A Theory for How Global Warming Mechanistically Depends on Cumulative Carbon Emissions Over Time

Abstract:

Climate model experiments reveal that transient global warming is nearly proportional to cumulative carbon emissions on multi-decadal to millennial timescales. However, it is not quantitatively understood how this near linear dependence between warming and cumulative carbon emissions arises in transient climate simulations, nor why the proportionality of warming is largely independent of emission scenario. Here, we present the first theoretical equation for how global warming depends on cumulative carbon emissions over time for an atmosphere-ocean system. For the present, our theory identifies a sensitivity of surface warming to emission of 1.5±0.7 K for every 1000 Pg of carbon emitted, reducing by only 10 to 20% by the end of the century and beyond. The sensitivity remaining nearly constant over time is due to partially-opposing thermal and carbon responses in a coupled atmosphere-ocean, as well as reflecting how warming is proportional to cumulative carbon emissions after many centuries. Incorporating estimates of terrestrial carbon uptake into our analysis reduces the sensitivity of surface warming to 1.1±0.5 K for every 1000 Pg of carbon emitted, but does not significantly alter the percentage reduction in warming sensitivity over the 21^st century. Our theory provides an analytical framework to interpret model projections of global warming.