Atmospheric lifetime ($\tau$)

For a well-mixed atmospheric burden $B$ removed by a single first-order sink, $dB/dt=-B/\tau$, the atmospheric lifetime is the exponential decay time $\tau$. At steady emission rate $E$, this model gives $B=E\tau$. Independent sinks acting on the same burden have additive inverse lifetimes. Local removal times in separate compartments cannot be combined this way without considering exchange and partitioning. A multi-reservoir perturbation, especially atmospheric carbon dioxide, generally needs more than one timescale.

The e-folding relaxation time of an added methane burden after accounting for chemical feedbacks. It need not equal burden divided by the contemporaneous methane loss rate: extra methane can consume hydroxyl radical and reduce its own removal. A fixed-OH exponential estimate omits that coupled adjustment.