## The Lifetime Of A Greenhouse Gas In The Earths Atmosphere

The microscopic radiative efficiency of a greenhouse gas is determined by measuring absolute absorption coefficients for infra-red-active vibrations in the range ca. 400 2000 cm 1 and integrating over this region of the electromagnetic spectrum. Its meaning is unambiguous. The lifetime, however, is a term that can mean different things to different scientists, according to their discipline. It is, therefore, pertinent to describe exactly what is meant by the lifetime of a greenhouse gas (penultimate row of Table 2), and how these values are determined.

To a physical chemist, the lifetime generally means the inverse of the pseudo-first-order rate constant of the dominant chemical or photolytic process that removes the pollutant from the atmosphere. Using CH4 as an example, it is removed in the troposphere via oxidation by the OH free radical, OH + CH4 ! H2O + CH3. The rate coefficient for this reaction at 298 K is 6.4 x 10 15 cm3 molecules 1s 1 [9], so the lifetime is approximately equal to (k298[OH]) 1. Assuming the tropospheric OH concentration to be 0.05 pptv or 1.2 x 106 molecules cm 3 [2], the lifetime of CH4 is calculated to be ca. 4 a. This is within a factor of three of the accepted value of 12 a (Table 2). The difference arises because CH4 is not emitted uniformly from the earth's surface, a finite time is needed to transport CH4 via convection and diffusion into the troposphere, and oxidation occurs at different altitudes in the troposphere where the OH concentration varies from its average value of 1.2 x 106 molecules cm 3. We can regard this as an example of a two-step kinetic process,

with first-order rate constants k1 and k2. The first step, A ! B, represents the transport of the pollutant into the atmosphere, whilst the second step, B ! C, represents the chemical or photolytic process (e.g., reaction with an OH radical in the troposphere) that removes the pollutant from the atmosphere. In general, the overall rate of the process (whose inverse is called the lifetime) will be a function of both k1 and k2, but its value will be dominated by the slower of the two steps. Thus, in calculating the lifetime of CH4 simply by determining (k298[OH]) 1, we are assuming that the first step, transport into the region of the atmosphere where chemical reactions occurs, is infinitely fast compared to the removal process.

The exceptionally long-lived greenhouse gases in Tables 1 and 2 (e.g., SF6, CF4, SF5CF3) behave in the opposite sense. Now, the slow, rate-determining process is the first step, that is, transport of the greenhouse gas from the surface of the earth into the region of the atmosphere where chemical removal occurs. The chemical or photolytic processes that ultimately remove SF6, etc., will have very little influence on the lifetime, that is, k1 ^ k2 in Eq. (6). These molecules do not react with OH or O* (1D) to any significant extent, and are not photolysed by visible or UV radiation in the troposphere or stratosphere. They therefore rise higher into the mesosphere (h > 60 km) where the dominant processes that can remove pollutants are electron attachment and vacuum-UV photodissociation at the Lyman-a wavelength of 121.6 nm [6]. We can define a chemical lifetime, tchemical, for such species as:

ke is the electron attachment rate coefficient, ct1216 is the absorption cross-section at this wavelength, [e ] is the average number density of electrons in the mesosphere, J1216 is the mesospheric solar flux and F1216 the quantum yield for dissociation at 121.6 nm. Often, the photolysis term is much smaller than the electron-attachment term, and the second term of the squared bracket in Eq. (7) is ignored. It is important to appreciate that the value of tchemical is a function of position, particularly altitude, in the atmosphere. In the troposphere, tchemical will be infinite because both the concentration of electrons and J1216 are effectively zero, but in the mesosphere tchemical will be much less. However, multiplication of ke for SF6, etc., by a typical electron density in the mesosphere, ca. 104 cm 3 [10], yields a chemical lifetime which is far too small and bears no relation to the true atmospheric lifetime, simply because most of the SF6, etc., does not reside in the mesosphere.

One may, therefore, ask where the quoted lifetimes for SF6, CF4 and SF5CF3 of 3200, 50 000 and 800 a, respectively, come from [8,11]. The lifetimes of such long-lived greenhouse gas can only be obtained from globally averaged loss frequencies. The psuedo-first-order destruction rate coefficient for each region of the atmosphere is weighted according to the number of molecules of compound in that region, tchemical — [ke [e ] + ^121.6^121.6^121.6]

(k) global

(k) global

where i is a region, ki is the pseudo-first-order removal rate coefficient for region i, Vi is the volume of region i, and ni is the number density of the greenhouse gas under study in region i. The lifetime is then the inverse of (k)global. The averaging process thus needs input from a 2- or 3-dimensional model of the atmosphere in order to supply values for ni. This is essentially a meteorological, and not a chemical problem. It may explain why meteorologists and physical chemists sometimes have different interpretations of what the lifetime of a greenhouse gas actually means.

Many such studies have been made for SF6 [8,12,13], and differences in the kinetic model (ki) and the atmospheric distributions (ni) from different climate or transport models account for the variety of atmospheric lifetimes that have been reported. The importance of both these factors has also been explored by Hall and Waugh [14]. Their results show that because the fraction of the total number of SF6 molecules in the mesosphere is very small, the global atmospheric lifetime given by Eq. (8) is very much longer than the mesospheric, chemical lifetime given by Eq. (7). Thus, they quote that if the mesospheric loss frequency is 9 x 10 8 s 1, corresponding to a local lifetime of 129 d (days), then the global lifetime ranges between 1425 and 1975 a, according to which climate or transport model is used.

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