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

==== 5.5.1.2 Assessment of Limits of the TCRE Concept ====

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===== 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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===== 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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===== 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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