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The finite-horizon GWP lifetime sensitivity follows because a longer lifetime leaves more methane from a given pulse at later times and raises the steady burden for a given constant emission rate. For the stipulated exponential pulse response and unchanged greenhouse gas radiative efficiency, the integrated methane forcing over horizon $H$ is proportional to $\tau (1-e^{-H/\tau })$. The same carbon dioxide reference pulse appears in both global warming potential denominators, so it cancels from their ratio:Thus the twenty-year GWP increases by $13.75\%$ under these fixed-efficiency assumptions. This is smaller than the $19.33\%$ lifetime increase because part of the extra forcing occurs beyond the finite horizon. For an infinite horizon the fractional increase would approach the lifetime ratio. Indirect forcing and the distinction between a chemical lifetime and a hydroxyl radical-coupled methane perturbation lifetime require a fuller chemical model; they are held fixed in this comparison.

For the chemical sink, ${\tau }_{\mathrm{C}{\mathrm{H}}_4}\sim 1/(k[\mathrm{OH}])$. Warming increases the methane–hydroxyl radical rate constant and, with increased water vapor, often increases hydroxyl radical production, tending to shorten the chemical lifetime. Changes in ozone photodissociation, radical recycling, lightning and competing carbon monoxide/VOC/methane consumption can reinforce or oppose that trend. Increasing methane itself consumes hydroxyl radicals and lengthens its methane perturbation lifetime. The physical/chemical warming tendency should therefore be separated from scenarios with changed emissions; shorter chemical lifetime at fixed precursor conditions is a tendency, not an unconditional prediction for the future atmosphere.^[ref]