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

=== 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]] .

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==== 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.

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==== 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.

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[[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).

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==== 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.

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