Finite-horizon GWP lifetime sensitivity ($\tau (1-e^{-H/\tau })$)

For a gas pulse with unchanged greenhouse gas radiative efficiency and decay $e^{-t/\tau }$, its integrated forcing through $H$ is proportional to $\tau (1-e^{-H/\tau })$. Comparing two such lifetimes at fixed carbon-dioxide reference gives the ratio of these two factors. A fractional lifetime increase is not generally the same fractional GWP increase at finite $H$.