Global inventory of the stable isotopic composition of methane surface emissions, augmented by new measurements in Europe

. Recent climate change mitigation strategies rely on the reduction of methane (CH 4 ) emissions. δ 13 C CH 4 and δ 2 H CH 4 measurements can be used to distinguish sources and thus to understand the CH 4 budget better. The CH 4 emission estimates by models are sensitive to the isotopic signatures assigned to each source category, so it is important to provide representative modern microbial fermentation sources (ruminants, landﬁlls, sewage treatment plants and biogas plants). of of including included. The new is a contribution from the European Methane Isotope Database, that results from the sampling activities performed within the 2 project. It represents a substantial contribution to the global dataset for fugitive fossil fuels and waste sources, mainly sampled in urban areas.


Introduction
The current change of the earth's climate is mainly caused by the emissions of greenhouse gases from anthropogenic activities (IPCC, 2013;IPCC 2021IPCC , 2021a. Methane (CH 4 ) is a strong greenhouse gas, with a global warming potential 32 times that of CO 2 over 100 years (Etminan et al., 2016). The increase in CH 4 concentration has contributed to an average warming of 0.5ºC in 2010-2019 compared to 1850-1900, which is slightly smaller than the contribution of CO 2 (IPCC 2021(IPCC , 2021b. The 20 global CH 4 mole fraction (χ(CH 4 )) in the atmosphere has drastically increased since 1984, when direct regular measurements started, changing from 1645 ppb to 1850 ppb in 2017 (Nisbet et al., 2019). Compared to pre-industrial times (before 1750), the global χ(CH 4 ) has increased by 160%, from 720 to 1850 ppb (IPCC 2021(IPCC , 2021a. In the past 30 years, we have not observed a steady growth of atmospheric CH 4 mole fraction. Instead the increase in χ(CH 4 ) levelled-off between 2000 and 2007, and has been increasing again since then, from 2014 at the highest rate since the 1980's 25 (Nisbet et al., 2019). This renewed increase presents a significant threat to reaching the goals of the Paris agreement, and mitigation policies are now also targeting CH 4 emissions (Shindell et al., 2017;Mayfield et al., 2017;. Efficient strategies require good knowledge of the different kinds of CH 4 sources, their location and relative contributions. While emission estimates are reported at a country-level using statistical indicators, atmospheric inversions, based on observations, can be used to verify the inventories (Houweling et al., 2000;Zavala-Araiza et al., 2015;Henne et al., 2016;Maasakkers et al., 30 2019). But the results from two approaches, respectively called bottom-up and top-down, are not fully compatible, reflecting a lack in our understanding of the CH 4 cycle (Etiope and Schwietzke, 2019;Saunois et al., 2020;Stavert et al., 2021).
Direct measurements of the isotopic signature of CH 4 sources allow us to characterise them well, and a lot of data is available in the literature. Several review articles on CH 4 isotopic source signatures were previously published (Rice and Claypool, 45 1981;Cicerone and Oremland, 1988;Bréas et al., 2001). The most recent one presented by Sherwood et al. (2017), and recently updated in Sherwood et al. (2021), gathered values from 13 489 locations (10 778 fossil fuel, 2711 non-fossil) from 347 published references. The 2017 study focused on (fugitive) fossil fuel sources, and allowed to re-evaluate the global δ 13 C CH4 value assigned to this emission category towards more depleted values (Schwietzke et al., 2016). A disadvantage of this database is that it is rather US-centered, and that the dataset is strongest for fossil fuel sources, but less robust for non-fossil sources.

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Therefore the database can be completed by more studies, especially concerning non-fossil sources.
The MEMO 2 project (MEthane goes MObile -MEasurements and MOdeling) was a H2020 MSCA European Training Network 1 with the goal to use innovative mobile measurement and modelling tools to improve the quantification of CH 4 emissions in Europe (Walter et al., 2019). An important component of MEMO 2 was the isotopic characterisation of CH 4 55 sources. Two laboratories involved in MEMO 2 , at Utrecht University, The Netherlands, and at the Royal Holloway University of London, UK, carried out a large number of high-precision measurements with isotope ratio mass spectrometry (IRMS).
Another method, using cavity ring-down spectroscopy (CRDS) was developed for the mobile measurements of ambient CH 4 isotopic composition. Several research groups were involved in field work with mobile measurements that targeted specific sources or environments in several European countries. Using this network, numerous CH 4 sources could be sampled for 60 isotopic measurements. The resulting isotopic source signatures were gathered in a publicly available database: The European Methane Isotope Database.
This article presents the data collected within MEMO 2 , and the implications for the global understanding of CH 4 source isotopic composition. To place the new data in context, we analyse it together with an updated version of the Sherwood et al. (2017Sherwood et al. ( , 2021 global database of measured CH 4 source signatures. G2201-i, and G4302, Picarro Inc., USA;MGGA-918 and UGGA, Los Gatos Research, ABB, USA;LI-7810 Trace Gas analyser, LI-COR, USA; Dual Laser Trace Gas Monitor, Aerodyne Research, USA). The samples were taken using a 80 small electric pump connected to an inlet outside of the vehicle. The sample receptacles were bags of 1 to 3 L (Supel™-Inert Multi-Layer Foil bags, Sigma-Aldrich Co. LLC, USA; Tedlar or FlexFoil sample bags, SKC Inc., USA). Surveys were made around known sources of CH 4 , where we sampled the elevated mole fractions as well as background CH 4 on the same day. If it was not practical to approach a source with the vehicle during mobile surveys, samples were taken on foot.

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-Mobile sampling onboard of an aircraft, during the ROMEO campaign. A CRDS instrument (G4302, Picarro Inc., USA) was installed in the aircraft, and samples were taken from the outflow of the instrument into bags of 2 L (Supel™-Inert Multi-Layer Foil bags, Sigma-Aldrich Co. LLC, USA) when an increase in CH 4 mole fractions was observed. The method is described in detail in Menoud et al. (in review).
-Mobile sampling on foot, without analyser. The samples were taken at regularly spread locations around a known CH 4 90 source, to make sure we collected air with CH 4 from the emission plume and background. In this case, the sample receptacles were bags of 2 to 3 L (Supel™-Inert Multi-Layer Foil bags, Sigma-Aldrich Co. LLC, USA; Tedlar sample bags, SKC Inc., USA), filled with a portable hand pump.
-Soil chambers on wetlands in north Sweden and coal waste disposal areas in Poland. In wetlands, we installed transparent Plexiglas chambers on top of stainless steel collars that were pushed 20 cm into the peat. Samples from the chambers 95 were taken during closure times, when χ(CH 4 ) increased, generally after 10 to 25 min. The soil chambers in Poland were made of plastic buckets covered with aluminum foil that were pushed about 5 cm in the ground and left for 30 min.
In both cases, air was pumped into 2L sample bags (Supel™-Inert Multi-Layer Foil, Sigma-Aldrich Co. LLC, USA) for further analysis in the lab.
-From an unmanned aerial vehicle (UAV), carrying an AirCore (coiled tubing) system to collect air samples (Andersen 100 et al., 2018). The air samples were continuously pulled into the AirCore while flying transects across the plume of a CH 4 emission source, and were transferred to a 0.5 or 1 L bag sample after landing (Supel™-Inert Multi-Layer Foil, Sigma-Aldrich Co. LLC, USA) for further analysis in the laboratory. Some photos taken in the field illustrate the different sampling procedures that were used, and are available in

Measurements of isotopic composition
The mass spectrometry measurements were performed at two laboratories: the IMAU (Institute for Marine and Atmospheric research Utrecht) at UU, and at the Department of Earth Sciences at RHUL. Both laboratories use a CF-IRMS (continuous flow isotopic ratio mass spectrometry) system to measure δ 13 C, and also δ 2 H at IMAU. The system at IMAU was described by Röckmann et al. (2016) and the one at RHUL by Fisher et al. (2006). The reproducibility both groups can achieve is of 0.05 110 to 0.1 ‰ for δ 13 C CH4 . At IMAU, δ 2 H measurements have a reproducibility lower than 2 ‰. For consistency of the results, the two laboratories measured a set of 5 cylinders that contained air with CH 4 of different isotopic composition. The resulting differences in δ 13 C CH4 for each cylinder ranged beetween 0.02 and 0.04 ‰. They were within the analytical error reported by the two laboratories, so that the isotopic results obtained within the MEMO 2 project are consistent across the laboratories. The inter-comparison exercise is presented in detail in a MEMO 2 deliverable report publically availabe 4 .
In the database, the method of isotopic measurements is specified by the "Measurement type" parameter, as either 'IRMS' or 'CRDS'. The laboratory where the measurements were performed is specified in the column "Measurement lab".

Calculation of isotopic signatures 120
The measurement results of δ 13 C and δ 2 H of CH 4 are for ambient air, and not the sources themselves. There are different methods to derive the isotopic source signatures from the sampled CH 4 enhancement signatures; the Keeling plot and Miller-Tans methods are commonly used mass balance approaches. The Keeling plot method is based on the assumption that the background is stable during the sampling period (Keeling, 1961;Pataki et al., 2003). The Miller-Tans method is also applicable when the condition of a stable background is not fulfilled (Miller and Tans, 2003). Because background samples were taken 125 on each survey day and in the same region, the condition of stable background was usually fulfilled. Defratyka (2021) showed that in this case, both methods lead to similar results within their uncertainty.
Both methods involve a linear regression model to fit the observed data. Different models were used: ordinary least squares (OLS) minimising the difference in the y-axis coordinate, bivariate correlated errors and intrinsic scatter (BCES) (Akritas and Bershady, 1996), and ordinary distance regression (ODR) (Boggs and Rogers, 1990). Zobitz et al. (2006) compared different 130 regression methods when applied in Keeling plots. The ODR can induce a bias towards lower values in the case the data points cover a relatively small range on the x-axis, so the OLS and BCES methods were usually prefered.
All the mass balance and regression methods are statistically valid. Therefore we did not work towards a uniform procedure, but the different approaches are specified for each entry of the database by the parameters "Mass balance approach" and "Regression method". We used the same parameters as in the database of Sherwood et al. (2017Sherwood et al. ( , 2021 for non-fossil data. That is because our objectives concern only values for δ 13 C and δ 2 H of emitted CH 4 , and do not include measurements of other gases or isotope signatures that Sherwood et al. (2017) reported in the fossil fuel database. The variables of interest are listed in Table 1 and 140 include the site description (country, region, group, category and sub-category) and the δ 13 C and δ 2 H of CH 4 . We grouped the sources reported in the European Methane Isotope Database by region and sub-category in order to integrate it in the literature database. We kept the categories and sub-categories as defined in Sherwood et al. (2017Sherwood et al. ( , 2021, but when the new entries from MEMO 2 measurements and published literature required it, we added additional source categories or sub-categories. The categories are grouped into the three main CH 4 formation pathways: modern microbial, pyrogenic, and fossil fuels. The 145 "modern microbial" CH 4 is formed by microorganisms in surface ecosystems or in animals through enteric fermentation, and are refered simply as "microbial" throughout the paper. Microbial CH 4 formations in the subsurface related to petroleum systems belongs to the "fossil fuels" category. Compared to Sherwood et al. (2017Sherwood et al. ( , 2021, we extended the biomass burning type to include emissions from all combustion sources, such as traffic or industry (Table 1). The analytical parameters reported in the database are δ 13 C CH4 and δ 2 H CH4 , which are defined as:

Literature data
We found additional data in the literature to complete the referred data listed in Sherwood et al. (2021). Because we aim at reflecting the actual CH 4 surface emissions to the atmosphere, we excluded studies that reported results from laboratory experiments, and of CH 4 dissolved in water (i.e. in oceans, wetlands and inland waters). We note that the search for data was biased because of the use of English language. The references we added concern published peer-reviewed articles and to a 160 lesser extent thesis and conference papers. The studies were performed from 1982 to 2021 in various laboratories in the world.
We did not perform additional data quality assessment.

Results and discussion
The data on isotopic source signatures from the measurement campaigns carried out within the MEMO 2 project (2017-2020) were compiled into one database: The European Methane Isotope Database. The first version was made accesssible 5 on October 165 1 st 2020, and described in a publicly available report 6 . The European data was used in several publications over the past 2 years by Menoud et al. (2020Menoud et al. ( , 2021b

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The isotopic signatures obtained within the MEMO 2 project concern 734 locations over 8 countries, with δ 2 H source signatures being measured at 54 % of the sites (Table 2). Figure 1 shows the geographical distribution of the sampled sites in the different countries, according to the type of source. The number of sources we sampled does not necessarily represent the emission magnitudes.

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We characterised 376 locations by both δ 13 C and δ 2 H values, and we compared the results to ranges reported in the literature in Fig. 2. The fossil fuel sources partly overlap with the range of thermogenic CH 4 , but also spread towards lower δ 13 C or higher δ 2 H. This is due to the presence of natural gas of microbial origin in the coal reservoirs of Silesia, in Poland (Kotarba, 2001;Kotarba and Pluta, 2009;Menoud et al., 2021b), as well as in Romania (Baciu et al., 2018;Fernandez et al., in review;Menoud 185 et al., in review). We concluded that this microbial CH 4 originates from the CO 2 reduction pathway, because of a relatively enriched δ 2 H (>-250 ‰), and relatively depleted δ 13 C (<-60 ‰) (Milkov and Etiope, 2018). The δ 2 H measurements were in these cases particularly useful to distinguish fossil fuels from microbial sources (Menoud et al., 2021b;Fernandez et al., in review;Menoud et al., in review).
The waste-related source signatures are generally more enriched in δ 13 C than the typical microbial fermentation range spec-190 ified in previous reviews. The most enriched values concern sewage treatment plants and biogas plants. Changes in waste management practices towards less disposal and more biogas production can likely explain the higher δ 13 C values found in recent studies (Bakkaloglu et al., 2021). A new study also reported surprisingly enriched δ 13 C CH4 (and δ 2 H) around a wastewater treatment plant in Australia: δ 13 C = -47.6 ± 2 ‰ (Lu et al., 2021). The δ 13 C of CH 4 emitted from sewage treatment plants depends on process parameters: oxic conditions lead to more enriched signatures than anaerobic treatment (Toyoda 195 et al., 2011). Regarding biogas facilities, Bakkaloglu et al. (in review) emphasised the link between the type of substrate and the emitted CH 4 isotopic signatures: facilities that operate with C4 plant substrates emit CH 4 with higher δ 13 C values in comparison with C3 plant substrates. Another driver for more or less enriched δ 13 C CH4 emissions from waste sources is isotopic fractionation when CH 4 reacts or diffuses. Diffusion and oxidation in the soil layers when CH 4 migrates from the deeper layers are secondary processes that cause isotopic fractionation (Bergamaschi et al., 1998;De Visscher, 2004;Conrad, 2005  Methane Isotope Database in Fig. 5.A. In western Europe, δ 13 C allows for a good separation between microbial and fossil fuel sources, which is well-established in the literature (Levin et al., 1993;Lowry et al., 2001;Röckmann et al., 2016;Zazzeri et al., 2017;Lowry et al., 2020). Yet we show that we can't use only δ 13 C data to distinguish microbial and fossil fuel CH 4 from 210 all European regions. Fortunately, the δ 2 H CH4 source signatures allow for a clear distinction between fossil fuel and modern microbial emissions of anthropogenic origin ( Fig. 3 and 5.A).

Global data overview and representativeness
The extended global database including all literature data and the aggregated MEMO 2 data consists of 13313 and 4337 measurements of δ 13 C and δ 2 H, respectively, from 64 countries. The map in Fig. 4 shows the partitioning of the data per country, 215 and Table 1 (Table 1), and the amount of measurements is not evenly spread geographically: significantly more measurements were made in North American and European countries, Australia, 220 Brazil and Japan. In Russia and China, there were relatively more measurements as well, but only for fossil fuel sources.
Despite including the first few measurements reported from Africa and the middle-east ; Al-Shalan et al., Fossil fuels Fugitive emissions from fossil fuel reservoirs are highly variable not only on a large scale, but also from one basin 225 to another, or even within the same basin (Sherwood et al., 2017;Milkov and Etiope, 2018;Lan et al., 2021). Therefore, CH 4 isotopic composition from one basin can't be simply upscaled to a country scale. Any new isotopic measurement from a production basin with large fugitive CH 4 emissions brings relevant information. Sherwood et al. (2017) pointed out the lack of data for a list of conventional oil and gas and coal production countries, in Africa, the middle-east, central and southern Asia, and South America. Previous estimates of global CH 4 isotopic 230 signatures from the exploitation of fossil fuels weighted the source signatures from one basin by its fuel production (Schwietzke et al., 2016). Recent work suggest that fuel production is not a reliable proxy to estimate CH 4 fugitive emissions (Zavala-Araiza et al., 2015;Alvarez et al., 2018;Rutherford et al., 2021;Chen et al., 2021;Maazallahi et al., 2021). Thus, the most relevant sampling locations would be ideally related to estimated emission rates from top-down measurements, instead of production or bottom-up emission estimates. Unfortunately, these data are lacking in many Modern microbial The isotopic signatures of CH 4 from modern microbial sources (mainly wetlands, ruminants, waste degradation, rice paddies, termites) are largely dependent on environmental parameters such as the type of substrate and other ecosystem conditions. Figures A3 and A4 show that our new data confirm the trends previously observed: the δ 13 C 240 sensitivity to C3 or C4 plants in ruminant diet (Rust, 1981;Levin et al., 1993;Klevenhusen et al., 2010;Brownlow et al., 2017), to wetland latitudes (δ 13 C depletion in polar regions because of less oxidation and the absence of C4 plants) (Fisher et al., 2017;Brownlow et al., 2017;Ganesan et al., 2018), and the δ 2 H dependency on δ 2 H H2O of precipitation, and ultimately on the latitude (established for freshwater emissions) (Waldron et al., 1999;Chanton et al., 2006;Douglas et al., 2021;Stell et al., 2021). Based on the correlation with the plant metabolism (C3 or C4), δ 13 C CH4 from wetlands 245 could be mapped on a global scale (Ganesan et al., 2018). Douglas et al. (2021) also suggested a spatial extrapolation of wetland δ 2 H CH4 using δ 2 H H2O data, which can be interesting for under-sampled locations, such as the southern hemisphere. However, a certain variability will always remain because of the influence of other parameters such as the dominant methanogenic pathway (acetate fermentation or CO 2 reduction) (Waldron et al., 1998;De Visscher, 2004;Conrad, 2005;McCalley et al., 2014;Inglett et al., 2015;Chan et al., 2019;Douglas et al., 2021), or the composition of

Global data distribution
The global distribution of CH 4 isotopic signatures in the complete extended database is shown in Fig. 5. The values were grouped in categories that correspond to the largest reported emissions (Saunois et al., 2020). The categories agriculture, waste, wetlands, and partly other natural are all of modern microbial origin, mainly following the fermentation pathway (Milkov and 255 Etiope, 2018). They show a normal distribution, and an overlap between the categories, except for the waste sources that are more enriched in 13 C. This difference is particularly visible in the MEMO 2 data, and from a relatively large number of sites from waste related sources. As mentioned in section 2.4, additional parameters control the isotopic signature of the emitted CH 4 , such as the type of substrate, the presence of oxygen, or secondary (e.g. oxidation) processes. We recommend to separate the waste category from the other microbial sources to minimise the uncertainty in the assigned isotopic signature. The 260 fractionation factors derived for CH 4 microbial oxidation are larger for δ 2 H (Coleman et al., 1981;Bergamaschi et al., 1998;Chanton et al., 2006), but we don't clearly see an influence of these additional parameters on the δ 2 H CH4 signatures of our dataset. Indeed, the range of δ 2 H signatures for waste is the same for as agriculture and wetlands (Fig. 5), but these are based on few measurements compared to δ 13 C (42 % of all measured waste sources reported δ 2 H signatures). The relation between δ 2 H CH4 from wetlands and the δ 2 H H2O from precipitation has been established (Waldron et al., 1999;Chanton et al., 2006;Dou-265 glas et al., 2021). But, further δ 2 H measurements are required to better define the isotopic dependancies to secondary processes.
In Sherwood et al. (2017Sherwood et al. ( , 2021, the pyrogenic category only contained biomass burning data, and the binary distribution clearly illustrates the difference between C3 and C4 plants in terms of δ 13 C CH4 signatures. The additional biomass burning data we added from published literature confirms the dependency of δ 13 C CH4 on the plant metabolism. We also added pyro-270 genic data of fossil fuel burning from both our measurements and the literature. The resulting distribution of the δ 13 C data is therefore smoother than in Sherwood et al. (2017) (Fig. 5), because δ 13 C CH4 from fossil fuel burning is more variable than from biomass burning, and does not show a clear distinction between C3/C4 plant metabolisms. δ 2 H CH4 isotopic signatures from pyrogenic sources cover a wide range of values, and overlap with the ones of fossil fuels. Data on δ 2 H H2O could help to parametrise the biomass burning δ 2 H CH4 in more detail (Vigano et al., 2010), similar to the above mentioned relation between δ 2 H CH4 and δ 2 H H2O (Waldron et al., 1999;Chanton et al., 2006;Röckmann et al., 2010;Douglas et al., 2021).  Gupta et al. (1996) This database, mean ± sem -44.5 ± 0.5 / -50.7 ± 1.3 1 -183 ± 3 / -210 ± 5 1 1 for natural gas/coal; 2 also in Lassey et al. (2000); Houweling et al. (2000); Bousquet et al. (2006); Thompson et al. (2018) Fugitive CH 4 emissions from fossil fuels cover a wide range of isotopic signatures: δ 13 C from -72.5 to -18.3 ‰ and δ 2 H from -349 to 14.0 ‰. The average δ 13 C of all fugitive CH 4 emissions from the exploitation of fossil fuels in the European Methane Isotope Database was -44.6 ± 0.4 ‰ (n=452), and the weighted average was -46.6 ± 1.8 ‰ according to the relative 280 emission from conventional and coal fuels production worldwide 7 . Our averages are lower than δ 13 C values used in global models, and than the mean of the global database (Table 3). But the value of -44 ± 0.7 ‰ suggested by Schwietzke et al. (2016), based on the database from Sherwood et al. (2017) scaled with the fossil fuel production in the different regions, is relatively close to our average. The mean values we calculated in Table 3 (bottom row)  basins. However, our averages are an indication of the general δ 13 C signatures from all measurements until now. Because of the high heterogeneity of the δ 13 C of CH 4 from fossil fuel related activities, and the temporal variations in the production from the different regions (Stavert et al., 2021;US Energy Information Administration, 2021;Lan et al., 2021), it is important to keep a relatively large uncertainty when estimating in the global signature of fossil fuel emissions.
In section 2.4, we have shown the use of δ 13 C CH4 to distinguish fossil fuel emissions in western Europe, and the need for The updated database is beneficial for deriving a representative concept of the isotopic composition of CH 4 sources, but it is important to note that applying appropriate weighting arithmetic is essential. Users need to define the dominant CH 4 sources impacting an area, as well as the relative source type emission rates. Emission inventories provide such estimates, but top-down approaches are essential to identify potential biases and evaluate the bottom-up approaches (Alvarez et al., 2018;Etiope and 300 Schwietzke, 2019; Rutherford et al., 2021;Stavert et al., 2021).
This study presents an updated dataset of isotopic source signatures of CH 4 from recent atmospheric measurements, while including additional data from published literature which were not previously included. The new data is a contribution from the European Methane Isotope Database, that results from the sampling activities performed within the MEMO 2 project. It 305 represents a substantial contribution to the global dataset for fugitive fossil fuels and waste sources, mainly sampled in urban areas.
We have highlighted two main improvements in our understanding of the CH 4 isotopic composition: (i) A more robust range of values for modern microbial sources, and a better characterisation of the δ 13 C enrichment in CH 4 from waste sources. (ii) Fossil fuel related sources could have more depleted values than previous estimates used in global models. In this respect, our 310 data confirm the analysis made by Schwietzke et al. (2016).