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Sensitivity of climate to cumulative carbon emissions due to compensation of ocean heat and carbon uptake


Climate model experiments reveal that transient global warming is nearly proportional to cumulative carbon emissions on multi-decadal to centennial timescales1,2,3,4,5. However, it is not quantitatively understood how this near-linear dependence between warming and cumulative carbon emissions arises in transient climate simulations6,7. Here, we present a theoretically derived equation of the dependence of global warming on cumulative carbon emissions over time. For an atmosphere–ocean system, our analysis identifies a surface warming response to cumulative carbon emissions of 1.5 ± 0.7 K for every 1,000 Pg of carbon emitted. This surface warming response is reduced by typically 10–20% by the end of the century and beyond. The climate response remains nearly constant on multi-decadal to centennial timescales as a result of partially opposing effects of oceanic uptake of heat and carbon8. The resulting warming then becomes proportional to cumulative carbon emissions after many centuries, as noted earlier9. When we incorporate estimates of terrestrial carbon uptake10, the surface warming response is reduced to 1.1 ± 0.5 K for every 1,000 Pg of carbon emitted, but this modification is unlikely to significantly affect how the climate response changes over time. We suggest that our theoretical framework may be used to diagnose the global warming response in climate models and mechanistically understand the differences between their projections.

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Figure 1: Global surface warming versus cumulative carbon emissions.
Figure 2: Cumulative carbon emissions, cumulative ocean carbon undersaturation and Δln CO2 over time in our coupled atmosphere–ocean model (GENIE) for six twenty-first century emission scenarios23.
Figure 3: Thermal and carbon response to cumulative carbon emissions over 3,000 years for six emission scenarios23 in our coupled atmosphere–ocean model.
Figure 4: A schematic depiction of the ocean thermal and carbon response to anthropogenic carbon emissions.


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This research was supported by UK NERC Postdoctoral Fellowship NE/I020725/2 and NERC grants NE/K012789/1 and NE/H017453/1.

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P.G. and R.G.W. provided the theory, with P.G. deriving the equations for the transient adjustment. A.R. conducted the supporting numerical modelling with GENIE. P.G. and R.G.W. led the writing of this study, and contributed equally, and A.R. provided comments on the manuscript.

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Correspondence to Philip Goodwin or Richard G. Williams.

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The authors declare no competing financial interests.

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Goodwin, P., Williams, R. & Ridgwell, A. Sensitivity of climate to cumulative carbon emissions due to compensation of ocean heat and carbon uptake. Nature Geosci 8, 29–34 (2015).

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