The relationship between peak warming and cumulative CO2 emissions, and its use to quantify vulnerabilities in the carbon–climate–human system

Interactions between the carbon cycle, climate and human societies are subject to several major vulnerabilities, broadly defined as factors contributing to the risk of harm from human-induced climate change. We assess five vulnerabilities: (1) effects of increasing CO₂ on the partition of anthropogenic carbon between atmospheric, land and ocean reservoirs; (2) effects of climate change (quantified by temperature) on CO₂ fluxes; (3) uncertainty in climate sensitivity; (4) non-CO₂ radiative forcing and (5) anthropogenic CO₂ emissions. Our analysis uses a physically based expression for T _p(Q _p), the peak warming T _p associated with a cumulative anthropogenic CO₂ emission Q_p to the time of peak warming. The approximations in this expression are evaluated using a non-linear box model of the carbon-climate system, forced with capped emissions trajectories described by an analytic form satisfying integral and smoothness constraints. The first four vulnerabilities appear as parameters that influence T _p(Q _p), whereas the last appears through the independent variable. In terms of likely implications for T _p(Q _p), the decreasing order of the first four vulnerabilities is: uncertainties in climate sensitivity, effects of non-CO₂ radiative forcing, effects of climate change on CO₂ fluxes and effects of increasing CO₂ on the partition of anthropogenic carbon.