Editing IPCC:AR6/WGI/Chapter-5 (section)

=== 5.5.1 Transient Climate Response to Cumulative Emissions of Carbon Dioxide (TCRE) ===

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<span id="contributing-physical-processes-and-theoretical-frameworks"></span>
==== 5.5.1.1 Contributing Physical Processes and Theoretical Frameworks ====

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The processes that translate emissions of CO <sub>2</sub> into a change in global temperature (terrestrial and oceanic carbon uptake, radiative forcing from CO <sub>2</sub> , and ocean heat uptake) are governed by complex mechanisms that all evolve in time (Sections 3.5, 4.3, 4.5, 5.4, and 7.3, and Cross-Chapter Box 5.3; [[#Gregory--2009|Gregory et al., 2009]] ). Starting with an initial description in AR5 (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ), a body of literature has since expanded the understanding of physical mechanisms from which a simple proportional relationship between cumulative emissions of CO <sub>2</sub> and change in global temperature arises – expressed in either global mean surface temperature (GMST) or global surface air temperature (GSAT).

Studies have focused on two key features of the transient climate response to cumulative CO <sub>2</sub> emissions (TCRE) relationship: (i) why the relationship is nearly constant in time ( [[#Goodwin--2015|Goodwin et al., 2015]] ; [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#Williams--2016|Williams et al., 2016]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ; [[#Katavouta--2018|Katavouta et al., 2018]] ); and (ii) why, and under which conditions, the relationship is independent of the historical rate (or pathway) of CO <sub>2</sub> emissions ( [[#MacDougall--2017|MacDougall, 2017]] ; [[#Seshadri--2017|Seshadri, 2017]] ).

There is increased confidence in the near-constancy of TCRE because of the variety of methods that have been used to examine this relationship: sensitivity studies with Earth system models of intermediate complexity (EMICs; [[#Herrington--2014|Herrington and Zickfeld, 2014]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ); theory-based equations used to examine ESM and EMIC output ( [[#Goodwin--2015|Goodwin et al., 2015]] ; R.G. [[#Williams--2016|Williams et al., 2016]] , 2017b); and simple analytical models that capture aspects of the TCRE relationship ( [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ). All studies agree that the near-constancy of the TCRE arises from compensation between the diminishing sensitivity of radiative forcing to CO <sub>2</sub> at higher atmospheric concentration and the diminishing ability of the ocean to take up heat and carbon at higher cumulative emissions ( [[#Allen--2009|Allen et al., 2009]] ; [[#Matthews--2009|Matthews et al., 2009]] ; [[#Frölicher--2015|Frölicher and Paynter, 2015]] ; [[#Goodwin--2015|Goodwin et al., 2015]] ; [[#Gregory--2015|Gregory et al., 2015]] ; [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#MacDougall--2016|MacDougall, 2016]] ; [[#Tokarska--2016|Tokarska et al., 2016]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ).

The question of whether, and under which conditions, the TCRE relationship is independent of the historical rate of CO <sub>2</sub> emissions (also referred to as ‘pathway independence of TCRE’) has been examined by using simple mathematically tractable models ( [[#MacDougall--2017|MacDougall, 2017]] ; [[#Seshadri--2017|Seshadri, 2017]] ). Based on the assumption that the cumulative fraction of carbon taken up by the terrestrial biosphere is constant, and that the climate feedback parameter and ocean heat uptake efficacy do not change in time, both studies agree that pathway independence is sensitive to the rate of CO <sub>2</sub> emissions, such that pathway independence is expected to break down at both very high and very low absolute CO <sub>2</sub> emissions rates ( [[#MacDougall--2017|MacDougall, 2017]] ; [[#Seshadri--2017|Seshadri, 2017]] ). Note that, in pathways with strongly declining emissions, the cumulative sink fraction by the combined terrestrial biosphere and ocean is expected to increase (Figure 5.25). The studies also agree that no similar relationship analogous to TCRE can be expected for short-lived non-CO <sub>2</sub> forcers, for which the annual emissions are a closer proxy for the implied warming (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; Sections 6.4, 7.6). [[#MacDougall--2017|MacDougall (2017)]] suggests that two additional constraints are required to create pathway independence: first, the transport of heat and carbon into the deep ocean should be governed by processes with similar time scales; and second, the ratio of the net change in the atmospheric carbon pool to the net change in the ocean carbon pool should be close to the ratio of the enhanced longwave radiation to space (i.e., the radiative response of the surface) to ocean heat uptake. If these ratios are identical, then TCRE would be completely path independent ( [[#MacDougall--2017|MacDougall, 2017]] ). If the ratios are close but not identical, TCRE would be only approximately path independent over a wide range of cumulative emissions (Cross-Chapter Box 5.3; [[#MacDougall--2017|MacDougall, 2017]] ).

The land carbon cycle does not appear to play a fundamental role in the origin of the linearity and path-independence of TCRE ( [[#Goodwin--2015|Goodwin et al., 2015]] ; [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ) but, in contrast to the ocean sink, dominates the uncertainty in the magnitude of TCRE by modulating the cumulative airborne fraction of carbon ( [[#Goodwin--2015|Goodwin et al., 2015]] ; [[#Williams--2016|Williams et al., 2016]] ; [[#Katavouta--2018|Katavouta et al., 2018]] ; [[#Jones--2020|Jones and Friedlingstein, 2020]] ). Some terrestrial carbon cycle feedbacks (such as the permafrost carbon feedback; [[#5.4.8|Section 5.4.8]] , Box 5.1) have the potential to alter both the linearity and pathway independence of TCRE, if such feedbacks significantly contribute carbon to the atmosphere (Sections 5.5.1.2.3 and 5.4.8, and Box 5.1; [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ). A recent study also shows how the value of TCRE can depend on the effect of ocean ventilation modulating ocean heat uptake ( [[#Katavouta--2019|Katavouta et al., 2019]] ).

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<span id="assessment-of-limits-of-the-tcre-concept"></span>
==== 5.5.1.2 Assessment of Limits of the TCRE Concept ====

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<span id="sensitivity-to-amount-of-cumulative-co-2-emissions"></span>
===== 5.5.1.2.1 Sensitivity to amount of cumulative CO <sub>2</sub> emissions =====

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The AR5 indicated that the concept of a constant ratio of cumulative emissions of CO <sub>2</sub> to temperature was applicable to scenarios with increasing cumulative CO <sub>2</sub> emissions up to 2000 PgC (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ). Recent analyses added confidence to this insight ( [[#Herrington--2014|Herrington and Zickfeld, 2014]] ; [[#Steinacher--2016|Steinacher and Joos, 2016]] ) and showed some evidence of a potentially larger window of constant TCRE ( [[#Leduc--2015|Leduc et al., 2015]] ; [[#Tokarska--2016|Tokarska et al., 2016]] ). Using an analytical approach, [[#MacDougall--2015|MacDougall and Friedlingstein (2015)]] quantified a window of constant TCRE – defined as the range in cumulative emissions over which the TCRE remains within 95% of its maximum value – as between 360 to 1560 PgC. However, models with a more sophisticated ocean representation suggest that TCRE could also remain constant for considerably larger quantities of cumulative emissions, up to at least 3000 PgC ( [[#Leduc--2015|Leduc et al., 2015]] ; [[#Tokarska--2016|Tokarska et al., 2016]] ). Beyond this upper limit, studies are inconclusive, with some suggesting that TCRE will decrease ( [[#Leduc--2015|Leduc et al., 2015]] ) and others indicating that the linearity would hold up to as much as 5000 PgC ( [[#Tokarska--2016|Tokarska et al., 2016]] ).

As cumulative emissions increase, weakening land and ocean carbon sinks increase the airborne fraction of CO <sub>2</sub> emissions (see Figure 5.25), but each unit increase in atmospheric CO <sub>2</sub> has a smaller effect on global temperature owing to the logarithmic relationship between CO <sub>2</sub> and its radiative forcing ( [[#Matthews--2009|Matthews et al., 2009]] ; [[#Etminan--2016|Etminan et al., 2016]] ). At high values of cumulative emissions, some models simulate less warming per unit CO <sub>2</sub> emitted, suggesting that the saturation of CO <sub>2</sub> radiative forcing becomes more important than the effect of weakened carbon sinks ( [[#Herrington--2014|Herrington and Zickfeld, 2014]] ; [[#Leduc--2015|Leduc et al., 2015]] ). The behaviour of carbon sinks at high emissions levels remains uncertain, as models used to assess the limits of the TCRE show a large spread in net land carbon balance ( [[#5.4.5|Section 5.4.5]] ), and most estimates did not include the effect of permafrost carbon feedbacks (Sections 5.5.1.2.3 and 5.4). The latter would tend to further increase the airborne fraction at high cumulative emissions levels, and could therefore extend the window of linearity to higher total amounts of emissions ( [[#MacDougall--2015|MacDougall et al., 2015]] ). [[#Leduc--2016|Leduc et al. (2016)]] suggested further that a declining strength of snow and sea ice feedbacks in a warmer world would also contribute to a smaller TCRE at high amounts of cumulative emissions. However, [[#Tokarska--2016|Tokarska et al. (2016)]] suggested that a large decrease in TCRE for high cumulative emissions is only associated with some EMICs; in the four ESMs analysed in their study, the TCRE remained approximately constant up to 5000 PgC, owing to stronger declines in the efficiency of ocean heat uptake in ESMs compared to EMICs.

Overall, there is ''high agreement'' between multiple lines of evidence ( ''robust evidence'' ) resulting in ''high confidence'' that TCRE remains constant for the domain of increasing cumulative CO <sub>2</sub> emissions until at least 1500 PgC, with ''medium confidence'' of it remaining constant up to 3000 PgC because of less agreement across available lines of evidence.

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<span id="sensitivity-to-the-rate-of-co-2-emissions"></span>
===== 5.5.1.2.2 Sensitivity to the rate of CO <sub>2</sub> emissions =====

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Global average temperature increase responds over a time scale of about 10 years following the emission of a 100 PgC pulse of CO <sub>2</sub> ( [[#Joos--2013|Joos et al., 2013]] ; [[#Ricke--2014|Ricke and Caldeira, 2014]] ), with larger emission pulses associated with longer time scales and smaller pulses with shorter ones ( [[#Joos--2013|Joos et al., 2013]] ; [[#Matthews--2013|Matthews and Solomon, 2013]] ; [[#Zickfeld--2015|Zickfeld and Herrington, 2015]] ). This behaviour is confirmed in other studies, including those that calculate the temperature response to an instantaneous doubling or quadrupling of atmospheric CO <sub>2</sub> ( [[#Matthews--2009|Matthews et al., 2009]] ; [[#Gillett--2013|Gillett et al., 2013]] ; [[#Herrington--2014|Herrington and Zickfeld, 2014]] ; [[#Leduc--2015|Leduc et al., 2015]] ; [[#Hajima--2020b|Hajima et al., 2020b]] ). These findings suggest that the TCRE is sensitive to the rate of emissions, but studies assessing this sensitivity have found diverging results. For example, an increase in TCRE and its surrounding uncertainty was reported for experiments that imply a gradual decline in annual CO <sub>2</sub> emissions ( [[#Tachiiri--2019|Tachiiri et al., 2019]] ). These studies suggest that, in most cases, TCRE would be expected to increase in scenarios with decreasing annual emissions rates. This increase in TCRE for annual CO <sub>2</sub> emissions declining towards zero can be the result of the zero emissions commitment (ZEC) which is the amount of warming projected to occur following a complete cessation of emissions (see [[IPCC:Wg1:Chapter:Chapter-4#4.7.1.1|Section 4.7.1.1]] for its assessment), as well as Earth system processes that are unrepresented in current TCRE estimates ( [[#5.5.2.2.4|Section 5.5.2.2.4]] ) and other factors. When using TCRE to estimate CO <sub>2</sub> emissions consistent with a specific maximum warming level, these factors have to be taken into account (see Figure 5.31). Combined with recent literature on the ZEC ( [[#MacDougall--2020|MacDougall et al., 2020]] ) and emissions pathways ( [[#Huppmann--2018|Huppmann et al., 2018]] ) and noting the lack of literature that disentangles these various contributions, there is ''medium evidence'' and ''high agreement'' resulting in ''medium confidence'' that the TCRE remains a good predictor of CO <sub>2</sub> -induced warming when applied in the context of emissions reduction pathways, provided that ZEC and long-term Earth system feedbacks are adequately accounted for when emissions decline towards zero (see also [[#5.5.1.2.3|Section 5.5.1.2.3]] ).

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<span id="reversibility-and-earth-system-feedbacks"></span>
===== 5.5.1.2.3 Reversibility and Earth system feedbacks =====

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There are relatively few studies that have assessed how the TCRE is expected to change in scenarios of declining emissions followed by net negative annual CO <sub>2</sub> emissions. Conceptually, the literature suggests that the small lag of about a decade between CO <sub>2</sub> emissions and temperature change ( [[#Ricke--2014|Ricke and Caldeira, 2014]] ; [[#Zickfeld--2015|Zickfeld and Herrington, 2015]] ) would result in more warming at a given amount of cumulative emissions in a scenario where that emissions level is first exceeded and then returned to by deploying negative emissions (referred to as an ‘overshoot’, as is often the case in scenarios that aim to limit radiative forcing in 2100 to 2.6 or 1.9 W m <sup>–2</sup> ( [[#Riahi--2017|Riahi et al., 2017]] ; [[#Rogelj--2018a|Rogelj et al., 2018a]] ). [[#Zickfeld--2016|Zickfeld et al. (2016)]] showed this to hold across a range of scenarios, with positive emissions followed by negative emissions, whereby the TCRE increased by about 10% across the transition from positive to negative emissions as a result of the thermal and carbon inertia of the deep ocean. However, CMIP6 results for the SSP5-3.4-overshoot scenario show diverging trends across various ESMs (Figure 5.30). In an idealized CO <sub>2</sub> -concentration-driven setting, [[#Tachiiri--2019|Tachiiri et al. (2019)]] also reported an increase in TCRE. Exploring pathways with emissions rates and overshoots closer to mitigation pathways considered over the 21st century (in this case up to about 300 PgC), a recent emissions-driven EMIC experiment showed pathway independence of TCRE ( [[#Tokarska--2019a|Tokarska et al., 2019a]] ). Furthermore, also in absence of net negative emissions, warming would not necessarily remain perfectly constant on time scales of centuries and millennia, but could decrease or increase ( [[#Frölicher--2015|Frölicher and Paynter, 2015]] ; R.G. [[#Williams--2017|Williams et al., 2017]] a; [[#Hajima--2020b|Hajima et al., 2020b]] ). These additional changes in global mean temperature increase at various time scales are known as the ZEC (C.D. [[#Jones--2019|]] [[#Jones--2019|Jones et al., 2019]] ; [[#MacDougall--2020|MacDougall et al., 2020]] ), assessed in [[IPCC:Wg1:Chapter:Chapter-4#4.7.1.1|Section 4.7.1.1]] , and have to be integrated when using TCRE to estimate warming or remaining carbon budgets in overshoot scenarios.

The AR5-assessed (W.J. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ) TCRE range was based in part on the ESMs available at the time, which did not include some potentially important Earth system feedbacks. Since then, a number of studies have assessed the importance of permafrost carbon feedbacks, in particular on remaining carbon budgets ( [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#MacDougall--2015|MacDougall et al., 2015]] ; [[#Burke--2017b|Burke et al., 2017b]] ; [[#Gasser--2018|Gasser et al., 2018]] ; [[#Lowe--2018|Lowe and Bernie, 2018]] ), a development highlighted and assessed in the IPCC Special Report on Global Warming of 1.5°C ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ). [[#MacDougall--2015|MacDougall and Friedlingstein (2015)]] reported a TCRE increase of about 15% when including permafrost carbon feedbacks. The overall linearity of the TCRE during the 21st century was not affected, but they also found that permafrost carbon feedbacks caused an increase in TCRE on multi-century time scales under declining CO <sub>2</sub> emissions rates. In addition, other processes that are not regarded, or are only partially considered in individual or all ESMs, could cause a further increase or decrease of TCRE ( [[#Matthews--2020|Matthews et al., 2020]] ). These are discussed in detail in [[#5.4|Section 5.4]] , but their quantitative effects on TCRE have not yet been explored by the literature.

Whether TCRE remains an accurate predictor of CO <sub>2</sub> -induced warming when annual CO <sub>2</sub> emissions reach zero and are followed by net carbon dioxide removal (also referred to as TCRE reversibility) therefore hinges on contributions of slow components of the climate system that cause unrealized warming from past CO <sub>2</sub> emissions. Such slow components can arise from either physical climate (i.e., ocean heat uptake) or carbon cycle (i.e., ocean carbon uptake and permafrost carbon release) processes. The combined effect of these processes determines the magnitude and sign of the ZEC ( [[#MacDougall--2020|MacDougall et al., 2020]] ), which in turn impacts TCRE reversibility. As discussed in [[IPCC:Wg1:Chapter:Chapter-4#4.7.1.1|Section 4.7.1.1]] , recent model estimates of the ZEC suggest a range of ±0.19°C centred on zero ( [[#MacDougall--2020|MacDougall et al., 2020]] ). This suggests ''low agreement'' among models as to the reversibility of the TCRE in response to net-negative CO <sub>2</sub> emissions. Furthermore, most models used for ZEC assessments to date do not represent permafrost carbon processes, although understanding their contribution is essential to quantify the TCRE contribution. There is therefore ''limited evidence'' that quantifies the impact of permafrost carbon feedbacks on the reversibility of TCRE, leading to ''low confidence'' that the TCRE remains an accurate predictor of temperature changes in scenarios of net-negative CO <sub>2</sub> emissions on time scales of more than a half a century.

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<span id="estimates-of-tcre"></span>
==== 5.5.1.3 Estimates of TCRE ====

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The AR5 (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ) assessed that the TCRE is ''likely'' to fall in the range of 0.8°C –2.5°C per 1000 PgC (or per exagrams of carbon, EgC <sup>–1</sup> ) for cumulative emissions up to 2000 PgC, based on multiple lines of evidence. These include estimates based on ESMs of varying complexity ( [[#Matthews--2009|Matthews et al., 2009]] ; [[#Gillett--2013|Gillett et al., 2013]] ; [[#Zickfeld--2013|Zickfeld et al., 2013]] ), simple climate modelling approaches ( [[#Allen--2009|Allen et al., 2009]] ; [[#Rogelj--2012|Rogelj et al., 2012]] ) or observational constraints and attributable warming ( [[#Gillett--2013|Gillett et al., 2013]] ).

Since AR5, new studies have further expanded the evidence base for estimating the value of TCRE. These studies rely on ESMs or EMICs, observational constraints and concepts of attributable warming, or theoretically derived equations (see Table 5.7 for an overview). Several studies have endeavoured to partition the uncertainty in the value of TCRE into constituent sources. For example, TCRE can be decomposed into terms of TCR and the airborne fraction of anthropogenic CO <sub>2</sub> emissions over time ( [[#Allen--2009|Allen et al., 2009]] ; [[#Matthews--2009|Matthews et al., 2009]] ). These two terms are assessed individually (see [[#5.4|Section 5.4]] and Chapter 7, respectively) and allow the integration of evidence assessed elsewhere in the report into the assessment of TCRE ( [[#5.5.1.4|Section 5.5.1.4]] ). Further studies use a variety of methods, including analysing the outputs from CMIP5 (R.G. [[#Williams--2017|Williams et al., 2017]] b) or CMIP6 ( [[#Arora--2020|Arora et al., 2020]] ; [[#Jones--2020|Jones and Friedlingstein, 2020]] ), conducting perturbed parameter experiments with a single model ( [[#MacDougall--2017|MacDougall et al., 2017]] ), Monte-Carlo methods applied to a simple climate model ( [[#Spafford--2020|Spafford and Macdougall, 2020]] ), or observations and estimates of the contribution of CO <sub>2</sub> and non-CO <sub>2</sub> forcers ( [[#Matthews--2021|Matthews et al., 2021]] ). All of the studies agree that uncertainty in climate sensitivity – either equilibrium climate sensitivity (ECS) or transient climate response (TCR) – is among the most important contribution to uncertainty in TCRE, with uncertainty in the strength of the land carbon feedback and ocean heat uptake or ventilation having also been identified as crucial to uncertainty in TCRE (Matthews et al., 2009; [[#Gillett--2013|Gillett et al., 2013]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ; [[#MacDougall--2017|MacDougall et al., 2017]] ; R.G. [[#Williams--2017|Williams et al., 2017]] a, 2020; [[#Katavouta--2019|Katavouta et al., 2019]] ; [[#Arora--2020|Arora et al., 2020]] ; [[#Jones--2020|Jones and Friedlingstein, 2020]] ; [[#Spafford--2020|Spafford and Macdougall, 2020]] ). Finally, internal variability has been shown to affect the maximum accuracy of TCRE estimates by ±0.1°C per 1000 PgC (5–95% range; [[#Tokarska--2020|Tokarska et al., 2020]] ).

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'''Table 5.7 |''' '''Overview of results from studies estimating the transient climate response to cumulative CO''' <sub>2</sub> '''emissions (TCRE)''' . GSAT = Global mean surface air temperature increase, SAT = surface air temperature (e.g., over land only), SST = sea surface temperature, ECS = equilibrium climate sensitivity. Studies that do not isolate the CO <sub>2</sub> -induced warming contribution in their TCRE estimates are not included.

{| class="wikitable"
|-
! Study

! TCRE Range (°C per 1000 PgC)

! Notes

|-
| colspan="3"| '''Studies available at the t''' '''ime of IPCC AR5'''

|-
| [[#Matthews--2009|Matthews et al. (2009)]]

| 1–2.1

| 5–95% range; GSAT; C <sup>4</sup> MIP model range

|-
| [[#Allen--2009|Allen et al. (2009)]]

| 1.4–2.5

| 5–95% range; blended global mean SAT and SSTs (no infilling of coverage gaps); simple model

|-
| [[#Zickfeld--2009|Zickfeld et al. (2009)]]

| 1.5

| Best estimate; GSAT, EMIC

|-
| [[#Williams--2012|Williams et al. (2012)]]

| 0.8–1.9

| Range consistent with 2°C to 4.5°C ECS; GSAT

|-
| [[#Rogelj--2012|Rogelj et al. (2012)]]

| About 1–2

| 5–95% range; historical constraint on GMST increase, but other constraints on GSAT increase MAGICC model calibrated to C <sup>4</sup> MIP model range and 2°C–4.5°C ''likely'' ECS

|-
| [[#Zickfeld--2013|Zickfeld et al. (2013)]]

| 1.4–2.5; mean: 1.9

| Model range; GSAT, EMICs

|-
| [[#Eby--2013|Eby et al. (2013)]]

| 1.1–2.1; mean: 1.6

| Model range; GSAT, EMICs

|-
| [[#Gillett--2013|Gillett et al. (2013)]]

| 0.8–2.4

| Model range; GSAT, CMIP5 ESMs

|-
| [[#Gillett--2013|Gillett et al. (2013)]]

| 0.7–2.0

| 5–95% range; blended global mean SAT and SSTs; observationally constrained estimates of historical warming and emissions

|-
| IPCC AR5 M. [[#Collins--2013|]] [[#Collins--2013|Collins et al. (2013)]]

| 0.8–2.5

| Assessed ''likely'' range; multiple lines of evidence; mixed definition of global average temperature increase

|-
| colspan="3"| '''Studies published''' '''since IPCC AR5'''

|-
| [[#Tachiiri--2015|Tachiiri et al. (2015)]]

| 0.3–2.4

| 5–95% range; blended global mean SAT and SSTs; JUMP-LCM model perturbed physics ensemble (EMIC)

|-
| [[#Tachiiri--2015|Tachiiri et al. (2015)]]

| 1.1–1.7

| 5–95% range; blended global mean SAT and SSTs; observationally constrained JUMP-LCM perturbed physics ensemble

|-
| [[#Goodwin--2015|Goodwin et al. (2015)]]

| 1.1 ± 0.5

| 5–95% range; theoretically derived TCRE equation constrained by surface warming, radiative forcing, and historic ocean and land carbon uptake from IPCC AR5

|-
| [[#Millar--2017a|Millar et al. (2017a)]]

| 1.0–2.5

| 5 to 95% range; blended global mean SAT and SSTs (HadCRUT4); observationally constrained probabilistic setup of simple climate model

|-
| [[#Steinacher--2016|Steinacher and Joos (2016)]]

| 1.0–2.7; median: 1.7

| 5–95% range; GSAT, observationally constrained BERN3D-LPJ EMIC

|-
| [[#MacDougall--2017|MacDougall et al. (2017)]]

| 0.9–2.5; mean: 1.7

| 5–95% range; GSAT, emulation of 23 CMIP5 ESMs

|-
| [[#Ehlert--2017|Ehlert et al. (2017)]]

| 1.2–2.1

| Model range; GSAT, UVIC EMIC with varying ocean mixing parameters

|-
| R.G. [[#Williams--2017b|Williams et al. (2017b)]]

| 1.4–2.1; mean: 1.8

| 1-sigma range; GSAT, diagnosed from 10 CMIP5 ESMs

|-
| [[#Millar--2018|Millar and Friedlingstein (2018)]]

| 0.9–2.6; best estimate: 1.3

| 5–95% range; blended global mean SAT and SSTs ( [[#Cowtan--2014|Cowtan and Way, 2014]] ); detection attribution with observational constraints

|-
| [[#Millar--2018|Millar and Friedlingstein (2018)]]

| Best estimate: 1.5

| Blended global mean SAT and SSTs (Berkeley Earth); detection attribution with observational constraints

|-
| [[#Millar--2018|Millar and Friedlingstein (2018)]]

| Best estimate: 1.2

| Blended global mean SAT and SSTs ( [[#Cowtan--2014|Cowtan and Way, 2014]] ); detection attribution with observational constraints, with updated historical CO <sub>2</sub> emissions ( [[#Le%20Quéré--2018b|Le Quéré et al., 2018b]] )

|-
| C.J. [[#Smith--2018|]] [[#Smith--2018|Smith et al. (2018)]]

| 1.0–2.2

| 5–95% range; blended global mean SAT and SSTs ( [[#Cowtan--2014|Cowtan and Way, 2014]] ); observationally constrained probabilistic setup of simple climate model

|-
| [[#Matthews--2021|Matthews et al. (2021)]]

| 1.0–2.2; median: 1.5

| 5–95% range; blended global mean SAT and SSTs; human-induced warming ( [[#Haustein--2017|Haustein et al., 2017]] ) based on an average of three full coverage datasets; observationally constrained estimate using the current non-CO <sub>2</sub> fraction of total anthropogenic forcing

|-
| [[#Arora--2020|Arora et al. (2020)]]

| 1.3–2.4; mean: 1.8; median: 1.65

| Model range; GSAT, diagnosed CO <sub>2</sub> emissions in CMIP6 ESMs

|-
| R.G. [[#Williams--2020|]] [[#Williams--2020|Williams et al. (2020)]]

| 1.2–2.1; mean: 1.6

| 1-sigma range; GSAT, diagnosed CO <sub>2</sub> emissions in 9 CMIP6 ESMs

|-
| [[#Jones--2020|Jones and Friedlingstein (2020)]]

| 1.2–2.7; median: 1.8

| 5–95% range; GSAT; estimate based on decomposition presented in ( [[#Jones--2020|Jones and Friedlingstein, 2020]] ) with ranges of carbon cycle feedback parameters from CMIP6 ( [[#Arora--2020|Arora et al., 2020]] ), see [[#5.4|Section 5.4]] .

|-
| [[#Spafford--2020|Spafford and Macdougall (2020)]]

| 1.1–2.9; mean: 1.9; median: 1.8

| 5–95% range; ratio of land SAT and SST; probabilistic assessment of with a zero-dimensional ocean diffusive model

|-
| colspan="3"| '''Cross-AR6 li''' '''nes of evidence'''

|-
| Transient Climate Response (TCR) and Airborne Fraction (AF)

| 1.0–2.3; median: 1.6

| 5–95% range; GSAT; TCR–AF decomposition-based estimate using the assessed range of TCR ( [[IPCC:Wg1:Chapter:Chapter-7#7.5|Section 7.5]] , 1.8°C median with 0.4°C 1-sigma range) and an airborne fraction of 53 ± 6% (1-sigma range)

|-
| colspan="3"| '''Ove''' '''rall assessment'''

|-
| IPCC AR6

| 1.0–2.3; best estimate: 1.65

| ''Likely'' range; GSAT; based on combination of cross-AR6 lines of evidence ( [[#5.5.1.4|Section 5.5.1.4]] ); normally distributed

|}

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==== 5.5.1.4 Combined Assessment of TCRE ====

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Studies differ in how they define TCRE, in the methods they use, and their assumptions, such as the assumed climate sensitivity distribution or the choice of metrics of global temperature change (e.g., GMST or GSAT, see Table 5.7). This makes TCRE estimates from individual studies difficult to compare. The combined assessment of TCRE therefore takes advantage of the well-established decomposition of TCRE in two factors: the TCR and the AF ( [[#5.5.1.3|Section 5.5.1.3]] ). This provides a TCRE assessment range for CO <sub>2</sub> -induced warming at the time of doubling CO <sub>2</sub> concentrations that builds on the broader Working Group 1 assessment. Expert judgement based on the airborne fraction range found in CMIP6 models ( [[#Arora--2020|Arora et al., 2020]] ; [[#Jones--2020|Jones and Friedlingstein, 2020]] ) suggest a value of 53% with a 1-sigma range of ±6%, which is double the sigma range based on the spread of CMIP6 models only. Combining this range with the AR6 TCR assessment ( [[IPCC:Wg1:Chapter:Chapter-7#7.5|Section 7.5]] , best estimate 1.8°C, 1.4°C–2.2°C ''likely'' and 1.2°C–2.4°C ''very likely'' range) results in a 5–95% range of 1.0–2.3°C per 1000 PgC (0.27°C–0.63°C per 1000 GtCO <sub>2</sub> ). Based on expert judgement that accounts for the incomplete coverage of all Earth system components, this results in a consolidated assessment that TCRE would fall ''likely'' in the range of 1.0–2.3°C per 1000 PgC, with a best estimate of 1.65°C per 1000 PgC (0.45°C per 1000 GtCO <sub>2</sub> ). Warming here reflects the human-induced GSAT increase and assumes a normal distribution. Some studies using observational constraints support a lognormal shape for the TCRE distribution ( [[#Spafford--2020|Spafford and Macdougall, 2020]] ), but such a distribution is currently not supported by the combined assessment of TCR and airborne fraction. Finally, this assessed TCRE range needs to be considered in combination with the ZEC ( [[IPCC:Wg1:Chapter:Chapter-4#4.7.1.1|Section 4.7.1.1]] ) when estimating the CO <sub>2</sub> -induced warming of low-emissions scenarios.

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'''Cross-Chapter Box 5.3 | The Ocean Carbon–Heat Nexus and Climate Change Commitment'''

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'''Contributors:''' Pedro M.S. Monteiro (South Africa), Jean-Baptiste Sallée (France), Piers Foster (United Kingdom), Baylor Fox-Kemper (United States of America), Helen T. Hewitt (United Kingdom), Masao Ishii (Japan), Joeri Rogelj (United Kingdom/Belgium), Kirsten Zickfeld (Canada/Germany)

'''Context'''
In the past 60 years, the ocean has taken up and stored 23 ± 5% of anthropogenic carbon emissions ( ''medium confidence'' ) ( [[#5.2.1.3|Section 5.2.1.3]] ) as well as more than 90% of the heat that has accumulated in the Earth system (referred to as excess heat) since the 1970s (Sections 7.2.2, 9.2.2 and 9.2.3, and Box 7.2; [[#Frölicher--2015|Frölicher et al., 2015]] ; [[#Talley--2016|Talley et al., 2016]] ; [[#Gruber--2019b|Gruber et al., 2019b]] ; [[#Hauck--2020|Hauck et al., 2020]] ). The interplay between heat and CO <sub>2</sub> uptake by the ocean has played a major role in slowing the rate of global warming, and also provides a first order influence in determining the unique properties of a metric of the coupled climate–carbon cycle response – transient climate response to cumulative CO <sub>2</sub> emissions (TCRE) – which is critical to setting the future remaining carbon emissions budget (Sections 5.5.1.3 and 5.5.4). This role of the ocean in the uptake of heat and anthropogenic CO <sub>2</sub> and related feedbacks is what we term the ‘ocean carbon–heat nexus’. The ocean processes behind this nexus are important in shaping and understanding the near-linear relationship between cumulative CO <sub>2</sub> emissions and global warming (TCRE) as well as the uncertainties in future projections of TCRE properties ( [[#Zickfeld--2016|Zickfeld et al., 2016]] ; [[#Bronselaer--2020|Bronselaer and Zanna, 2020]] ; [[#Jones--2020|Jones and Friedlingstein, 2020]] ), its path independence ( [[#MacDougall--2017|MacDougall, 2017]] ), and the warming commitment after cessation of greenhouse gas emissions – the zero emissions commitment (ZEC; [[#5.5.2|Section 5.5.2]] ; [[#Zickfeld--2016|Zickfeld et al., 2016]] ; [[#Ehlert--2017|Ehlert and Zickfeld, 2017]] ). In this box, we assess the role of the ocean and its physical and chemical thermodynamic processes that shape these striking characteristics.

The role of the ocean in setting the coupled climate–carbon cycle response is threefold. First, the ocean and land carbon sinks together set the airborne fraction (AF) of CO <sub>2</sub> in the atmosphere, which sets the radiative forcing that drives the additional heat in the atmosphere, most of which is taken up by the ocean (Sections 7.2 and 9.2; [[#Katavouta--2019|Katavouta et al., 2019]] ; [[#Williams--2019|Williams et al., 2019]] ). the land carbon sink does not appear to play an important role in determining the linearity and path-independence of TCRE ( [[#5.5.1.1|Section 5.5.1.1]] ; [[#Goodwin--2015|Goodwin et al., 2015]] ; [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ). Second, the ocean sets the thermal response through ocean heat uptake ( [[IPCC:Wg1:Chapter:Chapter-9#9.2|Section 9.2]] ; [[#Frölicher--2015|Frölicher et al., 2015]] ; [[#Bronselaer--2020|Bronselaer and Zanna, 2020]] ). Third, there is a feedback within the ocean carbon–heat nexus as ocean warming, particularly under low or no mitigation scenarios, weakens the ocean sink of CO <sub>2</sub> , which influences the AF, and hence the radiative forcing (Box 7.1; [[#Williams--2019|Williams et al., 2019]] ). The near-linear relationship between cumulative CO <sub>2</sub> emissions and global warming (TCRE) is thought to arise, to a large extent, from the compensation between the decreasing ability of the ocean to take up heat and CO <sub>2</sub> at higher cumulative CO <sub>2</sub> emissions, pointing to similar processes that determine ocean uptake of heat and carbon ( [[#5.5.1.1|Section 5.5.1.1]] ; [[#Goodwin--2015|Goodwin et al., 2015]] ; [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#Williams--2016|Williams et al., 2016]] ; [[#Zickfeld--2016|Zickfeld et al., 2016]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ).

'''Processes that drive the ocean carbon–heat nexus and its change'''
The air–sea flux of heat and all gases across the ocean interface is driven by a common set of complex and turbulent diffusion and mixing processes that are difficult to observe (Sections 5.2.1.3 and 9.2.1.2; [[#Wanninkhof--2009|Wanninkhof et al., 2009]] ; [[#Wanninkhof--2014|Wanninkhof, 2014]] ; [[#Cronin--2019|Cronin et al., 2019]] ; [[#Watson--2020|Watson et al., 2020]] ). These processes are typically simplified into widely verified expressions that link the flux to wind stress, the solubility and the gradient across the air–sea interface ( ''medium confidence'' ). Because the ocean has a higher heat capacity than the atmosphere (the heat capacity of the upper 100 m of the ocean is about 30 times larger than the heat capacity of the atmosphere), the partitioning of heat between the atmosphere and the ocean is primarily influenced by the temperature differences between air and seawater. Similarly, the unique seawater carbonate buffering capacity enables CO <sub>2</sub> to be stored in the ocean as dissolved salts, rather than just as dissolved gas; this increases the capacity of seawater to store CO <sub>2</sub> by two orders of magnitude beyond the solubility of CO <sub>2</sub> gas and approximates the partitioning ratio of heat between the atmosphere and the ocean ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.2.1|Section 9.2.2.1]] ; [[#Zeebe--2009|Zeebe and Wolf-Gladrow, 2009]] ; [[#Bronselaer--2020|Bronselaer and Zanna, 2020]] ). The role of the biological carbon pump in influencing the ocean sink of anthropogenic carbon into the ocean interior is assessed to be minimal during the historical period, but this may change, particularly in regional contexts, by 2100 ( ''medium confidence'' ) ( [[#Laufkötter--2015|Laufkötter et al., 2015]] ; [[#Kwiatkowski--2020|Kwiatkowski et al., 2020]] ). Its role is important in the natural or pre-industrial carbon cycle ( ''medium confidence'' ) ( [[#Henson--2016|Henson et al., 2016]] ).

Under climate change, the buffering capacity of the ocean decreases (increasing Revelle Factor), which reflects a decreasing capacity for the ocean to take up additional anthropogenic CO <sub>2</sub> and store it in the dissolved inorganic carbon reservoir ( [[#Egleston--2010|Egleston et al., 2010]] ). In contrast to CO <sub>2</sub> , there is no physical limitation that would reduce the ability of surface ocean temperature to equilibrate with the atmospheric temperature. However, both carbon and heat fluxes depend on air–sea heat fluxes that in turn depend on gradients of characteristics at the air–sea interface. These gradients at the air–sea interface respond to ocean dynamics, such as the volume of the surface mixed-layer that equilibrates with the atmosphere, and ocean circulation that can flush the surface layer with water masses that have not equilibrated with the atmosphere for a long time. Limited recent evidence suggests that the effect of small-scale dynamics absent in climate and Earth system models might be locally important ( [[#Bachman--2020|Bachman and Klocker, 2020]] ). In summary, changes in heat and carbon uptake by the ocean rely on a combination of unique chemical and shared physical processes, any of which have the potential to disrupt the coherence of heat and CO <sub>2</sub> change in the ocean.

'''Spatial pattern of air–sea fluxes and storage'''
Large-scale regional and global ocean circulation shape the spatial pattern of the uptake and storage of both CO <sub>2</sub> and heat (see Figure 5.8 for carbon; Figure 9.6 for heat observations; [[IPCC:Wg1:Chapter:Chapter-9#9.2|Section 9.2]] ; [[#Frölicher--2015|Frölicher et al., 2015]] ; [[#Bronselaer--2020|Bronselaer and Zanna, 2020]] ). This coherence of spatial patterns driven by the large-scale ocean circulation has three aspects. First, notwithstanding interannual-decadal variability in heat and CO <sub>2</sub> uptake, there is a spatial coherence of the temporally integrated uptake at the air–sea boundary, particularly in the Southern Ocean (Cross-Chapter Box 5.3, Figure 1; [[#Talley--2016|Talley et al., 2016]] ; [[#Keppler--2019|Keppler and Landschützer, 2019]] ; [[#Auger--2021|Auger et al., 2021]] ). Second, the importance of the meridional overturning circulation in the subsequent storage of both heat and CO <sub>2</sub> in mode, intermediate and deep waters of the ocean interior ( [[IPCC:Wg1:Chapter:Chapter-9#9.2|Section 9.2]] ). Third, of particular note, the roles of the North Atlantic Ocean ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.3.1|Section 9.2.3.1]] ) and the Southern Ocean ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.3.2|Section 9.2.3.2]] ) in linking the spatial pattern of air–sea fluxes, the storage of heat and carbon, and ultimately in understanding and predicting the sensitivity of the carbon-heat nexus to climate change ( [[#Frölicher--2015|Frölicher et al., 2015]] ; [[#Thomas--2018|Thomas et al., 2018]] ; [[#Wu--2019|Wu et al., 2019]] ).

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[[File:ef5d8d921b5a54a76f265843b8749cce IPCC_AR6_WGI_CCBox_5_3_Figure_1.png]]

'''Cross-Chapter Box 5.3, Figure 1 |'''

'''CMIP6 multi-model mean of changes in zonally integrated (a) heat and (b) carbon storage in the ocean''' '''between the pre-industrial and the modern period''' . Carbon corresponds to dissolved in organic carbon. Data are shown for the upper 2000 m. The modern period is 1995–2014. Adapted from [[#Frölicher--2015|Frölicher et al. (2015)]] .

The role of the large-scale circulation in shaping these fluxes is to: (i) flush the ocean surface layer with deep waters that are relatively cold and with weak or no anthropogenic CO <sub>2</sub> and heat content because they have been isolated from the atmosphere for centuries; and (ii) transport the anthropogenic CO <sub>2</sub> and heat at depth, away from the atmosphere ( [[#Frölicher--2015|Frölicher et al., 2015]] ; [[#Marshall--2015|Marshall et al., 2015]] ; [[#Armour--2016|Armour et al., 2016]] ). For instance, in the Southern Ocean, upwelled water masses take up a large amount of anthropogenic CO <sub>2</sub> and heat (Cross-Chapter Box 5.3, Figure 1), which are then exported northward by the circulation to be stored at depth in the Southern Hemisphere subtropical gyres (Cross-Chapter Box 5.3, Figure 1; Figure 9.7). In the North Atlantic, the signature of the Atlantic meridional overturning circulation (AMOC) is also clearly visible, with large amounts of heat and carbon being stored beneath the North Atlantic subtropical gyre at 1 km depth (Cross-Chapter Box 5.3, Figure 1). In summary, the net air–sea fluxes of anthropogenic CO <sub>2</sub> and heat depend on large-scale circulation, which is associated with upper ocean stratification, mixed-layer depth, and water-mass formation, transport and mixing (Sections 9.1–9.3).

'''Changes in ocean processes and impact on the ocean carbon–heat nexus'''
Future projections of the ocean carbon–heat nexus in the second half of the 21st century, particularly those under weak or no mitigation scenarios, are characterized by the strengthening of the two largest positive feedbacks: weakening surface ocean CO <sub>2</sub> buffering capacity (increasing Revelle Factor) and warming that further reduces CO <sub>2</sub> solubility and strengthens ocean stratification, which reduces exchange between the ocean surface and interior ( [[#Jiang--2019|Jiang et al., 2019]] ; [[#Bronselaer--2020|Bronselaer and Zanna, 2020]] ). These are offset by a growing but scenario-dependent negative feedback from increasing carbon and heat air–sea fluxes towards the ocean, due to increased atmospheric temperature and CO <sub>2</sub> concentrations ( [[#Talley--2016|Talley et al., 2016]] ; [[#Jiang--2019|Jiang et al., 2019]] ; [[#McKinley--2020|McKinley et al., 2020]] ). The Southern Ocean in particular is one of the regions where the projected feedback can be largest and where inter-model differences are strongest ( [[#Roy--2011|Roy et al., 2011]] ; [[#Frölicher--2015|Frölicher et al., 2015]] ; [[#Hewitt--2016|Hewitt et al., 2016]] ; [[#Mongwe--2018|Mongwe et al., 2018]] ). These projected trends in ocean carbonate chemistry ( [[#5.4.2|Section 5.4.2]] ), together with surface ocean warming ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.1.1|Section 9.2.1.1]] ), explain the slow down and long-term reduction of the ocean sink for anthropogenic CO <sub>2</sub> even as emissions continue to rise beyond 2050 under weak-to-no-mitigation scenarios (Figures 2.7.1 and 5.25, and Technical Summary TS Box 7). Projected change in the North Atlantic and Southern Ocean overturning circulation also impact air–sea fluxes of heat and carbon. The ''very likely'' decline in AMOC in the 21st century for all shared socio-economic pathways (SSP) scenarios ( [[IPCC:Wg1:Chapter:Chapter-9#9.2.3.1|Section 9.2.3.1]] ) tends to reduce heat and carbon uptake, resulting in a positive feedback. In contrast, in the Southern Ocean, the future 21st century projected increase in upper ocean overturning circulation ( ''low confidence'' ) – due to increasing wind forcing projected for all scenarios, except those with large mitigation (SSP1-2.6) – produces a negative feedback, with increasing heat and carbon uptake and storage despite the increasing stratification and outgassing of natural CO <sub>2</sub> in the upwelling zone (Sections 9.2.3.2 and 5.2.1.3).

In summary, a combination of unique chemical properties of seawater carbonate combined with shared physical ocean processes explain the coherence and scaling in the uptake and storage of both CO <sub>2</sub> and heat in the ocean, which is the basis for the carbon–heat nexus ( ''high confidence'' ). In this way, the processes of the ocean carbon-heat nexus help understand the quasi-linear and path independence of properties of TCRE, which forms the basis for the zero emissions commitment (ZEC; [[#5.5|Section 5.5]] ) ( ''medium confidence'' ). Future projections under low or no mitigation indicate with ''high confidence'' that carbon chemistry and warming will strengthen the positive feedback to climate change by reducing ocean carbon uptake, and ''medium confidence'' that ocean circulation may partially compensate that positive feedback by slightly increasing anthropogenic carbon storage. Increasing ocean warming and stratification may decrease exchanges between the surface and subsurface ocean, which could reduce the path independence of TCRE, though this effect can be partially counterbalanced regionally by increasing circulation associated with increasing winds ( ''l'' ''ow confidence'' ).

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