Oxygen Isotopic Composition of Carbon Dioxide in the Middle Atmosphere
Mao-Chang Liang1*, Geoffrey A. Blake1, Brenton R. Lewis2, and Yuk L. Yung1
1
Division of Geological and Planetary Sciences, California Institute of Technology, 1200 E.
California Blvd., Pasadena, CA 91125
2
Research School of Physical Sciences and Engineering, The Australian National
University, Canberra, ACT 0200, Australia
*
To whom all correspondence should be addressed. E-mail: mcl@gps.caltech.edu
The isotopic composition of long-lived trace molecules provides a window into
atmospheric transport and chemistry. Carbon dioxide is a particularly powerful
tracer, because its abundance remains >100 ppmv in the mesosphere. For the first
time, we successfully reproduce the isotopic composition of CO2 in the middle
atmosphere. The mass-independent fractionation of oxygen in CO2 can be
satisfactorily explained by the exchange reaction with O(1D). In the stratosphere, the
major source of O(1D) is O3 photolysis. Higher in the mesosphere, we discover that the
photolysis of 16O17O and 16O18O by solar Lyman- radiation yields O(1D) 10-100 times
more enriched in 17O and 18O than that from ozone photodissociation. New laboratory
and atmospheric measurements are proposed to test our model and validate the use of
CO2 isotopic fractionation as a tracer of atmospheric chemical and dynamical
processes. Coupled with climate models, the ‘anomalous’ oxygen signature in CO2 can
be used in turn to study biogeochemical cycles, in particular to constrain the gross
carbon fluxes between the atmosphere and terrestrial biosphere.
1
Of the many trace molecules that can be used to examine atmospheric transport processes
and chemistry (e.g., CH4, N2O, SF6, and the CFCs), carbon dioxide is unique in the middle
atmosphere, because of its high abundance (~370 ppmv in the stratosphere, dropping to
~100 ppmv at the homopause). The mass independent isotopic fractionation (MIF) of
oxygen first discovered in ozone (1, 2) is thought to be partially transferred to carbon
dioxide (3, 4) via the reaction O(1D) + CO2 in the middle atmosphere (5). Indeed, while the
reactions of trace molecules with O(1D) usually lead to their destruction, the O(1D) + CO2
reaction regenerates carbon dioxide. This ‘recycled’ CO2 is unique in its potential to trace
the chemical (reactions involving O(1D) in either a direct or indirect way) and dynamical
processes in the middle atmosphere. When transported to the troposphere, it will produce
measurable effects in biogeochemical cycles involving CO2 (6).
In particular, the extraordinary MIF seen initially in ozone (1, 2) has since been extended to
long-lived
trace
molecules
such
as
N 2O
and
CO2
(3,
4, 7-9).
The
first
stratospheric/mesospheric measurements of 17O(CO2) and 18O(CO2) at 30 N by
Thiemens et al. (4) led to a suggestion that the MIF in stratospheric CO2 is caused by
isotopic exchange between CO2 and O3, mediated by the reaction with O(1D) (5).
(17O(CO2) and 18O(CO2) are isotopic fractionation of 17O and 18O in CO2 relative to that
in a selected standard. See below.)
Subsequent stratospheric measurements at latitudes of 43.7 and 67.9 N (10) revealed
larger fractionations in both 17O(CO2) and 18O(CO2) than those seen at 30 N over a
similar altitude range. Yung et al. (5) suggested upwelling of tropospheric air from the
tropics and downwelling at about 30 N could dilute the magnitude of isotopic
fractionation, further illustrating the critical role that transport plays in establishing the
isotopic systematics of CO2 in the middle atmosphere.
2
In three-isotope plots, the mass-dependent fractionation of oxygen has a slope of 17O/18O
= m  0.5; yet least squares fits to the 30 N and 43.7/67.9 N CO2 data sets give m =
1.210.08 and 1.710.03, respectively, while m = 2.060.58 for samples from the Arctic
vortex (11) and 1.470.14 from the lower stratosphere (12). Slopes near 1.6-1.7 have been
successfully reproduced in the laboratory under ~stratospheric conditions (13). Within the
framework of Yung et al.'s mechanism (5), the range of measured slopes reflects the variety
of transport histories of air parcels and sources of O(1D), which have not yet been fully
established in previous studies. The magnitude of 17O(CO2) or 18O(CO2) can, in
principle, be used to determine how the air parcels are transported, but only if all sources of
O(1D) are accounted for. As we discuss below, while ozone photolysis is the dominant
source of O(1D) in the stratosphere, other sources must be considered at higher altitudes.
These have not been included in previous models, and, as a result, the transport history of
the air parcels as inferred by 17O(CO2) or 18O(CO2) alone tends to be ambiguous. This
ambiguity (sources of O(1D) and history of air parcels) can largely be resolved when both
17O(CO2) and 18O(CO2) are analyzed.
To avoid uncertainties due to stratosphere-troposphere exchange processes and possible
contamination from tropospheric water, we place our focus on the data taken above the
tropopause. Two data sets (4, 10) are selected for this study. We defer the discussion for the
rest of data (11, 12) to a later paper with results from multi-dimensional models.
Mechanism. The MIF of CO2 is the consequence of the following reactions (5):
16
O(1D) + C16O16O  C16O16O + 16O
17
O(1D) + C16O16O  C16O17O + 16O
k1 = 2k(1 + 1)
16
O(1D) + C16O17O  C16O16O + 17O
k2 = 2k(1 + 2)
18
O(1D) + C16O16O  C16O18O + 16O
k3 = 2k(1 + 3)
3k
3
16
O(1D) + C16O18O  C16O16O + 18O
k4 = 2k(1 + 4),
where O is either O(1D) or O(3P) (elastic or inelastic collisions) and 1-4 are the
fractionation in the rate coefficients. The resulting isotopic composition of CO2 in
equilibrium (in the absence of transport) is then determined simply by the isotopic
composition of O(1D), i.e., [C16O17O]/[C16O18O] = (k1k4)/(k2k3) [17O(1D)]/[18O(1D)].
However, the chemical exchange time ex is >> vertical mixing time tr, and, as a result, the
age of air can have a significant impact on the magnitude of 17O(CO2) and 18O(CO2). For
example, at an altitude of ~45 km, where O(1D) peaks, ex is ~108 s while that for tr is ~107
s; the ‘age’ of air entering from the troposphere is ~108 s (14). During the time air ascends
from the tropopause to this altitude, vertical mixing acts to dilute the isotopic fractionation
of CO2. Thus, as the system approaches steady state, the isotopic composition of CO2 is
determined by the combination of the isotopic composition of O(1D) and transport.
Limits to the slope m can be estimated by assuming isotopic equilibrium between CO2 and
O(1D), since transport will only dilute the magnitude of both 17O and 18O with equal
proportionality. Based on Yung et al.'s mechanism, 17O and 18O can be approximated by
17O(CO2)  1 - 2 + 17O(1D) - 17O(CO2)0
(1)
18O(CO2)  3 - 4 + 18O(1D) - 18O(CO2)0
(2)
where 17O(CO2) and 18O(CO2) are the enrichments of CO2 relative to the tropospheric
values of 17O(CO2)0  9 and 18O(CO2)0  17 per mil. In this paper, we follow the notation
used in a companion paper that discuss the isotopic fractionation of ozone (15) in which the
enrichments are referenced to atmospheric O2, unless otherwise stated. (Tropospheric
values of CO2 are, respectively, 21 and 41 per mil relative to the Vienna Standard Mean
Ocean Water.) If the reaction rate with O(1D) is scaled by the reduced mass of each
colliding pair, the 1-4 values are -21.8, -3.0, -41.6, -5.8 per mil. The quenching reactions
4
of O(1D) with O2/N2 provide additional enrichments of 19.8/18.9 and 37.7/36.0 to 17O(1D)
and 18O(1D), respectively, and since these effects are of opposite sign and similar in
magnitude the reduced mass effect in Eqs.(1) and (2) is small. The slope m can thus be well
approximated by (17O(1D) - 17O(CO2)0)/(18O(1D) - 18O(CO2)0).
Sources of O(1D). More quantitative calculations of the three-isotope slope m are obtained
via recent kinetic calculations that model the isotopic fractionation of ozone versus altitude
(15). Contributions to the enrichments of isotopically heavy ozone follow from two
processes: chemical formation (16) and UV photolysis (17, 18). Using the model that
reproduces the observed enrichments in a three-isotope plot of O3 (15), the computed
equilibrium values of m (in the absence of transport) at altitudes between 30 and 60 km,
where most of exchange reaction takes place, range from 1.3-3.0. Over the same altitude
range (after taking transport into account) as that of the CO2 measurements in the
stratosphere, the slope m is 1.60, which is in good agreement with the measured value of
~1.7 (10).
At altitudes greater than 70 km, the photodissociation of O2 becomes the dominant source
of O(1D). Exchange of O(1D) with CO2 at these altitudes could therefore modify the slope
m if the O(1D) from O2 photolysis is isotopically distinct from that generated in the
stratosphere. Using a semi-analytical calculation of the photolysis-induced fractionation
(17, 18) in the Schumann-Runge bands of O2, the calculated enrichment of heavy O(1D) is
100 per mil (Figure 1). However, a recent laboratory measurement of O2 dissociation near
Lyman- (121.567 nm) has shown that the cross section and O(1D) yield are strong
functions of wavelength, and suggests extremely large isotopic dependence (19). Although
the cross section near Lyman- is 2-3 orders of magnitude less than those in the SchumannRunge bands, the solar flux is correspondingly enhanced, compared with that in the
5
Schumann-Runge bands. For T = 100-300 K, we have computed the isotopic dependence of
the O2 dissociation cross section and O(1D) yield near Lyman- (Figure 2), using the model
described elsewhere (19). These cross sections, together with the solar spectrum, yield
calculated values of 17O(1D) and 18O(1D) resulting from O2 photolysis that peak at about
80 km with sizes of 3137.1 and 10578.6 per mil, respectively. These fractionations are
enormous and give m  0.3. Thus, even small amounts of mixing of mesospheric air with
the m = 1.6 gas that characterizes the stratosphere can provide an explanation for the m 
1.2 fractionation observed in CO2 by Thiemens et al. (4). We stress that Lyman-
photolysis of O2 as a source of heavy O(1D) has not been considered in previous models.
In addition to the mechanism of transferring heavy oxygen atoms from O3 and O2 to CO2,
we also include the effect of CO2 photolysis. We calculate the photolysis-induced isotopic
fractionation for CO2 based on Yung and Miller's model (20). Though the photolysisinduced fractionation of oxygen in CO2 can be as large as 100 per mil at selected
wavelengths (21), the overall effect of UV photolysis is always insignificant compared with
the exchange processes. Shown in Figure 3 are vertical profiles for two processes, CO2
photolysis and CO2 + O(1D) exchange reactions. Below ~70 km, although the fractionation
in CO2 photochemistry is >100 per mil, the photolysis rates are negligible compared with
the exchange reaction rates (Figure 3). Above 70 km, the photolysis-induced fractionation
is small, because most of absorption happens near the maximum of absorption cross
section, where only small photolytic isotopic effects are seen (17, 18).
One-Dimensional Model. To provide a more quantitative assessment of the probable
impact of the multiple sources of O(1D), the results of a one-dimensional atmospheric
model are summarized in Figure 4. The dominant slope of ~1.6-1.7 is produced by the
O(1D) from ozone photolysis, and reproduces the stratospheric data well. As the inset in
6
Figure 4 shows, the heavy O atoms from O2 Lyman- photolysis can greatly modify the
isotopic composition of CO2 at altitudes >40 km. To provide a better agreement with the
stratospheric data (10), the eddy coefficients below 40 km in this calculation have been
reduced by 30% compared to those derived by Allen et al. (22). The disagreement of the
model results with the measurements of Thiemens et al. (4) is most likely due to circulation
cells between the tropics and ~30 N, where the air is significantly younger than that at
higher latitudes and similar altitudes (5, 14), but this difference cannot be resolved
satisfactorily without two- or three-dimensional simulations. Indeed, we expect that multilatitude and, especially, additional mesospheric measurements of m, when combined with
proper models, should be able to refine our understanding of atmospheric transport and
chemical processesespecially in the remote regions of the mesosphere.
Three-Box Model. Finally, we use a three-box model to evaluate the potential impact of
transport on the slope and magnitude of the CO2 isotopic fractionation. Box 1 (fresh air
from the troposphere) has 17O(CO2)t = 9 and 18O(CO2)t = 17 per mil. Box 2 (the
stratosphere) has 17O(CO2)s = 17O(1D) = 93 and 18O(CO2)s = 18O(1D) = 69 per mil,
values defined by chemical equilibrium with O(1D) from O3. Box 3 (the mesosphere) has
17O(CO2)m = 17O(1D) = 3137 and 18O(CO2)m = 18O(1D) = 10579 per mil, that are
predicted from the Lyman- photolysis of O2. The isotopic composition of CO2 is
determined by the mixing of air from these boxes, or
17O(CO2) = xt17O(CO2)t + xs17O(CO2)s + xm17O(CO2)m - 17O(CO2)0
(3)
18O(CO2) = xt18O(CO2)t + xs18O(CO2)s + xm18O(CO2)m - 18O(CO2)0
(4)
7
where xt, xs, and xm are the fractions of air from boxes 1, 2, and 3, and xt + xs + xm = 1. For
atmospheric CO2, xm << xs < xt.
Figure 4 gives an illustration of this simple model. It is shown that the magnitude of
17O(CO2) increases with the age of the air parcel, i.e., more CO2 exchanging with O(1D)
from boxes 2 and 3. The solid line in this figure shows values of 17O(CO2) obtained by
varying xt while xm = 0. The symbols represent 17O(CO2) with different degrees of mixing
with box 3 after mixing of air from boxes 1 and 2.
The mixing of boxes 1 and 2 produces a slope of 1.6, as shown in the solid line of Figure 6.
When mixing in air from box 3 the slope is modified, and the dotted line represents the
cases for which (xt, xm) = (0.80, 0), (0.75, 0.0005) and (0.70, 0.001). The two extreme data
points from Figure 4 that are overplotted by asterisks can be explained by only ~0.02%
mixing with box 3. Similar analyses can be applied to the rest of the data. In general, we
predict that in the middle atmosphere air recently entrained from the troposphere would
have CO2 isotopic compositions characterized by stratospheric ozone, while the O(1D) from
O2 photolysis would play a part in air parcels exposed to the mesosphere.
In summary, we have demonstrated that the isotopic composition of CO2 is potentially an
exceptionally useful tracer in studying the dynamical and chemical processes in the middle
atmosphere. Furthermore, this ‘recycled’ CO2 carries an isotopic composition distinct from
that in the troposphere, and as such is a powerful tracer of biogeochemical CO2 cyclesin
particular those involving the terrestrial biosphere (6). The large isotopic fractionation of
O2 resulting from the Lyman- photolysis could be preserved in ice cores from polar
regions in which downwelling air is prevalent (23). The observed depletion of 18O(O2) at
53.3 and 59.5 km (4) is also likely the consequence of this O2 Lyman- photolysis.
Experimentally, laboratory measurements of the dissociation cross sections of isotopically
8
substituted O2 near Lyman- (121.567 nm) are urgently needed. Observationally, more
mesospheric measurements of CO2, along with two- or three-dimensional atmospheric
simulations, will significantly expand our understanding of the dynamical and chemical
history of trace molecules in the atmosphere.
9
References
1.
2.
3.
4.
Mauersberger, K. (1981) Geophysical Research Letters 8, 935-937.
Thiemens, M. H. & Heidenreich, J. E. (1983) Science 219, 1073-1075.
Thiemens, M. H. (1999) Science 283, 341-345.
Thiemens, M. H., Jackson, T., Zipf, E. C., Erdman, P. W. & Vanegmond, C. (1995)
Science 270, 969-972.
5. Yung, Y. L., Lee, A. Y. T., Irion, F. W., DeMore, W. B. & Wen, J. (1997) Journal of
Geophysical Research-Atmospheres 102, 10857-10866.
6. Hoag, K. J., Still, C. J., Fung, I. Y. & Boering, K. A. (2005) Geophysical Research
Letters 32.
7. Cliff, S. S., Brenninkmeijer, C. A. M. & Thiemens, M. H. (1999) Journal of Geophysical
Research-Atmospheres 104, 16171-16175.
8. Cliff, S. S. & Thiemens, M. H. (1997) Science 278, 1774-1776.
9. Röckmann, T., Kaiser, J., Crowley, J. N., Brenninkmeijer, C. A. M. & Crutzen, P. J.
(2001) Geophysical Research Letters 28, 503-506.
10. Lämmerzahl, P., Röckmann, T., Brenninkmeijer, C. A. M., Krankowsky, D. &
Mauersberger, K. (2002) Geophysical Research Letters 29.
11. Alexander, B., Vollmer, M. K., Jackson, T., Weiss, R. F. & Thiemens, M. H. (2001)
Geophysical Research Letters 28, 4103-4106.
12. Boering, K. A., Jackson, T., Hoag, K. J., Cole, A. S., Perri, M. J., Thiemens, M. &
Atlas, E. (2004) Geophysical Research Letters 31. 10
13. Chakraborty, S.&Bhattacharya, S. K. (2003) Journal of Geophysical ResearchAtmospheres 108.
14. Hall, T. M.,Waugh, D.W., Boering, K. A. & Plumb, R. A. (1999) Journal of
Geophysical Research-Atmospheres 104, 18815-18839.
15. Liang, M. C., Irion, F. W., Weibel, J. D., Miller, C. E., Blake, G. A. & Yung, Y. L.
(2005) Journal of Geophysical Research-Atmospheres, 111, D02302,
doi:10.1029/2005JD006342.
16. Gao, Y. Q. & Marcus, R. A. (2001) Science 293, 259-263.
17. Blake, G. A., Liang, M. C., Morgan, C. G. & Yung, Y. L. (2003) Geophysical
Research Letters 30, art. no.-1656.
18. Liang, M. C., Blake, G. A. & Yung, Y. L. (2004) Journal of Geophysical ResearchAtmospheres 109 (D10), art. No. D10308.
19. Lacoursi`ere, J., Meyer, S. A., Faris, G. W., Slanger, T. G., Lewis, B. R. & Gibson, S.
T. (1999) Journal of Chemical Physics 110, 1949-1958.
20. Yung, Y. L. & Miller, C. E. (1997) Science 278, 1778-1780.
21. Bhattacharya, S. K., Savarino, J.&Thiemens, M. H. (2000) Geophysical Research
Letters 27, 1459-1462.
22. Allen, M., Yung, Y. L. & Waters, J. W. (1981) Journal of Geophysical Research-Space
Physics 86, 3617-3627.
23. Luz, B., Barkan, E., Bender, M. L., Thiemens, M. H. & Boering, K. A. (1999) Nature
400, 547-550. 11
24. Anbar, A. D., Allen, M. & Nair, H. A. (1993) Journal of Geophysical Research-Planets
10
98, 10925-10931.
25. Lee, L. C., Slanger, T. G., Black, G. & Sharpless, R. L. (1977) Journal of Chemical
Physics 67, 5602-5606.
26. Nicolet, M. (1984) Planetary and Space Science 32, 1467-1468.
27. Samson, J. A. R., Rayborn, G. H. & Pareek, P. N. (1982) Journal of Chemical Physics
76, 393-397.
Acknowledgement
Special thanks to G. R. Gladstone for the solar Lyman- flux, and S. T. Gibson for
providing his coupled-channel code. We thank B. C. Hsieh, X. Jiang, and R. L. Shia for
helping us with the model, and M. Gerstell, H. Hartman, A. Ingersoll, J. Kaiser, C. Miller,
H. Pickett, T. Röckmann, and all of the members in our group for their helpful comments.
This work was supported by an NSF grant ATM-9903790.
11
Figure Captions
Figure 1. Fractionation factors of molecular oxygen in the vacuum ultraviolet calculated
using the model described in Liang et al. (15). Results using the Yung and Miller's model
(20) are shown by dotted lines. The fractionation factor is defined by 1000(/0 - 1),
where 0 and  are the photoabsorption cross sections of normal and isotopically
substituted molecules, respectively. The absorption cross section of normal O2 is taken
from literature (24-27).
Figure 2. Absorption cross sections for O2 that lead to the production of O(3P) and O(1D)
near Lyman-, the solar profile of which is shown by the dotted line. All quantities are
normalized by the maximum value in each spectrum. Normalization factors for the Lyman, cross sections at 100, 200, and 300 K are 5.11011 photons cm-2 s-1 Å-1, 1.7310-18,
1.7510-18, and 1.7610-18 cm2, respectively.
Figure 3. Vertical reaction rate profiles for the CO2 + O(1D) chemical exchange (solid line)
and CO2 photolysis (dotted line).
Figure 4. Three-isotope plot of oxygen in CO2, from which the tropospheric values have
been subtracted. The atmospheric measurements are from Lämmerzahl et al. (10) (circles)
and from Thiemens et al. (4) (asterisks). The solid line depicts the model, and the change in
slope at A corresponds to altitudes of ~60-80 km. At higher altitudes (and for fractionations
greater than these fiducial values), the slope m(A-B) is ~0.3as expected from oxygen
photolysis. Another change of slope in the calculation occurs at B for altitudes of ~90 km
and higher. Over this range, molecular diffusion dominates, and the slope becomes mass
dependent, that is ~0.5 (dash-dotted line). Inset: vertical profiles of 18O(CO2). The dotted
12
line represents the results excluding the fractionation of O(1D) from O2 photolysis over the
solar Lyman- emission.
Figure 5. A three-box mixing model for CO2 in the middle atmosphere. The solid line
represents the mixing of boxes 1 (troposphere) and 2 (stratosphere) only, while the symbols
denote additional mixing with box 3 to varying extent. Squares: no mixing with box 3.
Triangles: 0.05% of air from box 3. Diamonds: 0.1% of air from box 3. The two arrows
indicate the direction in which the fractionation changes as the age of the air is increased.
Figure 6. The notation and symbols are the same as those in Figs. 4 and 5. The solid line
illustrates the fractionation expected from the interaction of CO2 and O3 only, while the
dotted line presents an example of how the three isotope slope can be flattened by the
mixing of air from boxes 2 (stratosphere) and 3 (mesosphere).
13