  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.
