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

Abstract

Climate model experiments reveal that transient global warming is nearly proportional to cumulative carbon emissions on multi-decadal to centennial timescales 1-5 . However, it is not quantitatively understood how this near linear dependence between warming and cumulative carbon emissions arises in transient climate simulations 6,7 . 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 to 20% by the end of the century and beyond. The climate response remains nearly constant on multidecadal to centennial timescales as a result of partially-opposing effects of oceanic uptake of heat and carbon 8 . The resulting warming then becomes proportional to cumulative carbon emissions after many centuries, as noted earlier 9 . When we incorporate estimates of terrestrial carbon uptake 10 , the surface warming response is reduced to 1.1±0.5 K for every 1000 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.Warming of the Earth's surface, ΔT(t), depends on the increase in radiative forcing, R(t), from atmospheric CO 2 minus the net heat flux into the Earth System, N(t), 11where ΔT is the change in global mean surface temperature relative to the pre-industrial era, λ is the equilibrium climate feedback parameter [(W m -2 ) K -1 ] or equivalently λ -1 is the climate sensitivity 12 , R(t) and N(t) are positive when downward and in W m -2 . The net heat flux, N(t), is dominated by ocean heat uptake, since over 90% of N(t) passes into the ocean interior 13 . ε is the non-dimensional ocean heat uptake efficacy 11 , accounting for how ocean heat uptake may be more effective than radiative forcing in altering ΔT. The 2 radiative forcing, R(t), taken to be at the top of the troposphere, is directly linked to atmospheric CO 2 via a logarithmic relationship, 14where CO 2 is measured as a mixing ratio (ppmv), a=5.35 Wm -2 is a CO 2 radiative-forcing coefficient and Δln CO 2 (t) represents ln CO 2 (t) -ln CO 2 (t 0 ) where t 0 is the preindustrial. An increase in cumulative carbon emissions naturally leads to a longterm increase in atmospheric CO 2 , radiative forcing and surface warming, which might be augmented by further warming from non-CO 2 greenhouse gases or partly opposed by cooling from aerosols 6,7,15 . Focussing on the dominant effect of cumulative carbon emissions on global warming 15 , the relationship between the logarithmic change in atmospheric CO 2 , Δln CO 2 (t), and cumulative carbon emissions over time must be found.The rise in ln CO 2 from cumulative emissions is affected ...

How historic simulation–observation discrepancy affects future warming projections in a very large model ensemble

“…Also, the ranges of the Transient Climate Response to Emissions, TCRE, in the observation-consistent and simulation-consistent model ensembles are comparable to previous estimates based on models and Gillet et al 2013;Matthews et al 2009;Zickfield et al 2009Zickfield et al , 2012 and observationally constrained theory (Goodwin et al 2015). These agreements for the ECS, TCRE and projected warming ranges imply that the WASP model presented here ( Fig.…”

“…The WASP (simulation-consistent) ensemble contains 182,500 ensemble members that are consistent with 8 historic constraints based on the simulated historic ranges of the CMIP5 ensemble. The WASP (observation-consistent) ensemble contains 14,500 members that are consistent with 8 historic constraints from observations Goodwin et al (2015), with additional terms for radiative forcing from non-CO 2 agents (Meinshausen et al 2011) and for equivalent carbon emissions from the ocean temperature-CO 2 solubility feedback (Goodwin and Lenton 2009). A full description of the WASP model, including the model equations, is given in the "Appendix" section.…”

“…2): the Warming, Acidification and Sea-level Projector (WASP). In the WASP model, ocean carbonate chemistry is approximated using the buffered carbon inventory approach of Goodwin et al (2007Goodwin et al ( , 2015. Global mean surface air-temperature increase is calculated using the warming-carbon emissions relationship of (Flato et al 2013).…”

“…This future spread leads to significant uncertainty in the sensitivity of future warming to carbon emissions, termed the Transient Climate Response to Emission (Gillet et al 2013), or TCRE [K (1000 −1 ]. Based on the CMIP5-ensemble of 21 complex ESMs, the TCRE is estimated to be between 0.8 and 2.5 K (1000 PgC) −1 for the late twenty-first century Gillet et al 2013), while a separate observation constrained theoretical analysis (Goodwin et al 2015) suggests TCRE = 1.1 ± 0.5 K (1000 PgC) −1 . This large uncertainty in the TCRE introduces large uncertainty in the maximum cumulative carbon emission allowed to restrict CO 2 -induced warming to a policy-driven target ), noting that warming from non-CO 2 agents will also affect total anthropogenic warming (Pierrehumbert Abstract Projections of future climate made by modelensembles have credibility because the historic simulations by these models are consistent with, or near-consistent with, historic observations.…”

Quantifying the influence of the terrestrial biosphere on glacial–interglacial climate dynamics

“…For future climate changes studies, the response of atmospheric CO 2 concentrations (and hence climate) to changes in terrestrial carbon storage can be calculated using the transient response to cumulative emissions (TRCE) approach (Gillett et al, 2013), which demonstrated proportionality between carbon emissions and temperature rise (Goodwin et al, 2015). We include these estimates for completeness.…”