Interactive comment on “ The isotopic composition of methane in the stratosphere : high-altitude balloon sample measurements ” by T

Abstract. The isotopic composition of stratospheric methane has been determined on a large suite of air samples from stratospheric balloon flights covering subtropical to polar latitudes and a time period of 16 yr. 154 samples were analyzed for δ 13 C and 119 samples for δD, increasing the previously published dataset for balloon borne samples by an order of magnitude, and more than doubling the total available stratospheric data (including aircraft samples) published to date. The samples also cover a large range in mixing ratio from tropospheric values near 1800 ppb down to only 250 ppb, and the strong isotope fractionation processes accordingly increase the isotopic composition up to δ 13 C = −14‰ and δD = +190‰, the largest enrichments observed for atmospheric CH 4 so far. When analyzing and comparing kinetic isotope effects (KIEs) derived from single balloon profiles, it is necessary to take into account the residence time in the stratosphere in combination with the observed mixing ratio and isotope trends in the troposphere, and the range of isotope values covered by the individual profile. The isotopic composition of CH 4 in the stratosphere is affected by both chemical and dynamical processes. This severely hampers interpretation of the data in terms of the relative fractions of the three important sink mechanisms (reaction with OH, O( 1 D) and Cl). It is shown that a formal sink partitioning using the measured data severely underestimates the fraction removed by OH, which is likely due to the insensitivity of the measurements to the kinetic fractionation in the lower stratosphere. Full quantitative interpretation of the CH 4 isotope data in terms of the three sink reactions requires a global model.


Introduction
In the well-mixed troposphere, the CH 4 mixing ratio and its isotopic composition are determined by the principal balance between the sources (and their isotopic signatures) and sinks (and the corresponding kinetic fractionation factors) (Stevens and Rust, 1982;Quay et al., 1999;Miller et al., 2002).For a long-lived gas as methane, this leads to rather stable mixing ratio and isotope values throughout the troposphere that are modulated by the seasonal variations in the production and destruction rates and long-term temporal trends, resulting from disequilibrium of production and removal (Stevens and Rust, 1982;Lowe et al., 1997;Bergamaschi et al., 1998Bergamaschi et al., , 2000Bergamaschi et al., , 2001;;Quay et al., 1999;Tyler et al., 1999;Miller et al., 2002;Tarasova et al., 2006).
In the stratosphere the situation is different, since the only source for stratospheric methane is the tropospheric flux into the stratosphere, occurring mainly in the tropics.In the absence of in situ sources CH 4 mixing ratios decrease strongly in the stratosphere due to the removal by the three chemical (1st order) reactions with OH, O( 1 D) and Cl (Wahlen et al., 1989;Wahlen, 1993;Brenninkmeijer et al., 1995;Irion et al., 1996;Sugawara et al., 1997;Ridal and Siskind, 2002;Mc-Carthy et al., 2003;Rice et al., 2003).Removal of CH 4 by photolysis becomes important only in the mesosphere.However, throughout most of the stratosphere, the local chemical removal rates of CH 4 are actually slower than typical transport times (Zahn et al., 2006).Consequently, the CH 4 mixing ratio and its isotopic composition in an air parcel is dependent on the reaction with OH, O( 1 D) and Cl (chemical removal) on the one hand and its pathway through the stratosphere (physical transport, dynamics, see Sect. 2) on the other hand.In general, the longer the residence time of an air mass in the stratosphere, the more it is processed photochemically and the more CH 4 has been removed.
Published by Copernicus Publications on behalf of the European Geosciences Union.
T. Röckmann et al.: The isotopic composition of methane in the stratosphere As CH 4 is not fully oxidized in the stratosphere, but a large fraction returns to the troposphere, the isotope effects in the stratosphere have a significant effect on the tropospheric CH 4 isotope budget (Gupta et al., 1996;McCarthy et al., 2001;Wang et al., 2002).
Only a limited number of data on isotopic composition of stratospheric methane have been previously published.Sugawara et al. (1997) presented one δ 13 C profile from a balloon flight over Japan in 1994 and Rice et al. (2003) presented δ 13 C and δD values from various flights with the highaltitude aircraft ER-2 between 1996-2000 up to 21 km.Furthermore, Brenninkmeijer et al. (1995Brenninkmeijer et al. ( , 1996) ) published few δ 13 C data obtained on aircraft flights between New Zealand and Antarctica.
In this paper we present data from 13 stratospheric balloon flights, which increase the number of balloon observations in the literature by more than an order of magnitude and the number of total published data for the stratosphere by a factor of more than 2.

Short review of stratospheric dynamics and its effect on tracer distributions
After air enters the stratosphere, mainly in the tropics, it is first transported upwards in the tropics and then polewards and downwards, and it descends back to the troposphere at higher latitudes.The turnaround time for this global meridional circulation, the so-called Brewer-Dobson-circulation (BDC, Dobson et al., 1946;Brewer, 1949) is several years for the middle and upper stratosphere (Boering et al., 1996).
Next to this so-called deep branch of the BDC, which dominates the middle stratosphere, a shallow branch exists in which air is transported more directly from the tropics to the extratropics, without passing through high altitudes (Birner and Bönisch, 2011;Bönisch et al., 2011).The Brewer Dobson circulation is a combination of the net residual transport described above with fast mixing along isentropes.The global distributions and the surfaces of constant mixing ratio (isopleths) of long lived tracers are thus a result of two effects.First, the meridional net circulation lifts the tracer isopleths in the tropics and depresses them at high-latitudes and second, the quasi-horizontal mixing equilibrates the tracer distribution along the isentropes.For long-lived tracers, the fast quasi-horizontal mixing forms rapid exchange surfaces, common to all (sufficiently) long-lived tracers, on which local deviations are homogenized.As a consequence two longlived tracers will form a compact relation in a tracer:tracer plot, i.e. ideally a single curve for the correlation of their mixing ratios (Holton, 1986;Mahlman et al., 1986;Plumb and Ko, 1992).This idealized model is sometimes referred to as "global mixing scheme".It has successively been extended to better describe the situation in the tropics.Subtropical barriers split the global isopleths into the hemispheric "surf zones" and a "tropical pipe" (Plumb, 1996;Andrews et al., 2001).The "leaky tropical pipe" model allows for recirculation of mid latitude air back into the tropics (Avallone and Prather, 1996;Volk et al., 1996;Neu and Plumb, 1999).
The region below the tropical pipe corresponds to the shallow branch of the BDC where fast direct exchange between tropics and extratropics is possible.The polar vortices are seasonal transport barriers that are not included in these general global transport schemes.The radiative cooling in the polar night and the stronger downward forcing from the BDC in winter leads to a large-scale subsidence of air from the upper stratosphere and even mesosphere, which stays substantially isolated from extra-vortex air.Thus, the vortex edge, similar to the subtropical barrier, is characterised by strong horizontal tracer and potential vorticity gradients and the tracer isopleths are no more "almost parallel" to isentropes.Several mechanisms are known or discussed for interaction between vortex and extra-vortex air.Waugh et al. (1997) showed the occurrence of "anomalous mixing" lines, i.e. deviating from the general compact tracer:tracer relation, and related them to end member mixing between vortex and mid-latitudes.Plumb et al. (2000) offered two alternative mechanisms, a "continuous weak mixing" through the vortex edge and the intrusion of extra-vortex air in a single (or multiple) event(s) throughout the phase of descent, and its subsequent vertical redistribution inside the vortex.Such an intrusion was used in Engel et al. (2006) to explain the enclosure of mesospheric air observed in stratospheric balloon samples.With increasing solar heating after the polar night, the latitudinal temperature gradient, circumpolar jet, wave activities, and vortex isolation decrease and vortex air dissipates into the surrounding extra-vortex region (WMO, 2003).How the dynamical properties of the stratosphere affect the mixing ratio and isotopic composition of CH 4 will be discussed in detail in Sects.5 and 6.3.

Experimental
High-altitude samples (up to 35 km) from stratospheric balloon borne air samplers were provided by the Max-Planck-Institut (MPI) für Sonnensystemforschung (formerly Max-Planck-Institut für Aeronomie), Katlenburg-Lindau, Germany and the Institut für Atmosphäre und Umwelt (formerly Institut für Meteorologie und Geophysik), Universität Frankfurt, Germany.The samplers from both groups consist of 15 electro-polished stainless steel tubes immersed into liquid neon at a temperature of 27 K, but differ especially in the intake design (Schmidt et al., 1987).The sampling tubes have an internal volume of about 0.5 dm 3 that is filled to pressures between ∼5 to 50 bar (at room temperature).The vertical sampling resolution is usually about 1 km, sampling latitudes are essentially invariant, and longitude variations can be a few degrees, depending on the prevailing zonal winds during sample collection.(Gierzak et al., 1997) to match room temperature measurement.
The MPI group had stored a large number of stratospheric air samples from scientific balloon flights covering more than a decade (1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999) as stratospheric air archive.These samples were made available for isotope analysis on longlived greenhouse gases.From 2000 to 2003, samples from 5 more stratospheric flights with the BONBON cryogenic sampler operated by the Universität Frankfurt group were analyzed.Those samples were measured within few months after the flight.Table 2 gives an overview of the exact sampling dates and locations.
Mixing ratio and isotopic composition of the air samples were determined on a high-precision continuous flow isotope ratio mass spectrometry system (Brass and Röckmann, 2010) that has been used in various studies to determine the isotopic composition of CH 4 (Keppler et al., 2006(Keppler et al., , 2008;;Tarasova et al., 2006;Vigano et al., 2009Vigano et al., , 2010)).The samples are analyzed automatically relative to a laboratory standard air cylinder that is usually measured after each two samples.The reproducibility of the system, as determined from extensive tests, including subsets of the stratospheric samples presented here, is 18 ppb for CH 4 mixing ratios, 0.07 ‰ for δ 13 C and 2.3 ‰ for δD (Brass and Röckmann, 2010).For δ 13 C analysis we use the peak integration routine of the standard ISODAT software package, for δD an improved peak integration software has been developed (Brass and Röckmann, 2010).Isotope ratios are reported in the common δ notation relative to the international standard materials Vienna PeeDeeBelemnite for δ 13 C and Vienna Standard Mean Ocean Water for δD.CH 4 mixing ratios are reported on the NOAA04 scale (Dlugokencky et al., 2005).Most samples were attached to the analytical system directly from the original sampling containers, only a subset of samples was first expanded into 2 l volume stainless steel flasks and analyzed later.

General classification of flight profiles
Figure 1a shows the full set of methane mixing ratio profiles obtained from the balloon flights.As outlined in the introduction, mixing ratios decrease from tropospheric levels with altitude and latitude in the stratosphere.This is due to CH 4 destruction related to the photochemical processing of stratospheric air and the global transport and mixing patterns outlined in Sect. 2. The extent of chemical removal is clearly different for the individual profiles and the samples split into three groups, roughly according to the flight latitude, i.e. high latitudes (polar, here Arctic), mid latitudes and subtropics.
Generally, the δ 13 C and δD vertical profiles mirror the mixing ratio profiles (lower mixing ratio corresponds to higher δ-values) and therefore they generally show similar structural variations (Fig. 1b and c).The δ-values increase with altitude and latitude.Vortex air, with its very low CH 4 content, shows the highest isotope enrichments.The degree of this enrichment depends on the extent of photochemical processing in the stratosphere.

Polar profiles
The Arctic samples (all collected using Kiruna as operational base) show additional differences for different sampling seasons.The winter samples (KIR-92-01, -02, -03, KIR-00-01, KIR-03-03) reflect the presence of the polar vortex.Air that descends in the vortex has undergone massive methane oxidation.These profiles are characterised by the occurrence of very low CH 4 mixing ratios (down to ∼250 ppb) and strong  isotope enrichments.The spring and summer profiles (KIR-95-03, KIR-03-06) are similar to mid-latitudinal profiles.
The balloon profile KIR-03-03 shows a distinct feature, i.e. above 24 km the CH 4 mixing ratio increases and above 23 km δ 13 C and δD decrease again with height.A detailed analysis of this flight, using several tracers, shows that at least the two samples above this CH 4 minimum show clear mesospheric characteristics like high CO and H 2 mixing ratios (Engel et al., 2006).Above those "mesospheric" samples, the air exhibits stratospheric characteristics again, and the methane mixing ratio and isotope data suggest that midlatitudinal air is mixed into the resolving vortex from above.The samples will be discussed in detail in Sect.8.1.

Mid-latitude profiles
Four profiles from mid-latitudes are available (ASA-93-09, GAP-99-06, ASA-01-10, and ASA-02-09).Three flights took place in autumn and to some degree can be regarded as a stratospheric background.Photochemistry is decreased compared to summer and dynamical activity starts to intensify with the change from the summer to the winter circulation.All four profiles show wave structures in the vertical distribution of mixing ratio and isotopic composition with altitude, which indicate large-scale dynamical effects that disturb the smooth vertical evolution.In general, the mixing ratio and isotope values of the mid latitude flights are in the range of the Arctic summer profile (KIR-03-06), especially for altitudes above 20 km.

Subtropical profiles
The subtropical region is represented by samples from two balloon flights from Hyderabad, India, HYD-87-03 and HYD-99-04.Methane mixing ratios are rather constant up to the tropopause at 18 km and slightly decrease above the tropopause, followed by a significant decrease starting at 20-23 km.Only 5 samples were still available from the HYD-87-03 flight, resulting in two groups of similar characteristics.Thus, this dataset alone holds only limited information.Compared to HYD-99-04 the HYD-87-03 profile is shifted to lower mixing ratios and looks similar to a mid-latitudinal profile.One has to take into account that 12 yr passed between the two profiles.An age correction that takes the tropospheric trend into account will be applied in Sect.6.1.
Sample HYD-99-04/15 is the highest altitude subtropical sample with a mixing ratio ∼1200 ppb and an extremely high δ 13 C-value (for a sample with 1200 ppb).When the balloon samples are compared to CH 4 :N 2 O tracer correlations for different latitude bins taken from (Michelsen et al., 1998), the tracer:tracer-plot identifies HYD-99-04/15 as the only deep tropical sample in the balloon set.However, this was one of the samples that were only available as an aliquot (not the original balloon sample container) and were analysed for δ 13 C only at the very beginning of measurement.Also the original container had rather low pressure.Since experimental problems cannot definitely be excluded, this sample will not be interpreted further.: Arctic samples (blue: vortex, purple: non-vortex, : mid-latitudes (green, yellow), solid symbols: sampled in summer, : tropics (red).

Isotope -mixing ratio correlations
It is obvious from Fig. 1 that there is considerable variability between the individual flight profiles.However, the variations in mixing ratio and isotopic composition are closely correlated, and it is useful and common to investigate isotope results as isotope -mixing ratio correlations (Fig. 2).Two points are remarkable in these correlations.First, each flight profile shows up as a relatively compact correlation curve and second, isotope-mixing ratio correlations are relatively stable over the full period of time, in different seasons and at various latitudinal regions (subtropics, mid-latitudes and polar).Thus, most of the variation observed in the vertical profiles disappears when δ values are discussed on the mixing ratio scale (as alternative height coordinate) and the correlation curves can be regarded as (quasi) steady state functions for δ 13 C(c) and δD(c).Here and in the following, c represents the mixing ratio.
The first observation reflects the previous finding that compact stratospheric tracer-tracer correlations occur for trace gases whose chemical removal time constants are larger than the transport time constants (Plumb and Ko, 1992), which is the case for the individual CH 4 isotopologues.Thus this property can be explained by the global mixing scheme.The second observation shows the global validity of this scheme and that it is not strongly variable in time.This is expected, since CH 4 is a long-lived trace gas with only small temporal trends since 1990 (e.g.Dlugokencky et al., 1998).From these correlations we can already conclude that no major changes in dynamics in the stratosphere and/or changes in the chemical sinks are observed.
Nevertheless, two areas of variability can be easily identified in Fig. 2: first, there is increased variability in both δ values for methane mixing ratios <∼1000 ppb, which is mainly vortex or vortex edge air.For this region the assumptions of Plumb and Ko (1992) fail, since at the vortex edge the quasi-horizontal mixing on an isentrope is not fast enough to equilibrate mixing ratio variations.In the inner vortex region the time scale for vertical advection is of the same size as horizontal transport across the edge.Furthermore, the vortex undergoes dramatic changes over the seasons (it forms, breaks up and resolves).Secondly, there is comparably large scatter for δD at high methane mixing ratios, i.e. near the tropopause, where the δD -mixing ratio correlations are slightly shifted between individual flights.This point will be further investigated below.

Isotope -isotope correlations
Figure 3 shows the isotope -isotope correlation between δD and δ 13 C.In such a plot, air that is a result of mixing between two air parcels is found on a straight line connect-ing these two parcels.Such a linear mixing correlation in fact fits the mid-latitude data points well.This means that the spatial and temporal distribution of CH 4 and its isotopic composition can be explained by mixing of tropospheric air with a representative strongly processed reservoir in the upper stratosphere.Interestingly, the vortex samples significantly deviate from this straight (mid-latitudinal) correlation.For a global fit, the data was binned in 0.5 ‰ δ 13 C intervals to reduce the statistical weight of the more abundant higher mixing ratio (lower δ-values) samples.When the point with highest isotope enrichment (sample KIR-03-03/12) is disregarded, a parabolic fit of the form fits the data well without systematic structure in the residuals (Fig. 3c).The most interesting feature of the fit in Fig. 3b is its monotonically decreasing slope.This implies a decrease of D fractionation compared to 13 C fractionation at higher total enrichments (see below).Pure Rayleigh fractionation processes would actually show a slightly increasing slope, which is due to the non-linearity of the Rayleigh fractionation equation, so other process must contribute.Given the large differences in the fractionation constants associated with the three chemical sink reactions (see below), the overall monotonous decrease can only be caused by a continuously decreasing strength of the OH sink and the related increase of the O( 1 D) and Cl strength (and to a minor degree shifting from Cl to O( 1 D)).
The two vortex samples that fall below and above the mesospheric enclosure in flight KIR-03-03 deviate from this general description.According to Engel et al. (2006), sample KIR-03-03/8, has typical characteristics of upper stratospheric air from the mid-latitudes and indeed it accurately falls onto the mid-latitudinal mixing line and marks its most enriched end-point (Fig. 3a).The second sample, KIR-03-03/12, is more difficult to interpret, as it is completely isolated from the other samples in the isotope:isotope plane.It will be further discussed below.

δ 13 C comparison
In the published literature, there is a clear difference between the δ 13 C data from Sugawara et al. (1997) (balloon) and Rice et al. (2003) (ER-2 flights).The data from Sugawara et al. (1997) are approximately 0.5 ‰ more depleted, which has been attributed either to the different location/time period of sampling or to lab-specific calibration procedures (Rice et al., 2001).When compared to our data, the Rice et al. (2003Rice et al. ( ) data (1996Rice et al. ( -2000) ) fall in the range of the Arctic aircraft and balloon samples from 2003.At the same time, the KIR-92-01 profile agrees well with the Sugawara et al. (1997) data from the 1994 balloon profile.Thus, the new comprehensive measurements indicate that the difference between the Sugawara et al. (1997) and Rice et al. (2003) data is likely not an analytical artefact and probably due to the temporal trends.

δD comparison
In comparison to Rice et al. (2003) the δD values presented here are about 10 ‰ heavier.The difference appears to decrease towards lower mixing ratios and may disappear at 700 ppb.Several processes may contribute to the discrepancy.A fractionation in the sampling procedure is unlikely for our analyses, as samples from different sampling devices agree well.Given the fact that both δD datasets cover large regions of the stratosphere, it is unlikely that the observed difference indicates a real atmospheric difference.Most likely the deviation in δD originates from different, labspecific calibration scales.This typically leads to systematic deviations.Ideally, these deviations are constant, but they can also increase or decrease with mixing ratio, as observed.Because of this non-constant deviation, the ER-2 data discussed by Rice et al. (2003) and McCarthy et al. (2003) show a more pronounced relative vertical increase of δD in the stratosphere, i.e. a generally higher slope of δD(c) relation, and consequently slightly higher KIE D -values are reported by Rice et al. (2003) and McCarthy et al. (2003).

Chemical isotope fractionation in the removal reactions
In the stratosphere methane is oxidised by OH, O( 1 D) and Cl.Due to slightly different reaction rate coefficients for the different isotopologues, chemical removal by these reactions leads to a shift in the isotope ratio of the residual material.
Neglecting other effects, this can be described by the wellknown Rayleigh fractionation equation (Kaiser et al., 2002b).
δ and δ 0 are the initial and final δ-values and c 0 and c are the initial and final mixing ratios.KIE is the kinetic isotope effect, defined as the ratio of the reaction rate constants for the light (k) and heavy (k A normal kinetic isotope effect is characterised by k > k .In case of a constant KIE, it can be determined from the slope of a Rayleigh fractionation plot where (δ + 1) is plotted versus ln c c 0 (Eq.2).The corresponding fractionation constant ε is defined as As for δ-values, the numerical values of ε are usually stated in per mille.Note that in many publications ε is defined as α − 1 (where α = k /k = (KIE) −1 ).The same symbol ε is used in both cases, which are not equivalent.Saueressig et al. (2001) determined the KIE values and their temperature dependence for the reactions of OH, O( 1 D) and Cl with the three major isotopologues 12 CH 4 , 13 CH 4 , 12 CH 3 D (Table 1).Rice et al. (2003) showed that for three simultaneous sink reactions the combined effective KIE can be written as the sum of the KIEs weighted by the respective sink fractions a Y of methane oxidised by Y (Y = OH, O( 1 D), Cl).
Equation ( 5) is a set of 3 linear equations with 3 unknowns and can also be formulated as vector equation In this framework it is possible to formally derive the relative sink fractions (a OH , a O 1 D and a Cl ) from the measurement of both KIE eff values, if KIE eff is accessible from measurements in the stratosphere.

The effect of mixing
The isotopic composition in the stratosphere is not only determined by the KIE in the chemical removal reactions, but also by transport and mixing processes.Mixing always acts to reduce gradients, and therefore the actually observed apparent KIE app in the stratosphere is always smaller than the average effective KIE eff from the formal sink partitioning derived above (see e.g.Rahn et al., 1998;Kaiser et al., 2002a).The effect of mixing can be quantified by introducing two dynamical parameters f 13 C and f D .
Thus, f = 1 characterises an undisturbed Rayleigh fractionation process, whereas mixing generally leads to lower values of f , i.e.KIE app < KIE eff .f 13 C and f D can be included in the Eq. ( 6) to derive the sink partitioning as follows:  A consequence of the steady-state in the global mixing scheme is that the net vertical trace gas fluxes are purely diffusive (Plumb, 1996).For this specific case of pure diffusive mixing, a simplified discussion on the resulting isotope profile was already presented in Kaye (1987) (see also Erikson, 1965).In this idealised 1-D-diffusive steady-state model f -values between 0.5 and 1 are theoretically possible (independent of molecule and/or isotope), where f = 0.5 characterises the so-called diffusion-limited case, which describes the situation expected for the stratosphere (Rahn et al., 1998;Kaiser et al., 2002a).Thus, the apparent KIE app is only half of the expected KIE eff .It will be shown below that in general this 1-D-diffusive model (thus f = 0.5) already predicts the stratospheric fractionation surprisingly well.An additional effect in the real stratosphere occurs by mixing across transport barriers, where air masses (or parts of them) with distinct characteristics are irreversibly mixed.Also in this case, the observed KIE app will always be lower than KIE eff (i.e.f < 1) (Kaiser et al., 2002a).If the KIE app values of the mixing air masses themselves are already at the diffusion-limited extreme individually (f = 0.5), then the additional effect of mixing across a transport barrier (e.g. the polar vortex) will be to reduce f further to f < 0.5.

Mean fractionation factor
For each individual balloon profile, a mean KIE can be determined from a linear fit to the data in a double-logarithmic plot such as Fig. 4 according to Eq. ( 2).The results of those mean KIE values are shown in Table 3.The corresponding fractionation factors vary for the individual flights over the range 12-17 ‰ for ε 13 C and 122-160 ‰ for ε D .
In general the fits are of very good quality and give high accuracy KIE values with the following exceptions.The HYD-87-03 profile basically consists of only two groups of points.For HYD-99-04 half of the profile shows nearly constant (tropospheric) values, which effectively reduces the number of useful samples.Additionally, both HYD profiles occupy only a small c-interval in the δ(c) relations.Also for KIE D (ASA-02-09) the regression coefficient is lower, likely due to the limited number of samples analysed for δD.
Previously published mean KIE values are listed in Table 4 for comparison.The KIE 13 C derived by Sugawara et al. (1997), the only previously published result from a stratospheric balloon flight, is similar to the subtropical (HYD-99-04) result from this study.The overall average of Rice et al. (2003) is in very good agreement with the mid-latitudinal average of this work.Rice et al. (2003) observed an apparent increase of the KIE app towards decreasing mixing ratios in the regions of higher mixing ratios.For our data, a slight curvature towards lower mixing ratios can be detected for δ 13 C (Fig. 4a).For δD (Fig. 4b), including the results of highly processed polar air from our high altitude polar balloon samples leads to slightly lower values for ε D compared to Rice et al. (2003).The change of KIE app with mixing ratio will be discussed in detail in Sect.6.2.
The samples reported in Brenninkmeijer et al. (1995Brenninkmeijer et al. ( , 1996) ) were collected in the southern hemispheric lower stratosphere (10-12 km) at mid and high latitudes.They cover only a small range in mixing ratio (1620-1690 ppb).No comparable data set is available from this work.Nevertheless, similar KIEs are observed, if the new dataset is restricted to high mixing ratio samples only.
A long-term temporal trend in the KIE-values is not discernible from the data in Table 3.Nevertheless, one further factor needs to be corrected for, namely the correction of the bias introduced by the presence of the tropospheric temporal trends.

Correction for tropospheric trends
The evaluation of mean KIEs from each single profile as discussed so far relates the highest altitude sample, which has resided in the stratosphere for years, to the lowermost sam-      ple, which only recently entered the stratosphere or is still located in the upper troposphere.This method will only reflect the true chemical and dynamical stratospheric fractionation in the absence of tropospheric trends.If, however, tropospheric trends exist, then the higher altitude stratospheric samples are related to initial tropospheric values that do not reflect the conditions at the time the sample entered the stratosphere.The deviation is the bigger the larger the tropospheric trends are and the longer the sample of interest already resides in the stratosphere.A correction for the tropospheric trends using the concept of stratospheric "mean age" Kida (1983) is presented in Appendix A.
The mean age corrected fractionation constants are listed in Table 5 together with the absolute and relative change from the uncorrected values (Table 3).In general the mean age correction leads to higher KIE-values, and the effect increases towards lower latitudes.In tendency, it amplifies the KIE D signal relative to KIE 13 C .This is related to the relative size of the tropospheric δ-trend, which for δ 13 C is small.Figure 5 shows the uncorrected (a) and the mean age corrected (b) mean KIE values in direct comparison.After applying the correction the mean KIEs are grouped more closely together in the KIE -KIE plane, but the remaining scatter is still about 3 ‰ for KIE 13 C and ∼30 ‰ for KIE D .
The largest systematic feature in Fig. 5b is the rather low KIE 13 C for the subtropical flights.In addition, KIE D is lower for the vortex flights than for the mid latitude flights.These variations will be examined in the following sections.In the remainder of this paper only the mean age corrected fractionation constants are discussed.

Latitudinal mixing ratio cut-off bias and nonconstant apparent KIE
An additional effect can cause apparent differences between measurements at different latitudes.If the apparent KIE is not constant over the entire range of mixing ratios, the value of the minimum mixing ratio c min of each sample profile affects the mean KIEs at different latitudes.Due to the strong latitudinal mixing ratio gradient in the stratosphere, the minimum mixing ratio c min that is sampled on each balloon flight differs for the different regions.At altitudes of about 30 km (typical maximum altitude of the balloon flights) c min is around 1200 ppb for the subtropics, 650 ppb-900 ppb for mid latitudes and polar regions without vortex influence, and ∼300 ppb for vortex flights.The difference in c min can lead to a bias when comparing profiles from different regions if KIE increases with decreasing mixing ratio.In this case, the mean KIEs from the subtropical flights would be higher simply because only air with relatively high CH 4 mixing ratios was sampled.Figure 6 shows that indeed KIE 13 C decreases with decreasing c min .We call this effect "latitudinal cut-off" bias.
In order to assess whether a latitudinal cut-off bias occurs in our set of samples, Fig. 7 shows how the KIE changes when successively the highest points of each individual profile are truncated ("bottom-up" profiles).Conversely, each point in these figures presents the KIE calculated for each individual balloon profile when only the points up to the designated altitude (x-axis) are included.For KIE 13 C , it is evident that in particular for the vortex profiles, the value of KIE 13 C increases when successively lower mixing ratios are included in the evaluation of KIE 13 C .For the same mixing ratio range, KIE 13 C values for the subtropics are similar than  5 and include the correction for the tropospheric temporal trends.5 and include the correction for the tropospheric temporal trends.
those observed for mid and high latitudes.Thus, the fact that the tropical KIE 13 C values stand out low in Fig. 5b is mainly due to the latitudinal cut-off bias.There is even a tendency for the subtropical and mid latitude KIE's to be slightly higher than the vortex profiles in Fig. 7a.Except for a large scatter in the high mixing ratio regime, where the inverse mixing ratio spans only a small interval and high extrapolation errors are expected, no systematic cut-off bias is observed for KIE D (Fig. 7b).The values in this figure support the observation from Fig. 5b that the KIE D values for vortex air are generally slightly lower than for mid latitude air.

Limitations of global mean sink partitioning
In this section it will be investigated whether/how the derived mean KIE can be used to derive the mean relative strengths of the three stratospheric sink reactions.It is already clear from Eq. ( 8) that the results will depend on f 13 C and f D , but we will show that there are even more limitations.

Sink partitioning -results from previous models
Two extended 2-D-model studies on the isotopic composition of stratospheric methane have been published.Bergamaschi et al. (1996), updated in Saueressig et al. (2001), used a photochemical 2-D-model to predict the distribution of OH, O( 1 D) and Cl in the stratosphere.The model is able to reproduce the δ 13 C(c) fractionation profile from Sugawara et al. (1997).According to this model, in the middle and upper stratosphere (p < 10 hPa) Cl accounts for ∼20 % of the CH 4 sink strength at low and mid-latitudes and for ∼30 % at high latitudes.O( 1 D) is estimated to cause 30 % of the loss in the tropics and mid-latitudes (Fig. 5 in Bergamaschi The second modelling study from McCarthy et al. (2003) yields similar numbers for the sink partitioning.Using the available KIEs for the individual reactions (Table 1), this translates into effective KIEs of In an inverse approach, the model results from Eq. ( 9) can be used in Eq. ( 8) to calculate f 13 C and f D from the average KIE measurements (Table 5).To take the cut-off bias in the determination of mean KIEs into account, this was done separately for the different groups of flights and the results for f 13 C and f D are shown in Table 6.
It is obvious that f 13 C and f D differ significantly.
Whereas all f 13 C values exceed 0.5, f D is always below 0.5.This is surprising since the effects of transport on the different isotope signatures are expected to be similar.(Note that small differences can occur since δD values are much larger than δ 13 C values.)However, in the formal sink partitioning approach based on Rice et al. (2003) (Eq.8), the signal in δD appears strongly attenuated, when sink strengths from previous model studies are used.This is unexpected, since these models do agree with previous stratospheric observations.Given the good agreement of our dataset with previous measurements, we expect that the models would not strongly deviate from our data.Therefore, the low value of f D and the strong difference from f 13 C likely indicate other shortcomings.We will refer to this issue as KIE D -discrimination.
The KIE D -discrimination increases towards higher latitudes, which is mainly caused by the latitudinal cut-off bias in the determination of the mean KIE.Additionally, the attenuation increases when deuterium depleted vortex air (compare the vortex branch of the δD:δ 13 C relation, Sect.4.2.1) is included in the sample set.
The observed KIE D -discrimination and the fact that f D < 0.5 point towards conceptual limitations of the sink partitioning approach using Eq. ( 8), which will be further examined in the following.

Conceptual limitations of the partitioning approach and the origin of the KIE D -discrimination
The approach of deducing the sink partitioning from Eq. ( 8) is strictly applicable only for an idealized removal process where all three sink processes occur simultaneously in a well-mixed volume, i.e.KIE eff is constant.However, the stratospheric sink processes do not occur simultaneously.
The OH sink clearly dominates in the lower stratosphere and the other two sinks gain in importance with altitude.This partly sequential removal of CH 4 is generally masked by the fact that diffusive mixing removes most of the resulting gradients in the apparent fractionation constants.This on the one hand precludes deriving details of the altitude distribution of the different sink processes in the stratosphere from isotope data, but also limits the use of the mean kinetic isotope effects in Eq. ( 8).This can be demonstrated in a simple calculation: the isotope fractionation of a typical tropospheric air sample (c = 1750 ppb, δ 13 C = −47.5 ‰, δD = −81 ‰) is calculated when three times 300 ppb are subsequently removed by all three chemical sinks, but in different order.Table 7 lists the final δ values for all permutations of the sinks and clearly the final enrichments are very different.Although the perfect sequential removal in this idealized experiment exaggerates the issue, it illustrates that the order of removal is important for the final isotopic composition.In this idealized experiment we then use the final isotope composition to calculate again the apparent KIEs and the relative sink fractions (under the condition f 13 C = f D ) for each scenario.Theoretically the sink partitioning should be calculated to (1/3; 1/3; 1/3), but this result is only retrieved for case 7 when the removal in fact occurs simultaneously.
The results in Table 7 illustrate that the mean KIE eff , and thus the sink partitioning derived using the mean KIE approach, is pathway dependent.A fairly realistic sink partitioning is only retrieved when the chemical loss due to OH occurs last (case 2 and 4).In all other cases, the OH fraction is severely underestimated, especially if loss by OH occurs first.The fraction a O 1 D is always overestimated, especially if O( 1 D) is the last sink in the sequence.As a general rule, the last sink has the largest impact on the final δ-value.This is not surprising, because the relative fraction of the 300 ppb removed increases in the three successive steps (300/1750 in the first step, 300/1450 in the second step and 300/1150 in the third step).Since Rayleigh fractionation increases with the relative fraction removed, the last step has the largest impact.
In the stratosphere, the OH sink dominates at the lowest altitudes, which corresponds to case 1 or 6 in Table 7.It is clear that a OH is severely underestimated in both cases, and this can lead to the KIE D discrimination, as described Table 7. Final isotope fractionation (column 3 and 4) and effective kinetic isotope effect KIE eff (column 5 and 6) fractionation for different permutations (column 2) of the three methane sinks.The simulated δ-values are different and thus the KIE eff is pathway dependent.Case 7 is a parallel removal by all three sink processes of equal strength, i.e.KIE eff is constant along the fractionation pathway.8) has conceptual deficiencies.For a realistic treatment it is necessary to use global models, where both chemistry and transport can be included explicitly.

Global scale interpretation from the chemical and dynamical perspective
Building on previous studies on the isotopic composition of CH 4 and N 2 O in the stratosphere (e.g.Griffith et al., 2000;Röckmann et al., 2001;McCarthy et al., 2003;Rice et al., 2003;Park et al., 2004;Toyoda et al., 2001), Kaiser et al. (2006) presented a detailed interpretation of N 2 O isotope measurements from the majority of balloon samples presented in this study.Similar to N 2 O, the chemical lifetime of CH 4 throughout most of the stratosphere is longer than typical transport times and most of the CH 4 is actually removed in the middle to upper stratosphere.One interesting question is whether the distribution of the long-lived gases in the stratosphere can therefore be fully described by an idealized "two end member mixing" where tropospheric air simply mixes with a representative upper stratospheric reservoir that has been strongly processed photochemically.Kaiser et al. (2006) demonstrated that such a two end member mixing produces a straight line in a plot of δ value versus inverse mixing ratio, a so-called "Keeling" plot.Samples with N 2 O mixing ratios above 200 ppb actually show this behaviour.In the stratosphere, 200 ppb of N 2 O roughly corresponds to 1200 ppb of CH 4 (Park et al., 2004).Figure 8 shows that the CH 4 isotope data in this high mixing ratio regime (>1200 ppb) plot on a straight line on the Keeling plot.This subset of data contains all subtropical samples and most samples from the mid latitudes.However, for the samples from polar regions with much lower mixing ratios, the simple two end member mixing model actually deviates strongly from the observations.Figure 8 also shows that a Rayleigh fraction model with an apparent fractionation constant ε app = 16 ‰ (average value for the vortex flights) actually fits the general evolution of the entire dataset well (including the lower mixing ratios).This is equivalent to the observation that the data fall approximately on a straight line in a Rayleigh fractionation plot Fig. 4.However, the Rayleigh model attributes the vertical mixing and isotope ratio changes to chemistry only, which is conceptually inadequate given that transport time scales are slower than chemical timescales in the lower and middle stratosphere, as described above.
To investigate the role of mixing across the polar vortex, Kaiser et al. (2006) presented a simple advective-diffusive model of continuous weak mixing after Plumb et al. (2000) and showed that this model leads to a qualitatively similar trace in a Keeling plot as we find in Fig. 8.In that analysis, www.atmos-chem-phys.net/11/13287/2011/also samples from high-altitude aircraft flights that crossed the vortex edge horizontally were analyzed.Continuous weak mixing will certainly also affect our samples taken near the vortex edge, but a set of isolated vertical balloon profiles is less adequate to investigate this in detail.
Mixing of chemically different air masses across the polar vortex edge, in combination with descent of air from the mesosphere (see next section) is likely responsible for the remaining variability around the average isotope-mixing ratio correlation curve.The corresponding deviations are spatially and/or temporally confined and therefore result in a scatter.Points falling below the average curve represent air parcels that have experienced more than average mixing or less chemical fractionation.The opposite is true for points above the curve.In general, the interpretation of the CH 4 isotope signals is in agreement with the situation as discussed for N 2 O (Kaiser et al., 2006).

Mesosphere-stratosphere exchange in the vortex
It was already discussed above that the isotope:isotope correlation is different for mid-latitude and vortex samples Fig. 3.The correlation for the mid latitudes is practically linear.The correlation for the vortex samples becomes successively flatter, i.e. it has lower δD for a given δ 13 C value.Based on the KIE values in Table 1 this can be tentatively attributed to stronger removal by O( 1 D) for the vortex samples, since the reaction of CH 4 with O( 1 D) has the lowest KIE D .The vortex samples have descended from high altitudes where removal by O( 1 D) is expected to be relatively more important.The vortex region is generally characterized by subsidence of air from higher altitudes in the stratosphere and additionally mesospheric air can subside into the stratospheric polar vortex.For flight KIR-03-03, this has been investigated in detail in Engel et al. (2006), and it is interesting to note that the samples that were characterized there as having mesospheric influence do not show unusual behaviour in our isotope-isotope correlations.This suggests that the influence of mesospheric air on CH 4 in the vortex is not an exception in 2003 as it looks in the individual profiles, but that the descent of mesospheric air causes the general deviation of the isotope-isotope correlation in the vortex from the one at mid latitudes.
Surprisingly, the sample right below the mesospheric intrusion (KIR-03-03/12) deviates from this general classification.In Table 8 this sample is compared to sample KIR-03-03/6, which is the most enriched sample of the vortex branch of the isotope-isotope correlation, and clearly influenced by mesospheric air (Engel et al., 2006).Although KIR-03-03/06 contains less methane than KIR-03-03/12, i.e. it has undergone more methane removal, it is less enriched.This can be explained if KIR-03-03/12 has been processed more strongly by sink process with strong KIE, namely Cl.We propose that sample KIR-03-03/12, represents air that originates from the upper stratosphere, likely close to the stratopause, and from outside the vortex, which descends to the middle and lower stratosphere below the mesospheric intrusion.
Based on the previous results of this mesospheric air discussed in Engel et al. (2006) and the specific position of KIR-03-03/12 between the two characteristic lines in the isotope:isotope plot (Fig. 9), it can be speculated that sample KIR-03-03/12 is a result of an end-member mixing between the most enriched air sample on the vortex branch, i.e.KIR-03-03/6, and a suitable (unknown) end member from the upper stratosphere, denoted KIR-03-03/US.As the products of mixing are found on a straight line connecting the two end members, the unknown upper stratospheric member must also fall on an extrapolated line through KIR-03-03/6 (on the vortex branch) and KIR-03-03/12.We can further assume that KIR-03-03/US falls on the extrapolation of the mid-latitudinal isotope-isotope correlation (Fig. 9).The intersection then defines the isotopic composition of KIR-03-03/US under the given assumptions as given in Table 8.In this case, it is also straightforward to determine the relative contributions of the two end-members as 45 % of KIR-03-03/US and 55 % of KIR-03-03/6.Note that these relative fractions are slightly dependent on the choice of the end members on the vortex and mid latitude lines, since the vortex line has a curvature.

Conclusions
Measurements of the 13 C and D content of CH 4 on a large set of stratospheric air samples collected over a period of 16 yr provide the most comprehensive picture so far on the isotopic composition of stratospheric CH 4 .A method to take into account the residence time in the stratosphere in combination with the observed mixing ratio and isotope trends in the troposphere has been presented.The highest Table 8.Comparison of two samples from flight KIR-03-03, where mesospheric air was sampled.KIR-03-03/6 is found on the vortex branch of the isotope:isotope relation.It is evident that KIR-03-03/12 must have experienced a different fractionation/mixing history.Although its methane mixing ratio is higher than that of KIR-03-03/6, it is much more enriched.Interpreting KIR-03-03/12 as a result of mixing between vortex air and upper stratospheric air from mid latitudes, an appropriate upper stratospheric end-member is reconstructed (KIR-03-03/US).isotope enrichments are found in the polar vortex with values up to δ 13 C = −19 ‰ and δD = +190 ‰, strongly extending the range of isotope enrichments observed before.The previously available isotope data from different laboratories and on air samples collected at different locations and times can be linked and compared by relating them to the new large dataset.It also becomes apparent that inter-laboratory differences exist, especially for δD.
It has been shown that care has to be taken when mean kinetic isotope effects derived from single balloon profiles are compared.Due to the non-linearity of the isotope-mixing ratio relation in a Rayleigh fractionation plot the samples at the lowest mixing ratio have the strongest leverage on the overall slope.Therefore, only profiles that cover the same range of mixing ratios should be compared directly.If profiles from different times are compared, the temporal mixing ratio and isotope trends also need to be taken into account.
Isotope-isotope correlations show that samples from the polar vortex are less depleted in δD than at mid-latitudes, which is attributed to enhanced chemical destruction by O( 1 D) for the vortex samples.A critical analysis of methods to derive a sink partitioning from global mean kinetic isotope effects is carried out.The classical formal sink partitioning, which is based on the assumption that all sinks act simultaneously, underestimates the contribution from OH, because the KIE values derived in the stratosphere are less influenced by the removal in the lower stratosphere compared to the upper stratosphere.Therefore, global models that include the isotopic composition are needed to derive a reliable sink partitioning from the measurements, similar to the study by Mc-Carthy et al. (2003).
Figure 3: Isotope-isotope correlation (a) for tropical (red) mid-latitude (green) and polar (blue) samples, exceptional samples from KIR-03-03 (◊) in orange.Mid-latitude samples follow a linear fit, whereas polar samples follow a parabolic fit.The parabolic shape dominates in the fit to all data Fig. 3. Isotope-isotope correlation (a) for tropical (red) mid-latitude (green) and polar (blue) samples, exceptional samples from KIR-03-03 ( ) in orange.Mid-latitude samples follow a linear fit, whereas polar samples follow a parabolic fit.The parabolic shape dominates in the fit to all data (b).Here, the data was binned in 0.5 ‰ δ 13 C intervals to reduce the statistical weight of the more abundant higher mixing ratio (lower δ-values) samples.The residuals between parabolic fit and data (c), excluding the highest enrichment point, show no systematic structure.The error bars represent typical variations in a 0.5 ‰ δ 13 C bin.

Figure 7 :Fig. 4 .
Figure 7: Rayleigh plots used for deriving the mean fractionation factors for δ 13 C and δD.Some 840 exceptional points have been neglected for the fitting procedure.The lines in the graphs connect the 841 points of each flight according to the sampling altitude.Regression lines are left out, since the 842 principal linear dependence is obvious.843 844 845 846

Figure 9 :Fig. 5 .Figure 9 :
Figure 9: Mean KIE determined before (upper panel) and after (lower panel) applying the correction 851 for tropospheric trends.Errors result from fit uncertainty.Flights are grouped and colour-coded 852 according to their cut-off bias (subtropical: red •; mid-latitudes: green ■; Arctic vortex: dark blue 853 ▲ and Arctic non-vortex: light blue ▲).KIR-00-01 and ASA-01-10 in the bottom figure are based 854 on pseudo-δD values calculated from the isotope:isotope correlation.In the top figure only the real 855 KIE 13C values are shown for those flights, indicated by vertical lines.Additionally, the only 856 previous published balloon profile ( 13 C only) from Sugawara et al. (1997) is included for direct 857 comparison to the other flights.858

Fig. 5 .
Fig. 5. Mean KIE determined before (upper panel) and after (lower panel) applying the c rection for tropospheric trends.Errors result from fit uncertainty.Flights are grouped a colour-coded according to their cut-off bias (subtropical: red determined before (upper panel) and after (lower panel) applying the correction spheric trends.Errors result from fit uncertainty.Flights are grouped and colour-coded g to their cut-off bias (subtropical: red •; mid-latitudes: green ■; Arctic vortex: dark blue rctic non-vortex: light blue ▲).KIR-00-01 and ASA-01-10 in the bottom figure are based o-δD values calculated from the isotope:isotope correlation.In the top figure only the real alues are shown for those flights, indicated by vertical lines.Additionally, the only published balloon profile ( 13 C only) from Sugawara et al. (1997) is included for direct son to the other flights.

Figure 9 :;Figure 9 :
Figure 9: Mean KIE determined before (upper panel) and after (lower panel) applying the correction 851 for tropospheric trends.Errors result from fit uncertainty.Flights are grouped and colour-coded 852 according to their cut-off bias (subtropical: red •; mid-latitudes: green ■; Arctic vortex: dark blue 853 ▲ and Arctic non-vortex: light blue ▲).KIR-00-01 and ASA-01-10 in the bottom figure are based 854 on pseudo-δD values calculated from the isotope:isotope correlation.In the top figure only the real 855 KIE 13C values are shown for those flights, indicated by vertical lines.Additionally, the only 856 previous published balloon profile ( 13 C only) from Sugawara et al. (1997) is included for direct 857 comparison to the other flights.858

Fig. 5 .Figure 9 :
Fig. 5. Mean KIE determined before (upper panel) and a rection for tropospheric trends.Errors result from fit unc colour-coded according to their cut-off bias (subtropical: re

Fig. 5 .;Figure 9 :Figure 9 :
Fig. 5. Mean KIE determined before (upper panel) and after (lower panel) applying the correction for tropospheric trends.Errors result from fit uncertainty.Flights are grouped and colour-coded according to their cut-off bias (subtropical: red

Figure 10 :
Figure 10: Dependence of mean fractionation factors of each flight (ε 13C in blue ♦ , ε D in red ■) on the corresponding lowest mixing ratio cmin observed.Fractionation factors are taken from Table 5

Fig. 6 .
Fig. 6.Dependence of mean fractionation factors of each flight (ε 13 C in blue, ε D in red) on the corresponding lowest mixing ratio c min observed.Fractionation factors are taken from Table5and include the correction for the tropospheric temporal trends.

Figure 11 :Fig. 7 .
Figure 11: The bottom-up profiles show the increase in ε 13C with decreasing cmin, which illustrates 867 the decreasing importance of OH with increasing altitude (decreasing mixing ratio) and reduction of 868 δD relative to δ 13 C in the vortex.Some data points that include only lower stratospheric samples 869 have been left out in the graphs, since they reflect tropospheric variations.The last data point (on 870 the left side) of each line corresponds to the KIEmean results of Table5, but as exceptional samples 871have not been excluded here, they can slightly differ from the values given there.Typically the 872 topmost sample has the lowest methane mixing ratio in a profile and therefore defines cmin.The 873

Fig. 8 .
Fig. 8. δ 13 C plotted versus inverse mixing ratio.Mixing of two distinct air masses should result in a straight line in this plot (thick orange line), derived by a linear fit to all samples with mixing ratios below 1200 ppb, which is approximately equivalent to the high mixing ratio regime of >200 ppb N 2 O(Kaiser et al., 2006).Also shown is a Rayleigh fractionation curve with ε

Figure 12 :
Figure 12: Assuming that KIR-03-03/12 is the result of an end-member mixing process between vortex air (blue) and upper stratospheric air outside the vortex (green), an appropriate upper stratospheric member KIR-03-03/US can be constructed.

Fig. 9 .
Fig. 9.Assuming that KIR-03-03/12 is the result of an end-member mixing process between vortex air (blue) and upper stratospheric air outside the vortex (green), an appropriate upper stratospheric member KIR-03-03/US can be constructed.Note that the vortex and upper stratospheric end members may shift along the respective lines.

KIR
latitudinal upper stratosphere * Estimated from typical mid-latitude profile.

Table 1 .
Measured and calculated kinetic isotope effects and coefficients for their temperature dependence KIE(T ) = Aexp(B/T ).
* Adjusted T-dependence from

Table 2 .
Overview of balloon flights and number of samples analyzed for δ 13 C and δD (column 13 C and D).Each flight is given a flight ID as STA-JJ-MM, where STA is the 3-letter-code for the balloon launch station, JJ the year and MM the month of sampling.

Table 3 .
Mean KIE per flight, in brackets error on last digits.Additionally the column "c min " shows the minimal mixing ratio in a sample set used to derive the corresponding mean KIE.

Table 4 .
Previously published mean KIE values.

Table 5 .
Mean fractionation constants ε 13 C and ε D , corrected for tropospheric trends.The absolute differences in ‰ and the relative change in % to the uncorrected fractionation constants are stated in the right columns.

Table 6 .
Global mean dynamical factors f 13 C and f D inferred from the modelled sink partitioning and the averaged mean fractionation constants ε 13 C and ε D .The second column of values for a certain signature always gives the error.