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

==== 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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