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.

二氧化碳的累积排放量（\（\ hbox {CO} _ {2} \））是基于以下认识而建立的：地球系统模型中的全球变暖与累积\（\ hbox {CO} _ {2} \ ）排放，无论排放途径如何。但是，累积排放核算仅要求全球变暖与累积排放之间的关系图与排放路径（“路径独立性”）大致无关，而与这些变量之间的功能关系无关。对于能量平衡的气候模型，考虑了路径独立性的概念和数学，从而产生了全球变暖的封闭形式，并分析了排放后的大气循环。路径独立性取决于排放周期的时间与大气寿命之间的比率，如果排放周期的周期等于或小于大气寿命，则这是有效的近似值。这使得累积排放核算可能超越\（\ hbox {CO} _ {2} \）到最近开始排放的具有数十年使用寿命的其他温室气体。