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.