Rayleigh fractionation

Given that the emissions of N2O are enriched in light isotopologues, the isotopic composition of N2O in the troposphere is unexpectedly heavy. As there are no sinks of N2O in the troposphere, there must be an additional flux of heavy N2O to the troposphere. The source of this flux is the stratosphere. Moore (1974) first observed that the stratosphere is enriched in heavy N2O and since then many other measurements have confirmed this. The heavy N2O is introduced into the lower atmosphere through stratosphere-troposphere exchange processes, which balances the light N2O from the surface sources (Yoshida and Matsuo, 1983; Kim and Craig, 1993). All of the heavy N2O isotopologues are enriched in the stratosphere relative to the tropospheric mean and source emissions. Furthermore, the enrichment increases in altitude within the stratosphere as the N2O concentrations decrease (Figs 14.5 and 14.6). For example, d 15Nbulk increases from 7% in

Isotopomer ratio (%o) 0 20 40 60 80 100 120 140 160

Mixing ratio (ppbv)

Fig. 14.5. Vertical profiles of the isotopic enrichment of nitrous oxide (N2O) in the stratosphere over Japan on 31 May 1999. (From Toyoda et al., 2001. Reproduced by permission of American Geophysical Union.)

Mixing ratio (ppbv)

Fig. 14.5. Vertical profiles of the isotopic enrichment of nitrous oxide (N2O) in the stratosphere over Japan on 31 May 1999. (From Toyoda et al., 2001. Reproduced by permission of American Geophysical Union.)

the troposphere to more than 90%o at 35 km in the stratosphere. Likewise, 5448 increases from 20% to ~95% (Toyoda et al., 2001).

For some time the cause of this enrichment was unknown. Laboratory experiments suggested that neither photolysis nor the reaction with O(1D) fractionated N2O (Johnston et al., 1995). As there are no known sources of N2O in the stratosphere, new atmospheric processes were proposed to explain the stratospheric enrichment (McElroy and Jones, 1996; Prasad, 1997; Prasad et al., 1997).

There is now considerable theoretical and experimental evidence which confirms that photolysis is responsible for the enrichment of heavy N2O in the stratosphere (Table 14.2). At wavelengths important for stratospheric photolysis, light N2O is prefer entially dissociated, leaving the remaining N2O pool enriched in 456, 546 and 448. The evolution of the isotopic composition of the N2O pool can be modelled as a Rayleigh fractionation process, which describes how the composition changes after some fraction of the original N2O has been photolysed. For the Rayleigh model to be valid there can be no local N2O sources and the sink must be an irreversible loss process. As N2O is photolyzed, the enrichment of isotopologue X will change from an initial value of do to some later value d as governed by:

where co is the initial concentration of bulk N2O - usually set equal to the tropospheric c c

446 Mixing ratio (ppb)

446 Mixing ratio (ppb)

4

52 44 36 28 20 12

-90 -60 -30 0 30 60 90 Latitude (°)

Fig. 14.6. Modelled enrichments of nitrous oxide (N2O) and its heavy isotopologues. Units are ppbv for 446 and per mil (%o) for the isotopologues. (From McLinden et al., 2003. Reproduced by permission of American Geophysical Union.)

concentration as this is the source of non-photolysed N2O to the stratosphere, and ci is the concentration after some loss has occurred. The constant a is the 'fractionation factor', which is the ratio of isotopologue X's photolysis (or reaction) rate coefficient to that of 446. Since a is quite small, a 'fractionation constant' is defined as e = 1000(1 - a), which has units of per mil (%o). With this definition, the fractionation constant will be negative if the isotopologue is enriched by the loss process and will be positive if it is depleted.

Equation (14.7) can be linearized by making the approximation 8 <<1, in which case ln(1 + 8) ~ 8 and Eq. 14.7 becomes 8i = 8o + e x ln f, where f is the fraction of substrate remaining. The fractionation constant can then be found from a plot of 8i versus

Table 14.2. Fractionation constants measured in the laboratory, stratosphere and calculated in models.

e456 (%)

e546 (%)

15ebulk (%)

e448 (%)

15ebulk/e448 (y)

e456/e546 (n)

Reference

Photolysis experiments (l)

185 nm

-

-

-

< ± 0.3

-

-

Johnston et al. (1995)

-18.6 (0.5)

3.7 (0.2)

-7.5

4.5 (0.2)

-1.7

-5.0

Kaiser et al. (2003)

193 nm

-

-

-18.4

-14.5

1.2 7

-

Rahn et al. (1998)

-35.7 (0.5)

-10.9 (1.7)

-23.3 (0.5)

-17.3 (0.5)

1.35

3.27

Rockmann et al. (2000)

-25.7 (2)

-13.1 (2)

-19.4 (1.2)

-15.9 (3)

1.54

1.96

Turatti et al. (2000)

207 nm

-

-

-48.7

-46

1 .06

-

Rahn et al. (1998)

207.6 nm

-66.5 (5)

-27.1 (6)

-46.8 (5)

-49 (10)

0.96

2.45

Turatti et al. (2000)

211.5 nm

-65.3 (4)

-31.4 (8)

-48.3 (5)

-46 (11)

1.05

2.08

Turatti et al. (2000)

213 nm

-73.5 (5)

-41 (10)

-57 (15)

-

-

1.79

Zhang et al. (2000)

Broadband

-54.0 (1.6)

-21.9 (1.1)

-37.9 (1.1)

34.2 (0.8)

1.11

2.47

Rockmann et al. (2001)

Reaction with O(1D) experiments

-

-

-

-6

-

-

Johnston et al. (1995)

-2.21

-8.79

-

-12.23

0.45

0.25

Kaiser et al. (2002a)

Stratospheric measurements

14-22 km

-

-

-14.5

-12.9

1.12

-

Rahn and Wahlen (1997)

15-35 km

-57.1 (9.5)

-27.3 (13.5)

-42.3(10.1)

-42.6 (29.4)

0.99

2.09

Griffith et al. (2000)

<24 km

-22.9 (1.2)

-8.8 (1.4)

-15.9 (1.1)

-11.5 (1.8)

1.42

2.6

Toyoda et al. (2001)

>24 km

-40.9 (1.3)

-15.5 (0.4)

-28.6 (0.6)

-24.6 (0.6)

1.16

2.63

Toyoda et al. (2001)

10-320 ppbv

-33.4

-16.3 (0.6)

-24.9 (0.7)

-21.4 (0.6)

1.16

2.05

Rockmann et al. (2001a)

200-320 ppbv

-21.3 (1.5)

-12.9 (2.4)

-17.1 (1.6)

-14.0 (2.0)

1.22

1.65

Rockmann et al. (2001a)

<200 ppbv

-30.8 (6.4)

-12.9 (3.0)

-22.1 (4.2)

-18.9 (3.5)

1.17

2.35

Park et al. (2004)

>200 ppbv

-22.4 (2.5)

-7.1 (2.9)

-14.9 (1.1)

-13.3 (0.9)

1.12

2.65

Park et al. (2004)

Modelling studies

193 nm

-13.1

-7.5

-10.3

-9.1

1.13

1.75

Yung and Miller (1997)

207 nm

-30.6

-17.4

-24

-21.3

1.13

1.75

Yung and Miller (1997)

6-310 ppbv

-27.1

-10.6

-19.1

-19.3

0.99

2.56

McLinden et al. (2003)

200-310 ppbv

-19.5

-7.4

-13.4

-14.0

0.96

2.63

McLinden et al. (2003)

10-170 ppbv

-30.4

-11.7

-21.1

-21.8

0.97

2.60

McLinden et al. (2003)

k lnf. Although numerous authors use the linearized form, the approximation introduces errors of 1% for d = 20V and 5%0 for d = 100V (Kaiser et al., 2002a; Morgan et al., 2004). Therefore, it is more accurate to find e by plotting the whole left-hand side of Eq. 14.7 against ln f.

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