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On the contribution of anthropogenic Cl to the increase in d13C of atmospheric methane
James S. Wang, Michael B. McElroy, Clarissa M. Spivakovsky, and Dylan B. A. Jones
Department of Earth and Planetary Sciences and
Division of Engineering and Applied Sciences,
Harvard University
29 Oxford Street, Cambridge, MA 02138
Accepted for publication in Global Biogeochemical Cycles. Copyright 2002 American Geophysical Union. Further reproduction or electronic distribution is not permitted.
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Abstract. A two-dimensional model is used to evaluate the impact of stratospheric chlorine on
δ13C of CH4 at the surface and to analyze sensitivity to different chemical and transport processes. It is found that the impact of Cl depends on the relative strength of the lower and upper
branches of the stratospheric circulation, which emphasize regions of differing rates of methane
fractionation. It is estimated that the increase in concentrations of Cl associated with human
activity has contributed at most 0.54‰ to the 2‰ increase of δ13C observed over the past century.
It follows that growth in the relative importance of heavier sources of CH4 (associated for example with fossil fuels and biomass burning) has been largely responsible for the trend.
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1. Introduction
Methane (CH4) is important both as a greenhouse gas and as a chemically reactive trace
species in the atmosphere. Its concentration has increased rapidly over the past three centuries
[Etheridge et al., 1998]. Current levels are unprecedented over at least the past 420,000 years
[Petit et al., 1999]. The rate of growth slowed in the 1980s [Steele et al., 1992; Dlugokencky et
al., 1998; Dlugokencky et al., 2001], leading several groups to suggest that the CH4 source had
stabilized [Dlugokencky et al., 1998; Lassey et al., 2000]. Factors influencing trends in CH4 are
not well understood, however. There are significant uncertainties in the magnitudes and trends of
CH4 sinks and in the contributions of individual sources to overall emissions.
Measurements of the isotopic composition of CH4 can provide important constraints on
the contributions from individual sources (e.g. Stevens and Rust, 1982; Tyler, 1986). Methane
produced by bacterial activity (e.g. wetlands and domestic livestock) is isotopically depleted, or
“light”, while CH4 formed thermogenically (e.g. fossil fuels and biomass burning) is isotopically
enriched, or “heavy”. The isotopic composition (for carbon in this case) is defined conventionally
using the delta notation:
R sample
13
- – 1 × 1000 ,
δ C ≡  ------------------- R s tan dard

where Rsample is the ratio of 13C to 12C in the sample, and Rstandard equals 0.011237 (Peedee
belemnite); units are per mil (‰). The isotopic composition at a given location depends not only
on the mix of sources but also on the isotopic fractionation resulting from chemical reactions
undergone subsequent to emission. Typically, isotopically light species react more rapidly than
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their heavier isotopomers. The fractionation factor for a specific loss reaction is specified by η =
k12/k13, where k12 and k13 denote the rate coefficients for removal of 12CH4 and 13CH4 respectively; η is also known as the kinetic isotope effect (KIE). The experimentally and theoretically
determined values of KIE for individual CH4 sinks are given in Table 1. Note that the KIE for
reaction of Cl with CH4 is large compared to that for other loss processes.
From ice core measurements, Craig et al. [1988] determined that the δ13C of atmospheric
CH4 increased by close to 2‰ over the past century. Measurements on atmospheric and firn air
indicate a positive recent trend of 0.3-1.0‰ per decade [Stevens, 1988; Francey et al., 1999]. By
way of comparison, the current peak-to-peak amplitude of the seasonal variation of δ13C ranges
from 0.1‰ to 0.2‰ at Southern Hemisphere sites, and from 0.1‰ to 0.4‰ at Northern Hemisphere sites; the pole-to-pole difference is ~0.5‰ [Quay et al., 1999]. Since loss of CH4 is controlled primarily by reaction with OH in the troposphere, the potential influence of fractionation
contributed by loss processes in the stratosphere was omitted in a number of budget studies (e.g.
Craig et al., 1988; Francey et al., 1999). Gupta et al. [1996] pointed out however that the
increase in the concentration of Cl in the stratosphere as a result of anthropogenic emissions of
CFCs and other Cl precursors may have contributed significantly to the trend of δ13C, given the
large magnitude of the KIE for the Cl + CH4 reaction. Using a 2-D model of the atmosphere from
the surface to 24.5 km altitude, Gupta et al. concluded that growth in Cl over the past century
could have led to an increase in δ13C of 0.7‰ at the surface, assuming that pre-1930 concentrations of Cl were equal to 20% of present-day levels. According to their analysis, Cl in the stratosphere (natural plus anthropogenic) is responsible for a contemporary enrichment of δ13C of 1‰
at the surface. More recently, McCarthy et al. [2001], using a 2-D stratospheric model, reported a
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smaller value of 0.5‰ for enrichment by the total burden of Cl. The relative importance for δ13C
of a varying level of stratospheric Cl and a changing mix of emissions is re-examined in this
paper.
Tans [1997] noted that the isotopic composition of a species equilibrates more slowly after
a perturbation than the total concentration of the species. This suggests that the values for the
present-day impact of stratospheric Cl on δ13C calculated by Gupta et al. [1996] and McCarthy et
al. [2001] may be overestimated, given that they conducted steady-state simulations whereas
atmospheric CH4 is changing over time in reality. For the same reason, the contribution of
increasing Cl to the trend of δ13C estimated by Gupta et al. may also be too large. The present
study aims to estimate the Cl contribution more precisely through time-dependent simulations.
Another question examined in this paper is how sensitive the modeled distribution of δ13C is to
the treatment of chemistry and dynamics in the stratosphere. As we have seen, the studies by
Gupta et al. and McCarthy et al. arrived at values for the surface impact of Cl that differ by a factor of 2. In addition, several previous simulations of δ13C underestimated the magnitude of the
vertical gradient in the troposphere and lower stratosphere [Gupta et al., 1996; Bergamaschi et al.,
1996; Tyler et al., 1999]. These groups cited inaccuracies in model transport and in values of KIE
for the sink reactions as possible causes of the underestimation. The uncertainty implied by the
previous results motivated our analysis of chemical and transport processes, especially with
regard to their impact on δ13C at the surface. We use the Harvard 2-D model, which has been
tested against a variety of observations and applied in a number of studies of stratospheric transport and chemistry [Schneider et al., 2000a,b; Park et al., 1999; Jones et al., 2001]. A brief
description of the model is presented in Section 2. Our understanding of the processes controlling
the distribution of δ13C of CH4 in the stratosphere is evaluated in Section 3. Section 4 focuses on
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the implications for δ13C at the surface. Conclusions are presented in Section 5.
2. Model description and experiments
The Harvard 2-D model extends from pole to pole with a resolution of 5 degrees latitude.
It covers a range of altitudes from 0 to 80 km with a resolution of 2 km. It consists of four interacting modules describing dynamics, radiative transfer, chemistry, and transport. Heating rates in
the stratosphere are calculated using model-derived ozone and temperatures. Heating rates in the
troposphere are specified based on the parameterization of Cunnold et al. [1975]. Planetary wave
mixing is parameterized using seasonally varying eddy diffusion coefficients, Kyy, employed consistently in the zonal mean momentum equation and the diffusion term of the tracer transport
equation. The version of the model used in the present study reflects the large Kyy case described
in Schneider et al. [2000a]. Reaction rate coefficients are taken from Sander et al. [2000] except
where specified in some of the sensitivity runs. A detailed comparison of model results with satellite observations of tracers was presented by Schneider et al. [2000a]. Schneider et al. [2000b]
and Jones et al. [2001] compared calculated mean ages of air (defined as the mean time for air to
reach a given location in the stratosphere after passing through the tropical tropopause) with values inferred from CO2 and SF6 observations in the lower stratosphere. Comparisons of the model
with other models and additional data were presented in the report of the NASA Models and Measurements Intercomparison Workshop II (MMII) [Park et al., 1999].
We initialized model experiments using output from a steady state simulation of conditions for year 1970, with the exception of δ13C of CH4, for which we adopted an initial value of
-47.5‰ throughout the atmosphere. The model runs were started in 1970 and extended through
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1992, the year for which results are compared with observations. The procedure allows sufficient
time to damp out transient effects of the choice of initial distributions of CH4, CFCs and other
stratospheric Cl precursors, O3, and other species. The CH4 global source strength was set at 468
Tg in 1970, 520 Tg in 1980, and 546 Tg in 1990 with linear interpolation between those years and
extrapolation after 1990. The global mean value of δ13C for CH4 emissions, held constant over
time, was set equal to -53.2‰ to reproduce levels of δ13C in the troposphere observed for the
early 1990s. The strength of the CH4 source and the associated value of δ13C employed in the
study are consistent with the range of values reported in the literature. For example, Hein et al.
[1997] estimated a source of 575 Tg yr-1 for the period 1983-1989, Prather et al. [1995] estimated
510 Tg yr-1, while Quay et al. [1999] calculated a value for δ13C of the source of -53.4‰ for the
period 1990-1995. The source was partitioned among latitudinal bands in the same proportions as
in Gupta et al. [1996] with a corresponding variation in δ13C. The time-dependent lower boundary conditions for CFCs and other Cl precursors and long-lived trace gases were taken from WMO
[1995]. Concentrations of OH in the troposphere were adopted from Spivakovsky et al. [2000].
The model allowed for selective removal of 12CH4 by soils and by reactions with OH, Cl, and
O(1D); for the baseline run, we assumed KIE values similar to those adopted in the previous studies (Table 1). The soil sink was simulated as dry deposition amounting to 30 Tg CH4 yr-1 in the
year 1988, similar to the value assumed in the study by Gupta et al. [1996].
The issue of initial conditions is particularly relevant for δ13C, since the isotopic composition of CH4 requires a longer time to stabilize than does the concentration [Tans, 1997]. The
value of -47.5‰ assumed for the distribution in 1970 is perhaps higher than appropriate, given
that measurements by Francey et al. [1999] exhibited values of ~-47.7‰ for the late 1970s along
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with an increasing trend. Thus, results for 1992 could possibly be influenced significantly by an
inaccuracy in initial conditions. We conducted a test simulation in which the distribution of δ13C
in 1970 had an average value of -48.1‰. The values of δ13C in 1992 for this simulation were
only 0.16‰ lower than those of the original case throughout the atmosphere. The magnitude of
this difference lies well within the level of uncertainty for the δ13C value of the emissions, which
had been adjusted to produce agreement of model with observations in the troposphere as noted
above. Thus, an entirely acceptable readjustment of the δ13C value of emissions could be made to
restore the original values of atmospheric δ13C.
3. Analysis of model results in the stratosphere
To provide a framework for discussion of the model results, we first summarize the transport and chemical processes relevant to CH4 in the stratosphere. Air enters the stratosphere from
the troposphere at the tropical tropopause and returns to the troposphere in the extratropics (e.g.
Holton et al., 1995). There is considerable evidence that exchange between the tropics and extratropics is weak between 20-30 km altitude (e.g. Trepte and Hitchman, 1992; Randel et al., 1993;
Hitchman et al., 1994; Grant et al., 1996), effectively separating the mean meridional circulation
in the stratosphere into an upper and a lower branch. In the lower branch, air is moved from the
tropics to higher latitudes by advection and by eddy-induced transport; the time scale for this circulation is short, less than a year [Andrews et al., 2001; Jones et al., 2001]. In the upper branch,
air is advected from the tropical lower stratosphere to the upper stratosphere, and from there to the
extratropical lower stratosphere; the time scale for this path is about 5 years [Andrews et al., 2001;
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Jones et al., 2001].
Chemically, the stratosphere can be broadly divided into two regions based on the efficiency of carbon isotopic fractionation of CH4. Figure 1 shows a latitude-altitude cross-section
plot of the annual average KIE, weighted by the rates of the individual sink reactions, for year
1992 of the baseline run. The plot indicates relatively low KIE values for the troposphere and
most of the tropical stratosphere, with higher KIE values for the uppermost stratosphere and
extratropical stratosphere. The region of high KIE corresponds to locations where the Cl sink
makes up a large fraction of the total sink. The model accounts for heterogeneous processes
involving sulfate aerosols in the lower stratosphere but does not allow for the impact of polar
stratospheric clouds (PSCs). Results in Figure 1 do not account therefore for a possible elevation
of the average KIE as a consequence of high concentrations of Cl in the springtime polar environment.
The influences of the low-KIE and high-KIE regions on δ13C can be seen clearly in Figure
2. The figure contains a plot of δ13C against [CH4] for observations by Sugawara et al. [1997].
The observations consist of a vertical profile for [CH4] and δ13C from the surface to 34.7 km over
northern Japan (between 38.5˚ and 40.0˚ N), determined using air samples collected from a balloon in August of 1994. Plots of δ13C against [CH4] are useful for placing the data in the framework of Rayleigh distillation (e.g. Brenninkmeijer et al., 1995; 1996; Sugawara et al., 1997).
Rayleigh distillation describes the exponential increase in the relative abundance of the heavier
isotope in a system as a species undergoes fractionation. Mathematically, this is expressed as:
C η
R
------ =  ------
 C 0
R0
–1
–1
,
(1)
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where R is 13C/12C, C is the concentration of CH4, the subscripted zeros refer to a reference point
during the evolution of a given air parcel (e.g. when the parcel first enters the stratosphere at the
tropopause), and η, as before, is the fractionation factor k12/k13. As indicated in Figure 2, the
Rayleigh distillation plot for the observations exhibits dichotomous behavior as a function of
[CH4]. Where [CH4] is high, in the lower stratosphere between 16 and 21 km altitude, data points
fit a distillation curve with a KIE consistent with the OH sink (η = 1.0054) as the dominant loss
process, while the lower CH4 concentrations at higher altitudes suggest a value for KIE intermediate between those appropriate for losses by OH and Cl (1.0160). This behavior reflects the influences of transport and chemistry as discussed above. Air in the midlatitude lower stratosphere
exhibits a large tropospheric and tropical stratospheric influence due to the lower branch of stratospheric circulation; the relatively low KIE along this trajectory is reflected in the distillation plot.
In contrast, air above ~21 km in the midlatitude stratosphere does not mix rapidly with tropical air
because of the subtropical barrier; instead it is influenced more strongly by transport from higher
altitudes in the upper branch of the circulation. The high KIE values in the upper stratosphere and
extratropics are reflected in this portion of the distillation plot.
Figure 3a presents a comparison of baseline model results for [CH4] with observations
from the Halogen Occultation Experiment (HALOE) and Cryogenic Limb Array Etalon Spectrometer (CLAES) instruments on the Upper Atmosphere Research Satellite (UARS). The UARS
data represent the climatological distribution of CH4 in the stratosphere for the period 1992-1998,
referred to as the “extended data set”, Version 1.0 [Randel et al., 1998]. A cross-section plot for
modeled δ13C is shown in Figure 3b. We choose to illustrate the month of August in Figure 3a-b
for the sake of consistency with the analysis of model results for δ13C discussed below, which
uses observations obtained for the same month. There is agreement in Figure 3a between mod-
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eled and observed [CH4] in terms of the general shape of the isolines and the overall magnitudes
of concentrations. The model exhibits sharper latitudinal gradients in the lower stratosphere and
lower concentrations in the extratropical stratosphere than the observations; this is true of other
months as well. This pattern is consistent with a conclusion that the mean ages in the extratropical lower stratosphere as represented by the model are too high [Jones et al., 2001], and suggests
that tropical-extratropical exchange in the lower stratosphere is under-represented. In fact, Jones
et al. found that increasing the amount of gravity wave drag in the lower stratosphere improved
the agreement with observations of model results for chemical and age distributions. Gravity
wave drag enhances advection from the tropics to the extratropics.
Vertical profiles of [CH4] and δ13C computed for the latitude range 35˚N to 40˚N (heavy
solid lines) are compared with the observations of Sugawara et al. [1997] (diamonds) in Figure
4a-c. Model values of [CH4] displayed in Figure 4a are in agreement with observation between
22 km and 35 km altitude. As indicated in Figure 4b, model results for δ13C are accurate between
22 and 30 km. Model values of [CH4] are too high below 10 km altitude and too low from 12 to
22 km; model values of δ13C are too high between 14 and 22 km and too low above 30 km.
Agreement between modeled and observed values of [CH4] is unsatisfactory at most latitudes in
the troposphere: the latitudinal gradient for [CH4] is excessive in our model, with unrealistically
high concentrations at high latitudes in both hemispheres and concentrations that are too low in
the tropics (see Figure 3a). The large gradient results from insufficient horizontal diffusion in the
model’s simulation of tropospheric transport.
The discrepancy in [CH4] and δ13C between the model and the observational data of Sugawara et al. in the lower stratosphere below 22 km ([CH4] > 1.4 ppm) can be attributed to errors in
the treatment of transport. As we have seen, the model underestimates transport of CH4 from the
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tropics to midlatitudes in the lower stratosphere, the region encompassed by the observational
points in question. When gravity wave drag was increased in the lower stratosphere between 10
to 30 km altitude in a sensitivity run denoted by Gravity+ (with a maximum decrease in the damping time scale, from one year to one month, between 18 and 22 km), modeled profiles were found
to align more closely with the observations between 15 and 20 km as a result of enhanced transport from the tropics in the lower stratosphere (Figure 4a and b). The model thus simulates the
vertical gradient of δ13C in the lower stratosphere accurately when this adjustment is effected, in
contrast to the previous studies that underestimated the vertical gradient. Figure 4c indicates that
the change in transport had little effect on the relationship between δ13C and [CH4]; in both runs,
there is agreement between model and observation in the lower stratosphere. In contrast, above
22 km the relationship between δ13C and [CH4] in the model differs from observation: δ13C is
too low for specific values of [CH4]. This suggests that factors other than transport are responsible for the discrepancy in δ13C that is particularly noticeable above 30 km in Figure 4b. The
smaller curvature of the modeled Rayleigh curve in Figure 4c compared to observation implies a
smaller average KIE and points to errors in the model’s chemistry as the reason for the discrepancy above 30 km. The error in chemistry occurs specifically in the upper and/or extratropical
stratosphere, since this is the region that supplies most of the air in the midlatitudes above 22 km.
This suggests that the error is likely to involve Cl and/or O(1D) rather than OH, since the concentrations of the first two are significant mainly at higher altitudes of the stratosphere while OH is
abundant at most altitudes in the troposphere and the stratosphere.
To explore possible explanations for the apparent discrepancy between model and
observed values for average KIE in the upper/extratropical stratosphere, we carried out a number
of sensitivity runs in which individual chemical parameters were adjusted within their ranges of
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uncertainty. These runs focused on Cl and O(1D). Descriptions of the runs are summarized in
Table 2. Vertical profiles are displayed in Figure 4a-c.
A recent laboratory measurement [Saueressig et al., 2001] indicates a value for the KIE of
the O(1D) + CH4 reaction of 1.013, appreciably higher than the value of 1.001 reported earlier by
Davidson et al. [1987]. Run KIE.O1D+ accounts for this higher value of the KIE. Agreement
with observations is markedly improved as indicated in Figure 4c. An error in KIEO(1D) offers
thus a possible explanation for the discrepancy between results of the baseline model and observations.
The value of the KIE for the Cl + CH4 reaction was increased by 0.010 for all temperatures in the run KIE.Cl+ to consider effects of a possible error in KIECl (Saueressig et al. [1995]
determined a 2σ uncertainty of 0.002 to 0.005 for a range of xeperimental temperatures). This
simulation resulted in an increase in δ13C above ~20 km (Figure 4b). The relationship between
δ13C and [CH4] for the KIE.Cl+ run is in better agreement with observations than results for the
baseline run, although the discrepancy is not completely eliminated.
We investigated also the sensitivity of results to the choice of rate coefficient for the Cl +
CH4 reaction. Michelsen et al. [1996] suggested that the rate coefficient for this reaction recommended in the evaluation by DeMore et al. [1997] may be too low, a conclusion supported also by
Voss et al. [2001], in light of discrepancies between modeled and observed values of [ClONO2]/
[HCl]. Using a weighted fit to laboratory measurements, Michelsen et al. derived an expression
for the rate coefficient that is 10%-30% higher at lower- to mid- stratospheric temperatures than
that recommended by DeMore et al. [1997], and 5%-25% higher than the recommendation by
Sander et al. [2000]. Our sensitivity run k.Cl.Michelsen adopts the expression for kCl+CH4 recommended by Michelsen et al. [1996]. Michelsen and Simpson [2000] revised the rate coefficient
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upward further to model the non-Arrhenius behavior of the reaction. However, the value of the
coefficient from Michelsen and Simpson differs only slightly from that of Michelsen et al. [1996]
within the applicable range of stratospheric temperatures. The average KIE for run k.Cl.Michelsen would be expected to be higher than that for the baseline run, given the larger contribution
of the Cl sink to the total sink. As indicated in Figure 4b, δ13C is higher than in the baseline run
throughout the stratosphere, similar to the KIE.Cl+ run, although the difference between the
k.Cl.Michelsen and baseline runs is small, less than 0.5‰ over the altitude range covered by the
observations. Similarly, the distillation curve for k.Cl.Michelsen in Figure 4c has only a slightly
higher KIE than the baseline run.
Stratospheric concentrations of Cl and OH in the model are lower than those inferred from
observations [Flocke et al., 1999; Herman et al., 1999; and Wennberg et al., 1995], by as much as
a factor of 3 below 20 km, with agreement better above (e.g. within ~50% for OH). A similar
problem has been reported by other researchers and a variety of explanations have been proposed
to resolve the discrepancy, including the omission of minor precursors for Cly and HOx and
uncertainty in rates for reactions affecting the ratio of [Cl] to [ClO] (e.g. Flocke et al., 1999). We
conducted a sensitivity study to explore the impact of uncertainties in Cl and OH on [CH4] and
δ13C. First, [Cl] was increased in the lower stratosphere between 16 and 30 km by a factor of 2 in
a run denoted Clx2, close to the upper end of the uncertainty range suggested by observations
[Flocke et al., 1999]. This increase would be expected to raise the average KIE in the lower
stratosphere. In a second simulation, the uncertainty in [OH] was considered also: [OH] was
increased by a factor of 2 to its upper limit [Herman et al., 1999; Wennberg et al., 1995], while
[Cl] was increased by a factor of 1.5 to the lower end of uncertainty (run Clx1.5.OHx2). The
increase in average KIE in this simulation should be less than that for run Clx2 not only because
of the smaller increase in [Cl] but also because of the increased relative importance of the OH sink
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with its low value of KIE. Figure 4 indicates that values for δ13C for the two sensitivity runs are
higher than those for the baseline at all altitudes, and the distillation curves exhibit higher curvature. Interestingly, there is still a net increase in average KIE for run Clx1.5.OHx2 as implied by
the higher curvature of the distillation curve despite the larger fractional increase for [OH] than
for [Cl]. This can be attributed to a decrease in the relative importance of the O(1D) sink, which
has the lowest KIE value among all the sinks. As long as the fraction of the total sink contributed
by Cl is changed little, an increase in the relative strength of the OH sink along with a decrease in
the relative strength of the O(1D) sink leads to higher average KIE. The sensitivity study suggests
that insufficient Cl in the model may have contributed to the discrepancy between model and
observed values of δ13C and relationships between δ13C and [CH4] in the upper stratosphere.
In summary, our analysis supports the suggestion of Saueressig et al. [1998] of a higher
value for KIEO(1D). A higher value for KIECl may also be indicated. An increase in the rate coefficient for the Cl + CH4 reaction (e.g. that recommended by Michelsen et al., 1996) could contribute slightly to an improvement in agreement between model and observation. Values of [Cl] may
be too low in the model. A combination of these changes could eliminate the discrepancy
between model and observed Rayleigh distillation curves.
4. Influence of stratospheric sinks of CH4 on surface δ13C
Values of δ13C from surface air averaged over latitudes for 1992 for the baseline run and
each of the sensitivity runs are given in Table 3. To assess the influence of stratospheric Cl on
δ13C at the surface, we compared results for the runs with corresponding runs in which loss of
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CH4 due to Cl was omitted. The differences in average δ13C at the surface between the runs with
and without the Cl reaction are summarized in Table 3. Chlorine was responsible for an increase
of 0.23‰ for δ13C at the surface in the baseline case. This appears small, considering that Gupta
et al. [1996] reported an increase of 1‰ while McCarthy et al. [2001] obtained 0.5‰. But the
values from these studies were based on steady-state computations for present-day conditions. To
properly compare the present results with the earlier studies, we investigated the limiting case of
steady-state (specifically, emissions of CH4 and Cl were held constant at present-day levels for 70
years). We obtained a difference of 0.43‰ between runs with and without fractionation by Cl.
This is still smaller than the result of Gupta et al., but now similar to that of McCarthy et al.
Another factor lowering the magnitudes of the Cl impact we calculated (with the exception of the
result for the steady-state simulation) is that the same initial distribution of δ13C was used for the
runs with and without Cl. For the case of no Cl in the atmosphere, the values of δ13C in 1970
should actually be lower than those for the case with Cl. Because of the long equilibration time
for δ13C, the overestimate of δ13C for the former case persists through 1992, reducing the calculated Cl impact. However, the primary purpose of these runs was to examine the sensitivity of the
Cl impact to stratospheric parameters. To calculate the contribution of anthropogenic Cl to the
trend of δ13C, we use more accurate initial conditions, as described below.
An enhancement in chemical reactivity and/or fractionation efficiency in the stratosphere,
specifically an increase in the rate or KIE for the Cl + CH4 reaction, would be expected to
increase the influence of Cl on surface δ13C. This expectation is confirmed by the results for the
runs KIE.Cl+, k.Cl.Michelsen, Clx2, and Clx1.5.OHx2, all of which exhibit a larger magnitude of
the Cl impact than that of the baseline run. Run Clx2 yields the largest value (0.32‰) while
results from other runs are only slightly larger than the baseline.
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The overall velocities associated with the circulation of air in the stratosphere in our model
are low compared to those estimated from observations. For example, the upward advective mass
flow across 100 mb in the tropics in our model is 1.4 x 1017 kg air yr-1, as compared with fluxes of
2.7 x 1017 kg air yr-1 [Rosenlof and Holton, 1993] and 5.0 x 1017 kg air yr-1 [Follows, 1992]
reported in the literature. To explore the sensitivity of the Cl impact to the overturning rate in the
stratosphere, we carried out a run, Velocity+, in which the wind speeds were increased by a factor
of 3.7 everywhere in the atmosphere contributing to an advective mass flow across 100 mb of ~5.0
x 1017 kg air yr-1. This is a crude modification of the model transport that results in significant
disagreement between modeled and observed distributions of tracers and mean age; the purpose
of the run was simply to illustrate the potential response of the Cl impact to the rate of stratosphere-troposphere exchange (STE). The run resulted in a higher average value for δ13C in the
troposphere relative to the baseline run with a lower average value for δ13C in the stratosphere.
The surface impact of Cl increased to 0.38‰. The increase reflects a larger influx of highly fractionated air from the stratosphere to the troposphere.
An effect that complicates the above picture of mixing between the stratosphere and troposphere involves changes in [Cl] that arise in response to changes in [CH4]. For example, a higher
STE rate results in an increase in [CH4] in the stratosphere, shifting Cl to HCl, thus lowering [Cl].
We found that the average concentration of Cl in the stratosphere was 39% lower in run Velocity+
than in the baseline case (the average stratospheric mixing ratio of Cl changed from 0.79 pptv to
0.48 pptv). This results in a negative feedback on the impact of Cl. Model results indicate that
the effect of a larger supply of stratospheric air to the troposphere prevails over the effect of
decreased [Cl]. The lower [Cl] in run Velocity+ is reflected in the smaller curvature of the Rayleigh distillation plot in Figure 4c. Note that the faster circulation does not directly affect the Ray-
18
leigh distillation curve, since the velocities are increased uniformly across the atmosphere and
thus the contributions of the two branches of circulation to the air at any given location are
unchanged. This explanation was confirmed by a model run similar to Velocity+ except that concentrations of Cl were taken from the baseline run. The Rayleigh plot for this run had the same
curvature as that for the baseline run (not shown).
As mentioned above, transport is specifically sensitive to details in the treatment of gravity
wave drag and eddy diffusion (Kyy). For run Gravity+, in which gravity wave drag was increased
in the lower stratosphere, the surface impact of Cl was lowered slightly to 0.22‰. This is a consequence of strengthening of the meridional flow in the lower branch of the stratospheric circulation. A more efficient lower branch increases the influence of the “low KIE region” on air
returning to the troposphere, thus decreasing the influence of Cl. In another run, “Global.Diffuser”, Kyy was increased by a constant amount throughout the stratosphere in the transport module but not in the dynamics module (i.e. diffusive transport of tracers was enhanced but the mean
meridional circulation was unchanged), weakening tropical isolation in the stratosphere. The Cl
effect in this case was 0.14‰, appreciably less than in the baseline run. An increase in meridional
diffusion results in dilution of air in the midlatitude lower stratosphere with young air from the
“low KIE” tropics; the impact of Cl on surface air is reduced accordingly.
To isolate the contribution of anthropogenic Cl to the trend of δ13C at the surface, we
implemented a pair of runs from year 1930 through year 1992. CH3Cl was assumed to represent
the only source of stratospheric Cl in year 1930. The initial atmospheric distributions of tracers
including CH4 and its two isotopic forms and CH3Cl were taken from the output of a steady-state
run for conditions appropriate for 1930. The resulting [Cl] in 1930 was equal to about 20% of
levels appropriate for 1992, similar to the values used in Gupta et al. We allowed for an increase
in CH4 emissions with time (the global CH4 source strength was 332 Tg in 1930, interpolated lin-
19
early between 1930 and 1970, and the same as in the previously discussed runs for the years after
1970). The runs differed in that one accounted for a gradual increase in anthropogenic emissions
of Cl with time, while in the other the flux of anthropogenic Cl was held constant at zero. (The
boundary conditions at the surface for anthropogenic Cl precursors were linearly interpolated
between 1930 and 1970.) The resulting difference in the value of δ13C averaged over the surface
in year 1992 between the two runs, representing the contribution of anthropogenic Cl to the trend
of δ13C, was 0.18‰. This value is several times smaller than the 0.7‰ calculated by Gupta et al.
[1996]. The difference results mainly from differences in the chemistry and/or transport between
the models, as implied by the comparison of steady-state Cl impacts described earlier in this section. In addition, some of the difference is due to the fact that their result was based on steadystate runs for 1930 and 1988 (i.e. present-day) conditions. Hence, their value is an overestimate
of the trend from 1930 to the present day, since δ13C was allowed to equilibrate under present-day
conditions. In a calculation analogous to theirs, we obtained a value of 0.26‰ for the Cl contribution to the trend.
We investigated also the sensitivity of the contribution of anthropogenic Cl to the trend of
δ13C to uncertainties associated with different chemical and transport parameters. Recall that the
rate and/or the KIE of the Cl + CH4 reaction may be too low in our baseline model, as suggested
by the discrepancy between the modeled and observed distillation curves in the upper stratosphere. Therefore, the value of the Cl impact calculated for the baseline model may be too low.
(Note however that adjusting the KIE for the O(1D) + CH4 sink would improve agreement of the
distillation curves without magnifying the Cl impact.) In addition, the relatively sluggish simulation of stratospheric circulation may contribute to an underestimate of the Cl impact. To calculate
an upper bound to the Cl impact, we increased KIECl by 0.01, used the rate coefficient for Cl +
20
CH4 recommended by Michelsen et al. [1996], and multiplied velocities throughout the atmosphere by 3.7 for a run which included increasing anthropogenic Cl emissions and also for a run
in which Cl emissions were held at 1930 levels. Additionally, [Cl] was increased by a factor of 2
in the stratosphere below 30 km for the first run. This pair of runs indicated an upper-bound contribution of 0.54‰ by Cl to the trend. Therefore, our best guess lies between 0.18‰ and 0.54‰.
It follows that changes in the isotopic composition of the CH4 source rather than changes in [Cl]
must be largely responsible for the 2‰ trend in the past century. For the average δ13C of emissions to have risen, the strengths of one or both of the isotopically heavy sources (production and
distribution of fossil fuels, and biomass burning) must have increased relative to those of the isotopically light sources (for example wetlands, rice paddies, and livestock).
5. Conclusions
Features of the atmospheric distribution of δ13C, such as the two contrasting KIE regimes
in the vertical profile observed by Sugawara et al. [1997], can be explained with a simple picture
of the atmosphere in which there are two branches of stratospheric circulation and distinct regions
of high and low fractionation efficiency. The vertical gradient of δ13C in the lower stratosphere of
our 2-D model agrees with that of the observations by Sugawara et al. if we allow for an increase
in meridional mixing in the lower stratosphere. There is a significant discrepancy between our
model results and the observed δ13C vertical profile and distillation plot above ~30 km, suggesting that the average KIE is too low in the upper and/or extratropical stratosphere. Adjustments
that led to the largest improvements in model results include increases in the values of KIEO(1D)
21
and KIECl and the concentration of Cl.
The impact of stratospheric Cl on δ13C at the surface depends on the rate and KIE of the
Cl + CH4 reaction and the supply to the troposphere of highly fractionated air from the upper
stratosphere, where the Cl sink accounts for a large fraction of total CH4 removal. We estimate
that the increase in Cl concentrations due to anthropogenic emissions of CFCs and other Cl precursors has contributed only 0.18‰-0.54‰ to the +2‰ trend in δ13C at the surface observed over
the past century. We conclude that growth in the relative importance of heavier sources of CH4
(associated for example with fossil fuels and biomass burning) has been largely responsible for
the trend.
More extensive stratospheric measurements of δ13C of CH4, both spatially and temporally,
would provide useful tests and opportunities to refine current understanding of stratospheric
chemistry and transport and the global budget of CH4. With only one reliable vertical profile of
δ13C extending into the middle stratosphere, it is difficult to evaluate present model results with
certainty, since the effects of latitudinal, seasonal, and interannual variability cannot be examined.
The pattern of transport in the stratosphere suggests that Rayleigh distillation plots will exhibit
distinct curvatures at different latitudes. Therefore, simultaneous measurements of [CH4] and
δ13C across a wide range of latitudes and altitudes may be useful for evaluating the transport and
chemistry in models. Carbon isotopic composition may be particularly useful as a tracer of the
amount and distribution of Cl radical in the atmosphere, and more extensive observations could
help improve our understanding of Cly partitioning, an issue of critical importance for the understanding of ozone depletion. Another possible source of information on stratospheric chemistry
and transport is the hydrogen isotopic composition of CH4 (δD), which has been measured for
emissions (e.g. Snover et al., 2000 and references therein) and stratospheric air (e.g. Irion et al.,
22
1996) and for which KIEs have been determined (Saueressig et al., 1996--Cl + CH4; RobertoNeto et al., 1998--Cl + CH4; Tyler et al., 2000--Cl + CH4; Gierczak et al., 1997--OH + CH4;
Saueressig et al., 2001--O(1D) + CH4; Snover and Quay, 2000--soil sink). Future research applying the conceptual framework and modeling techniques of this study to δD might be fruitful.
Acknowledgements. This work was supported by an NSF Graduate Research Fellowship, NSF
grant ATM-9903529, and DOE grant DE-FG02-98ER62585. We thank Hans Schneider for his
help with the development of the model and numerous stimulating discussions. We also acknowledge discussions with Paul Voss, Ross Salawitch, Stanley Tyler, Carl Brenninkmeijer, Thomas
Roeckmann, Philip Cameron-Smith, Andrew Fusco, Daniel Jacob, and Karen Felzer. We thank
Michael McCarthy and Kristie Boering for the opportunity to review their manuscript prior to its
acceptance for publication.
23
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31
Table 1: Carbon Isotopic Fractionation Factors
CH4 Sink
OH
O(1D)
Cl
Soil oxidation
a. Used in baseline simulation.
b. Used in sensitivity test.
c. Not used in model.
Fractionation Factor (KIE,
=k12/k13)
Reference
1.0054 ± 0.0009
aCantrell
1.010 at 300 K
c
1.0039 0.0004 at 296 K
cSaueressig
1.001
aDavidson
1.013 (223-295 K)
b
1.043 exp(6.455/T) at 223297 K (1.066 ± 0.002 at 297
K)
aSaueressig
1.032-1.024 at 200-350 K
cTanaka
1.034 at 300 K
cGupta
1.06 at 297 K, 1.07 at 243 K
cRoberto-Neto
1.066 ± 0.002 at 298 K
cCrowley
1.0621 0.0001 at 299 K
cTyler
et al. [2000]
1.022
aTyler
et al. [1994]
1.022-1.025
cReeburgh
1.0121 to 1.0183
cSnover
et al. [1990]
Gupta et al. [1997]
et al. [2001]
et al. [1987]
Saueressig et al. [2001]
et al. [1995]
et al. [1996]
et al. [1997]
et al. [1998]
et al. [1999]
et al. [1997]
and Quay [2000]
32
Table 2: Model Sensitivity Runs
Name of Run
Description
Gravity+
Gravity wave drag increased in lower stratosphere-damping time scale decreased from several months to less
than a month
Velocity+
Velocities everywhere in atmosphere multiplied by 3.7
Global.Diffuser
Kyy increased uniformly by a constant amount in the
stratosphere in the transport but not in the dynamics
KIE.Cl+
KIECl increased by 0.010 at all temperatures
KIE.O1D+
KIEO(1D) set equal to 1.013 [Saueressig et al., 2001]
k.Cl.Michelsen
kCl+CH4 taken from Michelsen et al. [1996]
Clx2
[Cl] increased by factor of 2 in the lower stratosphere
(16-30 km)
Clx1.5.OHx2
[Cl] increased by factor of 1.5 and [OH] increased by factor of 2 in the lower stratosphere (16-30 km)
Trend.Baseline
Simulation extending from years 1930 through 1992 to
determine the contribution of anthropogenic Cl to the
trend of δ13C
Trend.Upperbound
Same as Trend.Baseline except KIECl increased by 0.010,
kCl+CH4 taken from Michelsen et al. [1996], [Cl]
increased by a factor of 2 between 16 and 30 km, and
velocities throughout the atmosphere increased by factor
of 3.7
33
Table 3: Global-average δ13C of CH4 at the surface in year 1992, and Cl impact /
contribution to trend of δ13C at the surface
Run
δ13C (‰)
Cl Effect at Surface (‰)
Baseline
-47.46
0.23
KIE.Cl+
-47.43
0.26
KIE.O1D+
-47.37
--
k.Cl.Michelsen
-47.44
0.25
Clx2
-47.37
0.32
Clx1.5.OHx2
-47.43
0.27
Gravity+
-47.52
0.22
Velocity+
-47.29
0.38
Global.Diffuser
-47.51
0.14
Trend.Baseline
-47.63
0.18
Trend.Upperbound
-47.21
0.54
34
Figure 1. Average KIE for year 1992 in the model weighted by the loss rates of the individual
sinks.
35
Figure 2. Plot of δ13C vs. [CH4] for observations by Sugawara et al. [1997] (diamonds),
along with hypothetical Rayleigh distillation curves for different values of KIE (solid
lines). The two curves with a KIE value of 1.016 differ in starting values for 13C/12C and
[CH4] (R0 and C0).
36
Figure 3. Results for baseline run. (a) Comparison of modeled [CH4] with measurements by
instruments aboard the UARS satellite for the month of August. Model results (solid contours) are for 1992; UARS observations (dashed contours) are an average for the period
1992-1998 (“extended data set”, version 1.0) [Randel et al., 1998]. Values in ppmv. (b)
Plot of modeled δ13C for August, 1992. Values in per mil.
37
Figure 4. Comparison of results from model runs with observations by Sugawara et al. [1997]: (a) [CH4]; (b) δ13C; and (c)
δ13C vs. [CH4] for the stratospheric points. Model values are from latitudes 35˚N to 40˚N for August of 1992; observations were made over northern Japan (38.5˚N to 40.0˚N) in late August of 1994. The uncertainty of the laboratory analyses was estimated to be ±0.07‰. The observational point at 16.5 km altitude only has a value for [CH4] and is missing
its δ13C value. Explanation of run names (see Table 2 for complete descriptions): Gravity+ = increased gravity wave
drag in lower stratosphere; KIE.O1D+ = value for KIEO(1D) taken from Saueressig et al. [1998]; KIE.Cl+ = KIECl
increased by 0.010; k.Cl.Michelsen = rate coefficient for Cl + CH4 taken from Michelsen et al. [1996]; Clx2 = [Cl]
increased by factor of 2 in lower stratosphere; Clx1.5.OHx2 = [Cl] increased by factor of 1.5 and [OH] increased by factor of 2 in lower stratosphere; Velocity+ = velocities increased by factor of 3.7 throughout atmosphere.