Origins and implications of the relationship between warming and cumulative carbon emissions

Abstract:

A near-linear relationship between warming (T) and cumulative carbon emissions (Q) is a robust finding from numerous studies. This finding opens biophysical questions concerning (1) its theoretical basis, (2) the treatment of non-CO2 forcings, and (3) uncertainty specifications. Beyond these biophysical issues, a profound global policy question is raised: (4) how can a quota on cumulative emissions be shared? Here, an integrated survey of all four issues is attempted.

(1) Proportionality between T and Q is an emergent property of a linear carbon-climate system forced by exponentially increasing CO2 emissions. This idealisation broadly explains past but not future near-proportionality between T and Q: in future, the roles of non-CO2 forcings and carbon-climate nonlinearities become important, and trajectory dependence becomes stronger.

(2) The warming effects of short-lived non-CO2 forcers depend on instantaneous rather than cumulative fluxes. However, inertia in emissions trajectories reinstates some of the benefits of a cumulative emissions approach, with residual trajectory dependence comparable to that for CO2.

(3) Uncertainties arise from several sources: climate projections, carbon-climate feedbacks, and residual trajectory dependencies in CO2 and other emissions. All of these can in principle be combined into a probability distribution P(T|Q) for the warming T from given cumulative CO2 emissions Q. Present knowledge of P(T|Q) allows quantification of the tradeoff between mitigation ambition and climate risk.

(4) Cumulative emissions consistent with a given warming target and climate risk are a finite common resource that will inevitably be shared, creating a tragedy-of-the-commons dilemma. Sharing options range from “inertia” (present distribution of emissions is maintained) to “equity” (cumulative emissions are distributed equally per-capita). Both extreme options lead to emissions distributions that are unrealisable in practice, but a blend of the two extremes may be realisable. This perspective provides a means for nations to compare the global consequences of their own proposed emissions quotas if others were to act in a consistent way, a critical step towards achieving consensus.