The global atmospheric lifetime (yr) characterises the time required to turn over the global atmospheric burden. It is defined as the burden (Tg) divided by the mean global sink (Tg/yr) for a gas in steady state (i.e., with unchanging burden). This quantity was defined as both �lifetime� and �turnover time� in the SAR (see also Bolin and Rodhe, 1973). Lifetimes calculated in this manner are listed in Table 4.1. A corollary of this definition is that, when in steady state (i.e., source strength = sink strength), the atmospheric burden of a gas equals the product of its lifetime and its emissions. A further corollary is that the integrated atmospheric abundance following a single emission is equal to the product of its steady-state lifetime for that emission pattern and the amount emitted (Prather, 1996). This latter, new result since the SAR supports the market-basket approach of aggregating the direct emissions of different greenhouse gases with a GWP (Global Warming Potential) weighting.

The atmospheric lifetime is basically a scale factor relating (i) constant emissions (Tg/yr) to a steady-state burden (Tg), or (ii) an emission pulse (Tg) to the time-integrated burden of that pulse (Tg/yr). The lifetime is often additionally assumed to be a constant, independent of the sources; and it is also taken to represent the decay time (e-fold) of a perturbation. These latter assumptions apply rigorously only for a gas whose local chemical lifetime is constant in space and time, such as for the noble gas radon, whose lifetime is fixed by the rate of its radioactive decay. In such a case the mean atmospheric lifetime equals the local lifetime: the lifetime that relates source strength to global burden is exactly the decay time of a perturbation.

This general applicability of the atmospheric lifetime breaks down for those greenhouse gases and pollutants whose chemical losses vary in space and time. NO_x, for instance, has a local lifetime of <1 day in the lower troposphere, but >5 days in the upper troposphere; and both times are less than the time required for vertical mixing of the troposphere. In this case emission of NO_x into the upper troposphere will produce a larger atmospheric burden than the same emission into the lower troposphere. Consequently, the definition of the atmospheric lifetime of NO_x is not unique and depends on the location (and season) of its emissions. The same is true for any gas whose local lifetime is variable and on average shorter than about 0.5 year, i.e., the decay time of a north-south difference between hemispheres representing one of the longer time-scales for tropospheric mixing. The majority of greenhouse gases considered here have atmospheric lifetimes greater than 2 years, much longer than tropospheric mixing times; and hence their lifetimes are not significantly altered by the location of sources within the troposphere. When lifetimes are reported for gases in Table 4.1, it is assumed that the gases are uniformly mixed throughout the troposphere. This assumption is unlikely for gases with lifetimes <1 year, and reported values must be viewed only as approximations.

Some gases have chemical feedbacks that change their lifetimes. For example, the increasing CH₄ abundance leads to a longer lifetime for CH₄ (Prather et al., 1995; Schimel et al., 1996). A chemical feedback with opposite effect has been identified for N₂O where a greater N₂O burden leads to increases in stratospheric NO_x which in turn depletes mid-stratospheric ozone. This ozone loss enhances the UV, and as a consequence N₂O is photolysed more rapidly (Prather, 1998). Such feedbacks cause the time-scale of a perturbation, henceforth called perturbation lifetime (PT), to differ from the global atmospheric lifetime (LT). In the limit of small perturbations, the relation between the perturbation lifetime of a gas and its global atmospheric lifetime can be derived from a simple budget relationship as PT = LT / (1 - s), where the sensitivity coefficient s = ðln(LT) / ðln(B) and B = burden. Without a feedback on lifetime, s = 0, and PT is identical to LT. The product, PT times a sustained change in emission, gives the resulting change in the burden. The ratio of PT/LT adopted here for CH₄, 1.4, is based on recent model studies (see Section 4.4) and is consistent with the SAR results.

To evaluate the total greenhouse effect of a given gas molecule, one needs to know, first, how long it remains in the atmosphere and, second, how it interacts chemically with other molecules. This effect is calculated by injecting a pulse of that gas (e.g., 1 Tg) into the atmosphere and watching the added abundance decay as simulated in a CTM. This decay is represented by a sum of exponential functions, each with its own decay time. These exponential functions are the chemical modes of the linearised chemistry-transport equations of the CTM (Prather, 1996). In the case of a CH₄ addition, the longest-lived mode has an e-fold time of 12 years, close to the perturbation lifetime (PT) of CH₄, and carries most of the added burden. (This e-fold time was called the adjustment time in the SAR.) In the case of a CO addition, this same mode is also excited, but at a reduced amplitude (Prather, 1996; Daniel and Solomon, 1998). The pulse of added CO, by causing the concentration of OH to decrease and thus the lifetime of CH₄ to increase temporarily, causes a build-up of CH₄ while the added burden of CO persists. After the initial period of a few months defined by the CO photochemical lifetime, this built-up CH₄ then decays in the same manner as would a direct pulse of CH₄. Similarly, an addition of NO_x (e.g., from aviation; see Isaksen and Jackman, 1999) will excite this mode, but with a negative amplitude. Thus, changes in the emissions of short-lived gases can generate long-lived perturbations as shown in 3-D CTMs (Wild and Prather, 2000; Derwent et al., 2001). Changes in tropospheric O₃ accompany the CH₄ decay on a 12 year time-scale as an inherent component of this mode, a key example of chemical coupling in the troposphere. Thus, any chemically reactive gas, whether a greenhouse gas or not, will produce some level of indirect greenhouse effect through its impact on atmospheric chemistry.

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