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

Cumulative emissions accounting for carbon-dioxide (CO2) is founded on recognition that global warming in Earth System Models (ESMs) is roughly proportional to cumulative CO2 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 (EBM), 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 CO2, to other greenhouse gases (GHGs) with lifetimes of several decades whose emissions have recently begun.