractional coverage of those clouds over the globe to give the global feedback, following an approach adopted in [[#Sherwood--2020|Sherwood et al. (2020)]] . This ‘bottom-up’ assessment is explained below with a summary of updated confidence of individual cloud feedback components (Table 7.9). Dependence of cloud feedbacks on evolving patterns of surface warming will be discussed in ( [[#7.4.4|Section 7.4.4]] and is not explicitly taken into account in the assessment presented in this section.

<div id="7.4.2.4.2" class="h4-container"></div>

<span id="assessment-for-individual-cloud-regimes"></span>
===== 7.4.2.4.2 Assessment for individual cloud regimes =====

<div id="h4-8-siblings" class="h4-siblings"></div>

<span id="high-cloud-altitude-feedback"></span>
====== High-cloud altitude feedback ======

It has long been argued that cloud-top altitude rises under global warming, concurrent with the rising of the tropopause at all latitudes ( [[#Marvel--2015|Marvel et al., 2015]] ; [[#Thompson--2017|Thompson et al., 2017]] ). This increasing altitude of high-clouds was identified in early generation GCMs and the tropical high-cloud altitude feedback was assessed to be positive with ''high confidence'' in AR5 ( [[#Boucher--2013|Boucher et al., 2013]] ). This assessment is supported by a theoretical argument called the ‘fixed anvil temperature mechanism’, which ensures that the temperature of the convective detrainment layer does not change when the altitude of high-cloud tops increases with the rising tropopause ( [[#Hartmann--2002|Hartmann and Larson, 2002]] ). Because the cloud-top temperature does not change significantly with global warming, cloud LW emission does not increase even though the surface warms, resulting in an enhancement of the high-cloud greenhouse effect (a positive feedback; [[#Yoshimori--2020|Yoshimori et al. (2020)]] ). The upward shift of high-clouds with surface warming is detected in observed interannual variability and trends in satellite records for recent decades ( [[#Chepfer--2014|Chepfer et al., 2014]] ; [[#Norris--2016|Norris et al., 2016]] ; [[#Saint-Lu--2020|Saint-Lu et al., 2020]] ). The observational detection is not always successful ( [[#Davies--2017|Davies et al., 2017]] ), but the cloud altitude shifts similarly in many CRM experiments ( [[#Khairoutdinov--2013|Khairoutdinov and Emanuel, 2013]] ; [[#Tsushima--2014|Tsushima et al., 2014]] ; [[#Narenpitak--2017|Narenpitak et al., 2017]] ). The high-cloud altitude feedback was estimated to be 0.5 W m <sup>–2</sup> °C <sup>–1</sup> based on GCMs in AR5, but is revised, using a recent re-evaluation that excludes aliasing effects by reduced low-cloud amounts, downward to 0.22 ± 0.12 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation; [[#Zhou--2014|Zhou et al., 2014]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ). In conclusion, there is ''high confidence'' in the positive high-cloud altitude feedback simulated in ESMs as it is supported by theoretical, observational, and process modelling studies.

<span id="tropical-high-cloud-amount-feedback"></span>
====== Tropical high-cloud amount feedback ======

Updrafts in convective plumes lead to detrainment of moisture at a level where the buoyancy diminishes, and thus deep convective clouds over high SSTs in the tropics are accompanied by anvil and cirrus clouds in the upper troposphere. These clouds, rather than the convective plumes themselves, play a substantial role in the global TOA radiation budget. In the present climate, the net CRE of these clouds is small due to a cancellation between the SW and LW components ( [[#Hartmann--2001|Hartmann et al., 2001]] ). However, high-clouds with different optical properties could respond to surface warming differently, potentially perturbing this radiative balance and therefore leading to a non-zero feedback.

A thermodynamic mechanism referred to as the ‘stability iris effect’ has been proposed to explain that the anvil cloud amount decreases with surface warming ( [[#Bony--2016|Bony et al., 2016]] ). In this mechanism, a temperature-mediated increase of static stability in the upper troposphere, where convective detrainment occurs, acts to balance a weakened mass outflow from convective clouds, and thereby reduce anvil cloud areal coverage (Figure 7.9). The reduction of anvil cloud amount is accompanied by enhanced convective aggregation that causes a drying of the surrounding air and thereby increases the LW emission to space that acts as a negative feedback ( [[#Bony--2020|Bony et al., 2020]] ). This phenomenon is found in many CRM simulations ( [[#Emanuel--2014|Emanuel et al., 2014]] ; [[#Wing--2014|Wing and Emanuel, 2014]] ; [[#Wing--2020|Wing et al., 2020]] ) and also identified in observed interannual variability ( [[#Stein--2017|Stein et al., 2017]] ; [[#Saint-Lu--2020|Saint-Lu et al., 2020]] ).

Despite the reduction of anvil cloud amount supported by several lines of evidence, estimates of radiative feedback due to high-cloud amount changes is highly uncertain in models. The assessment presented here is guided by combined analyses of TOA radiation and cloud fluctuations at interannual time scale using multiple satellite datasets. The observationally based local cloud amount feedback associated with optically thick high-clouds is negative, leading to its global contribution (by multiplying the mean tropical anvil cloud fraction of about 8%) of –0.24 ± 0.05 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation) for LW ( [[#Vaillant%20de%20Guélis--2018|Vaillant de Guélis et al., 2018]] ). Also, there is a positive feedback due to increase of optically thin cirrus clouds in the tropopause layer, estimated to be 0.09 ± 0.09 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation; [[#Zhou--2014|Zhou et al., 2014]] ). The negative LW feedback due to reduced amount of thick high-clouds is partly compensated by the positive SW feedback (due to less reflection of solar radiation), so that the tropical high-cloud amount feedback is assessed to be equal to or smaller than their sum. Consistently, the net high-cloud feedback in the tropical convective regime, including a part of the altitude feedback, is estimated to have the global contribution of –0.13 ± 0.06 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation; [[#Williams--2017|Williams and Pierrehumbert, 2017]] ). The negative cloud LW feedback is considerably biased in CMIP5 GCMs ( [[#Mauritsen--2015|Mauritsen and]] [[#Stevens--2015|Stevens, 2015]] ; [[#Su--2017|Su et al., 2017]] ; [[#Li--2019|Li et al., 2019]] ) and highly uncertain, primarily due to differences in the convective parametrization ( [[#Webb--2015|Webb et al., 2015]] ). Furthermore, high-resolution CRM simulations cannot alone be used to constrain uncertainty because the results depend on parametrized cloud microphysics and turbulence ( [[#Bretherton--2014|Bretherton et al., 2014]] ; [[#Ohno--2019|Ohno et al., 2019]] ). Therefore, the tropical high-cloud amount feedback is assessed as negative but with ''low confidence'' given the lack of modelling evidence. Taking observational estimates altogether and methodological uncertainty into account, the global contribution of the high-cloud amount feedback is assessed to be –0.15 ± 0.2 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation).

<span id="subtropical-marine-low-cloud-feedback"></span>
====== Subtropical marine low-cloud feedback ======

It has long been argued that the response of marine boundary-layer clouds over the subtropical ocean to surface warming was the largest contributor to the spread among GCMs in the net cloud feedback ( [[#Boucher--2013|Boucher et al., 2013]] ). However, uncertainty of the marine low-cloud feedback has been reduced considerably since AR5 through combined knowledge from theoretical, modelling and observational studies ( [[#Klein--2017|Klein et al., 2017]] ). Processes that control the low-clouds are complex and involve coupling with atmospheric motions on multiple scales, from the boundary-layer turbulence to the large-scale subsidence, which may be represented by a combination of shallow and deep convective mixing ( [[#Sherwood--2014|Sherwood et al., 2014]] ).

In order to disentangle the large-scale processes that cause the cloud amount either to increase or decrease in response to the surface warming, the cloud feedback has been expressed in terms of several ‘cloud controlling factors’ ( [[#Qu--2014|Qu et al., 2014]] , 2015; [[#Zhai--2015|Zhai et al., 2015]] ; [[#Brient--2016|Brient and Schneider, 2016]] ; [[#Myers--2016|Myers and Norris, 2016]] ; [[#McCoy--2017a|McCoy et al., 2017a]] ). The advantage of this approach over conventional calculation of cloud feedbacks is that the temperature-mediated cloud response can be estimated without using information of the simulated cloud responses that are less well-constrained than the changes in the environmental conditions. Two dominant factors are identified for the subtropical low-clouds: a thermodynamic effect due to rising SST that acts to reduce low-cloud by enhancing cloud-top entrainment of dry air, and a stability effect accompanied by an enhanced inversion strength that acts to increase low-cloud ( [[#Qu--2014|Qu et al., 2014]] , 2015; [[#Kawai--2017|Kawai et al., 2017]] ). These controlling factors compensate with a varying degree in different ESMs, but can be constrained by referring to the observed seasonal or interannual relationship between the low-cloud amount and the controlling factors in the environment as a surrogate. The analysis leads to a positive local feedback that has the global contribution of 0.14 to 0.36 W m <sup>–2</sup> °C <sup>–1</sup> ( [[#Klein--2017|Klein et al., 2017]] ), to which the feedback in the stratocumulus regime dominates over the feedback in the trade cumulus regime ( [[#Cesana--2019|Cesana et al., 2019]] ; [[#Radtke--2021|Radtke et al., 2021]] ). The stratocumulus feedback may be underestimated because explicit simulations using LES show a larger local feedback of up to 2.5 W m <sup>–2</sup> °C <sup>–1</sup> , corresponding to the global contribution of 0.2 W m <sup>–2</sup> °C <sup>–1</sup> by multiplying the mean tropical stratocumulus fraction of about 8% ( [[#Bretherton--2015|Bretherton, 2015]] ). Supported by different lines of evidence, the subtropical marine low-cloud feedback is assessed as positive with ''high confidence'' . Based on the combined estimate using LESs and the cloud controlling factor analysis, the global contribution of the feedback due to marine low-clouds equatorward of 30° is assessed to be 0.2 ± 0.16 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation), for which the range reflects methodological uncertainties.

<span id="land-cloud-feedback"></span>
====== Land cloud feedback ======

Intensification of the global hydrological cycle is a robust feature of global warming, but at the same time, many land areas in the subtropics will experience drying at the surface and in the atmosphere ( [[IPCC:Wg1:Chapter:Chapter-8#8.2.2|Section 8.2.2]] ). This occurs due to limited water availability in these regions, where the cloudiness is consequently expected to decrease. Reduction in clouds over land is consistently identified in the CMIP5 models and also in a GCM with explicit convection ( [[#Bretherton--2014|Bretherton et al., 2014]] ; [[#Kamae--2016a|Kamae et al., 2016a]] ). Because low-clouds make up the majority of subtropical land clouds, this reduced amount of low-clouds reflects less solar radiation and leads to a positive feedback similar to the marine low-clouds. The mean estimate of the global land cloud feedback in CMIP5 models is smaller than the marine low-cloud feedback, 0.08 ± 0.08 W m <sup>–2</sup> °C <sup>–1</sup> ( [[#Zelinka--2016|Zelinka et al., 2016]] ). These values are nearly unchanged in CMIP6 ( [[#Zelinka--2020|Zelinka et al., 2020]] ). However, ESMs still have considerable biases in the climatological temperature and cloud fraction over land, and the magnitude of this feedback has not yet been supported by observational evidence. Therefore, the feedback due to decreasing land clouds is assessed to be 0.08 ± 0.08 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation) with ''low confidence'' .

<span id="mid-latitude-cloud-amount-feedback"></span>
====== Mid-latitude cloud amount feedback ======

Poleward shifts in the mid-latitude jets are evident since the 1980s ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1.4.3|Section 2.3.1.4.3]] ) and are a feature of the large-scale circulation change in future projections ( [[IPCC:Wg1:Chapter:Chapter-4#4.5.1.6|Section 4.5.1.6]] ). Because mid-latitude clouds over the North Pacific, North Atlantic and Southern Ocean are induced mainly by extratropical cyclones in the storm tracks along the jets, it has been suggested that the jet shifts should be accompanied by poleward shifts in the mid-latitude clouds, which would result in a positive feedback through the reduced reflection of insolation ( [[#Boucher--2013|Boucher et al., 2013]] ). However, studies since AR5 have revealed that this proposed mechanism does not apply in practice ( [[#Ceppi--2015|Ceppi and Hartmann, 2015]] ). While a poleward shift of mid-latitude cloud maxima in the free troposphere has been identified in satellite and ground-based observations ( [[#Bender--2012|Bender et al., 2012]] ; [[#Eastman--2013|Eastman and Warren, 2013]] ), associated changes in net CRE are small because the responses in high and low-clouds to the jet shift act to cancel each other ( [[#Grise--2016|Grise and Medeiros, 2016]] ; [[#Tselioudis--2016|Tselioudis et al., 2016]] ; [[#Zelinka--2018|Zelinka et al., 2018]] ). This cancellation is not well captured in ESMs ( [[#Lipat--2017|Lipat et al., 2017]] ), but the above findings show that the mid-latitude cloud feedback is not dynamically driven by the poleward jet shifts, which are rather suggested to occur partly in response to changes in high clouds (Y. [[#Li--2018|]] [[#Li--2018|Li et al., 2018]] ).

Thermodynamics play an important role in controlling extratropical cloud amount equatorward of about 50° latitude. Recent studies showed, using observed cloud controlling factors, that the mid-latitude low-cloud fractions decrease with rising SST, which also acts to weaken stability of the atmosphere unlike in the subtropics ( [[#McCoy--2017a|McCoy et al., 2017a]] ). ESMs consistently show a decrease of cloud amounts and a resultant positive SW feedback in the 30°–40° latitude bands, which can be constrained using observations of seasonal migration of cloud amount ( [[#Zhai--2015|Zhai et al., 2015]] ). Based on the qualitative agreement between observations and ESMs, the mid-latitude cloud amount feedback is assessed as positive with ''medium confidence.'' Following these emergent constraint studies using observations and CMIP5/6 models, the global contribution of net cloud amount feedback over 30°–60° ocean areas, covering 27% of the globe, is assessed at 0.09 ± 0.1 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation), in which the uncertainty reflects potential errors in models’ low-cloud response to changes in thermodynamic conditions.

<span id="extratropical-cloud-optical-depth-feedback"></span>
====== Extratropical cloud optical depth feedback ======

Mixed-phase clouds that consist of both liquid and ice are dominant over the Southern Ocean (50°S–80°S), which accounts for 20% of the net CRE in the present climate ( [[#Matus--2017|Matus and L’Ecuyer, 2017]] ). It has been argued that the cloud optical depth (opacity) will increase over the Southern Ocean as warming drives the replacement of ice-dominated clouds with liquid-dominated clouds ( [[#Tan--2019|Tan et al., 2019]] ). Liquid clouds generally consist of many small cloud droplets, while the crystals in ice clouds are orders of magnitude fewer in number and much larger, causing the liquid clouds to be optically thicker and thereby resulting in a negative feedback ( [[#Boucher--2013|Boucher et al., 2013]] ). However, this phase-change feedback works effectively only below freezing temperature ( [[#Lohmann--2018|Lohmann and Neubauer, 2018]] ; [[#Terai--2019|Terai et al., 2019]] ) and other processes that increase or decrease liquid water path (LWP) may also affect the optical depth feedback ( [[#McCoy--2019|McCoy et al., 2019]] ).

Due to insufficient amounts of super-cooled liquid water in the simulated atmospheric mean state, many CMIP5 models overestimated the conversion from ice to liquid clouds with climate warming and the resultant negative phase-change feedback ( [[#Kay--2016a|Kay et al., 2016a]] ; [[#Tan--2016|Tan et al., 2016]] ; [[#Lohmann--2018|Lohmann and Neubauer, 2018]] ). This feedback can be constrained using satellite-derived LWP observations over the past 20 years that enable estimates of both long-term trends and the interannual relationship with SST variability ( [[#Gordon--2014|Gordon and Klein, 2014]] ; [[#Ceppi--2016|Ceppi et al., 2016]] ; [[#Manaster--2017|Manaster et al., 2017]] ). The observationally-constrained SW feedback ranges from –0.91 to –0.46 W m <sup>–2</sup> °C <sup>–1</sup> over 40°S–70°S depending on the methodology ( [[#Ceppi--2016|Ceppi et al., 2016]] ; [[#Terai--2016|Terai et al., 2016]] ). In some CMIP6 models, representation of super-cooled liquid water content has been improved, leading to weaker negative optical depth feedback over the Southern Ocean closer to observational estimates ( [[#Bodas-Salcedo--2019|Bodas-Salcedo et al., 2019]] ; [[#Gettelman--2019|Gettelman et al., 2019]] ). This improvement at the same time results in a positive optical depth feedback over other extratropical ocean where LWP decreased in response to reduced stability in those CMIP6 models ( [[#Zelinka--2020|Zelinka et al., 2020]] ). Given the accumulated observational estimates and an improved agreement between ESMs and observations, the extratropical optical depth feedback is assessed to be small negative with ''medium confidence.'' Quantitatively, the global contribution of this feedback is assessed to have a value of –0.03 ± 0.05 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation) by combining estimates based on observed interannual variability and the cloud controlling factors.

<span id="arctic-cloud-feedback"></span>
====== Arctic cloud feedback ======

Clouds in polar regions, especially over the Arctic, form at low altitude above or within a stable to neutral boundary layer and are known to co-vary with sea ice variability beneath. Because the clouds reflect sunlight during summer but trap LW radiation throughout the year, seasonality plays an important role in cloud effects on Arctic climate ( [[#Kay--2016b|Kay et al., 2016b]] ). AR5 assessed that Arctic low-cloud amount will increase in boreal autumn and winter in response to declining sea ice in a warming climate, due primarily to an enhanced upward moisture flux over open water. The cloudier conditions during these seasons result in more downwelling LW radiation, acting as a positive feedback on surface warming ( [[#Kay--2009|Kay and Gettelman, 2009]] ). Over recent years, further evidence of the cloud contribution to the Arctic amplification has been obtained ( [[#7.4.4.1|Section 7.4.4.1]] ; [[#Goosse--2018|Goosse et al., 2018]] ). Space-borne lidar (light detection and ranging) observations show that the cloud response to summer sea ice loss is small and cannot overcome the cloud effect in autumn ( [[#Taylor--2015|Taylor et al., 2015]] ; [[#Morrison--2019|Morrison et al., 2019]] ). The seasonality of the cloud response to sea ice variability is reproduced in GCM simulations ( [[#Laîné--2016|Laîné et al., 2016]] ; [[#Yoshimori--2017|Yoshimori et al., 2017]] ). The agreement between observations and models indicates that the Arctic cloud feedback is positive at the surface. This leads to an Arctic cloud feedback at TOA that is ''likely'' positive, but very small in magnitude, as found in some climate models ( [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Morrison--2019|Morrison et al., 2019]] ). The observational estimates are sensitive to the analysis period and the choice of reanalysis data, and a recent estimate of the TOA cloud feedback over 60°N–90°N using atmospheric reanalysis data and CERES satellite observations suggests a regional value ranging from –0.3 to +0.5 W m <sup>–2</sup> °C <sup>–1</sup> , which corresponds to a global contribution of –0.02 to +0.03 W m <sup>–2</sup> °C <sup>–1</sup> (R. [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|Zhang et al., 2018]] ). Based on the overall agreement between ESMs and observations, the Arctic cloud feedback is assessed to be small positive and has the value of 0.01 ± 0.05 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation). The assessed range indicates that a negative feedback is almost as probable as a positive feedback, and the assessment that the Arctic cloud feedback is positive is therefore given ''low confidence'' .

<div id="7.4.2.4.3" class="h4-container"></div>

<span id="synthesis-for-the-net-cloud-feedback"></span>
===== 7.4.2.4.3 Synthesis for the net cloud feedback =====

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The understanding of the response of clouds to warming and associated radiative feedback has deepened since AR5 (Figure 7.9 and FAQ 7.2). Particular progress has been made in the assessment of the marine low-cloud feedback, which has historically been a major contributor to the cloud feedback uncertainty but is no longer the largest source of uncertainty. Multiple lines of evidence (theory, observations, emergent constraints and process modelling) are now available in addition to ESM simulations, and the positive low-cloud feedback is consequently assessed with ''high confidence'' .

The best estimate of net cloud feedback is obtained by summing feedbacks associated with individual cloud regimes and assessed to be α C = 0.42 W m <sup>–2</sup> °C <sup>–1</sup> . By assuming that the uncertainties of individual cloud feedbacks are independent of each other, their standard deviations are added in quadrature, leading to the ''likely'' range of 0.12 to 0.72 W m <sup>–2</sup> °C <sup>–1</sup> and the ''very likely'' range of –0.10 to +0.94 W m <sup>–2</sup> °C <sup>–1</sup> (Table 7.10). This approach potentially misses feedbacks from cloud regimes that are not assessed, but almost all the major cloud regimes were taken into consideration ( [[#Gettelman--2016|Gettelman and Sherwood, 2016]] ) and therefore additional uncertainty will be small. This argument is also supported by an agreement between the net cloud feedback assessed here and the net cloud feedback directly estimated using observations. The observational estimate, which is sensitive to the period considered and is based on two atmospheric reanalyses (ERA-Interim and MERRA) and TOA radiation budgets derived from the CERES satellite observations for the years 2000–2010, is 0.54 ± 0.7 W m <sup>–2</sup> °C <sup>–1</sup> (one standard deviation; [[#Dessler--2013|Dessler, 2013]] ). The observational estimate overlaps with the assessed range of the net cloud feedback. The assessed ''very likely'' range is reduced by about 50% compared to AR5, but is still wide compared to those of other climate feedbacks (Table 7.10). The largest contribution to this uncertainty range is the estimate of tropical high-cloud amount feedback which is not yet well quantified using models.

In reality, different types of cloud feedback may occur simultaneously in one cloud regime. For example, an upward shift of high-clouds associated with the altitude feedback could be coupled to an increase/decrease of cirrus/anvil cloud fractions associated with the cloud amount feedback. Alternatively, slowdown of the tropical circulation with surface warming ( [[IPCC:Wg1:Chapter:Chapter-4#4.5.3|Section 4.5.3]] and Figure 7.9) could affect both high and low-clouds so that their feedbacks are co-dependent. Quantitative assessments of such covariances require further knowledge about cloud feedback mechanisms, which will further narrow the uncertainty range.

In summary, deepened understanding of feedback processes in individual cloud regimes since AR5 leads to an assessment of the positive net cloud feedback with ''high confidence'' . A small probability (less than 10%) of a net negative cloud feedback cannot be ruled out, but this would require an extremely large negative feedback due to decreases in the amount of tropical anvil clouds or increases in optical depth of extratropical clouds over the Southern Ocean; neither is supported by current evidence.

<div id="_idContainer041" class="Basic-Text-Frame"></div>

'''Table 7.9''' '''|''' '''Assessed sign and confidence level of cloud feedbacks in different regimes in AR5 and AR6.''' For some cloud regimes, the feedback was not assessed in AR5, indicated by N/A.

{| class="wikitable"
|-
| Feedback

| AR5

| AR6

|-
| High-cloud altitude feedback

| Positive ( ''high confidence'' )

| Positive ( ''high confidence'' )

|-
| Tropical high-cloud amount feedback

| N/A

| Negative ( ''low confidence'' )

|-
| Subtropical marine low-cloud feedback

| N/A ( ''low confidence'' )

| Positive ( ''high confidence'' )

|-
| Land cloud feedback

| N/A

| Positive ( ''low confidence'' )

|-
| Mid-latitude cloud amount feedback

| Positive ( ''medium confidence'' )

| Positive ( ''medium confidence'' )

|-
| Extratropical cloud optical depth feedback

| N/A

| Small negative ( ''medium confidence'' )

|-
| Arctic cloud feedback

| Small positive ( ''very low confidence'' )

| Small positive ( ''low confidence'' )

|-
| Net cloud feedback

| Positive ( ''medium confidence'' )

| Positive ( ''high confidence'' )

|}

<div id="7.4.2.5" class="h3-container"></div>

<span id="biogeophysical-and-non-co-2-biogeochemical-feedbacks"></span>
==== 7.4.2.5 Biogeophysical and Non-CO <sub>2</sub> Biogeochemical Feedbacks ====

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The feedbacks presented in the previous sections (Sections 7.4.2.1–7.4.2.4) are directly linked to physical climate variables (for example temperature, water vapour, clouds, or sea ice). The central role of climate feedbacks associated with these variables has been recognized since early studies of climate change. However, in addition to these physical climate feedbacks, the Earth system includes feedbacks for which the effect of global mean surface temperature change on the TOA energy budget is mediated through other mechanisms, such as the chemical composition of the atmosphere, or by vegetation changes. Among these additional feedbacks, the most important is the CO <sub>2</sub> feedback that describes how a change of the global surface temperature affects the atmospheric CO <sub>2</sub> concentration. In ESM simulations in which CO <sub>2</sub> emissions are prescribed, changes in surface carbon fluxes affect the CO <sub>2</sub> concentration in the atmosphere, the TOA radiative energy budget, and eventually the global mean surface temperature. In ESM simulations in which the CO <sub>2</sub> concentration is prescribed, changes in the carbon cycle allow compatible CO <sub>2</sub> emissions to be calculated, that is, the CO <sub>2</sub> emissions that are compatible with both the prescribed CO <sub>2</sub> concentration and the representation of the carbon cycle in the ESM. The CO <sub>2</sub> feedback is assessed in ( [[IPCC:Wg1:Chapter:Chapter-5|Chapter 5]] [[IPCC:Wg1:Chapter:Chapter-5#5.4|Section 5.4]] ). The framework presented in this chapter assumes that the CO <sub>2</sub> concentration is prescribed, and our assessment of the net feedback parameter, α , does not include carbon cycle feedbacks on the atmospheric CO <sub>2</sub> concentration ( [[#7.1|Section 7.1]] and Box 7.1). However, our assessment of α does include non-CO <sub>2</sub> biogeochemical feedbacks (including effects due to changes in atmospheric methane concentration; [[#7.4.2.5.1|Section 7.4.2.5.1]] ) and biogeophysical feedbacks ( [[#7.4.2.5.2|Section 7.4.2.5.2]] ). A synthesis of the combination of biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks is given in [[#7.4.2.5.3|Section 7.4.2.5.3]] .

<div id="7.4.2.5.1" class="h4-container"></div>

<span id="non-co-2-biogeochemical-feedbacks"></span>
===== 7.4.2.5.1 Non-CO <sub>2</sub> biogeochemical feedbacks =====

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The chemical composition of the atmosphere (beyond CO <sub>2</sub> and water vapour changes) is expected to change in response to a warming climate. These changes in greenhouse gases (methane, nitrous oxide and ozone) and aerosol amount (including dust) have the potential to alter the TOA energy budget and are collectively referred to as ‘non-CO <sub>2</sub> biogeochemical feedbacks’. Methane (CH <sub>4</sub> ) and nitrous oxide (N <sub>2</sub> O) feedbacks arise partly from changes in their emissions from natural sources in response to temperature change; these are assessed in ( [[IPCC:Wg1:Chapter:Chapter-5|Chapter 5]] [[IPCC:Wg1:Chapter:Chapter-5#5.4.7|Section 5.4.7]] ; see also Figure 5.29c). Here we exclude the permafrost CH <sub>4</sub> feedback ( [[IPCC:Wg1:Chapter:Chapter-5#5.4.9.1.2|Section 5.4.9.1.2]] ) because, although associated emissions are projected to increase under warming on multi-decadal to centennial time scales, on longer time scales these emissions would eventually substantially decline as the permafrost carbon pools were depleted ( [[#Schneider%20von%20Deimling--2012|Schneider von Deimling et al., 2012]] , 2015). This leaves the wetland CH <sub>4</sub> , land N <sub>2</sub> O, and ocean N <sub>2</sub> O feedbacks, the assessed mean values of which sum to a positive feedback parameter of +0.04 [0.02 to 0.06] W m <sup>–2</sup> °C <sup>–1</sup> [[IPCC:Wg1:Chapter:Chapter-5#5.4.7|Section 5.4.7]] . Other non-CO <sub>2</sub> biogeochemical feedbacks that are relevant to the net feedback parameter are assessed in [[IPCC:Wg1:Chapter:Chapter-6|Chapter 6]] (Section 6.4.5 and Table 6.8). These feedbacks are associated with sea salt, dimethyl sulphide, dust, ozone, biogenic volatile organic compounds, lightning, and CH <sub>4</sub> lifetime, and sum to a negative feedback parameter of –0.20 [–0.41 to +0.01] W m <sup>–2</sup> °C <sup>–1</sup> . The overall feedback parameter for non-CO <sub>2</sub> biogeochemical feedbacks is obtained by summing the [[IPCC:Wg1:Chapter:Chapter-5|Chapter 5]] and [[IPCC:Wg1:Chapter:Chapter-6|Chapter 6]] assessments, which gives –0.16 [–0.37 to +0.05] W m <sup>–2</sup> °C <sup>–1</sup> . However, there is ''low confidence'' in the estimates of both the individual non-CO <sub>2</sub> biogeochemical feedbacks as well as their total effect, as evident from the large range in the magnitudes of α from different studies, which can be attributed to diversity in how models account for these feedbacks and limited process-level understanding.

<div id="7.4.2.5.2" class="h4-container"></div>

<span id="biogeophysical-feedbacks"></span>

===== 7.4.2.5.2 Biogeophysical feedbacks =====

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Biogeophysical feedbacks are associated with changes in the spatial distribution and/or biophysical properties of vegetation, induced by surface temperature change and attendant hydrological cycle change. These vegetation changes can alter radiative fluxes directly via albedo changes, or via surface momentum or moisture flux changes and hence changes in cloud properties. However, the direct physiological response of vegetation to changes in CO <sub>2</sub> , including changes in stomatal conductance, is considered part of the CO <sub>2</sub> effective radiative forcing rather than a feedback ( [[#7.3.2.1|Section 7.3.2.1]] ). The time scale on which vegetation responds to climate change is relatively uncertain but can be from decades to hundreds of years ( [[#Willeit--2014|Willeit et al., 2014]] ), and could occur abruptly or as a tipping point (Sections 5.4.9.1.1, 8.6.2.1 and 8.6.2.2); equilibrium only occurs when the soil system and associated nutrient and carbon pools equilibrate, which can take millennia ( [[#Brantley--2008|Brantley, 2008]] ; [[#Sitch--2008|Sitch et al., 2008]] ). The overall effects of climate-induced vegetation changes may be comparable in magnitude to those from anthropogenic land-use and land-cover change ( [[#Davies-Barnard--2015|Davies-Barnard et al., 2015]] ). Climate models that include a dynamical representation of vegetation (e.g., [[#Reick--2013|Reick et al., 2013]] ; [[#Harper--2018|Harper et al., 2018]] ) are used to explore the importance of biogeophysical feedbacks ( [[#Notaro--2007|Notaro et al., 2007]] ; [[#Brovkin--2009|Brovkin et al., 2009]] ; [[#O’ishi--2009|O’ishi et al., 2009]] ; [[#Port--2012|Port et al., 2012]] ; [[#Willeit--2014|Willeit et al., 2014]] ; [[#Alo--2017|Alo and Anagnostou, 2017]] ; W. [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|Zhang et al., 2018]] ; [[#Armstrong--2019|Armstrong et al., 2019]] ). In AR5, it was discussed that such model experiments predicted that expansion of vegetation in the high latitudes of the Northern Hemisphere would enhance warming due to the associated surface-albedo change, and that reduction of tropical forests in response to climate change would lead to regional surface warming, due to reduced evapotranspiration (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ), but there was no assessment of the associated feedback parameter. The SRCCL stated that regional climate change can be dampened or enhanced by changes in local land cover, but that this depends on the location and the season; however, in general the focus was on anthropogenic land-cover change, and no assessment of the biogeophysical feedback parameter was carried out. There are also indications of a marine biogeophysical feedback associated with surface-albedo change due to changes in phytoplankton ( [[#Frouin--2002|Frouin and Iacobellis, 2002]] ; [[#Park--2015|Park et al., 2015]] ), but there is not currently enough evidence to quantitatively assess this feedback.

Since AR5, several studies have confirmed that a shift from tundra to boreal forests and the associated albedo change leads to increased warming in Northern Hemisphere high latitudes ( ''high confidence'' ) ( [[#Willeit--2014|Willeit et al., 2014]] ; W. [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|Zhang et al., 2018]] ; [[#Armstrong--2019|Armstrong et al., 2019]] ). However, regional modelling indicates that vegetation feedbacks may act to cool climate in the Mediterranean ( [[#Alo--2017|Alo and Anagnostou, 2017]] ), and in the tropics and subtropics the regional response is in general not consistent across models. On a global scale, several modelling studies have either carried out a feedback analysis ( [[#Stocker--2013|Stocker et al., 2013]] ; [[#Willeit--2014|Willeit et al., 2014]] ) or presented simulations that allow a feedback parameter to be estimated ( [[#O’ishi--2009|O’ishi et al., 2009]] ; [[#Armstrong--2019|Armstrong et al., 2019]] ), in such a way that the physiological response can be accounted for as a forcing rather than a feedback. The central estimates of the biogeophysical feedback parameter from these studies range from close to zero ( [[#Willeit--2014|Willeit et al., 2014]] ) to +0.13 W m <sup>–2</sup> °C <sup>–1</sup> ( [[#Stocker--2013|Stocker et al., 2013]] ). An additional line of evidence comes from the mid-Pliocene warm period (MPWP, Chapter 2, Cross-Chapter Box 2.1), for which paleoclimate proxies provide evidence of vegetation distribution and CO <sub>2</sub> concentrations. Model simulations that include various combinations of modern versus MPWP vegetation and CO <sub>2</sub> allow an associated feedback parameter to be estimated, as long as account is also taken of the orographic forcing ( [[#Lunt--2010|Lunt et al., 2010]] , 2012b). This approach has the advantage over pure modelling studies in that the reconstructed vegetation is based on (paleoclimate) observations, and is in equilibrium with the CO <sub>2</sub> forcing. However, there are uncertainties in the vegetation reconstruction in regions with little or no proxy data, and it is uncertain how much of the vegetation change is associated with the physiological response to CO <sub>2</sub> . This paleoclimate approach gives an estimate for the biogeophysical feedback parameter of +0.3 W m <sup>–2</sup> °C <sup>–1</sup> .

Given the limited number of studies, we take the full range of estimates discussed above for the biogeophysical feedback parameter, and assess the ''very likely'' range to be from 0.0 to +0.3 W m <sup>–2</sup> °C <sup>–1</sup> , with a central estimate of +0.15 W m <sup>–2</sup> °C <sup>–1</sup> ( ''low confidence'' ). Although this assessment is based on evidence from both models and paleoclimate proxies, and the studies above agree on the sign of the change, there is nonetheless ''limited evidence'' . Higher confidence could be obtained if there were more studies that allowed calculation of a biogeophysical feedback parameter (particularly from paleoclimates), and if the partitioning between biogeophysical feedbacks and physiological forcing were clearer for all lines of evidence.

<div id="7.4.2.5.3" class="h4-container"></div>

<span id="synthesis-of-biogeophysical-and-non-co-2-biogeochemical-feedbacks"></span>
===== 7.4.2.5.3 Synthesis of biogeophysical and non-CO 2 biogeochemical feedbacks =====

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The non-CO <sub>2</sub> biogeochemical feedbacks are assessed in ( [[#7.4.2.5.1|Section 7.4.2.5.1]] to be –0.16 [–0.37 to +0.05] W m <sup>–</sup> <sup>2</sup> °C <sup>–1</sup> and the biogeophysical feedbacks are assessed in ( [[#7.4.2.5.2|Section 7.4.2.5.2]] to be +0.15 [0.0 to +0.3] W m <sup>–2</sup> °C <sup>–1</sup> . The sum of the biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks is assessed to have a central value of –0.01 W m <sup>–2</sup> °C <sup>–1</sup> and a ''very likely'' range from –0.27 to +0.25 W m <sup>–2</sup> °C <sup>–1</sup> (Table 7.10). Given the relatively long time scales associated with the biological processes that mediate the biogeophysical and many of the non-CO <sub>2</sub> biogeochemical feedbacks, in comparison with the relatively short time scale of many of the underlying model simulations, combined with the small number of studies for some of the feedbacks, and the relatively small signals, this overall assessment has ''low confidence'' .

Some supporting evidence for this overall assessment can be obtained from the CMIP6 ensemble, which provides some pairs of instantaneous 4×CO <sub>2</sub> simulations carried out using related models, with and without biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks. This is not a direct comparison because these pairs of simulations may differ by more than just their inclusion of these additional feedbacks; furthermore, not all biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks are fully represented. However, a comparison of the pairs of simulations does provide a first-order estimate of the magnitude of these additional feedbacks. [[#Séférian--2019|Séférian et al. (2019)]] find a slightly more negative feedback parameter in CNRM-ESM2-1 (with additional feedbacks) then in CNRM-CM6-1 (a decrease of 0.02 W m <sup>–2</sup> °C <sup>–1</sup> , using the linear regression method from years 10–150). [[#Andrews--2019|Andrews et al. (2019)]] also find a slightly more negative feedback parameter when these additional feedbacks are included (a decrease of 0.04 W m <sup>–2</sup> °C <sup>–1</sup> in UKESM1 compared with HadGEM3-GC3.1). Both of these studies suggest a small but slightly negative feedback parameter for the combination of biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks, but with relatively large uncertainty given (i) interannual variability and (ii) that feedbacks associated with natural terrestrial emissions of CH <sub>4</sub> and N <sub>2</sub> O were not represented in either pair.

<div id="7.4.2.6" class="h3-container"></div>

<span id="long-term-radiative-feedbacks-associated-with-ice-sheets"></span>
==== 7.4.2.6 Long-Term Radiative Feedbacks Associated with Ice Sheets ====

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Although long-term radiative feedbacks associated with ice sheets are not included in our definition of ECS (Box 7.1), the relevant feedback parameter is assessed here because the time scales on which these feedbacks act are relatively uncertain, and the long-term temperature response to CO <sub>2</sub> forcing of the entire Earth system may be of interest.

Earth’s ice sheets (Greenland and Antarctica) are sensitive to climate change ( [[IPCC:Wg1:Chapter:Chapter-9#9.4|Section 9.4]] ; [[#Pattyn--2018|Pattyn et al., 2018]] ). Their time evolution is determined by both their surface mass balance and ice dynamic processes, with the latter being particularly important for the West Antarctic Ice Sheet. Surface mass balance depends on the net energy and hydrological fluxes at their surface, and there are mechanisms of ice-sheet instability that depend on ocean temperatures and basal melt rates ( [[IPCC:Wg1:Chapter:Chapter-9#9.4.1.1|Section 9.4.1.1]] ). The presence of ice sheets affects Earth’s radiative budget, hydrology, and atmospheric circulation due to their characteristic high albedo, low roughness length, and high altitude, and they influence ocean circulation through freshwater input from calving and melt (e.g., [[#Fyke--2018|Fyke et al., 2018]] ). Ice-sheet changes also modify surface albedo through the attendant change in sea level and therefore land area ( [[#Abe-Ouchi--2015|Abe-Ouchi et al., 2015]] ). The time scale for ice sheets to reach equilibrium is of the order of thousands of years ( [[#Clark--2016|Clark et al., 2016]] ). Due to the long time scales involved, it is a major challenge to run coupled climate–ice sheet models to equilibrium, and as a result, long-term simulations are often carried out with lower complexity models, and/or are asynchronously coupled.

In AR5, it was described that both the Greenland and Antarctic ice sheets would continue to lose mass in a warming world (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ), with a continuation in sea level rise beyond the year 2500 assessed as ''virtually certain'' . However, there was ''low confidence'' in the associated radiative feedback mechanisms, and as such, there was no assessment of the magnitude of long-term radiative feedbacks associated with ice sheets. That assessment is consistent with SROCC, wherein it was stated that ‘with limited published studies to draw from and no simulations run beyond 2100, firm conclusions regarding the net importance of atmospheric versus ocean melt feedbacks on the long-term future of Antarctica cannot be made.’

The magnitude of the radiative feedback associated with changes to ice sheets can be quantified by comparing the global mean long-term equilibrium temperature response to increased CO <sub>2</sub> concentrations in simulations that include interactive ice sheets with that of simulations that do not include the associated ice sheet–climate interactions ( [[#Swingedouw--2008|Swingedouw et al., 2008]] ; [[#Vizcaíno--2010|Vizcaíno et al., 2010]] ; [[#Goelzer--2011|Goelzer et al., 2011]] ; [[#Bronselaer--2018|Bronselaer et al., 2018]] ; [[#Golledge--2019|Golledge et al., 2019]] ). These simulations indicate that on multi-centennial time scales, ice-sheet mass loss leads to freshwater fluxes that can modify ocean circulation ( [[#Swingedouw--2008|Swingedouw et al., 2008]] ; [[#Goelzer--2011|Goelzer et al., 2011]] ; [[#Bronselaer--2018|Bronselaer et al., 2018]] ; [[#Golledge--2019|Golledge et al., 2019]] ). This leads to reduced surface warming (by about 0.2°C in the global mean after 1000 years; [[#7.4.4.1.1|Section 7.4.4.1.1]] ; [[#Goelzer--2011|Goelzer et al., 2011]] ), although other work suggests no net global temperature effect of ice-sheet mass loss ( [[#Vizcaíno--2010|Vizcaíno et al., 2010]] ). However, model simulations in which the Antarctic Ice Sheet is removed completely in a paleoclimate context indicate a positive global mean feedback on multi-millennial time scales due primarily to the surface-albedo change ( [[#Goldner--2014a|Goldner et al., 2014a]] ; [[#Kennedy-Asser--2019|Kennedy-Asser et al., 2019]] ); in ( [[IPCC:Wg1:Chapter:Chapter-9|Chapter 9]] [[IPCC:Wg1:Chapter:Chapter-9#9.6.3|Section 9.6.3]] ) it is assessed that such ice-free conditions could eventually occur given 7°C–13°C of warming. This net positive feedback from ice-sheet mass loss on long time scales is also supported by model simulations of the mid-Pliocene Warm Period (MPWP; Cross-chapter Box 2.1) in which the volume and area of the Greenland and West Antarctic ice sheets are reduced in model simulations in agreement with geological data ( [[#Chandan--2018|Chandan and Peltier, 2018]] ), leading to surface warming. As such, overall, on multi-centennial time scales the feedback parameter associated with ice sheets is ''likely'' negative ( ''medium confidence'' ), but on multi-millennial time scales by the time the ice sheets reach equilibrium, the feedback parameter is ''very likely'' positive ( ''high confidence'' ) (Table 7.10). However, a relative lack of models carrying out simulations with and without interactive ice sheets over centennial to millennial time scales means that there is currently not enough evidence to quantify the magnitude of these feedbacks, or the time scales on which they act.

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<span id="synthesis-1"></span>
==== 7.4.2.7 Synthesis ====

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Table 7.10 summarizes the estimates and the assessment of the individual and the net feedbacks presented in the above sections. The uncertainty range of the net climate feedback was obtained by adding standard deviations of individual feedbacks in quadrature, assuming that they are independent and follow the Gaussian distribution. It is ''virtually certain'' that the net climate feedback is negative, primarily due to the Planck temperature response, indicating that climate acts to stabilize in response to radiative forcing imposed to the system. Supported by the level of confidence associated with the individual feedbacks, it is also ''virtually certain'' that the sum of the non-Planck feedbacks is positive. Based on Table 7.10 these climate feedbacks amplify the Planck temperature response by about 2.8 [1.9 to 5.9] times ''.'' Cloud feedback remains the largest contributor to uncertainty of the net feedback, but the uncertainty is reduced compared to AR5. A secondary contribution to the net feedback uncertainty is the biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks, which together are assessed to have a central value near zero and thus do not affect the central estimate of ECS. The net climate feedback is assessed to be –1.16 W m <sup>–2</sup> °C <sup>–1</sup> , ''likely'' from –1.54 to –0.78 W m <sup>–2</sup> °C <sup>–1</sup> , and ''very likely'' from –1.81 to –0.51 W m <sup>–2</sup> °C <sup>–1</sup> ''.''

Feedback parameters in climate models are calculated assuming that they are independent of each other, except for a well-known co-dependency between the water vapour (WV) and lapse rate (LR) feedbacks. When the inter-model spread of the net climate feedback is computed by adding in quadrature the inter-model spread of individual feedbacks, it is 17% wider than the spread of the net climate feedback directly derived from the ensemble. This indicates that the feedbacks in climate models are partly co-dependent. Two possible co-dependencies have been suggested ( [[#Huybers--2010|Huybers, 2010]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ). One is a negative covariance between the LR and longwave cloud feedbacks, which may be accompanied by a deepening of the troposphere ( [[#O’Gorman--2013|O’Gorman and Singh, 2013]] ; [[#Yoshimori--2020|Yoshimori et al., 2020]] ) leading both to greater rising of high-clouds and a larger upper-tropospheric warming. The other is a negative covariance between albedo and shortwave cloud feedbacks, which may originate from the Arctic regions: a reduction in sea ice enhances the shortwave cloud radiative effect because the ocean surface is darker than sea ice ( [[#Gilgen--2018|Gilgen et al., 2018]] ). This covariance is reinforced as the decrease of sea ice leads to an increase in low-level clouds ( [[#Mauritsen--2013|Mauritsen et al., 2013]] ). However, the mechanism causing these co-dependences between feedbacks is not well understood yet and a quantitative assessment based on multiple lines of evidence is difficult. Therefore, this synthesis assessment does not consider any co-dependency across individual feedbacks.

The assessment of the net climate feedback presented above is based on a single approach (i.e., process understanding) and directly results in a value for ECS given in ( [[#7.5.1|Section 7.5.1]] ; this is in contrast to the synthesis assessment of ECS in ( [[#7.5.5|Section 7.5.5]] which combines multiple approaches. The total (net) feedback parameter consistent with the final synthesis assessment of the ECS and Equation 7.1 (Box 7.1) is provided there.

<div id="7.4.2.8" class="h3-container"></div>

<span id="climate-feedbacks-in-esms"></span>
==== 7.4.2.8 Climate Feedbacks in ESMs ====

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Since AR5, many modelling groups have newly participated in CMIP experiments, leading to an increase in the number of models in CMIP6 [[IPCC:Wg1:Chapter:Chapter-1#1.5.4|Section 1.5.4]] ). Other modelling groups that contributed to CMIP5 also updated their ESMs for carrying out CMIP6 experiments. While some of the CMIP6 models share components and are therefore not independent, they are analysed independently when calculating climate feedbacks. This, and more subtle forms of model inter-dependence, creates challenges when determining appropriate model weighting schemes ( [[IPCC:Wg1:Chapter:Chapter-1#1.5.4|Section 1.5.4]] ). Additionally, it must be kept in mind that the ensemble sizes of the CMIP5 and CMIP6 models are not sufficiently large to sample the full range of model uncertainty.

The multi-model mean values of all physical climate feedbacks are calculated using the radiative kernel method ( [[#7.4.1|Section 7.4.1]] ) and compared with the assessment in the previous sections (Figure 7.10). For CMIP models, there is a discrepancy between the net climate feedback calculated directly using the time evolutions of Δ ''T'' and Δ ''N'' in each model and the accumulation of individual feedbacks, but it is negligibly small (Supplementary Material 7.SM.4). Feedbacks due to biogeophysical and non-CO <sub>2</sub> biogeochemical processes are included in some models but neglected in the kernel analysis. In AR6, biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks are explicitly assessed ( [[#7.4.2.5|Section 7.4.2.5]] ).

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'''Table 7.10''' '''|''' '''Synthesis assessment of climate feedbacks (central estimate shown in bold).''' The mean values and their 90% ranges in CMIP5/6 models, derived using multiple radiative kernels ( [[#Zelinka--2020|Zelinka et al., 2020]] ) are also presented for comparison.

{| class="wikitable"
|-
| rowspan="2"| Feedback Parameter α x (W m <sup>–2</sup> °C <sup>–1</sup> )

| CMIP5 GCMs

| CMIP6 ESMs

| colspan="4"| AR6 Assessed Ranges

|-
| Mean and

5–95% Interval

| Mean and

5–95% Interval

| Central Estimate

| Very likely Interval

| Likely Interval

| Level of Confidence

|-
| Planck

| –3.20 [–3.3 to –3.1]

| –3.22 [–3.3 to –3.1]

| '''–3.22'''

| –3.4 to –3.0

| –3.3 to –3.1

| ''high''

|-
| WV+LR

| 1.24 [1.08 to 1.35]

| 1.25 [1.14 to 1.45]

| '''1.30'''

| 1.1 to 1.5

| 1.2 to 1.4

| ''high''

|-
| Surface albedo

| 0.41 [0.25 to 0.56]

| 0.39 [0.26 to 0.53]

| '''0.35'''

| 0.10 to 0.60

| 0.25 to 0.45

| ''medium''

|-
| Clouds

| 0.41 [–0.09 to 1.1]

| 0.49 [–0.08 to 1.1]

| '''0.42'''

| –0.10 to 0.94

| 0.12 to 0.72

| ''high''

|-
| Biogeophysical and non-CO <sub>2</sub> biogeochemical

| Not evaluated

| Not evaluated

| '''–0.01'''

| –0.27 to 0.25

| –0.16 to 0.14

| ''low''

|-
| Residual of kernel estimates

| 0.06 [–0.17 to 0.29]

| 0.05 [–0.18 to 0.28 ]

|
|-
| '''Net''' (i.e., relevant for ECS)

| –1.08 [–1.61 to –0.68]

| –1.03 [–1.54 to –0.62]

| '''–1.16'''

| –1.81 to –0.51

| –1.54 to –0.78

| ''medium''

|-
| Long-term ice-sheet feedbacks (millennial scale)

|
| &gt;0.0

|
| ''high''

|}

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[[File:abad03bd326a3f3e49cb28d9d362a7d5 IPCC_AR6_WGI_Figure_7_10.png]]

'''Figure 7.10''' '''|''' '''Global mean climate feedbacks estimated in''' ''abrupt 4xCO2'' '''simulations of 29 CMIP5 models (light blue) and 49 CMIP6 models (orange), compared with those assessed in this Report (red).''' Individual feedbacks for CMIP models are averaged across six radiative kernels as computed in [[#Zelinka--2020|Zelinka et al. (2020)]] . The white line, black box and vertical line indicate the mean, 66% and 90% ranges, respectively. The shading represents the probability distribution across the full range of GCM/ESM values and for the 2.5–97.5 percentile range of the AR6 normal distribution. The unit is W m <sup>–2</sup> °C <sup>–1</sup> . Feedbacks associated with biogeophysical and non-CO <sub>2</sub> biogeochemical processes are assessed in AR6, but they are not explicitly estimated from general circulation models (GCMs)/Earth system models (ESMs) in CMIP5 and CMIP6. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

All the physical climate feedbacks apart from clouds are very similar in the CMIP5 and CMIP6 model ensembles (see also Table 7.10). These values, where possible supported by other lines of evidence, are used for assessing feedbacks in Sections 7.4.2.1–7.4.2.3. A difference found between CMIP5 and CMIP6 models is the net cloud feedback, which is larger in CMIP6 by about 20%. This change is the major cause of less-negative values of the net climate feedback in CMIP6 than in CMIP5 and hence an increase in modelled ECs ( [[#7.5.1|Section 7.5.1]] ).

A remarkable improvement of cloud representation in some CMIP6 models is the reduced error of the too-weak negative shortwave CRE over the Southern Ocean ( [[#Bodas-Salcedo--2019|Bodas-Salcedo et al., 2019]] ; [[#Gettelman--2019|Gettelman et al., 2019]] ) due to a more realistic simulation of supercooled liquid droplets and associated cloud optical depths that were biased low commonly in CMIP5 models ( [[#McCoy--2014a|McCoy et al., 2014a]] , b). Because the negative cloud optical depth feedback occurs due to ‘brightening’ of clouds via phase change from ice to liquid cloud particles in response to surface warming ( [[#Cesana--2017|Cesana and]] [[#Storelvmo--2017|Storelvmo, 2017]] ), the extratropical cloud shortwave feedback tends to be less negative or even slightly positive in models with reduced errors ( [[#Bjordal--2020|Bjordal et al., 2020]] ; [[#Zelinka--2020|Zelinka et al., 2020]] ). The assessment of cloud feedbacks in ( [[#7.4.2.4|Section 7.4.2.4]] incorporates estimates from these improved ESMs. Yet, there still remain other shared model errors, such as in the subtropical low-clouds ( [[#Calisto--2014|Calisto et al., 2014]] ) and tropical anvil clouds ( [[#Mauritsen--2015|Mauritsen and]] [[#Stevens--2015|Stevens, 2015]] ), hampering an assessment of feedbacks associated with these cloud regimes based only on ESMs ( [[#7.4.2.4|Section 7.4.2.4]] ).

<div id="7.4.3" class="h2-container"></div>

<span id="dependence-of-feedbacks-on-climate-mean-state"></span>
=== 7.4.3 Dependence of Feedbacks on Climate Mean State ===

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In the standard framework of forcings and feedbacks ( [[#7.4.1|Section 7.4.1]] and Box 7.1), the approximation is made that the strength of climate feedbacks is independent of the background global mean surface temperature. More generally, the individual feedback parameters, α x , are often assumed to be constant over a range of climate states, including those reconstructed from the past (encompassing a range of states warmer and colder than today, with varying continental geographies) or projected for the future. If this approximation holds, then the equilibrium global surface temperature response to a fixed radiative forcing will be constant, regardless of the climate state to which that forcing is applied.

This approximation will break down if climate feedbacks are not constant, but instead vary as a function of, for example, background temperature ( [[#Roe--2007|Roe and Baker, 2007]] ; [[#Zaliapin--2010|Zaliapin and Ghil, 2010]] ; [[#Roe--2011|Roe and Armour, 2011]] ; [[#Bloch-Johnson--2015|Bloch-Johnson et al., 2015]] ), continental configuration ( [[#Farnsworth--2019|Farnsworth et al., 2019]] ), or configuration of ice sheets ( [[#Yoshimori--2009|Yoshimori et al., 2009]] ). If the real climate system exhibits this state-dependence, then the future equilibrium temperature change in response to large forcing may be different from that inferred using the standard framework, and/or different to that inferred from paleoclimates. Such considerations are important for the assessment of ECs ( [[#7.5|Section 7.5]] ). Climate models generally include representations of feedbacks that allow state-dependent behaviour, and so model results may also differ from the predictions from the standard framework.

In AR5 ( [[#Boucher--2013|Boucher et al., 2013]] ), there was a recognition that climate feedbacks could be state-dependent ( [[#Colman--2009|Colman and McAvaney, 2009]] ), but modelling studies that explored this (e.g., [[#Manabe--1985|Manabe and Bryan, 1985]] ; [[#Voss--2001|Voss and Mikolajewicz, 2001]] ; [[#Stouffer--2003|Stouffer and Manabe, 2003]] ; [[#Hansen--2005b|Hansen et al., 2005b]] ) were not assessed in detail. Also in AR5 ( [[#Masson-Delmotte--2013|Masson-Delmotte et al., 2013]] ), it was assessed that some models exhibited weaker sensitivity to Last Glacial Maximum (LGM; Cross-Chapter Box 2.1) forcing than to 4×CO <sub>2</sub> forcing, due to state-dependence in shortwave cloud feedbacks.

Here, recent evidence for state-dependence in feedbacks from modelling studies ( [[#7.4.3.1|Section 7.4.3.1]] ) and from the paleoclimate record ( [[#7.4.3.2|Section 7.4.3.2]] ) are assessed, with an overall assessment in ( [[#7.4.3.3|Section 7.4.3.3]] . The focus is on temperature-dependence of feedbacks when the system is in equilibrium with the forcing; evidence for transient changes in the net feedback parameter associated with evolving spatial patterns of warming is assessed separately in ( [[#7.4.4|Section 7.4.4]] .

<div id="7.4.3.1" class="h3-container"></div>

<span id="state-dependence-of-feedbacks-in-models"></span>
==== 7.4.3.1 State-dependence of Feedbacks in Models ====

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There are several modelling studies since AR5 in which ESMs of varying complexity have been used to explore temperature dependence of feedbacks, either under modern ( [[#Hansen--2013|Hansen et al., 2013]] ; [[#Jonko--2013|Jonko et al., 2013]] ; [[#Meraner--2013|Meraner et al., 2013]] ; [[#Good--2015|Good et al., 2015]] ; [[#Duan--2019|Duan et al., 2019]] ; [[#Mauritsen--2019|Mauritsen et al., 2019]] ; [[#Rohrschneider--2019|Rohrschneider et al., 2019]] ; [[#Stolpe--2019|Stolpe et al., 2019]] ; [[#Bloch-Johnson--2020|Bloch-Johnson et al., 2020]] ; [[#Rugenstein--2020|Rugenstein et al., 2020]] ) or paleo ( [[#Caballero--2013|Caballero and Huber, 2013]] ; [[#Zhu--2019a|Zhu et al., 2019a]] ) climate conditions, typically by carrying out multiple simulations across successive CO <sub>2</sub> doublings. A non-linear temperature response to these successive doublings may be partly due to forcing that increases more (or less) than expected from a purely logarithmic dependence ( [[#7.3.2|Section 7.3.2]] ; [[#Etminan--2016|Etminan et al., 2016]] ), and partly due to state-dependence in feedbacks; however, not all modelling studies have partitioned the non-linearities in temperature response between these two effects. Nonetheless, there is general agreement among ESMs that the net feedback parameter, α , increases (i.e., becomes less negative) as temperature increases from pre-industrial levels (i.e., sensitivity to forcing increases as temperature increases; e.g., [[#Meraner--2013|Meraner et al., 2013]] ; see Figure 7.11). The associated increase in sensitivity to forcing is, in most models, due to the water vapour ( [[#7.4.2.2|Section 7.4.2.2]] ) and cloud ( [[#7.4.2.4|Section 7.4.2.4]] ) feedback parameters increasing with warming ( [[#Caballero--2013|Caballero and Huber, 2013]] ; [[#Meraner--2013|Meraner et al., 2013]] ; [[#Zhu--2019a|Zhu et al., 2019a]] ; [[#Rugenstein--2020|Rugenstein et al., 2020]] ; [[#Sherwood--2020|Sherwood et al., 2020]] ). These changes are offset partially by the surface-albedo feedback parameter decreasing ( [[#Jonko--2013|Jonko et al., 2013]] ; [[#Meraner--2013|Meraner et al., 2013]] ; [[#Rugenstein--2020|Rugenstein et al., 2020]] ), as a consequence of a reduced amount of snow and sea ice cover in a much warmer climate. At the same time, there is little change in the Planck response ( [[#7.4.2.1|Section 7.4.2.1]] ), which has been shown in one model to be due to competing effects from increasing Planck emission at warmer temperatures and decreasing planetary emissivity due to increased CO <sub>2</sub> and water vapour ( [[#Mauritsen--2019|Mauritsen et al., 2019]] ). Analysis of the spatial patterns of the non-linearities in temperature response ( [[#Good--2015|Good et al., 2015]] ) suggests that these patterns are linked to a reduced weakening of the AMOC, and changes to evapotranspiration. The temperature dependence of α is also found in model simulations of high-CO <sub>2</sub> paleoclimates ( [[#Caballero--2013|Caballero and Huber, 2013]] ; [[#Zhu--2019a|Zhu et al., 2019a]] ). The temperature dependence is not only evident at very high CO <sub>2</sub> concentrations in excess of 4×CO <sub>2</sub> , but also apparent in the difference in temperature response to a 2×CO <sub>2</sub> forcing compared with to a 4×CO <sub>2</sub> forcing ( [[#Mauritsen--2019|Mauritsen et al., 2019]] ; [[#Rugenstein--2020|Rugenstein et al., 2020]] ), and as such is relevant for interpreting century-scale climate projections.

Despite the general agreement that α increases as temperature increases from pre-industrial levels (Figure 7.11), other modelling studies have found the opposite ( [[#Duan--2019|Duan et al., 2019]] ; [[#Stolpe--2019|Stolpe et al., 2019]] ). Modelling studies exploring state-dependence in climates colder than today, including in cold paleoclimates such as the LGM, provide conflicting evidence of either decreased ( [[#Yoshimori--2011|Yoshimori et al., 2011]] ) or increased ( [[#Kutzbach--2013|Kutzbach et al., 2013]] ; [[#Stolpe--2019|Stolpe et al., 2019]] ) temperature response per unit forcing during cold climates compared to the modern era.

In contrast to most ESMs, the majority of Earth system models of intermediate complexity (EMICs) do not exhibit state-dependence, or have a net feedback parameter that decreases with increasing temperature ( [[#Pfister--2017|Pfister and Stocker, 2017]] ). This is unsurprising since EMICs usually do not include process-based representations of water-vapour and cloud feedbacks. Although this shows that care must be taken when interpreting results from current generation EMICs, [[#Pfister--2017|Pfister and Stocker (2017)]] also suggest that non-linearities in feedbacks can take a long time to emerge in model simulations due to slow adjustment time scales associated with the ocean; longer simulations also allow better estimates of equilibrium warming ( [[#Bloch-Johnson--2020|Bloch-Johnson et al., 2020]] ). This implies that multi-century simulations ( [[#Rugenstein--2020|Rugenstein et al., 2020]] ) could increase confidence in ESM studies examining state-dependence.

The possibility of more substantial changes in climate feedbacks, sometimes accompanied by hysteresis and/or irreversibility, has been suggested from some theoretical and modelling studies. It has been postulated that such changes could occur on a global scaleand across relatively narrow temperature changes ( [[#Popp--2016|Popp et al., 2016]] ; [[#von%20der%20Heydt--2016|von der Heydt and Ashwin, 2016]] ; [[#Steffen--2018|Steffen et al., 2018]] ; [[#Schneider--2019|Schneider et al., 2019]] ; [[#Ashwin--2020|Ashwin and von der Heydt, 2020]] ; [[#Bjordal--2020|Bjordal et al., 2020]] ). However, the associated mechanisms are highly uncertain, and as such there is ''low confidence'' as to whether such behaviour exists at all, and in the temperature thresholds at which it might occur.

Overall, the modelling evidence indicates that there is ''medium confidence'' that the net feedback parameter, α , increases (i.e., becomes less negative) with increasing temperature (i.e., that sensitivity to forcing increases with increasing temperature), under global surface background temperatures at least up to 40°C ( [[#Meraner--2013|Meraner et al., 2013]] ; [[#Seeley--2021|Seeley and Jeevanjee, 2021]] ), and ''medium confidence'' that this temperature dependence primarily derives from increases in the water-vapour and shortwave cloud feedbacks. This assessment is further supported by recent analysis of CMIP6 model simulations ( [[#Bloch-Johnson--2020|Bloch-Johnson et al., 2020]] ) in the framework of nonlinMIP ( [[#Good--2016|Good et al., 2016]] ), which showed that out of 10 CMIP6 models, seven of them showed an increase of the net feedback parameter with temperature, primarily due to the water-vapour feedback.

<div id="7.4.3.2" class="h3-container"></div>

<span id="state-dependence-of-feedbacks-in-the-paleoclimate-proxy-record"></span>
==== 7.4.3.2 State-dependence of Feedbacks in the Paleoclimate Proxy Record ====

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Several studies have estimated ECS from observations of the glacial–interglacial cycles of the last approximately 2 million years, and found a state-dependence, with more-negative α (i.e., lower sensitivity to forcing) during colder periods of the cycles and less-negative α during warmer periods ( [[#von%20der%20Heydt--2014|von der Heydt et al., 2014]] ; [[#Köhler--2015|Köhler et al., 2015]] , 2017; [[#Friedrich--2016|Friedrich et al., 2016]] ; [[#Royer--2016|Royer, 2016]] ; [[#Snyder--2019|Snyder, 2019]] ); see summaries in [[#Skinner--2012|Skinner (2012)]] and [[#von%20der%20Heydt--2016|von der Heydt et al. (2016)]] . However, the nature of the state-dependence derived from these observations is dependent on the assumed ice-sheet forcing ( [[#Köhler--2015|Köhler et al., 2015]] ; [[#Stap--2019|Stap et al., 2019]] ), which is not well known, due to a relative lack of proxy indicators of ice-sheet extent and distribution prior to the LGM (Cross-Chapter Box 2.1). Furthermore, many of these glacial–interglacial studies estimate a very strong temperature-dependence of α (Figure 7.11) that is hard to reconcile with the other lines of evidence, including proxy estimates from warmer paleoclimates. However, if the analysis excludes time periods when the temperature and CO <sub>2</sub> data are not well correlated, which occurs in general at times when sea level is falling and obliquity is decreasing, the state-dependence reduces ( [[#Köhler--2018|Köhler et al., 2018]] ). Despite these uncertainties, due to the agreement in the sign of the temperature-dependence from all these studies, there is ''medium confidence'' from the paleoclimate proxy record that the net feedback parameter, α , was less negative in the warm periods than in the cold periods of the glacial–interglacial cycles.

Paleoclimate proxy evidence from past high-CO <sub>2</sub> time periods much warmer than present (the early Eocene and Paleocene–Eocene Thermal Maximum, PETM; Cross-Chapter Box 2.1) show that the feedback parameter increases as temperature increases ( [[#Anagnostou--2016|Anagnostou et al., 2016]] , 2020; [[#Shaffer--2016|Shaffer et al., 2016]] ). However, such temperature-dependence of feedbacks was not found in the warm Pliocene relative to the cooler Pleistocene ( [[#Martínez-Botí--2015|Martínez-Botí et al., 2015]] ), although the temperature changes are relatively small at this time, making temperature-dependence challenging to detect given the uncertainties in reconstructing global mean temperature and forcing. Overall, the paleoclimate proxy record provides ''medium confidence'' that the net feedback parameter, α , was less negative in these past warm periods than in the present day.

<div id="_idContainer046" class="Basic-Text-Frame"></div>

[[File:cede88dd139299f5d25e764a5f855c21 IPCC_AR6_WGI_Figure_7_11.png]]

'''Figure 7.11''' '''|''' '''Feedback parameter,''' α '''(W m''' –2 '''°C''' –1 '''), as a function of global mean surface air temperature anomaly relative to pre-industrial, for ESM simulations (red circles and lines)''' ( [[#Caballero--2013|Caballero and Huber, 2013]] ; [[#Jonko--2013|Jonko et al., 2013]] ; [[#Meraner--2013|Meraner et al., 2013]] ; [[#Good--2015|Good et al., 2015]] ; [[#Duan--2019|Duan et al., 2019]] ; [[#Mauritsen--2019|Mauritsen et al., 2019]] ; [[#Stolpe--2019|Stolpe et al., 2019]] ; [[#Zhu--2019a|Zhu et al., 2019a]] ), '''and derived from paleoclimate proxies (grey squares and lines)''' ( [[#von%20der%20Heydt--2014|von der Heydt et al., 2014]] ; [[#Anagnostou--2016|Anagnostou et al., 2016]] , 2020; [[#Friedrich--2016|Friedrich et al., 2016]] ; [[#Royer--2016|Royer, 2016]] ; [[#Shaffer--2016|Shaffer et al., 2016]] ; [[#Köhler--2017|Köhler et al., 2017]] ; [[#Snyder--2019|Snyder, 2019]] ; [[#Stap--2019|Stap et al., 2019]] ). For the ESM simulations, the value on The x -axis refers to the average of the temperature before and after the system has equilibrated to a forcing (in most cases a CO <sub>2</sub> doubling), and is expressed as an anomaly relative to an associated pre-industrial global mean temperature from that model. The light blue shaded square extends across the assessed range of '''α''' (Table 7.10) on The y -axis, and on The x -axis extends across the approximate temperature range over which the assessment of α is based (taken as from zero to the assessed central value of ECS; see Table 7.13). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

<div id="7.4.3.3" class="h3-container"></div>

<span id="synthesis-of-state-dependence-of-feedbacks-from-modelling-and-paleoclimate-records"></span>
==== 7.4.3.3 Synthesis of State-dependence of Feedbacks from Modelling and Paleoclimate Records ====

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Overall, independent lines of evidence from models ( [[#7.4.3.1|Section 7.4.3.1]] ) and from the paleoclimate proxy record ( [[#7.4.3.2|Section 7.4.3.2]] ) lead to ''high confidence'' that the net feedback parameter, α , increases (i.e., becomes less negative) as temperature increases; that is, that sensitivity to forcing increases as temperature increases (Figure 7.11). This temperature-dependence should be considered when estimating ECS from ESM simulations in which CO <sub>2</sub> is quadrupled ( [[#7.5.5|Section 7.5.5]] ) or from paleoclimate observations from past time periods colder or warmer than today ( [[#7.5.4|Section 7.5.4]] ). Although individual lines of evidence give only ''medium confidence'' , the overall high confidence comes from the multiple models that show the same sign of the temperature-dependence of α , the general agreement in evidence from the paleo proxy and modelling lines of evidence, and the agreement between proxy evidence from both cold and warm past climates. However, due to the large range in estimates of the magnitude of the temperature-dependence of α across studies (Figure 7.11), a quantitative assessment cannot currently be given, which provides a challenge for including this temperature-dependence in emulator-based future projections (Cross-Chapter Box 7.1). Greater confidence in the modelling lines of evidence could be obtained from simulations carried out for several hundreds of years ( [[#Rugenstein--2020|Rugenstein et al., 2020]] ), substantially longer than in many studies, and from more models carrying out simulations at multiple CO <sub>2</sub> concentrations. Greater confidence in the paleoclimate lines of evidence would be obtained from stronger constraints on atmospheric CO <sub>2</sub> concentrations, ice-sheet forcing, and temperatures, during past warm climates.

<div id="7.4.4" class="h2-container"></div>

<span id="relationship-between-feedbacks-and-temperature-patterns"></span>
=== 7.4.4 Relationship Between Feedbacks and Temperature Patterns ===

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The large-scale patterns of surface warming in observations since the 19th century ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ) and climate model simulations ( [[IPCC:Wg1:Chapter:Chapter-4#4.3.1|Section 4.3.1]] and Figure 7.12a) share several common features. In particular, surface warming in the Arctic is greater than for the global average and greater than in the Southern Hemisphere (SH) high latitudes; and surface warming is generally greater over land than over the ocean. Observations and climate model simulations also show some notable differences. ESMs generally simulate a weakening of the equatorial Pacific Ocean zonal (east–west) SST gradient on multi-decadal to centennial time scales, with greater warming in the east than the west, but this trend has not been seen in observations ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] and Figure 2.11b).

[[IPCC:Wg1:Chapter:Chapter-4|Chapter 4]] [[IPCC:Wg1:Chapter:Chapter-4#4.5.1|Section 4.5.1]] ) discusses patterns of surface warming for 21st-century climate projections under the Shared Socio-economic Pathways (SSP) scenarios. [[IPCC:Wg1:Chapter:Chapter-9|Chapter 9]] [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] ) assesses historical SST trends and the ability of coupled ESMs to replicate the observed changes. [[IPCC:Wg1:Chapter:Chapter-4|Chapter 4]] [[IPCC:Wg1:Chapter:Chapter-4#4.5.1|Section 4.5.1]] ) discusses the processes that cause the land to warm more than the ocean (land–ocean warming contrast). This section assesses process understanding of the large-scale patterns of surface temperature response from the perspective of a regional energy budget. It then assesses evidence from the paleoclimate proxy record for patterns of surface warming during past time periods associated with changes in atmospheric CO <sub>2</sub> concentrations. Finally, it assesses how radiative feedbacks depend on the spatial pattern of surface temperature, and thus how they can change in magnitude as that pattern evolves over time, with implications for the assessment of ECS based on historical warming (Sections 7.4.4.3 and 7.5.2.1).

<div id="7.4.4.1" class="h3-container"></div>

<span id="polar-amplification"></span>
==== 7.4.4.1 Polar Amplification ====

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Polar amplification describes the phenomenon where surface temperature change at high latitudes exceeds the global average surface temperature change in response to radiative forcing of the climate system. Arctic amplification, often defined as the ratio of Arctic to global surface warming, is a ubiquitous emergent feature of climate model simulations ( [[IPCC:Wg1:Chapter:Chapter-4#4.5.1|Section 4.5.1]] and Figure 7.12a; [[#Holland--2003|Holland and Bitz, 2003]] ; [[#Pithan--2014|Pithan and Mauritsen, 2014]] ) and is also seen in observations ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ). However, both climate models and observations show relatively less warming of the SH high latitudes compared to the Northern Hemisphere (NH) high latitudes over the historical record ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ), a characteristic that is projected to continue over the 21st century ( [[IPCC:Wg1:Chapter:Chapter-4#4.5.1|Section 4.5.1]] ). Since AR5 there is a much-improved understanding of the processes that drive polar amplification in the NH and delay its emergence in the Sh ( [[#7.4.4.1.1|Section 7.4.4.1.1]] ). Furthermore, the paleoclimate record provides evidence for polar amplification from multiple time periods associated with changes in CO <sub>2</sub> ( [[#Hollis--2019|Hollis et al., 2019]] ; [[#Cleator--2020|Cleator et al., 2020]] ; [[#McClymont--2020|McClymont et al., 2020]] ; [[#Tierney--2020b|Tierney et al., 2020b]] ), and allows an evaluation of polar amplification in model simulations of these periods ( [[#7.4.4.1.2|Section 7.4.4.1.2]] ). Research since AR5 identifies changes in the degree of polar amplification over time, particularly in the SH, as a key factor affecting how radiative feedbacks may evolve in the future ( [[#7.4.4.3|Section 7.4.4.3]] ).

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[[File:06a8b9db625dc756a4847f3a68f254f1 IPCC_AR6_WGI_Figure_7_12.png]]

'''Figure 7.12''' '''|''' '''Contributions of effective radiative forcing, ocean heat uptake, atmospheric heat transport, and radiative feedbacks to regional surface temperature changes at year 100 of''' ''abrupt 4xCO2'' '''simulations of CMIP6 Earth system models (ESMs).''' '''Figure 7.12: (a)''' Pattern of near-surface air temperature change. '''(b–d)''' Contributions to net Arctic (&gt;60°N), tropical (30°S–30°N), and Antarctic (&lt;60°S) warming calculated by dividing regional-average energy inputs by the magnitude of the regional-average Planck response. The contributions from radiative forcing, changes in moist, dry-static, and total atmospheric energy transport, ocean heat uptake, and radiative feedbacks (orange bars) all sum to the value of net warming (grey bar). Inset shows regional warming contributions associated with individual feedbacks, all summing to the total feedback contribution. Uncertainties (represented by black whiskers) show the interquartile range (25th and 75th percentiles) across models. The warming contributions (units of °C) for each process are diagnosed by calculating the energy flux (units of W m <sup>–2</sup> ) that each process contributes to the atmosphere over a given region, either at the top-of-atmosphere or surface, then dividing that energy flux by the magnitude of the regional Planck response (around 3.2 W m <sup>–2</sup> °C <sup>–1</sup> but varying with region). By construction, the individual warming contributions sum to the total warming in each region. Radiative kernel methods ( [[#7.4.1|Section 7.4.1]] ) are used to decompose the net energy input from radiative feedbacks into contributions from changes in atmospheric water vapour, lapse rate, clouds, and surface albedo ( [[#Zelinka--2020|Zelinka et al. (2020)]] using the [[#Huang--2017|Huang et al. (2017)]] radiative kernel). The CMIP6 models included are those analysed by [[#Zelinka--2020|Zelinka et al. (2020)]] and the warming contribution analysis is based on that of [[#Goosse--2018|Goosse et al. (2018)]] . Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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<span id="critical-processes-driving-polar-amplification"></span>
===== 7.4.4.1.1 Critical processes driving polar amplification =====

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Several processes contribute to polar amplification under greenhouse gas forcing, including the loss of sea ice and snow (an amplifying surface-albedo feedback), the confinement of warming to near the surface in the polar atmosphere (an amplifying lapse-rate feedback), and increases in poleward atmospheric and oceanic heat transport ( [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Goosse--2018|Goosse et al., 2018]] ; [[#Dai--2019|Dai et al., 2019]] ; [[#Feldl--2020|Feldl et al., 2020]] ). Modelling and process studies since AR5 have led to an improved understanding of the combined effect of these different processes in driving polar amplification and how they differ between the hemispheres.

Idealized modelling studies suggest that polar amplification would occur even in the absence of any amplifying polar surface-albedo or lapse-rate feedbacks owing to changes in poleward atmospheric heat transport under global warming ( [[#Hall--2004|Hall, 2004]] ; [[#Alexeev--2005|Alexeev et al., 2005]] ; [[#Graversen--2009|Graversen and Wang, 2009]] ; [[#Alexeev--2013|Alexeev and Jackson, 2013]] ; [[#Graversen--2014|Graversen et al., 2014]] ; [[#Roe--2015|Roe et al., 2015]] ; [[#Merlis--2018|Merlis and Henry, 2018]] ; [[#Armour--2019|Armour et al., 2019]] ). Poleward heat transport changes reflect compensating changes in the transport of latent energy (moisture) and dry-static energy (sum of sensible and potential energy) by atmospheric circulations ( [[#Alexeev--2005|Alexeev et al., 2005]] ; [[#Held--2006|Held and Soden, 2006]] ; [[#Hwang--2010|Hwang and Frierson, 2010]] ; [[#Hwang--2011|Hwang et al., 2011]] ; [[#Kay--2012|Kay et al., 2012]] ; [[#Huang--2014|Huang and Zhang, 2014]] ; [[#Feldl--2017a|Feldl et al., 2017a]] ; [[#Donohoe--2020|Donohoe et al., 2020]] ). ESMs project that within the mid-latitudes, where eddies dominate the heat transport, an increase in poleward latent energy transport arises from an increase in the equator-to-pole gradient in atmospheric moisture with global warming, with moisture in the tropics increasing more than at the poles as described by the Clausius–Clapeyron relation ( [[IPCC:Wg1:Chapter:Chapter-8#8.2|Section 8.2]] ). This change is partially compensated by a decrease in dry-static energy transport arising from a weakening of the equator-to-pole temperature gradient as the polar regions warm more than the tropics.

Energy balance models that approximate atmospheric heat transport in terms of a diffusive flux down the meridional gradient of near-surface moist static energy (sum of dry-static and latent energy) are able to reproduce the atmospheric heat transport changes seen within ESMs ( [[#Flannery--1984|Flannery, 1984]] ; [[#Hwang--2010|Hwang and Frierson, 2010]] ; [[#Hwang--2011|Hwang et al., 2011]] ; [[#Rose--2014|Rose et al., 2014]] ; [[#Roe--2015|Roe et al., 2015]] ; [[#Merlis--2018|Merlis and Henry, 2018]] ), including the partitioning of latent and dry-static energy transports ( [[#Siler--2018b|Siler et al., 2018b]] ; [[#Armour--2019|Armour et al., 2019]] ). These models suggest that polar amplification is driven by enhanced poleward latent heat transport and that the magnitude of polar amplification can be enhanced or diminished by the latitudinal structure of radiative feedbacks. Amplifying polar feedbacks enhance polar warming and in turn cause a decrease in the dry-static energy transport to high latitudes ( [[#Alexeev--2013|Alexeev and Jackson, 2013]] ; [[#Rose--2014|Rose et al., 2014]] ; [[#Roe--2015|Roe et al., 2015]] ; [[#Bonan--2018|Bonan et al., 2018]] ; [[#Merlis--2018|Merlis and Henry, 2018]] ; [[#Armour--2019|Armour et al., 2019]] ; [[#Russotto--2020|Russotto and Biasutti, 2020]] ). Poleward latent heat transport changes act to favour polar amplification and inhibit tropical amplification ( [[#Armour--2019|Armour et al., 2019]] ), resulting in a strongly polar-amplified warming response to polar forcing and a more latitudinally uniform warming response to tropical forcing within ESMs ( [[#Alexeev--2005|Alexeev et al., 2005]] ; [[#Rose--2014|Rose et al., 2014]] ; [[#Stuecker--2018|Stuecker et al., 2018]] ). The important role for poleward latent energy transport in polar amplification is supported by studies of atmospheric reanalyses and ESMs showing that episodic increases in latent heat transport into the Arctic can enhance surface downwelling radiation and drive sea ice loss on sub-seasonal time scales ( [[#Woods--2016|Woods and Caballero, 2016]] ; [[#Gong--2017|Gong et al., 2017]] ; [[#Lee--2017|Lee et al., 2017]] ; B. [[#Luo--2017|]] [[#Luo--2017|Luo et al., 2017]] ), however this may be a smaller driver of sea ice variability than atmospheric temperature fluctuations ( [[#Olonscheck--2019|Olonscheck et al., 2019]] ).

Regional energy budget analyses are commonly used to diagnose the relative contributions of radiative feedbacks and energy fluxes to polar amplification as projected by ESMs under increased CO <sub>2</sub> concentrations (Figure 7.12; [[#Feldl--2013|Feldl and Roe, 2013]] ; [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Goosse--2018|Goosse et al., 2018]] ; [[#Stuecker--2018|Stuecker et al., 2018]] ). These analyses suggest that a primary cause of amplified Arctic warming in ESMs is the latitudinal structure of radiative feedbacks, which warm the Arctic more than the tropics (Figure 7.12b), and enhanced latent energy transport into the Arctic. That net atmospheric heat transport into the Arctic does not change substantially within ESMs, on average, under CO <sub>2</sub> forcing (Figure 7.12b) reflects a compensating decrease in poleward dry-static energy transport as a response to polar amplified warming ( [[#Hwang--2011|Hwang et al., 2011]] ; [[#Armour--2019|Armour et al., 2019]] ; [[#Donohoe--2020|Donohoe et al., 2020]] ). The latitudinal structure of radiative feedbacks primarily reflects that of the surface-albedo and lapse-rate feedbacks, which preferentially warm the Arctic ( [[#Graversen--2014|Graversen et al., 2014]] ; [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Goosse--2018|Goosse et al., 2018]] ). Latitudinal structure in the lapse-rate feedback reflects weak radiative damping to space with surface warming in polar regions, where atmospheric warming is constrained to the lower troposphere owing to stably stratified conditions, and strong radiative damping in the tropics, where warming is enhanced in the upper troposphere owing to moist convective processes. This is only partially compensated by latitudinal structure in the water-vapour feedback ( [[#Taylor--2013|Taylor et al., 2013]] ), which favours tropical warming ( [[#Pithan--2014|Pithan and Mauritsen, 2014]] ). While cloud feedbacks have been found to play little role in Arctic amplification in CMIP5 models ( [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Goosse--2018|Goosse et al., 2018]] ; Figure 7.12b), less-negative cloud feedbacks at high latitude, as seen within some CMIP6 models ( [[#Zelinka--2020|Zelinka et al., 2020]] ), tend to favour stronger polar amplification ( [[#Dong--2020|Dong et al., 2020]] ). A weaker Planck response at high latitudes, owing to less efficient radiative damping where surface and atmospheric temperatures are lower, also contributes to polar amplification ( [[#Pithan--2014|Pithan and Mauritsen, 2014]] ). The effective radiative forcing of CO <sub>2</sub> is larger in the tropics than at high latitudes, suggesting that warming would be tropically amplified if not for radiative feedbacks and poleward latent heat transport changes (Figure 7.12b–d; [[#Stuecker--2018|Stuecker et al., 2018]] ).

While the contributions to regional warming can be diagnosed within ESM simulations (Figure 7.12), assessment of the underlying role of individual factors is limited by interactions inherent to the coupled climate system. For example, polar feedback processes are coupled and influenced by warming at lower latitudes ( [[#Screen--2012|Screen et al., 2012]] ; [[#Alexeev--2013|Alexeev and Jackson, 2013]] ; [[#Graversen--2014|Graversen et al., 2014]] ; [[#Graversen--2016|Graversen and Burtu, 2016]] ; [[#Rose--2016|Rose and Rencurrel, 2016]] ; [[#Feldl--2017a|Feldl et al., 2017a]] , 2020; [[#Yoshimori--2017|Yoshimori et al., 2017]] ; [[#Garuba--2018|Garuba et al., 2018]] ; [[#Po-Chedley--2018b|Po-Chedley et al., 2018b]] ; [[#Stuecker--2018|Stuecker et al., 2018]] ; [[#Dai--2019|Dai et al., 2019]] ), while atmospheric heat transport changes are in turn influenced by the latitudinal structure of regional feedbacks, radiative forcing, and ocean heat uptake ( [[#Hwang--2011|Hwang et al., 2011]] ; [[#Zelinka--2012|Zelinka and Hartmann, 2012]] ; [[#Feldl--2013|Feldl and Roe, 2013]] ; [[#Huang--2014|Huang and Zhang, 2014]] ; [[#Merlis--2014|Merlis, 2014]] ; [[#Rose--2014|Rose et al., 2014]] ; [[#Roe--2015|Roe et al., 2015]] ; [[#Feldl--2017b|Feldl et al., 2017b]] ; [[#Stuecker--2018|Stuecker et al., 2018]] ; [[#Armour--2019|Armour et al., 2019]] ). The use of different feedback definitions, such as a lapse-rate feedback partitioned into upper and lower tropospheric components ( [[#Feldl--2020|Feldl et al., 2020]] ) or including the influence of water vapour at constant relative humidity ( [[#Held--2012|Held and Shell, 2012]] ; [[#7.4.2|Section 7.4.2]] ), would also change the interpretation of which feedbacks contribute most to polar amplification.

The energy budget analyses (Figure 7.12) suggest that greater surface warming in the Arctic than the Antarctic under greenhouse gas forcing arises from two main processes. The first is large surface heat uptake in the Southern Ocean (Figure 7.12c) driven by the upwelling of deep waters that have not yet felt the effects of the radiative forcing; the heat taken up is predominantly transported away from Antarctica by northward-flowing surface waters ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] ; [[#Marshall--2015|Marshall et al., 2015]] ; [[#Armour--2016|Armour et al., 2016]] ). Strong surface heat uptake also occurs in the subpolar North Atlantic Ocean under global warming ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] ). However, this heat is partially transported northward into the Arctic, which leads to increased heat fluxes into the Arctic atmosphere (Figure 7.12b; [[#Rugenstein--2013|Rugenstein et al., 2013]] ; [[#Jungclaus--2014|Jungclaus et al., 2014]] ; [[#Koenigk--2014|Koenigk and Brodeau, 2014]] ; [[#Marshall--2015|Marshall et al., 2015]] ; [[#Nummelin--2017|Nummelin et al., 2017]] ; [[#Singh--2017|Singh et al., 2017]] ; [[#Oldenburg--2018|Oldenburg et al., 2018]] ). The second main process contributing to differences in Arctic and Antarctic warming is the asymmetry in radiative feedbacks between the poles ( [[#Yoshimori--2017|Yoshimori et al., 2017]] ; [[#Goosse--2018|Goosse et al., 2018]] ). This primarily reflects the weaker lapse-rate and surface-albedo feedbacks and more-negative cloud feedbacks in the SH high latitudes (Figure 7.12). However, note the SH cloud feedbacks are uncertain due to possible biases in the treatment of mixed phase clouds ( [[#Hyder--2018|Hyder et al., 2018]] ). Idealized modelling suggests that the asymmetry in the polar lapse-rate feedback arises from the height of the Antarctic Ice Sheet precluding the formation of deep atmospheric inversions that are necessary to produce the stronger positive lapse-rate feedbacks seen in the Arctic ( [[#Salzmann--2017|Salzmann, 2017]] ; [[#Hahn--2020|Hahn et al., 2020]] ). ESM projections of the equilibrium response to CO <sub>2</sub> forcing show polar amplification in both hemispheres, but generally with less warming in the Antarctic than the Arctic (C. [[#Li--2013|]] [[#Li--2013|Li et al., 2013]] ; [[#Yoshimori--2017|Yoshimori et al., 2017]] ).

Because multiple processes contribute to polar amplification, it is a robust feature of the projected long-term response to greenhouse gas forcing in both hemispheres. At the same time, contributions from multiple processes make projections of the magnitude of polar warming inherently more uncertain than global mean warming ( [[#Holland--2003|Holland and Bitz, 2003]] ; [[#Roe--2015|Roe et al., 2015]] ; [[#Bonan--2018|Bonan et al., 2018]] ; [[#Stuecker--2018|Stuecker et al., 2018]] ). The magnitude of Arctic amplification ranges from a factor of two to four in ESM projections of 21st-century warming ( [[IPCC:Wg1:Chapter:Chapter-4#4.5.1|Section 4.5.1]] ). While uncertainty in both global and tropical warming under greenhouse gas forcing is dominated by cloud feedbacks ( [[#7.5.7|Section 7.5.7]] ; [[#Vial--2013|Vial et al., 2013]] ), uncertainty in polar warming arises from polar surface-albedo, lapse-rate, and cloud feedbacks, changes in atmospheric and oceanic poleward heat transport, and ocean heat uptake ( [[#Hwang--2011|Hwang et al., 2011]] ; [[#Mahlstein--2011|Mahlstein and Knutti, 2011]] ; [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Bonan--2018|Bonan et al., 2018]] ).

The magnitude of polar amplification also depends on the type of radiative forcing applied ( [[IPCC:Wg1:Chapter:Chapter-4#4.5.1.1|Section 4.5.1.1]] ; [[#Stjern--2019|Stjern et al., 2019]] ), with ( [[IPCC:Wg1:Chapter:Chapter-6|Chapter 6]] (Section 6.4.3) discussing changes in sulphate aerosol emissions and the deposition of black carbon aerosols on ice and snow as potential drivers of amplified Arctic warming. The timing of the emergence of SH polar amplification remains uncertain due to insufficient knowledge of the time scales associated with Southern Ocean warming and the response to surface wind and freshwater forcing ( [[#Bintanja--2013|Bintanja et al., 2013]] ; [[#Kostov--2017|Kostov et al., 2017]] , 2018; [[#Pauling--2017|Pauling et al., 2017]] ; [[#Purich--2018|Purich et al., 2018]] ). ESM simulations indicate that freshwater input from melting ice shelves could reduce Southern Ocean warming by up to several tenths of a °C over the 21st century by increasing stratification of the surface ocean around Antarctica ( ''low confidence'' due to ''medium agreement'' but ''limited evidence'' ) (Sections 7.4.2.6 and 9.2.1, and Box 9.3; [[#Bronselaer--2018|Bronselaer et al., 2018]] ; [[#Golledge--2019|Golledge et al., 2019]] ; [[#Lago--2019|Lago and England, 2019]] ). However, even a large reduction in the Atlantic Meridional Overturning Circulation (AMOC) and associated northward heat transport due, for instance, to greatly increased freshwater runoff from Greenland would be insufficient to eliminate Arctic amplification ( ''medium confidence'' based on ''medium agreement'' and ''medium evidence'' ) ( [[#Liu--2017|Liu et al., 2017]] ; Y. [[#Liu--2018|]] [[#Liu--2018|Liu et al., 2018]] ; [[#Wen--2018|Wen et al., 2018]] ).

Arctic amplification has a distinct seasonality with a peak in early winter (November to January) owing to sea ice loss and associated increases in heat fluxes from the ocean to the atmosphere resulting in strong near-surface warming ( [[#Pithan--2014|Pithan and Mauritsen, 2014]] ; [[#Dai--2019|Dai et al., 2019]] ). Surface warming may be further amplified by positive cloud and lapse-rate feedbacks in autumn and winter ( [[#Burt--2016|Burt et al., 2016]] ; [[#Morrison--2019|Morrison et al., 2019]] ; [[#Hahn--2020|Hahn et al., 2020]] ). Arctic amplification is weak in summer owing to surface temperatures remaining stable as excess energy goes into thinning the summertime sea ice cover, which remains at the melting point, or into the ocean mixed layer. Arctic amplification can also be interpreted through changes in the surface energy budget ( [[#Burt--2016|Burt et al., 2016]] ; [[#Woods--2016|Woods and Caballero, 2016]] ; [[#Boeke--2018|Boeke and Taylor, 2018]] ; [[#Kim--2019|Kim et al., 2019]] ), however such analyses are complicated by the finding that a large portion of the changes in downward longwave radiation can be attributed to the lower troposphere warming along with the surface itself ( [[#Vargas%20Zeppetello--2019|Vargas Zeppetello et al., 2019]] ).

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<span id="polar-amplification-from-proxies-and-models-during-past-climates-associated-with-co-2-change"></span>
===== 7.4.4.1.2 Polar amplification from proxies and models during past climates associated with CO 2 change =====

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Paleoclimate proxy data provide observational evidence of large-scale patterns of surface warming in response to past forcings, and allow an evaluation of the modelled response to these forcings (Sections 3.3.1.1 and 3.8.2.1). In particular, paleoclimate data provide evidence for long-term changes in polar amplification during time periods in which the primary forcing was a change in atmospheric CO <sub>2</sub> , although data sparsity means that for some time periods this evidence may be limited to a single hemisphere or ocean basin, or the evidence may come primarily from the mid-latitudes as opposed to the polar regions. In this context, there has been a modelling and data focus on the Last Glacial Maximum (LGM) in the context of PMIP4 ( [[#Cleator--2020|Cleator et al., 2020]] ; [[#Tierney--2020b|Tierney et al., 2020b]] ; [[#Kageyama--2021|Kageyama et al., 2021]] ), the mid-Pliocene Warm Period (MPWP) in the context of PlioMIP2 (Cross-Chapter Box 2.4; [[#Salzmann--2013|Salzmann et al., 2013]] ; [[#Haywood--2020|Haywood et al., 2020]] ; [[#McClymont--2020|McClymont et al., 2020]] ), the Early Eocene Climatic Optimum (EECO) in the context of DeepMIP ( [[#Hollis--2019|Hollis et al., 2019]] ; [[#Lunt--2021|Lunt et al., 2021]] ), and there is growing interest in the Miocene ( [[#Goldner--2014b|Goldner et al., 2014b]] ; [[#Steinthorsdottir--2021|Steinthorsdottir et al., 2021]] ; for definitions of time periods see Cross-Chapter Box 2.1). For all these time periods, in addition to the CO <sub>2</sub> forcing there are long-term feedbacks associated with ice sheets ( [[#7.4.2.6|Section 7.4.2.6]] ), and in particular for the Early Eocene there is a forcing associated with paleogeographic change ( [[#Farnsworth--2019|Farnsworth et al., 2019]] ). However, because these non-CO <sub>2</sub> effects can all be included as boundary conditions in model simulations, these time periods allow an assessment of the patterns of modelled response to known forcing (although uncertainty in the forcing increases further back in time). Because these changes to boundary conditions can be complex to implement in models, and because long simulations (typically longer than 500 years) are required to approach equilibrium, these simulations have been carried out mostly by pre-CMIP6 models, with relatively few (or none for the Early Eocene) fully coupled CMIP6 models in the ensembles.

At the time of AR5, polar amplification was evident in proxy reconstructions of paleoclimate sea surface temperature (SST) and surface air temperature (SAT) from the LGM, MPWP and the Early Eocene, but uncertainties associated with proxy calibrations ( [[#Waelbroeck--2009|Waelbroeck et al., 2009]] ; [[#Dowsett--2012|Dowsett et al., 2012]] ; [[#Lunt--2012a|Lunt et al., 2012a]] ) and the role of orbital forcing (for the MPWP; [[#Lisiecki--2005|Lisiecki and Raymo, 2005]] ) meant that the degree of polar amplification during these time periods was not accurately known. Furthermore, although some models (CCSM3; [[#Winguth--2010|Winguth et al., 2010]] ; [[#Huber--2011|Huber and Caballero, 2011]] ) at that time were able to reproduce the strong polar amplification implied by temperature proxies of the Early Eocene, this was achieved at higher CO <sub>2</sub> concentrations (&gt;2000 ppm) than those indicated by CO <sub>2</sub> proxies (&lt;1500 ppm; [[#Beerling--2011|Beerling and Royer, 2011]] ).

Since AR5 there has been progress in improving the accuracy of proxy temperature reconstructions of the LGM ( [[#Cleator--2020|Cleator et al., 2020]] ; [[#Tierney--2020b|Tierney et al., 2020b]] ), the MPWP ( [[#McClymont--2020|McClymont et al., 2020]] ), and the Early Eocene ( [[#Hollis--2019|Hollis et al., 2019]] ) time periods. In addition, reconstructions of the MPWP have been focused on a short time slice with an orbit similar to modern-day (isotopic stage KM5C; [[#Haywood--2013|Haywood et al., 2013]] , 2016b). Furthermore, there are more robust constraints on CO <sub>2</sub> concentrations from the MPWP ( [[#Martínez-Botí--2015|Martínez-Botí et al., 2015]] ; [[#de%20la%20Vega--2020|de la Vega et al., 2020]] ) and the Early Eocene ( [[#Anagnostou--2016|Anagnostou et al., 2016]] , 2020). As such, polar amplification during the LGM, MPWP, and Early Eocene time periods can now be better quantified than at the time of AR5, and the ability of climate models to reproduce this pattern can be better assessed; model-data comparisons for SAT and SST for these three time periods are shown in Figure 7.13.

Since AR5, there has been progress in the simulation of polar amplification by paleoclimate models of the Early Eocene. Initial work indicated that changes to model parameters associated with aerosols and/or clouds could increase simulated polar amplification and improve agreement between models and paleoclimate data ( [[#Kiehl--2013|Kiehl and Shields, 2013]] ; [[#Sagoo--2013|Sagoo et al., 2013]] ), but such parameter changes were not physically based. In support of these initial findings, a more recent (CMIP5) climate model, that includes a process-based representation of cloud microphysics, exhibits polar amplification in better agreement with proxies when compared to the models assessed in AR5 ( [[#Zhu--2019a|Zhu et al., 2019a]] ). Since then, some other CMIP3 and CMIP5 models in the DeepMIP multi-model ensemble ( [[#Lunt--2021|Lunt et al., 2021]] ) have obtained polar amplification for the EECO that is consistent with proxy indications of both polar amplification and CO <sub>2</sub> . Although there is a lack of tropical proxy SAT estimates, both proxies and DeepMIP models show greater terrestrial warming in the high latitudes than the mid-latitudes in both hemispheres (Figure 7.13a,d). SST proxies also exhibit polar amplification in both hemispheres, but the magnitude of this polar amplification is too low in the models, in particular in the south-west Pacific (Figure 7.13g,j).

For the MPWP, model simulations are now in better agreement with proxies than at the time of AR5 ( [[#Haywood--2020|Haywood et al., 2020]] ; [[#McClymont--2020|McClymont et al., 2020]] ). In particular, in the tropics new proxy reconstructions of SSTs are warmer and in better agreement with the models, due in part to the narrower time window in the proxy reconstructions. There is also better agreement at higher latitudes (primarily in the North Atlantic), due in part to the absence of some very warm proxy SSTs due to the narrower time window ( [[#McClymont--2020|McClymont et al., 2020]] ), and in part to a modified representation of Arctic gateways in the most recent Pliocene model simulations ( [[#Otto-Bliesner--2017|Otto-Bliesner et al., 2017]] ), which have resulted in warmer modelled SSTs in the North Atlantic ( [[#Haywood--2020|Haywood et al., 2020]] ). Furthermore, as for the Eocene, improvements in the representation of aerosol–cloud interactions have also led to improved model-data consistency at high latitudes ( [[#Feng--2019|Feng et al., 2019]] ). Although all PlioMIP2 models exhibit polar amplification of SAT, due to the relatively narrow time window there are insufficient terrestrial proxies to assess this (Figure 7.13b,e). However, polar SST amplification in the PlioMIP2 ensemble mean is in reasonably good agreement with that from SST proxies in the Northern Hemisphere (Figure 7.13h,k).

The Last Glacial Maximum (LGM) also gives an opportunity to evaluate model simulation of polar amplification under CO <sub>2</sub> forcing, albeit under colder conditions than today ( [[#Kageyama--2021|Kageyama et al., 2021]] ). Terrestrial SAT and marine SST proxies exhibit clear polar amplification in the Northern Hemisphere, and the PMIP4 models capture this well (Figure 7.13c,f,i,l), particularly for SAT. There is less proxy data in the mid- to high latitudes of the Southern Hemisphere, but here the models exhibit polar amplification of both SST and SAT. LGM regional model-data agreement is also assessed in ( [[IPCC:Wg1:Chapter:Chapter-3|Chapter 3]] [[IPCC:Wg1:Chapter:Chapter-3#3.8.2|Section 3.8.2]] ).

Overall, the proxy reconstructions give ''high confidence'' that there was polar amplification in the LGM, MPWP and EECO, and this is further supported by model simulations of these time periods (Figure 7.13; [[#Zhu--2019a|Zhu et al., 2019a]] ; [[#Haywood--2020|Haywood et al., 2020]] ; [[#Kageyama--2021|Kageyama et al., 2021]] ; [[#Lunt--2021|Lunt et al., 2021]] ). For both the MPWP and EECO, models are more consistent with the temperature and CO <sub>2</sub> proxies than at the time of AR5 ( ''high confidence'' ). For the LGM Northern Hemisphere, which is the region with the most data and the time period with the least uncertainty in model boundary conditions, polar amplification in the PMIP4 ensemble mean is in good agreement with the proxies, especially for SAT ( ''medium confidence'' ). Overall, the confidence in the ability of models to accurately simulate polar amplification is higher than at the time of AR5, but a more complete model evaluation could be carried out if there were more CMIP6 paleoclimate simulations included in the assessment.

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<span id="overall-assessment-of-polar-amplification"></span>
===== 7.4.4.1.3 Overall assessment of polar amplification =====

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Based on mature process understanding of the roles of poleward latent heat transport and radiative feedbacks in polar warming, a high degree of agreement across a hierarchy of climate models, observational evidence, paleoclimate proxy records of past climates associated with CO <sub>2</sub> change, and ESM simulations of those past climates, there is ''high confidence'' that polar amplification is a robust feature of the long-term response to greenhouse gas forcing in both hemispheres. Stronger warming in the Arctic than the global average has already been observed ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ) and its causes are well understood. It is ''very likely'' that the warming in the Arctic will be more pronounced than the global average over the 21st century ( ''high confidence'' ) [[IPCC:Wg1:Chapter:Chapter-4#4.5.1.1|Section 4.5.1.1]] ). This is supported by models’ improved ability to simulate polar amplification during past time periods, compared with at the time of AR5 ( ''high confidence'' ); although this is based on an assessment of mostly non-CMIP6 models.

Southern Ocean SSTs have been slow to warm over the instrumental period, with cooling since about 1980 owing to a combination of upper-ocean freshening from ice-shelf melt, intensification of surface westerly winds from ozone depletion, and variability in ocean convection ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] ). This stands in contrast to the equilibrium warming pattern either inferred from the proxy record or simulated by ESMs under CO <sub>2</sub> forcing. There is ''high confidence'' that the SH high latitudes will warm more than the tropics on centennial time scales as the climate equilibrates with radiative forcing and Southern Ocean heat uptake is reduced. However, there is only ''low confidence'' that this feature will emerge this century.

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<span id="tropical-pacific-sea-surface-temperature-gradients"></span>

==== 7.4.4.2 Tropical Pacific Sea Surface Temperature Gradients ====

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Research published since AR5 identifies changes in the tropical Pacific Ocean zonal SST gradient over time as a key factor affecting how radiative feedbacks may evolve in the future ( [[#7.4.4.3|Section 7.4.4.3]] ). There is now a much-improved understanding of the processes that govern the tropical Pacific SST gradient ( [[#7.4.4.2.1|Section 7.4.4.2.1]] ) and the paleoclimate record provides evidence for its equilibrium changes from time periods associated with changes in CO <sub>2</sub> [[#7.4.4.2.2|Section 7.4.4.2.2]] ).

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<span id="critical-processes-determining-changes-in-tropical-pacific-sea-surface-temperature-gradients"></span>
===== 7.4.4.2.1 Critical processes determining changes in tropical Pacific sea surface temperature gradients =====

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A weakening of the equatorial Pacific Ocean east–west SST gradient, with greater warming in the east than the west, is a common feature of the climate response to greenhouse gas forcing as projected by ESMs on centennial and longer time scales (e.g., Figure 7.14b; see ( [[IPCC:Wg1:Chapter:Chapter-4#4.5.1|Section 4.5.1]] ). There are thought to be several factors contributing to this pattern. In the absence of any changes in atmospheric or oceanic circulations, the east–west surface temperature difference is theorized to decrease owing to weaker evaporative damping, and thus greater warming in response to forcing, where climatological temperatures are lower in the eastern Pacific cold tongue ( [[#Xie--2010|Xie et al., 2010]] ; [[#Luo--2015|Luo et al., 2015]] ). Within atmospheric ESMs coupled to a mixed-layer ocean, this gradient in damping has been linked to the rate of change with warming of the saturation specific humidity, which is set by the Clausius–Clapeyron relation ( [[#Merlis--2011|Merlis and Schneider, 2011]] ). Gradients in low-cloud feedbacks may also favour eastern equatorial Pacific warming ( [[#DiNezio--2009|DiNezio et al., 2009]] ).

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[[File:60bc04f65baf68bf30b88df95e74c1aa IPCC_AR6_WGI_Figure_7_14.png]]

'''Figure''' '''7.14 |''' '''Illustration of tropospheric temperature and low-cloud response to observed and projected Pacific Ocean sea surface temperature trends. (a)''' Atmospheric response to linear sea surface temperature trend observed over 1870–2019 (HadISST1 dataset; [[#Rayner--2003|Rayner et al., 2003]] ). '''(b)''' Atmospheric response to linear sea-surface temperature trend over 150 years following ''abrupt 4xCO2'' forcing as projected by CMIP6 ESMs ( [[#Dong--2020|Dong et al., 2020]] ). Relatively large historical warming in the western tropical Pacific has been communicated aloft (a shift from grey to red atmospheric temperature profile), remotely warming the tropical free troposphere and increasing the strength of the inversion in regions of the tropics where warming has been slower, such as the eastern equatorial Pacific. In turn, an increased inversion strength has increased the low-cloud cover ( [[#Zhou--2016|Zhou et al., 2016]] ) causing an anomalously negative cloud and lapse-rate feedbacks over the historical record ( [[#Andrews--2018|Andrews et al., 2018]] ; [[#Marvel--2018|Marvel et al., 2018]] ). Relatively large projected warming in the eastern tropical Pacific is trapped near the surface (shift from grey to red atmospheric temperature profile), decreasing the strength of the inversion locally. In turn, a decreased inversion strength combined with surface warming is projected to decrease the low-cloud cover, causing the cloud and lapse-rate feedbacks to become less negative in the future. Figure adapted from [[#Mauritsen--2016|Mauritsen (2016)]] . Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

In the coupled climate system, changes in atmospheric and oceanic circulations will influence the east-west temperature gradient as well. It is expected that as global temperature increases and as the east–west temperature gradient weakens, east–west sea level pressure gradients and easterly trade winds (characterizing the Walker circulation) will weaken as well (Sections 4.5.3, 8.2.2.2 and 8.4.2.3, and Figure 7.14b; [[#Vecchi--2006|Vecchi et al., 2006]] , 2008). This would, in turn, weaken the east–west temperature gradient through a reduction of equatorial upwelling of cold water in the east Pacific and a reduction in the transport of warmer water to the western equatorial Pacific and Indian Ocean ( [[#England--2014|England et al., 2014]] ; [[#Dong--2017|Dong and McPhaden, 2017]] ; [[#Li--2017|Li et al., 2017]] ; [[#Maher--2018|Maher et al., 2018]] ).

Research published since AR5 ( [[#Burls--2014b|Burls and Fedorov, 2014b]] ; [[#Fedorov--2015|Fedorov et al., 2015]] ; [[#Erfani--2019|Erfani and Burls, 2019]] ) has built on an earlier theory ( [[#Liu--1997|Liu and Huang, 1997]] ; [[#Barreiro--2008|Barreiro and Philander, 2008]] ) linking the east–west temperature gradient to the north–south temperature gradient. In particular, model simulations suggest that a reduction in the equator-to-pole temperature gradient (polar amplification) increases the temperature of water subducted in the extra-tropics, which in turn is upwelled in the eastern Pacific. Thus, polar amplified warming, with greater warming in the mid-latitudes and subtropics than in the deep tropics, is expected to contribute to the weakening of the east–west equatorial Pacific SST gradient on decadal to centennial time scales.

The transient adjustment of the equatorial Pacific SST gradient is influenced by upwelling waters which delay surface warming in the east since they have not been at the surface for years-to-decades to experience the greenhouse gas forcing. This ‘thermostat mechanism’ ( [[#Clement--1996|Clement et al., 1996]] ; [[#Cane--1997|Cane et al., 1997]] ) is not thought to persist to equilibrium since it does not account for the eventual increase in temperatures of upwelled waters ( [[#Liu--2005|Liu et al., 2005]] ; [[#Xie--2010|Xie et al., 2010]] ; Y. [[#Luo--2017|]] [[#Luo--2017|Luo et al., 2017]] ) which will occur as the subducting waters in mid-latitudes warm by more than the tropics on average as polar amplification emerges. An individual CMIP5 ESM (GFDL’s ESM2M) has been found to exhibit a La Niña-like pattern of Pacific temperature change through the 21st century, similar to the SST trends seen over the historical record ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] and Figure 7.14a), owing to a weakening asymmetry between El Niño and La Niña events ( [[#Kohyama--2017|Kohyama et al., 2017]] ), but this pattern of warming may not persist to equilibrium ( [[#Paynter--2018|Paynter et al., 2018]] ).

Since 1870, observed SSTs in the tropical western Pacific Ocean have increased while those in the tropical eastern Pacific Ocean have changed less (Figure 7.14a and ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] ). Much of the resultant strengthening of the equatorial Pacific temperature gradient has occurred since about 1980 due to strong warming in the west and cooling in the east (Figure 2.11b) concurrent with an intensification of the surface equatorial easterly trade winds and Walker circulation (Sections 3.3.3.1, 3.7.6, 8.3.2.3 and 9.2, and Figures 3.16f and 3.39f; [[#England--2014|England et al., 2014]] ). This temperature pattern is also reflected in regional ocean heat content trends and sea level changes observed from satellite altimetry since 1993 ( [[#Bilbao--2015|Bilbao et al., 2015]] ; [[#Richter--2020|Richter et al., 2020]] ). The observed changes may have been influenced by one or a combination of temporary factors including sulphate aerosol forcing ( [[#Smith--2016|Smith et al., 2016]] ; [[#Takahashi--2016|Takahashi and Watanabe, 2016]] ; [[#Hua--2018|Hua et al., 2018]] ), internal variability within the Indo-Pacific Ocean ( [[#Luo--2012|Luo et al., 2012]] ; [[#Chung--2019|Chung et al., 2019]] ), teleconnections from multi-decadal tropical Atlantic SST trends ( [[#Kucharski--2011|Kucharski et al., 2011]] , 2014, 2015; [[#McGregor--2014|McGregor et al., 2014]] ; [[#Chafik--2016|Chafik et al., 2016]] ; X. [[#Li--2016|]] [[#Li--2016|Li et al., 2016]] ; [[#Kajtar--2017|Kajtar et al., 2017]] ; [[#Sun--2017|Sun et al., 2017]] ), teleconnections from multi-decadal Southern Ocean SST trends ( [[#Hwang--2017|Hwang et al., 2017]] ), and coupled ocean–atmosphere dynamics which slow warming in the equatorial eastern Pacific ( [[#Clement--1996|Clement et al., 1996]] ; [[#Cane--1997|Cane et al., 1997]] ; [[#Seager--2019|Seager et al., 2019]] ). CMIP3 and CMIP5 ESMs have difficulties replicating the observed trends in the Walker circulation and Pacific Ocean SSTs over the historical record ( [[#Sohn--2013|Sohn et al., 2013]] ; [[#Zhou--2016|Zhou et al., 2016]] ; [[#Coats--2017|Coats and Karnauskas, 2017]] ), possibly due to model deficiencies including insufficient multi-decadal Pacific Ocean SST variability ( [[#Laepple--2014|Laepple and Huybers, 2014]] ; [[#Bilbao--2015|Bilbao et al., 2015]] ; [[#Chung--2019|Chung et al., 2019]] ), mean state biases affecting the forced response or the connection between Atlantic and Pacific basins ( [[#Kucharski--2014|Kucharski et al., 2014]] ; [[#Kajtar--2018|Kajtar et al., 2018]] ; [[#Luo--2018|Luo et al., 2018]] ; [[#McGregor--2018|McGregor et al., 2018]] ; [[#Seager--2019|Seager et al., 2019]] ), and/or a misrepresentation of radiative forcing (Sections 9.2.1 and 3.7.6). However, the observed trends in the Pacific Ocean SSTs are still within the range of internal variability as simulated by large initial condition ensembles of CMIP5 and CMIP6 models ( [[#Olonscheck--2020|Olonscheck et al., 2020]] ; Watanabe et al., 2021). Because the causes of observed equatorial Pacific temperature gradient and Walker circulation trends are not well understood ( [[IPCC:Wg1:Chapter:Chapter-3#3.3.3.1|Section 3.3.3.1]] ), there is ''low confidence'' in their attribution to anthropogenic influences ( [[IPCC:Wg1:Chapter:Chapter-8#8.3.2.3|Section 8.3.2.3]] ), while there is ''medium confidence'' that the observed changes have resulted from internal variability (Sections 3.7.6 and 8.2.2.2).

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<span id="tropical-pacific-temperature-gradients-in-past-high-co-2-climates"></span>
===== 7.4.4.2.2 Tropical Pacific temperature gradients in past high-CO 2 climates =====

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The AR5 stated that paleoclimate proxies indicate a reduction in the longitudinal SST gradient across the equatorial Pacific during the Mid-Pliocene Warm Period (MPWP; [[#Masson-Delmotte--2013|Masson-Delmotte et al., 2013]] ; see Cross-Chapter Box 2.1 and Cross-Chapter Box 2.4 in this Report). This assessment was based on SST reconstructions between two sites situated very close to the equator in the heart of the western Pacific warm pool and eastern Pacific cold tongue, respectively. Multiple SST reconstructions based on independent paleoclimate proxies generally agreed that during the Pliocene the SST gradient between these two sites was reduced compared with the modern long-term mean ( [[#Wara--2005|Wara et al., 2005]] ; [[#Dekens--2008|Dekens et al., 2008]] ; [[#Fedorov--2013|Fedorov et al., 2013]] ).

Since AR5, the generation of new SST records has led to a variety of revised gradient estimates, specifically the generation of a new record for the warm pool ( [[#Zhang--2014|Zhang et al., 2014]] ), the inclusion of SST reconstructions from sites in the South China Sea as warm pool estimates ( [[#O’Brien--2014|O’Brien et al., 2014]] ; [[#Zhang--2014|Zhang et al., 2014]] ), and the inclusion of several new sites from the eastern Pacific as cold tongue estimates ( [[#Zhang--2014|Zhang et al., 2014]] ; [[#Fedorov--2015|Fedorov et al., 2015]] ). Published estimates of the reduction in the longitudinal SST difference for the Late Pliocene, relative to either Late Quaternary (0–0.5 million years ago) or pre-industrial values, include 1°C to 1.5°C ( [[#Zhang--2014|Zhang et al., 2014]] ), 0.1°C to 1.9°C ( [[#Tierney--2019|Tierney et al., 2019]] ), and about 3°C ( [[#Ravelo--2014|Ravelo et al., 2014]] ; [[#Fedorov--2015|Fedorov et al., 2015]] ; [[#Wycech--2020|Wycech et al., 2020]] ). All of these studies report a further weakening of the longitudinal gradient based on records extending into the Early Pliocene. While these revised estimates differ in magnitude due to differences in the sites and SST proxies used, they all agree that the longitudinal gradient was weaker, and this is supported by the probabilistic approach of [[#Tierney--2019|Tierney et al. (2019)]] . However, given that there are currently relatively few western equatorial Pacific records from independent site locations, and due to uncertainties associated with the proxy calibrations ( [[#Haywood--2016a|Haywood et al., 2016a]] ), there is only ''medium confidence'' that the average longitudinal gradient in the tropical Pacific was weaker during the Pliocene than during the Late Quaternary.

To avoid the influence of local biases, changes in the longitudinal temperature difference within Pliocene model simulations are typically evaluated using domain-averaged SSTs within chosen east and west Pacific regions and as such there is sensitivity to methodology. Unlike the reconstructed estimates, longitudinal gradient changes simulated by the Pliocene Model Intercomparison Project Phase 1 (PlioMIP1) models do not agree on the change in sign and are reported as spanning approximately –0.5°C to +0.5°C by [[#Brierley--2015|Brierley et al. (2015)]] and approximately –1°C to +1°C by [[#Tierney--2019|Tierney et al. (2019)]] . Initial PlioMIP Phase 2 (PlioMIP2) analysis suggests responses similar to PlioMIP1 ( [[#Feng--2019|Feng et al., 2019]] ; [[#Haywood--2020|Haywood et al., 2020]] ). Models that include hypothetical modifications to cloud albedo or ocean mixing are required to simulate the substantially weaker longitudinal differences seen in reconstructions of the Early Pliocene ( [[#Fedorov--2013|Fedorov et al., 2013]] ; [[#Burls--2014a|Burls and Fedorov, 2014a]] ).

While more western Pacific warm pool temperature reconstructions are needed to refine estimates of the longitudinal gradient, several Pliocene SST reconstructions from the east Pacific indicate enhanced warming in the centre of the eastern equatorial cold tongue upwelling region ( [[#Liu--2019|Liu et al., 2019]] ). This enhanced warming in the east Pacific cold tongue appears to be dynamically consistent with reconstruction of enhanced subsurface warming ( [[#Ford--2015|Ford et al., 2015]] ) and enhanced warming in coastal upwelling regions, suggesting that the tropical thermocline was deeper and/or less stratified during the Pliocene. The Pliocene data therefore suggest that the observed cooling trend over the last 60 years in parts of the eastern equatorial Pacific ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1.1|Section 9.2.1.1]] and Figure 9.3; [[#Seager--2019|Seager et al., 2019]] ), whether forced or due to internal variability, involves transient processes that are probably distinct from the longer-time scale process ( [[#Burls--2014a|Burls and Fedorov, 2014a]] , b; [[#Luo--2015|Luo et al., 2015]] ; [[#Heede--2020|Heede et al., 2020]] ) that maintained warmer eastern Pacific SST during the Pliocene.

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<span id="overall-assessment-of-tropical-pacific-sea-surface-temperature-gradients-under-co-2-forcing"></span>
===== 7.4.4.2.3 Overall assessment of tropical Pacific sea surface temperature gradients under CO 2 forcing =====

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The paleoclimate proxy record and ESM simulations of the MPWP, process understanding, and ESM projections of climate response to CO <sub>2</sub> forcing provide ''medium evidence'' and a ''medium agreement'' and thus ''medium confidence'' that equilibrium warming in response to elevated CO <sub>2</sub> will be characterized by a weakening of the east–west tropical Pacific SST gradient.

Overall the observed pattern of warming over the instrumental period, with a warming minimum in the eastern tropical Pacific Ocean (Figure 7.14a), stands in contrast to the equilibrium warming pattern either inferred from the MPWP proxy record or simulated by ESMs under CO <sub>2</sub> forcing. There is ''medium confidence'' that the observed strengthening of the east–west SST gradient is temporary and will transition to a weakening of the SST gradient on centennial time scales. However, there is only ''low confidence'' that this transition will emerge this century owing to a low degree of agreement across studies about the factors driving the observed strengthening of the east–west SST gradient and how those factors will evolve in the future. These trends in tropical Pacific SST gradients reflect changes in the climatology, rather than changes in ENSO amplitude or variability, which are assessed in ( [[IPCC:Wg1:Chapter:Chapter-4|Chapter 4]] [[IPCC:Wg1:Chapter:Chapter-4#4.3.3|Section 4.3.3]] ).

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<span id="dependence-of-feedbacks-on-temperature-patterns"></span>
==== 7.4.4.3 Dependence of Feedbacks on Temperature Patterns ====

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The expected time-evolution of the spatial pattern of surface warming in the future has important implications for values of ECS inferred from the historical record of observed warming. In particular, changes in the global top-of-atmosphere (TOA) radiative energy budget can be induced by changes in the regional variations of surface temperature, even without a change in the global mean temperature ( [[#Zhou--2016|Zhou et al., 2016]] ; [[#Ceppi--2019|Ceppi and Gregory, 2019]] ). Consequently, the global radiative feedback, characterizing the net TOA radiative response to global surface warming, depends on the ''spatial pattern'' of that warming. Therefore, if the equilibrium warming pattern under CO <sub>2</sub> forcing (similar to CMIP6 projections in Figure 7.12a) is distinct from that observed over the historical record or indicated by paleoclimate proxies (Sections 7.4.4.1 and 7.4.4.2), then ECS will be different from the effective ECS (Box 7.1) that is inferred from those periods. Accounting for the dependence of radiative feedbacks on the spatial pattern of warming has helped to reconcile values of ECS inferred from the historical record with values of ECS based on other lines of evidence and simulated by climate models ( [[#7.5.2.1|Section 7.5.2.1]] ; [[#Armour--2017|Armour, 2017]] ; [[#Proistosescu--2017|Proistosescu and Huybers, 2017]] ; [[#Andrews--2018|Andrews et al., 2018]] ) but has not yet been examined in the paleoclimate context.

This temperature ‘pattern effect’ ( [[#Stevens--2016|Stevens et al., 2016]] ) can result from both internal variability and radiative forcing of the climate system. Importantly, it is distinct from potential radiative feedback dependencies on the global surface temperature, which are assessed in ( [[#7.4.3|Section 7.4.3]] . While changes in global radiative feedbacks under transient warming have been documented in multiple generations of climate models ( [[#Williams--2008|Williams et al., 2008]] ; [[#Andrews--2015|Andrews et al., 2015]] ; [[#Ceppi--2017|Ceppi and Gregory, 2017]] ; [[#Dong--2020|Dong et al., 2020]] ), research published since AR5 has developed a much-improved understanding of the role of evolving SST patterns in driving feedback changes ( [[#Armour--2013|Armour et al., 2013]] ; [[#Andrews--2015|Andrews et al., 2015]] , 2018; [[#Gregory--2016|Gregory and Andrews, 2016]] ; [[#Zhou--2016|Zhou et al., 2016]] , 2017b; [[#Ceppi--2017|Ceppi and Gregory, 2017]] ; [[#Haugstad--2017|Haugstad et al., 2017]] ; [[#Proistosescu--2017|Proistosescu and Huybers, 2017]] ; [[#Andrews--2018|Andrews and Webb, 2018]] ; [[#Marvel--2018|Marvel et al., 2018]] ; [[#Silvers--2018|Silvers et al., 2018]] ; [[#Dong--2019|Dong et al., 2019]] , 2020). This section assesses process understanding of the pattern effect, which is dominated by the evolution of SSTs. [[#7.5.2.1|Section 7.5.2.1]] describes how potential feedback changes associated with the pattern effect are important to interpreting ECS estimates based on historical warming.

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[[File:84e2e550237af9033963917321af870b IPCC_AR6_WGI_Figure_7_13.png]]

'''Figure 7.13''' '''|''' '''Polar amplification in paleo proxies and models of the Early Eocene Climatic Optimum (EECO), the Mid-Pliocene Warm Period (MPWP) and the Last Glacial Maximum (LGM).''' '''Figure 7.13:''' Temperature anomalies compared with pre-industrial (equivalent to CMIP6 simulation ‘piControl’) are shown for the high-CO <sub>2</sub> EECO and MPWP time periods, and for the low-CO <sub>2</sub> LGM (expressed as pre-industrial minus LGM). '''(a), (b) and (c)''' Modelled near-surface air temperature anomalies for ensemble-mean simulations of the (a) EECO ( [[#Lunt--2021|Lunt et al., 2021]] ); (b) MPWP ( [[#Haywood--2020|Haywood et al., 2020]] ; [[#Zhang--2021|Zhang et al., 2021]] ); and (c) LGM ( [[#Kageyama--2021|Kageyama et al., 2021]] ; [[#Zhu--2021|Zhu et al., 2021]] ). Also shown are proxy near-surface air temperature anomalies (coloured circles). '''(d), (e) and (f)''' Proxy near-surface air temperature anomalies (grey circles), including published uncertainties (grey vertical bars), model ensemble mean zonal mean anomaly (solid red line) for the same model ensembles as in (a–c), light-red lines show the modelled temperature anomaly for the individual models that make up each ensemble (LGM, N=9; MPWP, N=17; EECO, N=5). Black dashed lines show the average of the proxy values in each latitude band: 90°S–30°S, 30°S–30°N, and 30°N–90°N. Red dashed lines show the same banded average in the model ensemble mean, calculated from the same locations as the proxies. Black and red dashed lines are only shown if there are five or more proxy points in that band. Mean differences between the 90°S/N to 30°S/N and 30°S to 30°N bands are quantified for the models and proxies in each plot. Panels '''(g), (h) and (i)''' are like panels (d–f) but for sea surface temperature (SST) instead of near-surface air temperature. Panels '''(j), (k) and (l)''' are like panels (a–c) but for SST instead of near-surface air temperature. For the EECO maps – (a) and (j) – the anomalies are relative to the zonal mean of the pre-industrial, due to the different continental configuration. Proxy datasets are: (a) and (d) [[#Hollis--2019|Hollis et al. (2019)]] ; (b) and (e) [[#Salzmann--2013|Salzmann et al. (2013)]] ; [[#Vieira--2018|Vieira et al. (2018)]] , (c) and (f) [[#Cleator--2020|Cleator et al. (2020)]] at the sites defined in [[#Bartlein--2011|Bartlein et al. (2011)]] ; (g) and (j) [[#Hollis--2019|Hollis et al. (2019)]] ; (h) and (k) [[#McClymont--2020|McClymont et al. (2020)]] ; (i) and (l) [[#Tierney--2020b|Tierney et al. (2020b)]] . Where there are multiple proxy estimations at a single site, a mean is taken. Model ensembles are (a), (d), (g) and (j) DeepMIP (only model simulations carried out with a mantle-frame paleogeography, and carried out under CO <sub>2</sub> concentrations within the range assessed in Table 2.2, are shown); (b), (e), (h) and (k) PlioMIP; and (c), (f), (i) and (l) PMIP4. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

The radiation changes most sensitive to warming patterns are those associated with low-cloud cover (affecting global albedo) and the tropospheric temperature profile (affecting thermal emission to space) ( [[#Ceppi--2017|Ceppi and Gregory, 2017]] ; [[#Zhou--2017b|Zhou et al., 2017b]] ; [[#Andrews--2018|Andrews et al., 2018]] ; [[#Dong--2019|Dong et al., 2019]] ). The mechanisms and radiative effects of these changes are illustrated in Figure 7.14a,b. SSTs in regions of deep convective ascent (e.g., in the western Pacific warm pool) govern the temperature of the tropical free troposphere and, in turn, affect low-clouds through the strength of the inversion that caps the boundary layer (i.e., the lower-tropospheric stability) in subsidence regions ( [[#Wood--2006|Wood and Bretherton, 2006]] ; [[#Klein--2017|Klein et al., 2017]] ). Surface warming within ascent regions thus warms the free troposphere and increases low-cloud cover, causing an increase in emission of thermal radiation to space and a reduction in absorbed solar radiation. In contrast, surface warming in regions of overall descent preferentially warms the boundary layer and enhances convective mixing with the dry free troposphere, decreasing low-cloud cover ( [[#Bretherton--2013|Bretherton et al., 2013]] ; [[#Qu--2014|Qu et al., 2014]] ; [[#Zhou--2015|Zhou et al., 2015]] ). This leads to an increase in absorption of solar radiation but little change in thermal emission to space. Consequently, warming in tropical ascent regions results in negative lapse-rate and cloud feedbacks while warming in tropical descent regions results in positive lapse-rate and cloud feedbacks (Figure 7.14; [[#Rose--2016|Rose and Rayborn, 2016]] ; [[#Zhou--2017b|Zhou et al., 2017b]] ; [[#Andrews--2018|Andrews and Webb, 2018]] ; [[#Dong--2019|Dong et al., 2019]] ). Surface warming in mid-to-high latitudes causes a weak radiative response owing to compensating changes in thermal emission (Planck and lapse-rate feedbacks) and absorbed solar radiation (shortwave cloud and surface-albedo feedbacks; [[#Rose--2016|Rose and Rayborn, 2016]] ; [[#Dong--2019|Dong et al., 2019]] ), however this compensation may weaken due to less-negative shortwave cloud feedbacks at high warming ( [[#Frey--2018|Frey and Kay, 2018]] ; [[#Bjordal--2020|Bjordal et al., 2020]] ; [[#Dong--2020|Dong et al., 2020]] ).

The spatial pattern of SST changes since 1870 shows relatively little warming in key regions of less-negative radiative feedbacks, including the eastern tropical Pacific Ocean and Southern Ocean (Sections 7.4.4.1 and 7.4.4.2, and Figures 2.11b and 7.14a). Cooling in these regions since 1980 has occurred along with an increase in the strength of the capping inversion in tropical descent regions, resulting in an observed increase in low-cloud cover over the tropical eastern Pacific (Figure 7.14a; [[#Zhou--2016|Zhou et al., 2016]] ; [[#Ceppi--2017|Ceppi and Gregory, 2017]] ; [[#Fueglistaler--2021|Fueglistaler and Silvers, 2021]] ). Thus, tropical low-cloud cover increased over recent decades even as global surface temperature increased, resulting in a negative low-cloud feedback which is at odds with the positive low-cloud feedback expected for the pattern of equilibrium warming under CO <sub>2</sub> forcing ( [[#7.4.2.4|Section 7.4.2.4]] and Figure 7.14b).

[[#Andrews--2018|Andrews et al. (2018)]] analysed available CMIP5/6 ESM simulations (six in total) comparing effective feedback parameters diagnosed within atmosphere-only ESMs using prescribed historical SST and sea ice concentration patterns with the equilibrium feedback parameters as estimated within coupled ESMs (using identical atmospheres) driven by abrupt 4×CO <sub>2</sub> forcing. The atmosphere-only ESMs show pronounced multi-decadal variations in their effective feedback parameters over the last century, with a trend towards strongly negative values since about 1980 owing primarily to negative shortwave cloud feedbacks driven by warming in the western equatorial Pacific Ocean and cooling in the eastern equatorial Pacific Ocean ( [[#Zhou--2016|Zhou et al., 2016]] ; [[#Andrews--2018|Andrews et al., 2018]] ; [[#Marvel--2018|Marvel et al., 2018]] ; [[#Dong--2019|Dong et al., 2019]] ). Yet, all six models show a less-negative net feedback parameter under ''abrupt 4xCO2'' than for the historical period (based on regression since 1870 following [[#Andrews--2018|Andrews et al., 2018]] ). The average change in net feedback parameter between the historical period and the equilibrium response to CO <sub>2</sub> forcing, denoted here as α ''’'' , for these simulations is α ''’'' = +0.6 W m <sup>–2</sup> °C <sup>–1</sup> (+0.3 to +1.0 W m <sup>–2</sup> °C <sup>–1</sup> range across models; Figure 7.15b). These feedback parameter changes imply that the value of ECS may be substantially larger than that inferred from the historical record ( [[#7.5.2.1|Section 7.5.2.1]] ). These findings can be understood from the fact that, due to a combination of internal variability and transient response to forcing ( [[#7.4.4.2|Section 7.4.4.2]] ), historical sea surface warming has been relatively large in regions of tropical ascent (Figure 7.14a), leading to an anomalously large net negative radiative feedback; however, future warming is expected to be largest in tropical descent regions, such as the eastern equatorial Pacific, and at high latitudes (Sections 7.4.4.1 and 7.4.4.2 and Figure 7.14b), leading to a less-negative net radiative feedback and higher ECS.

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[[File:b7b4983aa5e6275bb417a83cb5cbc191 IPCC_AR6_WGI_Figure_7_15.png]]

'''Figure 7.15''' '''|''' '''Relationship between''' ''historical'' '''and''' ''abrupt 4xCO2'' '''net radiative feedbacks in ESMs. (a)''' Radiative feedbacks in CMIP6 ESMs estimated under historical forcing (values for GFDL CM4.0 and HadGEM3-CG3.1-LL from [[#Winton--2020|Winton et al. (2020)]] and [[#Andrews--2019|Andrews et al. (2019)]] , respectively); horizontal lines show the range across ensemble members. The other points show effective feedback values for 29 ESMs estimated using regression over the first 50 years of ''abrupt 4xCO2'' simulations as an analogue for historical warming ( [[#Dong--2020|Dong et al., 2020]] ). '''(b)''' Historical radiative feedbacks estimated from atmosphere-only ESMs with prescribed observed sea-surface temperature and sea-ice concentration changes ( [[#Andrews--2018|Andrews et al., 2018]] ) based on a linear regression of global top-of-atmosphere (TOA) radiation against global near-surface air temperature over the period 1870–2010 (pattern of warming similar to Figure 7.14a) and compared with equilibrium feedbacks in ''abrupt 4xCO2'' simulations of coupled versions of the same ESMs (pattern of warming similar to Figure 7.14b). In all cases, the equilibrium feedback magnitudes are estimated as CO <sub>2</sub> ERF divided by ECS where ECS is derived from regression over years 1–150 of ''abrupt 4xCO2'' simulations (Box 7.1); similar results are found if the equilibrium feedback is estimated directly from the slope of the linear regression. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

A similar behaviour is seen within transient simulations of coupled ESMs, which project SST warming patterns that are initially characterized by relatively large warming rates in the western equatorial Pacific Ocean on decadal time scales and relatively large warming in the eastern equatorial Pacific and Southern Ocean on centennial time scales ( [[#Andrews--2015|Andrews et al., 2015]] ; [[#Proistosescu--2017|Proistosescu and Huybers, 2017]] ; [[#Dong--2020|Dong et al., 2020]] ). Recent studies based on simulations of 1% yr <sup>–1</sup> CO <sub>2</sub> increase ( ''1pctCO'' 2 ) or ''abrupt 4xCO2'' as analogues for historical warming suggest characteristic values of α ''’'' = +0.05 W m <sup>–2</sup> °C <sup>–1</sup> (–0.2 to +0.3 W m <sup>–2</sup> °C <sup>–1</sup> range across models) based on CMIP5 and CMIP6 ESMs (Armour 2017, Lewis and Curry 2018, Dong et al. 2020). Using historical simulations of one CMIP6 ESM (HadGEM3-GC3.1-LL), [[#Andrews--2019|Andrews et al. (2019)]] find an average feedback parameter change of α ''’'' = +0.2 W m <sup>–2</sup> °C <sup>–1</sup> (–0.2 to +0.6 W m <sup>–2</sup> °C <sup>–1</sup> range across four ensemble members). Using historical simulations from another CMIP6 ESM (GFDL CM4.0), [[#Winton--2020|Winton et al. (2020)]] find an average feedback parameter change of α ''’'' = +1.5 W m <sup>–2</sup> °C <sup>–1</sup> (+1.2 to +1.7 W m <sup>–2</sup> °C <sup>–1</sup> range across three ensemble members). This value is larger than The α ''’'' = +0.7 W m <sup>–2</sup> °C <sup>–1</sup> within GFDL CM4.0 for historical CO <sub>2</sub> forcing only, suggesting that the value of α ''’'' may depend on historical non-CO <sub>2</sub> forcings such as those associated with tropospheric and stratospheric aerosols ( [[#Marvel--2016|Marvel et al., 2016]] ; [[#Gregory--2020|Gregory et al., 2020]] ; [[#Winton--2020|Winton et al., 2020]] ).

The magnitude of the net feedback parameter change α ''’'' found within coupled CMIP5 and CMIP6 ESMs is generally smaller than that found when prescribing observed warming patterns within atmosphere-only ESMs (Figure 7.15; [[#Andrews--2018|Andrews et al., 2018]] ). This arises from the fact that the forced spatial pattern of warming within transient simulations of most coupled ESMs are distinct from observed warming patterns over the historical record in key regions such as the equatorial Pacific Ocean and Southern Ocean (Sections 7.4.4.1 and 7.4.4.2), while being more similar to the equilibrium pattern simulated under ''abrupt 4xCO2'' . However, historical simulations with HadGEM3-GC3.1-LL ( [[#Andrews--2019|Andrews et al., 2019]] ) and GFDL CM4.0 ( [[#Winton--2020|Winton et al., 2020]] ) show substantial spread in the value of α ''’'' across ensemble members, indicating a potentially important role for internal variability in setting the magnitude of the pattern effect over the historical period. Using the 100-member historical simulation ensemble of MPI-ESM1.1, [[#Dessler--2018|Dessler et al. (2018)]] find that internal climate variability alone results in a 0.5 W m <sup>–2</sup> °C <sup>–1</sup> spread in the historical effective feedback parameter, and thus also in the value of α ''’'' . Estimates of α ''’'' using prescribed historical warming patterns provide a more realistic representation of the historical pattern effect because they account for the net effect of the transient response to historical forcing and internal variability in the observed record ( [[#Andrews--2018|Andrews et al., 2018]] ).

The magnitude of α ''’'' , as quantified by ESMs, depends on the accuracy of both the projected patterns of SST and sea ice concentration changes in response to CO <sub>2</sub> forcing and the radiative response to those patterns ( [[#Andrews--2018|Andrews et al., 2018]] ). Model biases that affect the long-term warming pattern (e.g., SST and relative humidity biases in the equatorial Pacific cold tongue as suggested by [[#Seager--2019|Seager et al., 2019]] ) will affect the value of α ''’'' . The value of α ''’'' also depends on the accuracy of the historical SST and sea ice concentration conditions prescribed within atmosphere-only versions of ESMs to quantify the historical radiative feedback (Figure 7.15b). Historical SSTs are particularly uncertain for the early portion of the historical record ( [[IPCC:Wg1:Chapter:Chapter-2#2.3.1|Section 2.3.1]] ), and there are few constraints on sea ice concentration prior to the satellite era. Using alternative SST datasets, [[#Andrews--2018|Andrews et al. (2018)]] found little change in the value of α ''’'' within two models (HadGEM3 and HadAM3), while [[#Lewis--2021|Lewis and Mauritsen (2021)]] found a smaller value of α ''’'' within two other models (ECHAM6.3 and CAM5). The sensitivity of results to the choice of dataset represents a major source of uncertainty in the quantification of the historical pattern effect using atmosphere-only ESMs that has yet to be systematically explored, but the preliminary findings of [[#Lewis--2021|Lewis and Mauritsen (2021)]] and [[#Fueglistaler--2021|Fueglistaler and Silvers (2021)]] suggest that α ''’'' could be smaller than the values reported in [[#Andrews--2018|Andrews et al. (2018)]] .

While there are not yet direct observational constraints on the magnitude of the pattern effect, satellite measurements of variations in TOA radiative fluxes show strong co-variation with changing patterns of SSTs, with a strong dependence on SST changes in regions of deep convective ascent (e.g., in the western Pacific warm pool; [[#Loeb--2018a|Loeb et al., 2018a]] ; [[#Fueglistaler--2019|Fueglistaler, 2019]] ). Cloud and TOA radiation responses to observed warming patterns in atmospheric models have been found to compare favourably with those observed by satellite ( [[#7.2.2.1|Section 7.2.2.1]] and Figure 7.3; [[#Zhou--2016|Zhou et al., 2016]] ; [[#Loeb--2020|Loeb et al., 2020]] ). This observational and modelling evidence indicates the potential for a strong pattern effect in nature that will only be negligible if the observed pattern of warming since pre-industrial levels persists to equilibrium – an improbable scenario given that Earth is in a relatively early phase of transient warming and that reaching equilibrium would take multiple millennia (C. [[#Li--2013|]] [[#Li--2013|Li et al., 2013]] ). Moreover, paleoclimate proxies, ESM simulations, and process understanding indicate that strong warming in the eastern equatorial Pacific Ocean (with ''medium confidence'' ) and Southern Ocean (with ''high confidence'' ) will emerge on centennial time scales as the response to CO <sub>2</sub> forcing dominates temperature changes in these regions (Sections 7.4.4.1, 7.4.4.2 and 9.2.1). However, there is ''low confidence'' that these features, which have been largely absent over the historical record, will emerge this century (Sections 7.4.4.1, 7.4.4.2 and ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1|Section 9.2.1]] ). This leads to ''high confidence'' that radiative feedbacks will become less negative as the CO <sub>2</sub> -forced pattern of surface warming emerges ( α ''’'' &gt; 0 W m <sup>–2</sup> °C <sup>–1</sup> ), but ''low confidence'' that these feedback changes will be realized this century. There is also substantial uncertainty in the magnitude of the net radiative feedback change between the present warming pattern and the projected equilibrium warming pattern in response to CO <sub>2</sub> forcing owing to the fact that its quantification currently relies solely on ESM results and is subject to uncertainties in historical SST patterns. Thus, based on the pattern of warming since 1870, α ''’'' is estimated to be in the range 0.0 to 1.0 W m <sup>–2</sup> °C <sup>–1</sup> but with a ''low confidence'' in the upper end of this range. A value of α ''’'' = +0.5 ± 0.5 W m <sup>–2</sup> °C <sup>–1</sup> is used to represent this range in Box 7.2 and ( [[#7.5.2|Section 7.5.2]] , which respectively assess the implications of changing radiative feedbacks for Earth’s energy imbalance and estimates of ECS based on the instrumental record. The value of α ''’'' is larger if quantified based on the observed pattern of warming since 1980 (Figure 2.11b) which is more distinct from the equilibrium warming pattern expected under CO <sub>2</sub> forcing ( ''high confidence'' ) (similar to CMIP6 projections shown in Figure 7.12a; [[#Andrews--2018|Andrews et al., 2018]] ).

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