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===== 5.5.1.2.1 Sensitivity to amount of cumulative CO <sub>2</sub> emissions ===== <div id="h4-8-siblings" class="h4-siblings"></div> 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 β defined as the range in cumulative emissions over which the TCRE remains within 95% of its maximum value β 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. <div id="5.5.1.2.2" class="h4-container"></div> <span id="sensitivity-to-the-rate-of-co-2-emissions"></span>
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