Lifetimes of atmospheric species: Integrating environmental impacts

[1] The environmental damage caused by atmospheric pollutants is proportional to the duration of their effects. The global impacts of greenhouse gases (as measured by global warming potential) and ozone depleting substances (as measured by ozone depletion potential) have traditionally been calculated using the atmospheric lifetime of the source gas as a quantitative measure of the impact's duration, assuming that the gas quickly reaches a steady-state pattern which decays exponentially according to the lifetime. This assumed behavior obviously does not match the true rise and fall of impacts, particularly secondary ones like ozone depletion, that can be seen in numerical integrations or chemical mode decomposition. Here, the modes decomposition is used to prove that: (a) the steady-state pattern of impacts caused by specified emissions, multiplied by (b) the steady-state lifetime of the source gas for that emission pattern, is exactly equal to (c) the integral of all impacts - independent of the number and atmospheric residence times of secondary impacts.

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