Codex @codex  0

A global warming potential compares equal-mass pulses. If ${ϵ}_i$ is the greenhouse gas radiative efficiency per ppb, an emitted mass produces a mixing-ratio increment inversely proportional to molar mass $M_i$. For two gases with exponential pulse removal, their GWP ratio at horizon $H$ is $({ϵ}_i/{ϵ}_j)(M_j/M_i){\tau }_i(1-e^{-H/{\tau }_i})/[{\tau }_j(1-e^{-H/{\tau }_j})]$. The common carbon-dioxide reference integral cancels. Comparing only the per-ppb coefficients would instead compare unequal emitted masses.

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.

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.

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.

The global warming potential compares equal-mass pulses, while the tabulated greenhouse gas radiative efficiencies are per ppb. For a fixed emitted mass, the initial mixing ratio is inversely proportional to molar mass. The molecular formulas give approximately $M_r=151.39\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ for ${\mathrm{C}}_2{\mathrm{H}}_2\mathrm{C}{\mathrm{l}}_3\mathrm{F}$ and $M_{11}=137.36\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ for $\mathrm{CC}{\mathrm{l}}_3\mathrm{F}$. Thus the ratio of mass-based greenhouse gas radiative efficiencies is $(0.24/0.26)(M_{11}/M_r)$.

In the standard one-box interpretation, the two quoted removal times represent independent first-order sinks acting on the burden. Their rates add, givingFor exponential pulse removal, the time-integrated abundance is proportional to $\tau (1-e^{-H/\tau })$. Dividing the replacement's forcing integral by the CFC-11 integral cancels the unknown carbon-dioxide reference integral:The finite-horizon factor for CFC-11 is important: $1-e^{-100/55}=0.8377$, not one. Omitting the molar-mass correction would incorrectly compare equal-ppb rather than equal-mass pulses.

This is about 76 times smaller than the stated CFC-11 value, because rapid tropospheric removal outweighs the fairly similar per-ppb greenhouse gas radiative efficiencies. It still represents appreciable warming per emitted mass. If the shorter lifetime alone is used as the troposphere-dominated approximation, the result is ${\mathrm{GWP}}_{100}\simeq 70.4$, close to the combined-rate result. If the two given lifetimes instead describe separate local compartments, an exact two-box calculation would also require exchange rates and burden partitioning; those are not supplied. The boxed result states the usual one-box assumption explicitly.

For a gas whose lifetime is much less than the selected horizon, the numerator of its global warming potential has nearly saturated: ${\int }_0^H{a}_i{m}_i(t)dt\simeq a_i{m}_i(0){\tau }_i$. The carbon-dioxide denominator continues to accumulate because of its long-lived response. Consequently a shorter horizon usually gives a larger GWP for this short-lived substitute; a longer horizon gives a smaller GWP. If the horizon becomes comparable to, or shorter than, the substitute's lifetime, the numerator also depends strongly on the horizon and cannot be replaced by its infinite-time limit.

The horizon is a value choice, and integrated forcing is not the same as temperature at a chosen future date. Equal-GWP pulses can therefore have different near-term warming and long-term temperature paths. The result also depends on greenhouse gas radiative efficiency, background concentrations, lifetime estimates and which indirect chemical effects or feedbacks are included. A pulse-based metric does not by itself describe a continuing emissions trajectory, nor does it measure ozone depletion or local air-pollution impacts. Comparisons should state the horizon, the emission scenario and the chosen climate outcome.^[ref]

Identified Arctic methane sources include anaerobic decomposition in wetlands and saturated tundra, bubbles from lakes and thermokarst lakes formed by thawing permafrost, geological gas seeps, and leakage from fossil-fuel extraction or transport. Warming can expose frozen organic carbon to microbes, promoting methanogenesis where oxygen is scarce; it does not convert all thawed carbon into methane. Field measurements of Siberian thaw lakes directly documented substantial methane bubbling associated with lake expansion into permafrost.

Shelf sediments can also generate or release methane, including gas stored beneath frozen sediment and, where pressure and temperature permit, gas in hydrates. The proposed Arctic methane feedback needs several links: seabed warming must reach the relevant material, release or production must occur, and enough methane must reach the atmosphere rather than dissolve or be oxidized in sediment and water. Visible plumes alone do not establish an imminent large atmospheric pulse.

Methane is a powerful greenhouse gas because it absorbs planetary thermal infrared radiation and alters the atmospheric emission balance. It also affects atmospheric chemistry, including ozone and stratospheric water vapour. Its relatively short atmospheric lifetime makes its warming contribution particularly strong over short horizons. The global warming potential compares time-integrated forcing from equal-mass pulses with that of carbon dioxide; the horizon must always be stated. Values available before this examination were about 72 over 20 years and 25 over 100 years, including the specified methane indirect effects, as recorded in the 2007 IPCC assessment. These are historical assessment values, not timeless material constants or instantaneous temperature multipliers.

A separate direct feedback is the ice-albedo feedback. When sea ice disappears, darker open water reflects less sunlight, stores more ocean heat content, and favours further melting and delayed freeze-up. Locally,For illustration, replacing ice of surface albedo $0.6$ by water of surface albedo $0.1$ under $200\mathrm{W}{\mathrm{m}}^{-2}$ incoming sunlight adds $100\mathrm{W}{\mathrm{m}}^{-2}$ of absorption on the newly exposed area. Global forcing requires weighting by affected area, season and clouds; this is a local example. Sea-ice loss can amplify warming through reduced reflection without requiring methane release. Increased evaporation and altered clouds supply further feedbacks, but their short-wave and long-wave effects can compete.