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

Journal name:
Nature Geoscience
Volume:
8,
Pages:
29–34
Year published:
DOI:
doi:10.1038/ngeo2304
Received
Accepted
Published online

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.

At a glance

Figures

  1. Global surface warming versus cumulative carbon emissions.
    Figure 1: Global surface warming versus cumulative carbon emissions.

    a, Surface warming over the twenty-first century versus cumulative emissions based on our theory, equation (4) with inputs from our coupled atmosphere–ocean model of intermediate complexity (GENIE; ref. 22), from year 2010 to 2100 for either IPCC concentration pathways6 or emission scenarios23. b, The discrepancy in surface warming direct from model output of ΔT andΔIem minus the theory (a) is less than 0.2 K. c, Surface warming evaluated after many centuries up to 5,000 years (dots) from our equilibrium theory9 (dashed line) and our model output forced by the emission scenarios22 (the theory uses model values of a, λ and IB, using equation (4) with N = 0 and IUsat = 0).

  2. Cumulative carbon emissions, cumulative ocean carbon undersaturation and [Delta]ln CO2 over time in our coupled atmosphere-ocean model (GENIE) for six twenty-first century emission scenarios.
    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.

    a, Cumulative emissions. b, Ocean undersaturation, where IUsat is diagnosed in the model configuration without climate feedbacks permitted. c, Δln CO2 calculated from equation (3), assuming no climate feedbacks altering the ocean carbon cycle (the equivalent radiative heat flux, ΔlnCO2(t) ranges from +2 to +5 W m−2 at year 5000). d, The error in ΔlnCO2 from the model minus the theory, equation (3), for the model configurations without climate feedbacks (solid lines) and with climate feedbacks (dashed lines), where climate feedbacks lead to a consistent slight increase in CO2.

  3. Thermal and carbon response to cumulative carbon emissions over 3,000 years for six emission scenarios in our coupled atmosphere-ocean model.
    Figure 3: Thermal and carbon response to cumulative carbon emissions over 3,000 years for six emission scenarios23 in our coupled atmosphere–ocean model.

    a, The sensitivity of surface warming to radiative forcing diagnosed from theory, ΔT/R = (1 − εN/R)/λ, increases over time (left-hand axis) as the entire ocean approaches a thermal equilibrium and the normalized heat uptake, εN/R, goes to zero (right-hand axis). b, The sensitivity of radiative forcing to cumulative emissions diagnosed from theory, R/Iem = (a/IB)(1 + IUsat/Iem), decreases over time (left-hand axis) as the entire ocean approaches a carbon equilibrium and the normalized ocean carbon undersaturation, IUsat/Iem, goes to zero (right-hand axis). c, The surface warming response to cumulative emissions (TCRE) diagnosed from theory, ΔT/Iem = (a/(λIB))(1 − εN/R)(1 + IUsat/Iem), decreases only slowly over time owing to the competing effects of the ocean thermal and carbon responses, expressed in (1 − εN/R)(1 + IUsat/Iem) (right-hand axis). d, The error in the TCRE from the difference between c and a. The model warming response is slightly larger than theory owing to positive carbon-climate feedbacks in the model, such as ocean solubility-CO2 feedback29 and ocean biological feedback to changes in nutrient supply and circulation.

  4. A schematic depiction of the ocean thermal and carbon response to anthropogenic carbon emissions.
    Figure 4: A schematic depiction of the ocean thermal and carbon response to anthropogenic carbon emissions.

    ac, Initial response (a), subsequently followed by the upper ocean (b) and deep ocean (c) approaching an equilibrium with the atmosphere. The ocean is depicted as a two-layer system: warm waters with low dissolved inorganic carbon (DIC) within the thermocline, overlying high DIC in the cold, deep ocean. Surface waters take up heat and excess CO2 from the atmosphere, then are physically transferred via ventilation pathways (grey arrows, nominally for the Atlantic). In a, carbon emissions lead to radiative forcing, R, inducing surface warming, ΔT, and an ocean heat uptake, N, as well as an ocean uptake of CO2. In b, after several decades, much of the upper ocean approaches an equilibrium, such that that ocean uptake continues only at high latitudes. Eventually in c, after many centuries, the deep ocean also approaches an equilibrium, such that the ocean uptake of heat and CO2 then ceases.

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Author information

Affiliations

  1. Department of Ocean and Earth Sciences, National Oceanography Centre Southampton, University of Southampton, Southampton SO14 3ZH, UK

    • Philip Goodwin
  2. Department of Earth, Ocean and Ecological Sciences, School of Environmental Science, University of Liverpool, Liverpool L69 3GP, UK

    • Richard G. Williams
  3. School of Geographical Science, University of Bristol, Bristol BS8 1SS, UK

    • Andy Ridgwell

Contributions

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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The authors declare no competing financial interests.

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