Cumulative emissions accounting of greenhouse gases due to path independence for a sufficiently rapid emissions cycle

Abstract

Cumulative emissions accounting for carbon-dioxide ($\hbox {CO}_{2}$) is founded on recognition that global warming in earth system models is roughly proportional to cumulative $\hbox {CO}_{2}$ emissions, regardless of emissions pathway. However, cumulative emissions accounting only requires the graph between global warming and cumulative emissions to be approximately independent of emissions pathway (“path-independence”), regardless of functional relationship between these variables. The concept and mathematics of path-independence are considered for an energy-balance climate model, giving rise to a closed-form expression of global warming, together with analysis of the atmospheric cycle following emissions. Path-independence depends on the ratio between the period of the emissions cycle and the atmospheric lifetime, being a valid approximation if the emissions cycle has period comparable to or shorter than the atmospheric lifetime. This makes cumulative emissions accounting potentially relevant beyond $\hbox {CO}_{2}$, to other greenhouse gases with lifetimes of several decades whose emissions have recently begun.