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.