Abstract. Projections of the response to anthropogenic emission scenarios, evaluation of some greenhouse gas metrics and estimates of the social cost of carbon, often require a simple model that links emissions of carbon dioxide CO2 to atmospheric concentrations and global temperature changes. An essential requirement of such a model is to reproduce the behaviour of more complex models as well as an ability to sample their range of response in a transparent, accessible and reproducible form. Here we adapt the simple model of the Intergovernmental Panel on Climate Change 5th Assessment Report (IPCC-AR5) to explicitly represent the state-dependence of the CO2 airborne fraction and reproduce several idealised experiments performed with more complex models. We find that a simple linear increase in 100-year integrated airborne fraction with cumulative carbon uptake and global temperature change is both necessary and sufficient to represent the response of the climate system to CO2 on a range of timescales and under a range of experimental designs. Quantified ranges of uncertainty (analogous to current assessed ranges in Equilibrium Climate Sensitivity and Transient Climate Response) in integrated airborne fraction over the 21st century under a representative mitigation scenario, and an assessed range in how much this quantity may have changed relative to pre-industrial conditions, would be valuable in future scientific assessments.