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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.

Methane is an infrared-active greenhouse gas with absorption in the terrestrial thermal spectrum. Its direct forcing is supplemented by chemically induced changes in tropospheric ozone and stratospheric water vapor. Its finite atmospheric lifetime makes sustained emissions and emission pulses different experiments: stopping emissions permits the methane burden to decline much faster than the long tail of a carbon-dioxide perturbation. Quantitative comparisons require a specified emission mass, time horizon and treatment of indirect effects, as formalized by global warming potential.

Absorption depends on an allowed transition with a nonzero transition dipole moment and appreciable line strength at wavelengths carrying terrestrial thermal radiation. Molecular vibration and molecular rotation, level populations and pressure/temperature-dependent line shapes determine the spectrum. A band in an atmospheric window can be more effective incrementally than one already strongly absorbed by water or carbon dioxide. Symmetry can make a vibration infrared inactive even when the molecule has many normal modes. Atmospheric lifetime affects the persistence of a released gas, not the intrinsic absorption strength of one molecule.

A small global warming potential requires both a small greenhouse gas radiative efficiency per unit emitted mass and a short atmospheric lifetime. Weak absorption in the terrestrial atmospheric window is desirable, particularly where absorption by existing gases is weak; strong carbon–fluorine vibrational bands can make even an ozone-safe substitute an efficient greenhouse gas. Rapid removal by lower-atmospheric chemistry limits the integrated burden, provided it does not generate abundant, long-lived radiatively active products. The atmospheric residence time and the absorption spectrum must therefore be assessed separately.

TODO: user-deferred biological component. Biological carbon uptake, storage and release are outside the current scope. The physical and ocean-chemistry explanation is given here; the deferred component means this is not a complete all-process answer.

There is no single first-order atmospheric lifetime for an added carbon dioxide pulse. Air–sea gas exchange and adjustment of the surface mixed layer act on years-to-decades scales; redistribution into the ocean interior takes centuries to millennia. These transfers partition carbon between atmosphere and ocean rather than making the entire added carbon inventory disappear. Dissolution also changes the ocean's carbonate speciation: conversion among dissolved carbon dioxide, bicarbonate and carbonate buffers the uptake, but provides a finite capacity at a given alkalinity. A substantial perturbation therefore remains airborne after the faster exchanges have adjusted.

Further removal involves dissolution of carbonate sediments and carbonate compensation over several thousand years, followed by the much slower silicate-weathering and burial pathway, typically tens to hundreds of thousands of years. The exact fractions and times depend on pulse size and model conditions. A thousand years exceeds the fast exchange times but not the complete ocean–solid-Earth adjustment time, so a residual atmospheric perturbation is expected. An intercomparison found a substantial long tail after ocean equilibration, with further carbonate neutralization on roughly 3–7 kyr scales.^[ref]