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

== 5.5 Remaining Carbon Budgets ==

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Science at the time of AR5 established a near-linear relationship between cumulative emissions of CO <sub>2</sub> and the resulting global warming ( [[#Allen--2009|Allen et al., 2009]] ; [[#Matthews--2009|Matthews et al., 2009]] ; [[#Meinshausen--2009|Meinshausen et al., 2009]] ; [[#Zickfeld--2009|Zickfeld et al., 2009]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ). The amount of global warming per unit of cumulated carbon dioxide emissions is called the transient climate response to cumulative CO <sub>2</sub> emissions (TCRE). This TCRE relationship is now used to estimate the amount of CO <sub>2</sub> emissions that would be consistent with limiting global warming to specific levels ( [[#Allen--2009|Allen et al., 2009]] ; [[#Matthews--2009|Matthews et al., 2009]] , 2012; [[#Meinshausen--2009|Meinshausen et al., 2009]] ; [[#Zickfeld--2009|Zickfeld et al., 2009]] ; M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ; [[#Knutti--2015|Knutti and Rogelj, 2015]] ; [[#Rogelj--2016|Rogelj et al., 2016]] , 2019; [[#Goodwin--2018|Goodwin et al., 2018]] ). The remainder of CO <sub>2</sub> emissions that would be in line with limiting global warming to a specific temperature level (while accounting for all other factors affecting global warming) can be estimated with the help of the TCRE and is referred to as the remaining carbon budget ( [[#Rogelj--2019|Rogelj et al., 2019]] ; [[#Matthews--2020|Matthews et al., 2020]] ). [[#5.5.1|Section 5.5.1]] first assesses the TCRE as one of the core concepts underlying the notion of a remaining carbon budget, and [[#5.5.2|Section 5.5.2]] then integrates this with other contributing factors from across this assessment to provide a consolidated assessment following the approach of the Special Report on Global Warming of 1.5°C (SR1.5) ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ). The historical carbon budget of CO <sub>2</sub> already emitted is assessed in [[#5.2.1.5|Section 5.2.1.5]] .

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<span id="transient-climate-response-to-cumulative-emissions-of-carbon-dioxide-tcre"></span>
=== 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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<span id="combined-assessment-of-tcre"></span>
==== 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.

<div id="cross-chapter-box-5.3" class="h2-container box-container mb-3"></div>

'''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'' ).

<div id="5.5.2" class="h2-container"></div>

<span id="remaining-carbon-budget-assessment"></span>
=== 5.5.2 Remaining Carbon Budget Assessment ===

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Estimates of remaining carbon budgets consistent with holding global warming below a specific temperature threshold depend on a range of factors which are increasingly being studied and quantified. These factors include: (i) well-understood methodological and definitional choices (Sections 5.5.2.1 and 5.5.2.2; [[#Friedlingstein--2014a|Friedlingstein et al., 2014a]] ; [[#Rogelj--2016|Rogelj et al., 2016]] , 2018b); and (ii) a set of contributing factors such as historical warming, the TCRE and its limitations, the ZEC (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]] ), as well as contributions of non-CO <sub>2</sub> climate forcers ( [[#5.5.2.2|Section 5.5.2.2]] ; [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#Rogelj--2015a|Rogelj et al., 2015a]] , b; [[#MacDougall--2016|MacDougall, 2016]] ; [[#Simmons--2016|Simmons and Matthews, 2016]] ; [[#Ehlert--2017|Ehlert et al., 2017]] ; [[#Matthews--2017|Matthews et al., 2017]] , 2021; [[#Millar--2017b|Millar et al., 2017b]] ; [[#Goodwin--2018|Goodwin et al., 2018]] ; [[#Mengis--2018|Mengis et al., 2018]] ; [[#Pfleiderer--2018|Pfleiderer et al., 2018]] ; [[#Tokarska--2018|Tokarska et al., 2018]] ; [[#Cain--2019|Cain et al., 2019]] ). These contributing factors are integrated in an overarching assessment of remaining carbon budgets for limiting global average warming to levels ranging from 1.5°C to 2.5°C relative to pre-industrial levels provided in [[#5.5.2.3|Section 5.5.2.3]] . Box 5.2 provides an overview of the methodological advances since AR5 (W.J. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ).

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<span id="framework-and-earlier-approaches"></span>
==== 5.5.2.1 Framework and Earlier Approaches ====

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The AR6 Glossary (Annex VII) defines remaining carbon budgets as the maximum amount of cumulative net global anthropogenic CO <sub>2</sub> emissions expressed from a recent specified date that would result in limiting global warming to a given level with a given probability, taking into account the effect of other anthropogenic climate forcers, consistent with the definition used inSR1.5 ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ). Studies, however, apply a variety of definitions that result in published remaining carbon budget estimates informing to cumulative emissions at the time when global-mean temperature increase would reach, exceed, avoid, or peak at a given warming level with a given probability (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ; [[#Clarke--2014|Clarke et al., 2014]] ; [[#Friedlingstein--2014a|Friedlingstein et al., 2014a]] ; [[#IPCC--2014|IPCC, 2014]] ; [[#Rogelj--2016|Rogelj et al., 2016]] ; [[#Millar--2017b|Millar et al., 2017b]] ).

This section provides an assessment of remaining carbon budgets consistent with the AR6 Glossary definition (Annex VII). Given that some feedbacks are time dependent, the values in this section apply to limiting warming over the 21st century, consistent with recent studies highlighting the usefulness of time-limited carbon budgets ( [[#Sanderson--2020|Sanderson, 2020]] ). Irrespective of the exact definition of the remaining carbon budget, the finding that higher cumulative CO <sub>2</sub> emissions lead to higher temperatures implies that annual net CO <sub>2</sub> emissions have to decline to close to zero in order to halt global warming, whether at 1.5°C, 2°C or another level ( [[#Allen--2018|Allen et al., 2018]] ).

Two approaches were used in AR5 to determine carbon budgets (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ; [[#Clarke--2014|Clarke et al., 2014]] ; [[#IPCC--2014|IPCC, 2014]] ; [[#Rogelj--2016|Rogelj et al., 2016]] ). Working Group I (WGI) reported threshold exceedance budgets (TEB) that correspond to the amount of cumulative CO <sub>2</sub> emissions at the time a specific temperature threshold is exceeded, with a given probability in a particular greenhouse-gas and aerosol (pre-cursor) emissions scenario (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; [[#IPCC--2013b|IPCC, 2013b]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ). WGI also reported TEBs for the hypothetical case that only CO <sub>2</sub> would be emitted by human activities (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; [[#IPCC--2013b|IPCC, 2013b]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ). The AR5 Working Group III used threshold avoidance budgets (TAB) that correspond to the cumulative CO <sub>2</sub> emissions over a given time period of a subset of greenhouse-gas and aerosol (precursor) emissions scenarios in which global-mean temperature increase stays below a specific temperature threshold with at least a given probability ( [[#Clarke--2014|Clarke et al., 2014]] ). The AR5 synthesis report used TABs defined until the time of peak warming over the 21st century ( [[#IPCC--2014|IPCC, 2014]] ). Drawbacks have been identified for TEBs and TABs ( [[#Rogelj--2016|Rogelj et al., 2016]] ). TABs provide an estimate of the cumulative CO <sub>2</sub> emissions under pathways that have as a common characteristic the fact that they do not exceed a specific global warming threshold. However, the actual level of maximum warming can vary between pathways, leading to an unnecessary and poorly constrained spread in TAB estimates ( [[#Rogelj--2016|Rogelj et al., 2016]] ). Therefore, the TAB approach typically does not result in accurate projections of the remaining carbon budget. One drawback of TEBs is that they provide an estimate of the cumulative CO <sub>2</sub> emissions at the time global warming crosses a given threshold of interest in a specific emissions scenario – for example, most of the standard scenarios used in climate change research, such as the Representative Concentration Pathways (RCPs) or Shared Socio-economic Pathways (SSPs), exceed global warming of 1.5°C or 2°C (see Cross-Chapter Box 1.5) (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ; [[#Friedlingstein--2014a|Friedlingstein et al., 2014a]] ; [[#Millar--2017b|Millar et al., 2017b]] ). Because of potential variations in non-CO <sub>2</sub> warming at that point in time, or potential lags of about a decade in CO <sub>2</sub> warming ( [[#Joos--2013|Joos et al., 2013]] ; [[#Ricke--2014|Ricke and Caldeira, 2014]] ; [[#Rogelj--2015a|Rogelj et al., 2015a]] , 2016, 2018b; [[#Zickfeld--2015|Zickfeld and Herrington, 2015]] ) TEBs also do not provide a precise estimate of the remaining carbon budget for limiting warming to a specific level.

Since the publication of AR5 (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ), several new approaches have been proposed that provide a solution to the identified limitations of TABs and TEBs. Most of these approaches indirectly rely on the concept of TCRE ( [[#5.5.1|Section 5.5.1]] ), for example, because they estimate modelled cumulative CO <sub>2</sub> emissions until a temperature threshold is crossed and use this budget to infer insights for pathways that attempt to limit warming to below this threshold and thus need to follow a different path ( [[#Friedlingstein--2014a|Friedlingstein et al., 2014a]] ; [[#Matthews--2017|Matthews et al., 2017]] ; [[#Millar--2017b|Millar et al., 2017b]] ; [[#Goodwin--2018|Goodwin et al., 2018]] ; [[#Tokarska--2018|Tokarska and Gillett, 2018]] ). In this report, the assessment framework of SR1.5 for remaining carbon budgets is applied ( [[#Rogelj--2018b|Rogelj et al., 2018b]] , 2019). This framework allows integration of multiple lines of evidence to assess the contributions of five components that together result in a consolidated assessment of the remaining carbon budget (TCRE, historical human-induced warming, non-CO <sub>2</sub> warming, the ZEC, and adjustments due to additional Earth system feedbacks, see [[#5.5.2.2|Section 5.5.2.2]] ). It builds on the advances in estimating remaining carbon budgets or related quantities that have been published since AR5 ( [[#Rogelj--2015a|Rogelj et al., 2015a]] ; [[#Haustein--2017|Haustein et al., 2017]] ; [[#Matthews--2017|Matthews et al., 2017]] , 2021; [[#Millar--2017b|Millar et al., 2017b]] ; [[#Gasser--2018|Gasser et al., 2018]] ; [[#Lowe--2018|Lowe and Bernie, 2018]] ; [[#Tokarska--2018|Tokarska et al., 2018]] ; [[#Nicholls--2020|Nicholls et al., 2020]] ).

Recent studies suggest further changes to this framework by including non-linear adjustments to the TCRE contribution ( [[#Nicholls--2020|Nicholls et al., 2020]] ), or including non-CO <sub>2</sub> forcers in different ways by accounting for their different forcing effects ( [[#Matthews--2021|Matthews et al., 2021]] ). Figure 5.31 provides a conceptual schematic of how the various individually assessed contributions are combined into a consolidated assessment of the remaining carbon budget. Together with estimates of historical CO <sub>2</sub> emissions to date ( [[#5.2.1|Section 5.2.1]] ), these remaining carbon budgets provide the overall amount of cumulative CO <sub>2</sub> emissions consistent with limiting global warming to specific levels. A comparison with the approach applied in AR5 (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; [[#Clarke--2014|Clarke et al., 2014]] ) is available in SR1.5 [[IPCC:Wg1:Chapter:Chapter-2#2.2.2|Section 2.2.2]] ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ) as well as Box 5.2.

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[[File:fd897abc34bb54789178645dac08d60e IPCC_AR6_WGI_Figure_5_31.png]]

'''Figure 5.31 |''' '''Illustration of relationship between cumulative emissions of carbon dioxide (CO''' <sub>2</sub> ''') and global mean surface air temperature (GSAT) increase (left) and conceptual schematic of the assessment of the remaining carbon budget from its constituting components (right).''' Carbon budgets consistent with various levels of additional warming are provided in Table 5.8 and should not be read from the illustrations in either panel. Left-hand panel: Historical data (thin black line data) shows historical CO <sub>2</sub> emissions as reported in [[#Friedlingstein--2020|Friedlingstein et al. (2020)]] together with the assessed global mean surface air temperature increase from 1850–1900 as assessed in [[IPCC:Wg1:Chapter:Chapter-2|Chapter 2]] (Box 2.3, GSAT). The orange-brown range with its central line shows the estimated human-induced share of historical warming ( [[#Haustein--2017|Haustein et al., 2017]] ). The vertical orange-brown line shows the assessed range of historical human-induced warming for the 2010–2019 period relative to 1850–1900 (Chapter 3). The grey cone shows the assessed range for the transient climate response to cumulative CO <sub>2</sub> emissions (TCRE) assessed to fall ''likely'' in the 1.0°C–2.3°C per 1000 PgC range ( [[#5.5.1.4|Section 5.5.1.4]] ), starting from 2015. Thin coloured lines show CMIP6 simulations for the five scenarios of the AR6 core set (SSP1-1.9, sky blue; SSP1-2.6, dark blue; SSP2-4.5, yellow; SSP3-7.0, red; SSP5-8.5, maroon), starting from 2015. Diagnosed carbon emissions ( [[#Arora--2020|Arora et al., 2020]] ) are complemented with estimated land-use change emissions for each respective scenario ( [[#Gidden--2019|Gidden et al., 2019]] ). Coloured areas show the [[IPCC:Wg1:Chapter:Chapter-4|Chapter 4]] assessed ''very likely'' range of GSAT projections and thick coloured central lines the median estimate, for each respective scenario. These projections are expressed relative to the cumulative CO <sub>2</sub> emissions that are available for emissions-driven CMIP6 ScenarioMIP experiments for each respective scenario ( [[#Riahi--2017|Riahi et al., 2017]] ; [[#Rogelj--2018a|Rogelj et al., 2018a]] ; [[#Gidden--2019|Gidden et al., 2019]] ). Right-hand panel: schematic illustration of assessment of remaining carbon budget based on multiple lines of evidence. The remaining allowable warming is estimated by combining the global warming limit of interest with the assessed historical human induced warming ( [[#5.5.2.2.2|Section 5.5.2.2.2]] ), the assessed future potential non-CO <sub>2</sub> warming contribution ( [[#5.5.2.2.3|Section 5.5.2.2.3]] ) and the zero emissions commitment ( [[#5.5.2.2.4|Section 5.5.2.2.4]] ). Note that contributions in the right-hand panel are illustrative and contributions are not to scale. For example, the central ZEC estimate was assessed to be zero. The remaining allowable warming (vertical blue bar) is subsequently combined with the assessed TCRE (Sections 5.5.1.4 and 5.5.2.2.1) and contribution of unrepresented Earth system feedbacks in models used to estimate ZEC and TCRE ( [[#5.5.2.2.5|Section 5.5.2.2.5]] ) to provide an assessed estimate of the remaining carbon budget (horizontal blue bar; see Table 5.8). Further details on data sources and processing are available in the chapter data table (Table 5.SM.6).

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<span id="assessment-of-individual-components"></span>
==== 5.5.2.2 Assessment of Individual Components ====

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Remaining carbon budgets are assessed through the combination of five separate components ( [[#Forster--2018|Forster et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ). Each component is discussed and assessed separately in the sections below, based on all available lines of evidence. Box 5.1 details the differences compared to AR5 and SR1.5 estimates(W.J. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ).

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<span id="tcre"></span>
===== 5.5.2.2.1 TCRE =====

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The first and central component for estimating remaining carbon budgets is the TCRE. Based on the assessment in [[#5.5.1.4|Section 5.5.1.4]] , an assessed ''likely'' range for TCRE of 1.0°C–2.3°C per 1000 PgC with a normal distribution is used.

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<span id="historical-warming"></span>
===== 5.5.2.2.2 Historical warming =====

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Advances in methods to estimate remaining carbon budgets have shown the importance of applying an estimate of historical warming to date that is as accurate as possible ( [[#Millar--2017b|Millar et al., 2017b]] ; [[#Tokarska--2018|Tokarska and Gillett, 2018]] ). This becomes particularly important when assessing remaining carbon budgets for global warming levels that are relatively close to present-day warming, such as a 1.5°C or 2°C levels ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ). Also shown to be important is the definition of global average temperature by which historical warming is estimated (Cross-Chapter Box 2.3; [[#Cowtan--2014|Cowtan and Way, 2014]] ; [[#Allen--2018|Allen et al., 2018]] ; [[#Pfleiderer--2018|Pfleiderer et al., 2018]] ; [[#Richardson--2018|Richardson et al., 2018]] ; [[#Tokarska--2019b|Tokarska et al., 2019b]] ), as is the correct isolation of human-induced global warming ( [[#Haustein--2017|Haustein et al., 2017]] ; [[#Allen--2018|Allen et al., 2018]] ) to remove the effect of internal variability. Based on the assessment in [[IPCC:Wg1:Chapter:Chapter-3#3.3|Section 3.3]] (Table 3.1), here we apply an assessedbest-estimate of historical warming expressed as an increase in GSAT of 1.07°C (0.8–1.3°C, ''likely'' range) between 1850–1900 and 2010–2019. This choice implies global coverage and is consistent with AR5 where carbon budgets were reported in GSAT (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ), SR1.5 where GSAT was the central metric for remaining carbon budgets ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ), and recent studies that highlight how GSAT enables an easy translation with AR5 ( [[#Tokarska--2019b|Tokarska et al., 2019b]] ). The use of other historical reference periods (Cross-Chapter Box 1.2) or temperature metrics and updated data products (Cross-Chapter Box 2.3) can result in a different estimated historical warming and thus a changed remaining carbon budget.

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<span id="non-co-2-warming-contribution"></span>
===== 5.5.2.2.3 Non-CO <sub>2</sub> warming contribution =====

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Non-CO <sub>2</sub> emissions contribute either cumulatively (N <sub>2</sub> O, and other long-lived climate forcers) or in proportion to their annual emissions (CH <sub>4</sub> and other short-lived climate forcers) to global warming, and thus also affect estimates of remaining carbon budgets by reducing the amount of warming that could still result from CO <sub>2</sub> emissions ( [[#Meinshausen--2009|Meinshausen et al., 2009]] ; [[#Friedlingstein--2014a|Friedlingstein et al., 2014a]] ; [[#Knutti--2015|Knutti and Rogelj, 2015]] ; [[#Rogelj--2015a|Rogelj et al., 2015a]] , 2016; R.G. [[#Williams--2016|Williams et al., 2016]] , 2017b; [[#Matthews--2017|Matthews et al., 2017]] ; [[#Collins--2018|Collins et al., 2018]] ; [[#Mengis--2018|Mengis et al., 2018]] ; [[#Tokarska--2018|Tokarska et al., 2018]] ; [[#Zickfeld--2021|Zickfeld et al., 2021]] ). The size of this contribution has been estimated both implicitly ( [[#Meinshausen--2009|Meinshausen et al., 2009]] ; [[#Friedlingstein--2014a|Friedlingstein et al., 2014a]] ; [[#Rogelj--2016|Rogelj et al., 2016]] ; [[#Matthews--2017|Matthews et al., 2017]] ; [[#Mengis--2018|Mengis et al., 2018]] ; [[#Tokarska--2018|Tokarska et al., 2018]] ) and explicitly ( [[#Rogelj--2015a|Rogelj et al., 2015a]] , 2018b; [[#Collins--2018|Collins et al., 2018]] ; [[#Matthews--2021|Matthews et al., 2021]] ) by varying the assumptions of non-CO <sub>2</sub> emissions and associated warming. Internally consistent evolutions of future CO <sub>2</sub> and non-CO <sub>2</sub> emissions allow for derivation of non-CO <sub>2</sub> warming contributions consistent with global CO <sub>2</sub> emissions reaching net zero levels, and therewith capping maximum future CO <sub>2</sub> emissions ( [[#Smith--2013|Smith and Mizrahi, 2013]] ; [[#Clarke--2014|Clarke et al., 2014]] ; [[#Huppmann--2018|Huppmann et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ; [[#Matthews--2021|Matthews et al., 2021]] ). Pathways that reflect such development typically show a stabilization or decline in non-CO <sub>2</sub> radiative forcing and warming at, and after the time of, global CO <sub>2</sub> emissions reaching net zero levels, as illustrated in the scenario database underlying SR1.5 ( [[#Huppmann--2018|Huppmann et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ).

The impact of non-CO <sub>2</sub> emissions on remaining carbon budgets is assessed with emulators ( [[#Meinshausen--2009|Meinshausen et al., 2009]] ; [[#Millar--2017b|Millar et al., 2017b]] ; [[#Gasser--2018|Gasser et al., 2018]] ; [[#Goodwin--2018|Goodwin et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ; C.J. [[#Smith--2018|]] [[#Smith--2018|Smith et al., 2018]] ; [[#Matthews--2021|Matthews et al., 2021]] ) that incorporate synthesized climate and carbon-cycle knowledge (Cross-Chapter Box 7.1). The estimated implied non-CO <sub>2</sub> warming can subsequently be applied to reduce the remaining allowable warming for estimating the remaining carbon budget (Figure 5.31; [[#Rogelj--2018b|Rogelj et al., 2018b]] , 2019). Alternative methods estimate the non-CO <sub>2</sub> fraction of total anthropogenic forcing ( [[#Matthews--2021|Matthews et al., 2021]] ), or do not correct for non-CO <sub>2</sub> warming directly. The latter methods instead consider CO <sub>2</sub> and non-CO <sub>2</sub> warming together to define a CO <sub>2</sub> -forcing equivalent carbon budget from which eventual non-CO <sub>2</sub> contributions expressed in CO <sub>2</sub> -forcing-equivalent emissions have to be subtracted to obtain a remaining carbon budget ( [[#Jenkins--2018|Jenkins et al., 2018]] ; [[#Matthews--2020|Matthews et al., 2020]] ). These studies also use emulators to invert a specified evolution of non-CO <sub>2</sub> forcing to a corresponding amount of equivalent CO <sub>2</sub> emissions ( [[#Matthews--2020|Matthews et al., 2020]] ), or alternatively use empirical relationships linking changes in non-CO <sub>2</sub> greenhouse gas emissions to warming ( [[#Cain--2019|Cain et al., 2019]] ). Methods to express non-CO <sub>2</sub> emissions in CO <sub>2</sub> equivalence are assessed in [[IPCC:Wg1:Chapter:Chapter-7#7.6|Section 7.6]] , yet their applicability and related uncertainties for remaining carbon budgets have not yet been covered in-depth in the literature.

Application of the SR1.5 method ( [[#Forster--2018|Forster et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ) with AR6-calibrated emulators (Box 7.1) suggests a median additional non-CO <sub>2</sub> warming contribution at the time global CO <sub>2</sub> emissions reach net zero levels of about 0.1°C–0.2°C relative to 2010–2019. Uncertainty surrounding this range due to geophysical uncertainties such as non-CO <sub>2</sub> -forcing uncertainties and TCR is of the order of ±0.1°C. Differences in the choices of mitigation strategies considered in low-emissions scenarios ( [[#Huppmann--2018|Huppmann et al., 2018]] ) result in a potential additional variation around the central range of at least ±0.1°C (spread across scenarios, referred to as non-CO <sub>2</sub> scenario uncertainty in Table 5.8).

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'''Table 5.8 |''' '''The assessed remaining carbon budget and corresponding uncertainties''' . Assessed estimates are provided for additional human-induced warming expressed as global average surface air temperature since the recent past (2010–2019), which ''likely'' amounted to 0.8 to 1.3 with a best estimate of 1.07°C relative to 1850–1900 (Table 3.1 in Chapter 3).

{| class="wikitable"
|-
! Additional Warming Since 2010–2019 <sup>a</sup>

! Warming Since 1850–1900 <sup>a</sup>

! colspan="5"| Remaining Carbon Budget <sup>b</sup> starting from 1 January 2020 and subject to variations and uncertainties quantified in the columns on the right

! Scenario Variation

! colspan="4"| Geophysical Uncertainties

|-
| ''°C''

| ''°C''

| colspan="5"| Percentiles of TCRE <sup>c,d</sup> ''PgC (GtCO'' 2 '')''

| Non-CO <sub>2</sub> scenario variation <sup>e</sup>

| Non-CO <sub>2</sub> forcing and response uncertainty <sup>f</sup>

| Historical temperature uncertainty <sup>a</sup>

| Zero emissions commitment (ZEC)uncertainty <sup>g</sup>

| Recent emissions uncertainty <sup>h</sup>

|-
|
| ''17th''

| ''33rd''

| ''50th''

| ''67th''

| ''83rd''

| ''PgC (GtCO'' 2 '')''

| ''PgC (GtCO'' 2 '')''

| ''PgC (GtCO'' 2 '')''

| ''PgC (GtCO'' 2 '')''

| ''PgC (GtCO'' 2 '')''

|-
| 0.23

| 1.3

| ''100 (400)''

| ''60 (250)''

| ''40 (150)''

| ''30 (100)''

| ''10 (50)''

| rowspan="12"| Values can vary by at least ±60 PgC (±220 GtCO <sub>2</sub> ) due to choices related to non-CO <sub>2</sub> emissions mitigation

| rowspan="12"| Values can vary by at least ±60 PgC (±220 GtCO <sub>2</sub> ) due to uncertainty in the warming reponse to future non-CO <sub>2</sub> emissions

| rowspan="12"| ±150 PgC (±550 GtCO <sub>2</sub> )

| rowspan="12"| ±115 PgC (±420 GtCO <sub>2</sub> )

| rowspan="12"| ±6 PgC (±20 GtCO <sub>2</sub> )

|-
| 0.33

| 1.4

| ''180 (650)''

| ''120 (450)''

| ''90 (350)''

| ''70 (250)''

| ''50 (200)''

|-
| 0.43

| 1.5

| ''250 (900)''

| ''180 (650)''

| ''140 (500)''

| ''110 (400)''

| ''80 (300)''

|-
| 0.53

| 1.6

| ''330 (1200)''

| ''230 (850)''

| ''180 (650)''

| ''150 (550)''

| ''110 (400)''

|-
| 0.63

| 1.7

| ''400 (1450)''

| ''290 ('' ''1050'' '')''

| ''230 (850)''

| ''190 (700)''

| ''150 (550)''

|-
| 0.73

| 1.8

| ''470 (1750)''

| ''350 (1250)''

| ''280 (1000)''

| ''230 (850)''

| ''180 (650)''

|-
| 0.83

| 1.9

| ''550 (2000)''

| ''400 (1450)''

| ''320 ('' ''1200'' '')''

| ''270 (1000)''

| ''210 (800)''

|-
| 0.93

| 2

| ''620 (2300)''

| ''460 (1700)''

| ''370 ('' ''1350'' '')''

| ''310 (1150)''

| ''250 (900)''

|-
| 1.03

| 2.1

| ''700 (2550)''

| ''510 (1900)''

| ''420 ('' ''1500'' '')''

| ''350 (1250)''

| ''280 ('' ''1050'' '')''

|-
| 1.13

| 2.2

| ''770 (2850)''

| ''570 (2100)''

| ''460 ('' ''1700'' '')''

| ''390 (1400)''

| ''310 (1150)''

|-
| 1.23

| 2.3

| ''850 (3100)''

| ''630 (2300)''

| ''510 ('' ''1850'' '')''

| ''430 (1550)''

| ''350 ('' ''1250'' '')''

|-
| 1.33

| 2.4

| ''920 (3350)''

| ''680 (2500)''

| ''550 (2050)''

| ''470 (1700)''

| ''380 ('' ''1400'' '')''

|}

<sup>a</sup> Human-induced global surface air temperature increase between 1850–1900 and 2010–2019 is assessed at 0.8–1.3°C ( ''likely'' range; Chapter 3) with a best estimate of 1.07°C. Warming reflects changes in GSAT, as TCRE and other estimates are GSAT-based. Combined with a central estimate of TCRE (1.65°C EgC <sup>–1</sup> ) the uncertainty in historical human-induced GSAT warming results in a potential variation of remaining carbon budgets of ±150 PgC or ±550 GtCO <sub>2</sub> .

<sup>b</sup> Historical CO <sub>2</sub> emissions between 1850 and 2019 have been estimated at about 655 ± 65 PgC ( ''likely'' range, or 2390 ± 240 GtCO <sub>2</sub> , see Table 5.1). Note that 57 PgC (210 GtCO <sub>2</sub> ) have been emitted from the middle of the 2010–2019 reference period (2015) until the end of 2019 ( [[#Friedlingstein--2020|Friedlingstein et al., 2020]] ).

<sup>c</sup> TCRE: transient climate response to cumulative CO <sub>2</sub> emissions, assessed to fall ''likely'' between 1.0–2.3°C EgC <sup>–1</sup> with a normal distribution. PgC values are rounded to the nearest 10; GtCO <sub>2</sub> values to the nearest 50. For comparison, assuming a lognormal distribution with a 1.0–2.3°C EgC <sup>–1</sup> central 66% range instead of a normal distribution would increase remaining carbon budgets at the 17th, 33rd, 50th, 67th, and 83rd percentile with 3%, 10%, 12%, 9%, 2%, respectively. Future non-CO <sub>2</sub> contributions in these remaining carbon budget estimates are based on the scenarios assessed in the SR1.5 report and estimated as the median quantile regression of non-CO <sub>2</sub> warming since 2010–2019 relative to total additional warming since 2010–2019 at the time scenarios reach net-zero CO <sub>2</sub> emissions ( [[#Forster--2018|Forster et al., 2018]] ; [[#Huppmann--2018|Huppmann et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ).

<sup>d</sup> Additional Earth system feedbacks are included in the remaining carbon budget estimates as discussed in [[#5.5.2.2.5|Section 5.5.2.2.5]] . The tropospheric ozone and methane lifetime contributions are included through the non-CO <sub>2</sub> warming projections by the AR6-calibrated Model for the Assessment of Greenhouse Gas Induced Climate Change (MAGICC) emulator, while the remaining feedbacks are assessed totalling a combined feedback of magnitude 7 ± 27 PgC K <sup>–1</sup> (1-sigma range, or 26 ± 97 GtCO <sub>2</sub> °C <sup>–1</sup> ).

<sup>e</sup> Variations due to different scenario assumptions related to the future evolution of non-CO <sub>2</sub> emissions in mitigation scenarios reaching net zero CO <sub>2</sub> emissions ( [[#Huppmann--2018|Huppmann et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ) of at least ±0.1°C (spread across scenarios). Combined with a central estimate of TCRE (1.65°C EgC <sup>–1</sup> ) this results in at least ±60 PgC or ±220 GtCO <sub>2</sub> . This spread reflects the variation in the underlying scenario ensemble but is not a formal likelihood. WGIII will re-assess the potential for non-CO <sub>2</sub> mitigation based on literature since SR1.5.

<sup>f</sup> Remaining carbon budget variation due to geophysical uncertainty in forcing and temperature response of non-CO <sub>2</sub> emissions of the order of ±0.1°C, ''very'' ''likely'' range (5–95%) of non-CO <sub>2</sub> response ( [[#5.5.2.2.3|Section 5.5.2.2.3]] ). Combined with a central estimate of TCRE (1.65°C EgC <sup>–1</sup> ) this results in at least ±60 PgC or ±220 GtCO <sub>2</sub> .

<sup>g</sup> The variation due to the ZEC is estimated for a central TCRE value of 1.65°C EgC <sup>–1</sup> and a 1-sigma ZEC range of 0.19°C. In real-world pathways, the magnitude of this effect will depend on the pace of CO <sub>2</sub> emissions reductions to net zero.

<sup>h</sup> Historical emissions uncertainty reflects the ±10% uncertainty in the historical emissions estimate since 1 January 2015.

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<span id="adjustments-due-to-the-zero-emissions-commitment"></span>
===== 5.5.2.2.4 Adjustments due to the zero emissions commitment =====

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Use of TCRE for estimating remaining carbon budgets needs to consider the zero emissions commitment (ZEC), the potential additional warming after a complete cessation of net CO <sub>2</sub> emissions. Based on the ZEC assessment presented in [[IPCC:Wg1:Chapter:Chapter-4#4.7.1.1|Section 4.7.1.1]] , the ZEC’s central value is taken to be zero with a ''likely'' range of ±0.19°C, noting that it might either increase or decrease after half a century. ZEC uncertainty is assessed for a time frame of half a century, as this most appropriately reflects the time between stringent mitigation pathways reaching net zero CO <sub>2</sub> emissions and the end of the century. For shorter time horizons, a similar central zero value applies, but with a smaller range ( [[#MacDougall--2020|MacDougall et al., 2020]] ). Experiments that ramped up and down emissions following a bell-shaped trajectory ( [[#MacDougall--2016a|MacDougall and Knutti, 2016a]] ) show that when annual CO <sub>2</sub> emissions decline to zero at a pace consistent with those currently assumed in mitigation scenarios ( [[#Huppmann--2018|Huppmann et al., 2018]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] ), the ZEC will already be realized to a large degree at the time of reaching net zero CO <sub>2</sub> emissions ( [[#MacDougall--2020|MacDougall et al., 2020]] ).

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===== 5.5.2.2.5 Adjustments for additional Earth system feedbacks =====

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( [[#5.5.1.2|Section 5.5.1.2]] highlighted recent literature describing potential impacts of Earth system feedbacks that have typically not been included in standard ESMs ( [[#MacDougall--2015|MacDougall and Friedlingstein, 2015]] ; [[#Schneider%20von%20Deimling--2015|Schneider von Deimling et al., 2015]] ; [[#Schädel--2016|Schädel et al., 2016]] ; [[#Burke--2017b|Burke et al., 2017b]] ; [[#Mahowald--2017|Mahowald et al., 2017]] ; [[#Comyn-Platt--2018|Comyn-Platt et al., 2018]] ; [[#Gasser--2018|Gasser et al., 2018]] ; [[#Lowe--2018|Lowe and Bernie, 2018]] ), the most important of which is carbon release from thawing permafrost. The SR1.5 estimated unrepresented Earth system processes to result in a reduction of remaining carbon budgets of up to 100 GtCO <sub>2</sub> over the course of this century, and more thereafter ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ). Here this assessment is updated based on the Earth system feedback assessment of ( [[#5.4.8|Section 5.4.8]] and synthesized in Figure 5.29 by applying the reverse method by [[#Gregory--2009|Gregory et al. (2009)]] .

The assessment in [[#5.4|Section 5.4]] and Box 5.1 highlights the different nature, magnitude and uncertainties surrounding additional Earth system feedback. The remaining carbon budgets reported in Table 5.8 account for these feedbacks, including corrections due to permafrost CO <sub>2</sub> and CH <sub>4</sub> feedbacks as well as those due to aerosol and atmospheric chemistry ( [[#5.4.8|Section 5.4.8]] ). Two of these additional feedbacks (tropospheric ozone and methane lifetime feedbacks) are included in the projections of non-CO <sub>2</sub> warming carried out with AR6-calibrated emulators (Box 7.1). The remainder of these independent Earth system feedbacks combine to a feedback of about 7 ± 27 PgC K <sup>–1</sup> (1-sigma range, or 26 ± 97 GtCO <sub>2</sub> °C <sup>–1</sup> ). Overall, [[#5.4.8|Section 5.4.8]] assessed there to be ''low confidence'' in the exact magnitude of these feedbacks and they represent identified additional amplifying factors that scale with additional warming, and mostly increase the challenge of limiting global warming to or below specific temperature levels.

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==== 5.5.2.3 Remaining Carbon Budget ====

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The combination of the five components assessed in Sections 5.5.2.2.1–5.5.2.2.5 allows for an overall assessment of the remaining carbon budget in line with different levels of global average warming, as documented in SR1.5 ( [[#Rogelj--2018b|Rogelj et al., 2018b]] ). The overall assessment of remaining carbon budgets (Table 5.8) reflects the uncertainty in TCRE quantification and provides estimates of the uncertainties surrounding the contributions of each of the respective further components. A formal combination of all uncertainties is not possible because they are not all independent, or because they represent choices rather than probabilistic uncertainties ( [[#Matthews--2021|Matthews et al., 2021]] ). In light of all uncertainties related to TCRE, non-CO <sub>2</sub> forcing and response, the level of non-CO <sub>2</sub> mitigation, and historical warming, there is a small probability that the remaining carbon budget for limiting warming to 1.5°C since the 1850–1900 period is effectively zero. However, applying best estimate values for all but uncertainties in Earth system feedbacks and TCRE, the remaining carbon budgets in line with the Paris Agreement are generally small yet not zero (see Table 5.8).

There is ''robust evidence'' supporting the concept of TCRE as well as ''high confidence'' in the range of historical human-induced warming. Combined with the assessed uncertainties in the Earth system’s response to non-CO <sub>2</sub> emissions and less well-established quantification of some of the effect of non-linear Earth system feedbacks, this leads to ''medium confidence'' being assigned to the assessed remaining carbon budget estimates while noting the identified and assessed uncertainties and potential variations. The reported values are applicable to warming and cumulative emissions over the 21st century. For climate stabilization beyond the 21st century, this confidence would decline to ''very low confidence'' due to uncertainties in Earth system feedbacks and the ZEC. For estimates of total carbon budgets in line with limiting global warming to a specific level, an estimate of historical CO <sub>2</sub> emissions should be added to the remaining carbon budget values reported in Table 5.8. Historical CO <sub>2</sub> emissions between 1850 and 2019 have been estimated at about 655 ± 65 PgC (1-sigma range, or 2390 ± 240 GtCO <sub>2</sub> , see Table 5.1), while since 1 January 2015, an additional 57 PgC (210 GtCO <sub>2</sub> ) has been emitted until the end of 2019 ( [[#Friedlingstein--2020|Friedlingstein et al., 2020]] ).

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'''Box 5.2 | Implications of Methodological Advancements in Estimating the Remaining Carbon Budget since the IPCC’s Fifth Assessme''' '''nt Report (AR5)'''

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Methodological advancements since AR5 (M. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; [[#IPCC--2013b|IPCC, 2013b]] , 2014; T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ; [[#Clarke--2014|Clarke et al., 2014]] ) result in an updated and strengthened assessment of remaining carbon budgets. Methods and approaches at the time of AR5 are described in [[#5.5.2.1|Section 5.5.2.1]] . Since AR5, strengths and weaknesses of various approaches have been more clearly articulated in the literature (e.g., in [[#Rogelj--2016|Rogelj et al., 2016]] ; [[#Millar--2017b|Millar et al., 2017b]] ; [[#Tokarska--2018|Tokarska and Gillett, 2018]] ; [[#Matthews--2020|Matthews et al., 2020]] ), resulting in a new consolidated framework applied in SR1.5 ( [[#Rogelj--2018b|Rogelj et al., 2018b]] , 2019) that is also used in AR6. This framework incorporates five methodological advancements compared to AR5, the implications of which are discussed in this box.

First, publications since AR5 applied methods that limit the effect of uncertainties in historical, diagnosed emissions in coupled Earth system models (ESMs) on estimates of the remaining carbon budget ( [[#Millar--2017b|Millar et al., 2017b]] ; [[#Tokarska--2018|Tokarska and Gillett, 2018]] ). These new methods express remaining carbon budget estimates relative to a recent reference period instead of relative to the pre-industrial period ( [[#Millar--2017b|Millar et al., 2017b]] ; [[#Tokarska--2019b|Tokarska et al., 2019b]] ). Estimates of the full carbon budget since the pre-industrial period can still be obtained by adding estimates of historical CO <sub>2</sub> emissions (Table 5.1) to the estimates in Table 5.8. This methodological update resulted, all other aspects being equal, in median estimates of remaining carbon budgets being about 350–450 GtCO <sub>2</sub> larger compared to AR5 ( [[#IPCC--2014|IPCC, 2014]] ; [[#Millar--2017b|Millar et al., 2017b]] ).

At the time of AR5, Coupled Model Intercomparison Project Phase 5 (CMIP5; [[#Taylor--2012|Taylor et al., 2012]] ) provided global surface air temperature (GSAT) projections for the representative concentration pathways ( [[#Meinshausen--2011c|Meinshausen et al., 2011c]] ), which were used to determine carbon budgets while taking into account the effects of non-CO <sub>2</sub> forcers (T.F. [[#Stocker--2013|]] [[#Stocker--2013|Stocker et al., 2013]] ). Their use came with two recognized limitations: first, the model spread of the CMIP5 represents an ensemble of opportunity with limited statistical value ( [[#Tebaldi--2007|Tebaldi and Knutti, 2007]] ); and second, the evolution of non-CO <sub>2</sub> emissions as a function of cumulative CO <sub>2</sub> emissions can differ markedly between high and low emissions pathways ( [[#Meinshausen--2011c|Meinshausen et al., 2011c]] ; [[#Friedlingstein--2014a|Friedlingstein et al., 2014a]] ; [[#Rogelj--2016|Rogelj et al., 2016]] ; [[#Matthews--2017|Matthews et al., 2017]] ). Solutions to these two limitations have been published since AR5 and represent the second and third methodological improvement compared to AR5.

The reliance on an ensemble of opportunity (i.e., a serendipitous collection of scenario data from a variety of sources and studies) is avoided by methodologically separating the assessment of future warming contributions of non-CO <sub>2</sub> emissions from the spread in transient climate response to cumulative CO <sub>2</sub> emissions (TCRE; [[#5.5.2|Section 5.5.2]] ; [[#Rogelj--2018b|Rogelj et al., 2018b]] , 2019). This facilitates the explicit representation of TCRE uncertainty by a formal distribution, in this case a normal distribution with a 1.0–2.3°C 1000 PgC <sup>–1</sup> 1–sigma range ( [[#5.5.1.4|Section 5.5.1.4]] ). The effect of this methodological advance can be estimated from a direct comparison of the frequency distribution of TCRE in CMIP5 models that were used in AR5, and the formal TCRE distribution used in AR6, but is limited in precision. For estimates of the remaining carbon budget in line with limiting warming to 1.5°C or 2°C relative to pre-industrial levels, this improvement is estimated to lead to a reduction of budgets of the order of about 100 GtCO <sub>2</sub> between AR5 and AR6.

The third methodological improvement is a more direct estimation of the warming contribution of non-CO <sub>2</sub> emissions, consistent with pathways that bring global CO <sub>2</sub> emissions down to net zero. Instead of deriving this contribution implicitly from the CMIP5 ensemble, climate emulators ( [[#Meinshausen--2011b|Meinshausen et al., 2011b]] ; C.J. [[#Smith--2018|]] [[#Smith--2018|Smith et al., 2018]] ; [[#Schwarber--2019|Schwarber et al., 2019]] ) that are calibrated to the combined AR6 assessment (Cross-Chapter Box 7.1) are used to estimate the non-CO <sub>2</sub> contribution across a wide variety of stringent mitigation scenarios ( [[#Huppmann--2018|Huppmann et al., 2018]] ). The specific relative effect of this advance compared to AR5 is not calculable because CMIP5 data does not isolate non-CO <sub>2</sub> from CO <sub>2</sub> -induced warming.

The fourth and fifth methodological advancements are to explicitly account for the zero emissions commitment (ZEC; [[#5.5.2.2.4|Section 5.5.2.2.4]] ) and adjust estimates for Earth system feedbacks that are typically not represented in Earth system models (ESMs; [[#5.5.2.2.5|Section 5.5.2.2.5]] ). The central estimate of the assessed ZEC used in SR1.5 and AR6 is zero ( [[IPCC:Wg1:Chapter:Chapter-4#4.7.1.1|Section 4.7.1.1]] ). ZEC uncertainties are reported separately (Table 5.8), and the additional consideration of ZEC therefore does result in a better understanding but not in a net shift of central estimates of the remaining carbon budget compared to AR5. Furthermore, AR5 did not explicitly account for Earth system feedbacks not represented in ESMs. The SR1.5 assessed that they could reduce the remaining carbon budgets by about 100 GtCO <sub>2</sub> over centennial time scales. This assessment has been updated in AR6, including a wider range of biogeochemical feedbacks and new evidence ( [[#5.5.2.2.5|Section 5.5.2.2.5]] ). Some of these feedbacks are captured in the estimation of non-CO <sub>2</sub> warming (see below), while the combined effect of remaining positive and negative feedbacks is assessed to reduce the remaining carbon budget estimates by 7 ± 27 PgC K <sup>–1</sup> (1-sigma range, or 26 ± 97 GtCO <sub>2</sub> °C <sup>–1</sup> ) compared to AR5.

Between SR1.5 and AR6, each of the five components described in [[#5.5.2.1|Section 5.5.2.1]] and Figure 5.31 have been re-assessed (see Sections 5.5.2.2.1–5.5.2.2.5). Their updated assessments in turn affect the assessment of the remaining carbon budget. The new and narrower assessment of TCRE in AR6 compared to SR1.5 ( ''likely'' range of 1.0°C–2.3°C EgC <sup>–1</sup> compared to 0.8°C–2.5°C EgC <sup>–1</sup> , respectively, with the same central estimate) leads to no change in median estimates and about a 50 and 100 GtCO <sub>2</sub> increase in remaining carbon budgets estimates at the 67th percentile in AR6 compared to SR1.5 for 1.5°C and 2°C of global warming, respectively.

For historical warming, SR1.5 used GSAT increase between 1850–1900 and 2006–2015 of 0.97°C as its main starting point, while also providing values for other temperature metrics. Remaining carbon budgets were expressed starting from 1 January 2018 by accounting for historical emissions emitted from 1 January 2011 until the end of 2017. AR6 uses anthropogenic (human-induced) warming until the 2010–2019 period, which is assessed at the 0.8-1.3°C range, with a best estimate of 1.07°C (Table 3.1), and subsequently accounts for historical emissions from 1 January 2015 until the end of 2019 to express remaining carbon budget estimates from 1 January 2020 onwards. The human-induced warming between the 1850–1900 and 2006–2015 periods used in SR1.5 was assessed by AR6 at 0.97°C (Table 3.1). In a like-with-like comparison, the combined effect of data and methodological updates in historical warming estimates thus results in no shift in estimated remaining carbon budgets between SR1.5 and AR6. However, the emissions of the years passed since SR1.5 reduce the remaining carbon budget by about 85 GtCO <sub>2</sub> . Note that AR6 also updated its GSAT assessment for total warming between the 1850–1900 and 2006–2015 periods, reporting 0.94°C of warming. On a like-with-like basis, this would have resulted in slightly larger remaining carbon budgets compared to SR1.5 (Cross-Chapter Box 2.3).

The non-CO <sub>2</sub> contribution to future warming in emissions scenarios ( [[#Huppmann--2018|Huppmann et al., 2018]] ) is re-assessed with AR6-calibrated emulators, in this case MAGICC7 (Cross-Chapter Box 7.1; [[#Meinshausen--2009|Meinshausen et al., 2009]] , 2011a, 2020). The re-assessment of non-CO <sub>2</sub> warming with MAGICC7 results in a relationship that closely matches the average relationship applied in SR1.5 (shown in Section 2.SM.1.1.2 in [[#Forster--2018|Forster et al., 2018]] ), and therefore does not change estimates of the remaining carbon budget relative to SR1.5. The median ZEC assessment remained the same between SR1.5 and AR6, and therefore does not change the median remaining carbon budget estimates. Finally, as indicated above, AR6 expanded the assessment of Earth system feedbacks compared to SR1.5 and included it in its central remaining carbon budget estimates. Some feedbacks are accounted for through the non-CO <sub>2</sub> warming estimate ( [[#5.5.2.2.5|Section 5.5.2.2.5]] ), while the remainder combines to reduce the median remaining carbon budget estimates for 1.5°C and 2°C of warming by about 10 to 20 GtCO <sub>2</sub> , respectively, compared to SR1.5.

All methodological improvements and new evidence combined result in median and 67th percentile remaining carbon budget estimates for limiting warming to 1.5°C being about 300–350 GtCO <sub>2</sub> larger compared to an assessment that would use the evidence and methods available at the time of the AR5. For limiting warming to 2°C, the difference is about 400–500 GtCO <sub>2</sub> . Since SR1.5, fewer key advancements had to be integrated. In a like-with-like comparison, the combined effects of all AR6 updates result in median remaining carbon budget estimates for limiting warming to 1.5°C and 2°C being the same and about 60 GtCO <sub>2</sub> smaller, respectively, in AR6 compared to SR1.5. At the 67th percentile, remaining carbon budget estimates for limiting warming to 1.5°C and 2°C are about 40 to 60 GtCO <sub>2</sub> larger, respectively, mainly as a result of a narrower assessed TCRE range.

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