Sensitivity of Global Warming to Carbon Emissions: Effects of Heat and Carbon Uptake in a Suite of Earth System Models

1. Introduction

Climate model projections reveal a simple emergent relationship for our future climate: surface warming increases nearly linearly with the cumulative CO2 emitted since the preindustrial age. This relationship has been illustrated in terms of how surface warming increases with the cumulative CO2 emission using a climate model emulator (Allen et al. 2009), an Earth system model of intermediate complexity (Matthews et al. 2009; Zickfeld et al. 2009), and a suite of Earth system models forced by an annual rise in atmospheric CO2 (Gillett et al. 2013).

Our aim is to understand how the sensitivity of surface warming to cumulative carbon emissions from fossil fuels is controlled: this sensitivity ΔT/ΔI is defined by the ratio of the change in global-mean surface air temperature ΔT (K) and the change in fossil-fuel cumulative carbon emission ΔI (in petagrams of carbon denoted by PgC) since the preindustrial age. This sensitivity of surface warming to carbon emissions relates to two climate metrics: for experiments with only atmospheric CO2 forcing, ΔT/ΔI is identical to the transient climate response to cumulative carbon emissions (TCRE) on decadal to centennial time scales (Gillett et al. 2013; Collins et al. 2013) and approaches the equilibrium climate response to cumulative carbon emissions (ECRE) on centennial to millennial time scales (Frölicher and Paynter 2015).

The sensitivity of surface warming to carbon emissions is examined here, exploiting our recent theory highlighting the role of the ocean in taking up heat and carbon (Goodwin et al. 2015; Williams et al. 2016). Two sets of Earth system model experiments are diagnosed: 10 Earth system models with an annual 1% rise in atmospheric CO2 and nine Earth system models following representative concentration pathways (RCPs) (Moss et al. 2010) until year 2100, including non-CO2 radiative forcing and carbon emissions from land-use and land-cover changes (Collins et al. 2013). In both sets of experiments, the sensitivity of the surface warming to fossil-fuel cumulative carbon emissions ΔT/ΔI remains nearly constant in time for each individual model (Figs. 1a,b), although its value differs for each model.