Variability in Atmospheric Methane From Fossil Fuel and Microbial Sources Over the Last Three Decades

Atmospheric measurements show an increase in CH4 from the 1980s to 1998 followed by a period of near-zero growth until 2007. However, from 2007, CH4 has increased again. Understanding the variability in CH4 is critical for climate prediction and climate change mitigation. We examine the role of CH4 sources and the dominant CH4 sink, oxidation by the hydroxyl radical (OH), in atmospheric CH4 variability over the past three decades using observations of CH4, C2H6, and δ CCH4 in an inversion. From 2006 to 2014, microbial and fossil fuel emissions increased by 36 ± 12 and 15 ± 8 Tg y , respectively. Emission increases were partially offset by a decrease in biomass burning of 3 ± 2 Tg y 1 and increase in soil oxidation of 5 ± 6 Tg y . A change in the atmospheric sink did not appear to be a significant factor in the recent growth of CH4. Plain Language Summary Methane is the second most important greenhouse gas and is responsible for approximately 17% of the direct radiative forcing from all long-lived greenhouse gases. Observations of methane in the atmosphere have shown a dramatic increase from 2007 after a period of relative stability between the late 1990s and early 2000s, but the cause of this increase is still under scientific debate. This study uses atmospheric observations of methane and two related tracers, the isotopic ratio of carbon in methane and ethane, to constrain the sources and sinks of methane over the past three decades. The increase in methane between 2007 and 2014 is likely due to an increase in microbial sources, of 24–48 Tg/y (predominantly natural wetlands and agricultural), as well as fossil fuel sources, of 7–23 Tg/y. In contrast to other recent studies, a reduction in the atmospheric sink of methane was found not to be a significant factor in explaining the recent atmospheric increase.


Introduction
Atmospheric methane (CH 4 ) grew throughout the 20th century, from~880 nmol mol À1 (or parts per billion, ppb) in 1900 (Etheridge et al., 1998) to~1,750 ppb in 1999(Dlugokencky et al., 2003 based on measurements in the remote marine boundary layer. The increase was largely due to human activities, particularly the extraction, transport and storage of fossil fuels, and agriculture . On top of this predominantly increasing trend are significant interannual and decadal variations. The most pertinent of these since the late 20th century are a decrease in the growth rate from the mid 1980s to late 1990s, a period of little growth between 1999 to 2007, and a significant CH 4 increase from 2007 (Nisbet et al., 2014(Nisbet et al., , 2016. Despite the importance of these changes for climate scenarios and emission mitigation, their causes are not well understood owing to the large uncertainties in the sources, anthropogenic and natural, as well as the primary sink, that is, oxidation by the hydroxyl radical (OH) in the atmosphere.
A number of recent studies have sought to improve understanding of CH 4 variability using box models or 3-D atmospheric transport models to compare different source and sink scenarios with atmospheric observations (Kirschke et al., 2013;Nisbet et al., 2016;Rice et al., 2016;Rigby et al., 2017;Saunois et al., 2017;Schaefer et al., 2016;Schwietzke et al., 2016;Turner et al., 2017). As observations of atmospheric CH 4 alone do not provide a sufficient constraint to resolve the sources and sinks, these studies have used the additional information given by the change in the 13 C: 12 C ratio in atmospheric CH 4 (recorded as the change with respect to a standard ratio with the notation δ 13 C CH4 and in units of per mil or ‰; Nisbet et al., 2016). Microbial sources, such as wetlands, enteric fermentation in ruminant animals, and landfills, are relatively depleted in 13  negative δ 13 C CH4 ), while thermogenic sources, such as fugitive emissions from fossil fuels, natural gas seepage, and biomass burning (especially of tropical grasslands), are relatively rich in 13 C (less negative δ 13 C CH4 ; Dlugokencky et al., 2011).
Even with the additional information from δ 13 C CH4 , these studies have found contradicting explanations for the variability in atmospheric CH 4 . For example, the observed increase in CH 4 from 2007, and the accompanying decrease in δ 13 C CH4 , has been interpreted in a few studies as an indication of an increase in microbial sources, particularly subtropical and tropical wetlands and agriculture (Nisbet et al., 2016;Schaefer et al., 2016). In contrast, other recent studies have highlighted that the observations may also be explained by a decrease in the OH sink of CH 4 with little or no change in the sources, since OH preferentially oxidizes 12 CH 4 (Rigby et al., 2017;Turner et al., 2017). However, these studies only infer changes in OH indirectly and it is unclear what would cause a decrease in the OH sink of the magnitude required to explain the trends in CH 4 and δ 13 C CH4 . Moreover, if the oxidative capacity of the atmosphere has declined, the consequences should be seen on other atmospheric species and not just on CH 4 . In fact, there is evidence to suggest that the OH sink of CH 4 may have increased as a result of a decrease in the atmospheric abundance of CO (Gaubert et al., 2017). In another study it was suggested that biomass burning (a 13 C-rich source of CH 4 ) has decreased from 2007 and may have masked an increase in fossil fuel emissions with an overall small decrease in δ 13 C CH4 in the global source . Given the change in biomass burning, Worden et al. (2017) propose that the most likely scenario to explain the CH 4 and δ 13 C CH4 trends from 2007 is an increase in both fossil fuel and microbial emissions.
Owing to the persisting ambiguities in the sources and sinks, even when using both CH 4 and δ 13 C CH4 observations, additional atmospheric tracers have been proposed. For instance, methylchloroform has been used to help constrain the OH sink . However, since errors in methylchloroform emissions are folded into the estimates of OH, these consequently also affect estimates of the CH 4 source (Krol et al., 2005). This problem has been exacerbated by the fact that methylchloroform emissions and atmospheric mixing ratios have now reached low levels, thus increasing the relative uncertainties (Liang et al., 2017). Also, it cannot be ruled out that emissions of methylchloroform may be significantly underestimated with large sources going undetected, as was the case for CFC-11 (Montzka et al., 2018). The D:H isotope ratio in CH 4 , δD CH4 , has also been used similarly to δ 13 C CH4 to help constrain the sources and sinks (Rice et al., 2016); however, δD CH4 measurements are very sparse.
In this study, we use ethane (C 2 H 6 ) as an additional tracer to constrain the sources and sinks of CH 4 . Ethane is co-emitted with CH 4 by fossil fuel extraction and distribution (Kort et al., 2016;Smith et al., 2015) as well as in natural gas seepage from land (Etiope & Ciccioli, 2009) and is a particularly interesting tracer as its other sources are relatively minor, that is, biomass burning and marine seeps (Etiope & Ciccioli, 2009). In addition, C 2 H 6 is also primarily lost via OH oxidation (Rudolph, 1995) with the result that changes in OH will affect both CH 4 and C 2 H 6 in a similar way. A further advantage of C 2 H 6 is that observations are available from discrete samples (flasks) at a multitude of sites globally since the early 1980s. Ethane levels in the atmosphere decreased from 1984 to 2009, leading to the hypothesis that the decline in CH 4 growth rate around the same time was at least partly due to a reduction in fossil fuel sources (Simpson et al., 2012). More recently, C 2 H 6 levels at Northern Hemisphere (NH) sites have risen again leading to speculation that fossil fuel emissions have increased and have contributed to the recent increase in CH 4 (Hausmann et al., 2016;Helmig et al., 2016), although an increase in fossil fuel emissions alone is inconsistent with the observed negative trend in δ 13 C CH4 .
Here we exploit C 2 H 6 , in addition to CH 4 and δ 13 C CH4 , in a formal statistical optimization to estimate the sources and atmospheric sink of CH 4 and to determine the primary causes of atmospheric variation over the period of 1980 to 2014.

Methodology
We use a Bayesian atmospheric inversion to optimize the sources and the OH sink to best match observations of CH 4 , δ 13 C CH4 , and C 2 H 6 within the uncertainty ranges of the observations, prior emissions, and prior sinks. Atmospheric chemistry and transport were calculated using the AGAGE 2-D model of the atmosphere, which is suited to the focus on multiannual trends because of its computational efficiency. This model has four equal area boxes in the latitudinal direction and three vertical layers representing the lower troposphere, upper troposphere, and stratosphere (Cunnold et al., 2002). We adapted the AGAGE model to compute monthly CH 4 and C 2 H 6 mixing ratios and changes in δ 13 C CH4 based on sources and the sinks due to reactions with OH and Cl (for details see Text S1 and Tables S1-S4 in the supporting information).
Emissions of CH 4 were grouped into six categories based on their δ 13 C CH4 values: microbial (including wetlands, rice cultivation, enteric fermentation, and termites with a mean value of À63.2 ± 0.8‰), fugitive emissions from fossil fuel (including natural gas seepage from land, À40.0 ± 1.0‰), landfills (À55.6 ± 0.7‰), biomass burning (À22.2 ± 1.9‰), ocean (assumed to have no effect on δ 13 C CH4 ), and soil oxidation (a negative emission to the atmosphere, À19.7 ± 2.9‰). The δ 13 C CH4 values for each of the six CH 4 source categories were based on literature values and are summarized in Text S2 and Table S4. Atmospheric loss of CH 4 by OH and Cl oxidation is also associated with a kinetic isotope effect; for OH we used À4.7 ± 0.7‰ and for Cl À61.9 ± 1.0‰ (Table S4). Although the total loss due to Cl oxidation is relatively small, with estimates ranging from 12 to 37 Tg y À1 (Allan et al., 2007;Hossaini et al., 2016), the resulting 13 C enrichment is significant but has previously not been considered in inversions for CH 4 .
Emissions of C 2 H 6 were grouped into two categories: fugitive emissions from fossil fuel (including natural gas seepage from land) and other emissions (including biomass burning and ocean sources). The fugitive emissions of CH 4 and C 2 H 6 were related to one another by an ethane to methane mass emission ratio of 0.15 ± 0.025. This ratio was calculated as the weighted average of observed emission ratios for coal, 0.19 (Strępoć et al., 2007), oil and gas, 0.33 and 0.09, respectively (Jones et al., 1999) with a weighting by the relative contribution of coal, oil and gas to the total fossil fuel CH 4 source based on the data set of Schwietzke et al. (2014). Using this data set, no significant trend in the ratio was found from 1980 to 2011 (the period covered by the data) at the scale of the latitudinal boxes. It is still possible though that the actual ratio has varied, especially more recently owing to the changing importance of nonconventional versus conventional sources of natural gas and oil, particularly in the USA, which may have impacted the emission ratio. However, without detailed information about the amount of gas and oil produced from all sources and their emission ratios, as a first approximation, we have used the mean ratio over the inversion period. We estimate the uncertainty in the optimized emissions due to the uncertainty in this ratio using Monte Carlo ensembles (described below). In addition, we include a sensitivity test in which the ratio is increased in one step to 0.175 after 2007 (see Text S4 and Figure S7). The other sources of CH 4 and C 2 H 6 are treated as independent from one another.
Prior emissions estimates of CH 4 were compiled for each latitudinal box and each month using EDGAR-4.2 for anthropogenic sources (enteric fermentation and fugitive emissions from fossil fuels), the LPX-Bern land ecosystem model for wetlands, rice cultivation, and dry-soil oxidation (Spahni et al., 2013), Petrenko et al. (2017) for geological emissions, GFED-4.1s for biomass burning (van der Werf et al., 2010), Lambert and Schmidt (1993) for the ocean source, and Sanderson (1996) for emissions from termites (for prior emission values see Table S2). The emission estimates were resolved monthly and included interannual variations except for oceans and termites, which were only available as monthly climatologies.  Table S3). Our prior estimate for the global C 2 H 6 source, of 22 Tg y À1 , is close to the recent estimate from Dalsøren et al. (2018) of 20 Tg y À1 .
The six CH 4 and two C 2 H 6 sources, as well as the OH sink, were optimized in the inversion. Sources were optimized monthly for the four latitudinal boxes, and the OH sink in each box and month was optimized by scaling it globally and annually. Note that, although the (relatively minor) Cl sink is not optimized, its influence on the results was determined using sensitivity tests and its uncertainty is factored into the overall posterior uncertainty estimates (see next paragraph). For the inversion we used Bayesian inference to find the solution of maximum posterior probability (Rodgers, 2000). Details on the inversion method are given in Text S3, and a summary of the optimized variables is provided in Table S5.
A number of sensitivity tests were performed to assess the robustness of the results to changes in the source and sink uncertainties, to changes in the mean δ 13 C CH4 value of fugitive emissions, to variations in the strength of the Cl sink, and to an increase in the ethane to methane ratio after 2007 (see Text S4 and Figure S7). All tests gave consistent results, but the inversion that resulted in the closest fit to all observations (Test 3 in Table S7) was selected as the best scenario (from here on "reference" inversion). We estimate the posterior source uncertainty using a Monte Carlo ensemble to account for the uncertainties in the mean δ 13 C CH4 values of the sources and sinks, as well as in the C 2 H 6 :CH 4 ratio (see Text S5). Furthermore, we used five additional Monte Carlo ensembles to determine which of the parameters (i.e., the δ 13 C CH4 values and C 2 H 6 :CH 4 ratio) has the largest influence on the source uncertainty. The ensembles contained 500 members each and had a Gaussian distribution for the prior fluxes and δ 13 C CH4 values and a truncated Gaussian distribution for the C 2 H 6 :CH 4 ratio (with truncation for the lower limit at 0.1).

Observational Data
We use monthly mean observations of CH 4 from the National Oceanic and Atmospheric Administration (NOAA) cooperative global air sampling network (Dlugokencky et al., 2009), δ 13 C CH4 from the University of Colorado's Institute of Arctic and Alpine Research (INSTAAR) and the University of Washington's (UW) networks (Quay et al., 1999;White & Vaughn, 2015), and C 2 H 6 from the University of California Irvine (UCI) and NOAA/INSTAAR networks (Blake, 2013;Helmig et al., 2011;Schultz et al., 2015). The reported uncertainties of the measurements are approximately 0.2% for CH 4 , 3% for C 2 H 6 , and 0.1‰ for δ 13 C CH4 . Observations were used from sites that had quasi-continuous records (maps of all sites are shown in Figures S1-S3 in the supporting information). For C 2 H 6 , the UCI observations are available from 1984 and NOAA data start in 2005. Closely located sites from both networks were used to check for consistency during the overlapping period of 2005-2014. For δ 13 C CH4 , the UW observations are available until 1996 and INSTAAR data are available from 1998. The offset between these two laboratories' scales has been estimated to be 0.074‰ (based on the comparison with a third laboratory's measurements at Baring Head, New Zealand; Levin et al., 2012) and is less than the reported precision of approximately 0.1‰ (Miller et al., 2002;Quay et al., 1999).
Average mixing ratios of CH 4 and C 2 H 6 , and values of δ 13 C CH4 , were calculated for each lower tropospheric box and each month when observations were available. For the mean CH 4 mixing ratio for each box and month, observations from three sites were averaged (except for 0°-30°S where only two sites were available). For the mean δ 13 C CH4 in each box and month, we used data from two sites (except 90°-30°N where four sites were available), and for C 2 H 6 numerous sites were used to calculate the average for each box and month (see Figure S2). The greater number of sites used for the C 2 H 6 averages was necessary owing to ethane's greater spatial variability owing to its shorter lifetime of~60 days. The monthly mean data were filtered for outliers, defined as points outside 2-sigma standard deviations around the running mean. The total numbers of monthly averaged observations for CH 4 , C 2 H 6 , and δ 13 C CH4 were 1527, 836, and 1082, respectively. Figure 1 shows the interannual variations in the observed mixing ratios of CH 4 , C 2 H 6 , and δ 13 C CH4 , along with the values modeled using the prior and posterior emissions from the reference inversion. (Note that the interannual variations shown here are calculated from the monthly observed and modeled values.) The prior emissions lead to large biases, especially in CH 4 and δ 13 C CH4 , whereas the posterior estimates reproduce the trends in CH 4 , C 2 H 6 , and δ 13 C CH4 comparatively well (see also Figures S4 to S6). The posterior emissions capture the period of near zero growth between 1998 and 2007 as well as the upward trend in CH 4 and downward trend in δ 13 C CH4 from 2007. The total posterior CH 4 emission has a mean δ 13 C CH4 value of À53.4 ± 5.0‰ (see Figure S7) and is enriched in 13 C compared to the prior (mean of À55.9 ± 7.6‰) but still has less 13 C relative to the atmosphere, which is enriched by the preferential loss of 12 C by OH and Cl oxidation. For C 2 H 6 , the posterior emissions reproduce the decreasing trend in the NH from the 1980s to the mid-1990s and its stabilization thereafter. In the NH, there is an observed increase in the annual mean mixing ratio of 23 ± 3 ppt y À1 from 2010 to 2014, as has previously been identified (Hausmann et al., 2016;Helmig et al., 2016), and is also captured by the posterior model with an increase of 20 ± 2 ppt y À1 . In general, the model has a low bias for C 2 H 6 , which could be due to a possible overestimate of C 2 H 6 loss due to OH and/or Cl oxidation. Note also that the constraint from C 2 H 6 is weaker owing to the higher uncertainty in the observation space for this species (~12.5% of the mean atmospheric value compared to~0.5% and ~0.3% for CH 4 and δ 13 C CH4 , respectively) to account for the larger measurement uncertainty and the uncertainty in the sink terms.

Results
We focus the discussion of the results over the period 1985-2014, as prior to 1985 the observations are sparse, especially for C 2 H 6 and δ 13 C CH4 . The global mean CH 4 emission for 1985-2014 found in our inversion was 505 ± 29 Tg y À1 and is close to the prior value of 525 ± 105 Tg y À1 . However, the trends are considerably different; the prior emissions increase steadily until 2010, while the optimized emissions have little trend until 2006 and then increase (see Figure S7). The inversion finds an increase in the global source of 43 ± 10 Tg y À1 between 2006 and 2014. Also noteworthy is the positive anomaly seen in 1997 owing to large biomass burning emissions associated with the strong El Niño event at this time (see Figure S8), as has previously been reported (Bousquet et al., 2006;Langenfelds et al., 2002). The OH sink increased from 429 ± 3 Tg y À1 in 1985 to 488 ± 4 Tg y À1 in 2014 approximately in proportion to the atmospheric CH 4 abundance. In contrast to the emissions, we found only small interannual variations in OH with small positive anomalies in 2004 and 2005 but fairly stable concentrations from 2007 (see Figure S9). Furthermore, the global CH 4 source and OH sink are robust against variations in the uncertainty assigned to the prior emissions and OH sink, as well as to the uncertainty in the mean δ 13 C CH4 value of fossil fuel emissions (see Text S4 and Figures S7 and S9).
In our inversion, the global fossil fuel emission decreased by 14 ± 9 Tg y À1 from 1990 to 1996 but gradually increased again by 15 ± 8 Tg y À1 from 2006 to 2014. More recently, from 2010 to 2014, the inversion also found the C 2 H 6 emissions to increase at a rate of 0.4 ± 0.3 Tg y À2 , which is consistent with the recent estimate of Helmig et al. (2016). The decrease in fossil fuel emissions in the 1990s is due to changes in the 90°-30°N box

10.1029/2018GL078127
Geophysical Research Letters ( Figure 2a). This result agrees well with previous studies, which point to a reduction in fossil fuel emissions in the early 1990s associated with the collapse of the Soviet Union and a subsequent large investment to reduce leaks associated with natural gas and oil production and distribution (Aydin et al., 2011;Bousquet et al., 2006;Dlugokencky et al., 1994Dlugokencky et al., , 2003Simpson et al., 2012). In the late 1980s and early 1990s, an estimated 25-35 Tg y À1 of CH 4 was leaked to the atmosphere from Russia (Reshetnikov et al., 2000), but with the decline in production from 1991 to 1996, and likely reduction in leaks, the fugitive emission of CH 4 in the post-Soviet era dropped significantly, to an estimated 4 Tg y À1 (Dedikov et al., 1999). The estimated reduction from these bottom-up studies, of approximately 20-30 Tg y À1 , is larger than the mean estimate found by the inversion, but the lower estimate is still within the uncertainty range of the inversion result.
For the microbial source (which includes wetlands and enteric fermentation) the inversion finds significant interannual variations (Figure 2b), which explain up to 62% of the variation in the global CH 4 source. One notable change is the negative anomaly in the tropical and subtropical emissions in the SH during the 1997/1998 El Niño, as has previously been documented (Bousquet et al., 2006;Pison et al., 2013). In the inversion, the posterior microbial emissions in the SH tropics and subtropics (0°-30°S) decreased by 8.5 ± 7.0 Tg y À1 between 2000 and 2005. Previous atmospheric inversion studies have also found a decrease in tropical and subtropical microbial emissions during this period (Bousquet et al., 2006;Pison et al., 2013). From 2006 to 2014, we find a total increase in microbial emissions of 36 ± 12 Tg y À1 , which was mostly located in the tropics and subtropics. An increase in tropical and subtropical microbial emissions since 2006 has similarly been suggested in other recent studies (McNorton et al., 2016;Nisbet et al., 2016;Schaefer et al., 2016).
Since wetlands are the largest microbial source and are sensitive to changes in meteorology, particularly precipitation (which also influences wetland extent), we examined observed precipitation changes using the University of Delaware precipitation data set (https://www.esrl.noaa.gov/psd/data/gridded/data.UDel_AirT_ Precip.html#detail). In subtropical and tropical wetland regions, where the largest changes were seen, we found a negative anomaly in precipitation from 2001  From our Monte Carlo ensembles, we calculated the posterior uncertainties for all sources and the OH sink, and their dependence on the uncertainties in the δ 13 C CH4 values of the sources and the OH and Cl sinks, as well as the C 2 H 6 :CH 4 ratio. Taking into account all these contributions, the uncertainty reduction for the CH 4 emissions was approximately 40% for the microbial and 15% for the fossil fuel emissions and negligible for the remaining more minor sources. Overall uncertainties in the δ 13 C CH4 values of the sources and sinks contributed similarly to the posterior uncertainty. The more minor sources were less well constrained and changed little compared to the prior estimates (<3 Tg y À1 ) and similarly for the nonfossil fuel emissions of C 2 H 6 (<0.2 Tg y À1 ; see Figure S8). The soil oxidation loss of CH 4 , however, was on average~15 Tg y À1 smaller than the prior ( Figure S8), but the uncertainty reduction for this source was negligible. Noteworthy is that the biomass burning emissions, though largely unchanged compared to the prior, decreased by 3.4 ± 1.7 Tg y À1 from 2006 to 2014, which is comparable to the result of Worden et al. (2017), who found a reduction in this source of 3.7 ± 1.4 Tg y À1 based on satellite retrievals of CH 4 , CO, and fire activity. The decrease in the CH 4 growth rate from 1990 to 1996 is symptomatic of the budget approaching steady state as the global total emission ceased to increase in the late 1980s and actually decreased between 1990 and 1996 by 11 ± 9 Tg y À1 . This decrease was likely driven by a reduction in fossil fuel emissions of 14 ± 9 Tg y À1 but was partially offset by increases in other sources ( Figure S11). The subsequent near-zero growth rate between 1998 and 2006 is owing to approximately stable total emissions, with changes in the fossil fuel emissions largely compensating those in the microbial emissions. Moreover, we find that the increase in CH 4 from~1,779 ppb in 2007 to~1,820 ppb in 2014 is driven by a net increase in the source of 43 ± 10 Tg y À1 , which is the balance of an increase in microbial and fossil fuel emissions of 36 ± 12 and

Conclusions
We find that the increase in CH 4 from 2007 was largely driven by an increase in microbial emissions of 36 ± 12 Tg y À1 , predominantly in the tropics and subtropics, and fossil fuel emissions of 15 ± 8 Tg y À1 . In the tropics and subtropics, changes in the microbial emissions are broadly consistent with those expected from a wetland source responding to variations in precipitation. However, the period from 2005 to 2014 is only weakly correlated with precipitation anomaly; thus, other driving factors or contributions from other microbial sources, such as those from agriculture, likely also play a role. In addition, we find that the most likely explanation for the decline in the C 2 H 6 mixing ratio, and a contributing factor in the decline of the CH 4 growth rate, from the late 1980s to the mid-1990s is a reduction in fossil fuel emissions of 14 ± 9 Tg y À1 (CH 4 ), which has probably occurred as a consequence of improvements in leak control in the oil and gas industries (Aydin et al., 2011).
Including C 2 H 6 , in supplement to CH 4 and δ 13 C CH4 , in the inversion provided an additional constraint on the fossil fuel source of CH 4 and thus indirectly on the other sources and, to some extent, also on the OH sink. Our results contrast with two recent studies that suggest that the increase in growth rate from 2007 may have been driven by a decrease in OH (Rigby et al., 2017;Turner et al., 2017), although we agree with their emphasis on the persisting large uncertainties in the CH 4 budget. Considering that the CH 4 increase is likely to be partially due to an increase in the fossil fuel source, there may be a possibility to curb the growth by mitigating these emissions. NOAA CH 4 and C 2 H 6 data are available from https://www.esrl.noaa.gov/gmd/ dv/data/, INSTAAR δ 13 C CH4 data from ftp://aftp.cmdl.noaa.gov/data/trace_ gases/ch4c13/flask/, UW δ 13 C CH4 data from http://cdiac.ornl.gov/ndps/quay. html (doi:10.3334/CDIAC/atg.026), and UCI C 2 H 6 data from http://cdiac.ornl. gov/trends/otheratg/blake/blake.html. The modified version of the AGAGE 2-D model, the inversion code, and the optimized emissions are available on request to R.L.T. We kindly thank P. Quay (UW) for the use of the δ 13 C CH4 data. R.L.T. and I.P. acknowledge the financial support of NordForsk to the eSTICC Nordic Centre of Excellence (grant 57001). E.G.N. was supported by the NERC Project MOYA (grant NE/N016211/1).