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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.

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Notes

  1. 1.

    The choice of perturbation in the conduct of the path independence analysis is not unique. Other choices could well be made, for example one might perturb proportionally to \(\triangle M\left( s\right)\), which would then be varying in time and be present in the integral from 0 to t. Our choice of constant perturbation \(\triangle M\left( t\right)\) for all past times \(0<s<t\) is motivated by the resulting simplicity of the analysis and its interpretation.

  2. 2.

    The minus sign in Eq. (11) is because although the airborne fraction is generally decreasing with time, we would prefer this timescale to generally take positive values.

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Acknowledgements

The author thanks Prof. Govindasamy Bala, and seminar participants at Imperial College, London, and University of Exeter for helpful discussions.

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Correspondence to Ashwin K. Seshadri.

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Seshadri, A.K. Cumulative emissions accounting of greenhouse gases due to path independence for a sufficiently rapid emissions cycle. Clim Dyn 57, 787–798 (2021). https://doi.org/10.1007/s00382-021-05739-3

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