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in recent literature on how carbon sinks (and resultant airborne fraction) are
affected by both elevated CO 2 and climate changes (concentration-carbon
and climate-carbon feedbacks; see Friedlingstein et al., 2006, Gregory et
al., 2009, and Section 2.4). There is also a large body of literature aimed at
estimating the temperature response to elevated CO 2 , typically defined as
equilibrium climate sensitivity or transient climate response (Meehl et al.,
2007; see also Sections 3.2 and 3.3). Each stage in the progression from
carbon emissions to the resultant climate warming carries large uncertainty
due to our incomplete understanding of the magnitude of both physical and
biochemical feedbacks in the climate system.
Matthews et al. (2009) proposed a new metric of the temperature re-
sponse to carbon emissions, the “carbon climate response,” which includes
the net effects of both carbon cycle and physical climate feedbacks. The
carbon-climate response is defined as the globally averaged temperature
response to 1 trillion tons of carbon emissions (3.7 trillion tons of CO 2 ),
thus framing the climate response to emissions in the context of cumulative
emissions of carbon dioxide over time. In effect, the carbon-climate reponse
is a generalization of the concept of climate sensitivity as it pertains to car-
bon dioxide forcing. By including the carbon cycle response to emissions
in addition to the temperature response to CO 2 forcing, the carbon-climate
response represents a metric that relates global mean temperature change
directly to cumulative carbon emissions. This concept of measuring the cli-
mate response to cumulative emissions was also proposed concurrently by
three other studies (Allen et al., 2009; Meinshausen et al., 2009; Zickfeld et
al., 2009), all of which demonstrated a remarkably consistent temperature
response to a given level of cumulative carbon emissions. Although CO 2
radiative forcing decreases logarithmically with increasing CO 2 concentra-
tions, this is balanced by a near-exponential increase in the airborne fraction
of emissions due to weakening carbon sinks at higher CO 2 concentrations
(Caldeira and Kasting, 1993). As a result, global mean temperature change
is almost linearly related to cumulative carbon emission and is independent
of the time during which the emissions occur (Matthews et al., 2009).
Estimates of the Temperature Response to Cumulative Emissions
Matthews et al. (2009) estimated the temperature response to cumulative
carbon emissions as 1-2.1°C per trillion tons of carbon (1000 GtC) emitted,
based both on 21st century simulations by coupled climate-carbon cycle
models and on historical observations of CO 2 -induced temperature change
and anthropogenic CO 2 emissions (Figure 3.5). This study produced a best
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