Measurements of the isotopic ratio in atmospheric methane for 2012 come from five northern high-latitude surface sites (White et al., 2018). The locations of these sites are shown in Fig. 1, and their characteristics are given in Table 1. Most of them are considered to be sampling background air: Alert is located in northern Canada; Zeppelin (Ny-Ålesund) is on a mountaintop in the Svalbard archipelago; Cold Bay is in the Alaska Peninsula; and Summit is at the top of the Greenland Ice Sheet. The Barrow observatory (now known as Utqiaġvik), located in the North Slope of Alaska, is more affected by local wetland emissions. The NOAA Earth System Research Laboratory (NOAA ESRL) is responsible for the collection and analysis of the weekly flask samples. The isotopic composition is determined by INSTAAR (Institute of Arctic and Alpine Research) of the University of Colorado. All data are reported in conventional delta notation, in per mil (‰). The δ13CCH4 observations are given with a precision of better than 0.1 ‰ (White et al., 2018). All data without reported issues in collection or analyses are selected; outliers above 3σ of the variability at the station are discarded.

Other sites where atmospheric methane is measured are also included in this study. They do not provide δ13CCH4 observations, but we evaluate their potential in doing so. Their description is given in Table 1.

The Eulerian chemistry-transport model CHIMERE (Vautard et al., 2001; Menut et al., 2013) is used to simulate tropospheric 12CH4 and 13CH4 concentrations separately, with the isotope ratio being computed offline a posteriori. Following Thonat et al. (2017), the domain has a regular kilometric resolution of 35 km, which avoids numerical issues due to grid cells that are too small, close to the pole, and encountered in regular latitude–longitude grids. It covers all longitudes above 64∘ N but extend partially to 39∘ N, as illustrated in Fig. 1. The troposphere is divided into 29 vertical levels from the surface to 300 hPa (∼ 9000 m).

CHIMERE solves the advection–diffusion equation and is forced using meteorological fields from the ECMWF (European Centre for Medium Range Weather Forecasts, http://www.ecmwf.int/; last access: 18 September 2019) forecasts and reanalyses. Wind, temperature, water vapour, and other meteorological variables are given with a 3 h time resolution, at ∼ 0.5∘ spatial resolution, and 70 vertical levels in the troposphere. Initial and boundary concentrations of 12CH4 and 13CH4 come from a global simulation of the general circulation model LMDZ (Hourdin et al., 2006) for the year 2012. This global simulation used emission fluxes (including ORCHIDEE for wetland emissions, EDGARv4.2 for anthropogenic emissions other than biomass burning, and GFED4.1 for biomass burning emissions) that were adjusted in order to obtain a reasonable agreement at the global scale between the simulated isotopic signal and the flask measurements of the NOAA ESRL network (Dlugokencky et al., 1994). These global fields have a 3 h time resolution and 3.75∘×1.875∘ spatial resolution. These meteorological and concentration fields are interpolated in time and space within the grid of the CHIMERE domain.

The model is run with various tracers, each one corresponding either to the 12CH4 or to the 13CH4 component of a methane source. Simulated 12CH4 and 13CH4 of all sources are then used in the calculation of δ13CCH4. This allows us to analyse the contribution of each source in δ13CCH4. Three pairs of tracers correspond to anthropogenic sources: emissions from oil and gas, emissions from solid fuels (coal), and other anthropogenic emissions (mostly from enteric fermentation and solid waste disposal). One pair of tracers corresponds to biomass burning. Two pairs correspond to geological sources: continental micro- and macroseepages; and marine seepages. Three pairs correspond to other natural sources: wetlands, freshwater systems, and emissions from the ESAS. Another pair of tracers corresponds to soil uptake and is considered as a negative surface source. Finally, one pair of tracers corresponds to the boundary conditions. No pair of tracers is implemented for the initial conditions: simulations in January are partly influenced by prescribed initial conditions from global fields during the spin-up period of 2–4 weeks (typical mixing time of air masses in the domain with the chosen model set-up spanning high northern-latitude regions), but this has little impact on our conclusions. No chemistry is included in the multi-tracers simulation, but another simulation including the reaction with OH is carried out in order to assess the contribution of this major sink. More details on the aforementioned emission categories are given below in Sect. 2.3.

Surface emissions used as inputs in the model come from various inventories, models, and data-driven studies. The emissions used are the same as in Thonat et al. (2017), in which they are described and discussed in more detail; we provide a summary below and in Table 2.

All anthropogenic emissions are taken from the EDGARv4.2FT2010 yearly product (Olivier and Janssens-Maenhout, 2012). When possible, the 2010 data are updated using FAO (Food and Agriculture Organization, http://www.fao.org/faostat/en/\#data/, last access: 18 September 2019) and BP (http://www.bp.com/, last access: 18 September 2019) statistics (on enteric fermentation, and manure management, and on oil and gas production, fugitive from solid, respectively). For 2012, anthropogenic emissions amount to 20.5 Tg CH4 yr-1 in our domain, mostly from the fossil fuel industry. Biomass burning emissions come from the GFED4.1 (van der Werf et al., 2010; Giglio et al., 2013) daily product and represent 3.1 Tg CH4 yr-1 in our domain.

Wetland emissions are derived from the ORCHIDEE global vegetation model (Ringeval et al., 2010, 2011) on a monthly basis. Annual emissions from wetlands in our domain correspond to 29.5 Tg CH4 yr-1. A large uncertainty affects wetland emissions, which can vary widely depending on the chosen land vegetation model and wetland area dynamics (e.g. Bohn et al., 2015). Emissions from geological sources stem from the GLOGOS database (Etiope, 2015) and amount to 4.0 Tg CH4 yr-1 in our domain. ESAS emissions are prescribed to 2 Tg CH4 yr-1 in agreement with the estimate made by Thornton et al. (2016a) based on a ship measurement campaign and with the estimate made by Berchet et al. (2016) based on atmospheric observations at surface stations. The temporal and geographic variability of the ESAS emissions is based on the description by Shakhova et al. (2010), following the modelling framework of Berchet et al. (2016).

Following Thonat et al. (2017), we consider that 15 Tg CH4 yr-1 is emitted by all lakes and reservoirs located at latitudes above 50∘ N. The localization of these freshwater systems relies on the Global Lakes and Wetlands Database (GLWD) level 3 map (Lehner and Döll, 2004). Our inventory was built based on some simplifications: the emissions are uniformly distributed among lakes and reservoirs, no emissions occur when the lake is frozen, and emissions are constant otherwise. Freeze-up and ice-out dates are estimated based on surface temperature data from ECMWF ERA-Interim reanalyses. Freshwater emissions amount to 9.3 Tg CH4 yr-1 in our domain, which is consistent with recent pan-Arctic studies (e.g. Wik et al., 2016; Tan and Zhuang, 2015).

Source signatures are chosen constant in time and space in our modelling framework. Regional seasonal variations of microbial signatures are expected to be small (e.g. Sriskantharajah et al., 2012); some homogeneity can be assumed at the scale of our domain, which only comprises high northern latitudes, and possible heterogeneity is assumed to be smoothed out by the model 35 km horizontal resolution. Also, considering that most atmospheric sites are located far from large emission areas, the signals in the emissions are mixed by the atmospheric transport. Therefore, we have chosen to use only one value for each source but to test various scenarios with different isotopic signatures (see Sect. 3.2).

The Sherwood et al. (2017) data on fossil fuel emissions for countries within our domain show a wide range of measured isotopic signatures. For conventional gas and shale gas, data range between -76 ‰ and -24 ‰, with means for Russia (number of data, n=556), Canada (n=490), Norway (n=28), and the US (Alaska) (n=20), of -46 ‰, -51 ‰, -44 ‰, and -43 ‰, respectively. Heavier signatures (typically -40 ‰) are generally used for oil and gas related emissions in global studies (e.g. Houweling et al., 2006; Lassey et al., 2007) and also for Arctic studies (Warwick et al., 2016), but more depleted signatures have also been used for Russia (-50 ‰ in Levin et al., 1999). Given that Russia is by far the largest emitter of methane from natural gas production and distribution, we chose here a mean value of -46 ‰ for the whole domain, but test our results over a range spanning -40 ‰ to -50 ‰. As it is difficult to distinguish between methane associated with gas and oil exploitation, the same signature is used for both.

The range of isotopic values is also very large for emissions from coalfields: from -80 ‰ to -17 ‰ (Rice, 1993). In the Sherwood et al. (2017) database, isotopic signatures from coal exploitation are fewer than those from natural gas, with only one reference for Russia and 92 values reported for Canada, with a mean value of -55 ‰. Russia is again the top emitter in this category, but the paucity of the data prevents us from using the single value for the whole domain. Zazzeri et al. (2016) highlighted the dependence of the isotopic value on the coal rank and type of mining, although national and regional specificities remain. Basically, the higher the coal rank (i.e. the carbon content), the heavier the isotopic signature. The main Russian coal basins, the Kuznetsk and Kansk-Achinsk basins, located in southern Siberia, where low rank coal is extracted, are not part of our domain. The few major hotspots of emission associated with coal in our domain, according to EDGARv4.2FT2020, correspond to basins where hard coal is exploited, mainly bituminous coal (Podbaronova, 2010). According to the broad classification suggested by Zazzeri et al. (2016) for modellers, this means rather light isotopic signatures between -55 ‰ and -65 ‰. Consequently, we chose here a mean value of -55 ‰ for emissions associated with coal in our domain, which is lighter than the values usually used in global methane budgets (e.g. -37 ‰ in Bousquet et al., 2006, and Tyler et al., 2007; -35 ‰ in Monteil et al., 2011), but we test our results over the range of -50 ‰ to -65 ‰.

Other non-negligible anthropogenic sectors in our domain are enteric fermentation and waste disposal. For the former, the δ13C signature depends strongly on the ruminants' diets and on the species. Klevenhusen et al. (2010) found signatures from cows of -68 ‰ (C3 plants) or -57 ‰ (C4 plants), depending on the diet, in agreement with previous studies by Levin et al. (1999) and Bilek et al. (2001). Here, a value of -62 ‰ was used, as in other methane isotopic budgets (e.g. Tyler et al., 2007; Monteil et al., 2011). Methane emitted by organic waste is enriched as a result of methane oxidation after its production in the anoxic layer. Here, a value of -52 ‰ was used, in agreement with Chanton et al. (1999) (-58 ‰ to -49 ‰) and close to what was found by Bergamaschi et al. (1998) (-55 ‰). The emissions of those two sources are an order of magnitude lower than anthropogenic emissions from fossil fuel production; thus, their isotopic signature does not significantly impact the isotopic signal at observation sites.

Anthony et al. (2012) found natural seeps concentrated along the boundaries of permafrost thaw and retreating glaciers in Alaska and Greenland, with a wide range of isotopic signatures, originating from fossil and also younger methane. However, geological methane is mostly of thermogenic origin (Etiope, 2009), and this is also true for submarine seepage (e.g. Brunskill et al., 2011). In this region, geological manifestations occur through submarine seepages and microseepages with mean isotopic signatures of about -51.2 ‰ and -51.4 ‰ with uncertainty on the order of 7 ‰ and 2 ‰, respectively (Etiope et al., 2019). As a consequence, the isotopic signature used here for geological methane, both continental and submarine, is -52 ‰, following Etiope et al. (2019), associated with the range -50 ‰ to -55 ‰.

The values of isotopic signatures for biomass burning are found within a small range, despite their dependency on the fuel type (C3 vs. C4 plants) and combustion efficiency. For example, Chanton et al. (2000) reported values comprised between -30 ‰ and -21 ‰ for US forests. Yamada et al. (2006) estimated the global biomass burning δ13CCH4 at -24 ‰, while Whiticar and Schaefer (2007) suggested -25 ‰. Here, the value of -24 ‰ was used as a mean value, but signatures ranging from -30 ‰ to -21 ‰ have been tested (Table 3).

Microbial methane from wetlands has a wide range of isotopic signatures, varying from -110 ‰ to -50 ‰ (Whiticar, 1999). Acetoclastic fermentation results in methane relatively less depleted in 13C (δ13CCH4 of -65 ‰ to -50 ‰), while CO2 reduction produces methane highly depleted in 13C (δ13CCH4 of -110 ‰ to -60 ‰) (Whiticar, 1999; McCalley et al., 2014). The partition between these two production pathways depends partly on the ecosystem type and season. The isotopic signature of the emitted methane also depends on other factors, such as the pathways of transport and oxidation (Chasar et al., 2000). Several studies on the isotopic signature of wetlands, focusing on high northern latitudes, are compiled in Table 3. All studies report values generally ranging between -75 ‰ and -60 ‰. Here again, the difficulty in dealing with these reported source signatures has to do with their representativity. Some observations are from chamber studies, which, by nature, focus on very local signals; others are given by ambient air samplings and can be representative of several hundred square kilometres, so possibly encompassing other source and sink determinants. The chamber studies present a wide variety of values for the same site. For example, Fisher et al. (2017) reported values at the Stordalen mire ranging from -112 ‰ to -48 ‰, and even in the same week, changes can be as large as 30 ‰. The signals can also vary significantly with the time of year and the kind of ecosystem (McCalley et al., 2014). For example, for three different peatland systems in Finland, Galand et al. (2010) report values that differed by 30 ‰. Consequently, values in Table 3 are mostly derived from ambient air samplings rather than chamber measurements, and we give means rather than the whole measured ranges. The value of -70 ‰ was used in our study and is close to the recommendation to modellers made by Fisher et al. (2017) (-71‰±1‰) and France et al. (2016) for wetlands above 60∘ N. However we tested a wide range of signatures for wetland emissions between -80 ‰ and -50 ‰.

Most values labelled “Wetlands” in Table 3 encompass not only wetlands but also a mix of wetlands and other exposed freshwater systems. Shallow lakes, ponds, and pools, common in the Arctic, have not always been considered a distinct source (Bastviken et al., 2011). This is another limitation in estimating the global methane budget (Saunois et al., 2016). Signature estimates based on air sampling are representative of a wide area, where exposed freshwaters are undoubtedly present. Moreover, signature ranges reported specifically from Arctic lakes are not precise enough to distinguish between water body types and overlap those of wetlands (Wik, 2016). In the range of recent reported values (Walter et al., 2008; Brosius et al., 2012; Bouchard et al., 2015; Wik, 2016; Thompson et al., 2016), and close to the value used for Arctic wetlands, the value of -66 ‰ was used for the isotopic signature of freshwater system (here lakes and reservoirs) emissions in our domain. We also tested a wide range of signatures for freshwater emissions between -80 ‰ and -55 ‰.

Sources of methane in the ESAS are varied, and it is still a challenge to determine the origin of methane produced and emitted there (Ruppel, 2015). The shallow ESAS is underlain by formerly subaerial permafrost that has been flooded by sea level rise since the Pleistocene (Dmitrenko et al., 2011). Carbon can be released via the degradation of permafrost or decomposition of gas hydrates. Sapart et al. (2017) showed that sediments in ESAS have isotopic signatures ranging between the two main microbial methane formation pathways. In an earlier study, Cramer and Franke (2005) observed significantly heavier CH4 (δ13CCH4 ∼ -39.9 ‰) in the Laptev Sea near-surface sediments, which are attributed to a deep thermogenic source. A wider range, with much lighter CH4 was detected in the Laptev seawater column. Methane in the water is more enriched in 13C than in sediments, but the signature of methane emitted in the atmosphere is in the range of wetland emissions. Based on fewer data than Sapart et al. (2017), Overduin et al. (2015) reported more positive values, associated with strong 13C enrichment in the upper thawed permafrost layers. Oxidation in marine systems can be coupled to sulfate reduction as well in suboxic environments. This will not affect the atmospheric values directly but will shift the source signatures of the methane that is emitted from the surface to heavier values after having been diffusively advected from its sedimentary sites of production through the water column to the atmosphere. A mean signature of -58 ‰ (range -80 ‰ to -50 ‰) was used here for emissions from ESAS, in the range of the literature (Etiope et al., 2019).

The main sinks of methane in the troposphere are its oxidation by hydroxyl radicals (OH), which accounts for about 90 % of the total sinks (Saunois et al., 2016), its reaction with chlorine (Cl) in the marine boundary layer (about 3 %), and its uptake by soils (about 3 %, on a global scale; Kirshke et al., 2013).

Due to the difference in mass between the 12CH4 and 13CH4 isotopologues, chemical reactions in the atmosphere preferentially consume the lighter isotopologue, potentially causing significant fractionation. This is one of the reasons why the δ13C of methane in the atmosphere is not the same as that of the total source.

The chlorine sink is not included in our regional simulation. We have shown in Thonat et al. (2017) that this sink has a negligible impact of CH4 mixing ratio (below 1 ppb in our polar domain).

Methane uptake occurs in unsaturated oxic soils due to the presence of methanotrophic bacteria. This sink may be particularly important in high-latitude regions with wetlands. In our domain of simulation, its magnitude is equal to -3.1 Tg CH4 yr-1 (see Table 2).

Sinks can be characterized by their kinetic isotope effect (KIE). The ratio of the reaction rate coefficients (k) for two different isotopologues of the same molecule is klight/kheavy. For the reaction with OH this value is 1.0039 (Saueressig et al., 2001). For the soil uptake, the KIE is 1.020, which is represented by a fixed δ13CCH4 source signature of -65.7 ‰ in our model set-up. Despite a high KIE, including the chlorine sink in the regional simulation will not change significantly our conclusions on the local source detectability.

Most of the five sites, where weekly δ13CCH4 measurements are available, are remote from any emitting areas (Fig. 1) with the exception of Barrow, where significant methane enhancements from nearby wetlands can happen in summer (Sweeney et al., 2016). The boundary conditions are the dominant signal in our domain, especially in winter, both in terms of total methane mixing ratio (in ppb) and δ13CCH4 value (in ‰), as illustrated in Fig. 2. The boundary conditions represent methane coming from lower latitudes south of the polar domain (Fig. 1). However, they cannot be fully considered as a background level of methane given that (i) they may be due to emissions from the northern high latitudes that have left our domain and then re-entered it, and (ii) they may bring to the domain air masses that are particularly depleted or enriched in methane.

For most remote sites, the maximum δ13CCH4 is reached in May–June and ranges between -47.3 ‰ and -47.1 ‰ (Fig. 2). Then wetlands and freshwater systems start emitting 13C-depleted methane and the minimum is reached in September to early November, with values around -47.8 ‰. One exception is Cold Bay, where δ13CCH4 in January was much lower than other sites. In Barrow, the minimum reaches -48.2 ‰. The yearly mean is -47.6 ‰ at Barrow and -47.5 ‰ at the other sites. The seasonal amplitude is about 0.6 ‰. The variability of the measurements is higher in Barrow and Cold Bay compared to the three others, highlighting that these two sites are the most sensitive to northern high-latitude sources (mainly wetland emissions) at the synoptic scale.

The contribution of the boundary conditions to simulated δ13CCH4 is approximately between -47.2 ‰ and -47.6 ‰. The increment added by northern high-latitude sources lies between -0.1 ‰ and -0.2 ‰ in summer (June–October), except in Barrow where it is -0.4 ‰ and is close to zero in winter (November–May). Barrow is more sensitive to the regional sources (mainly wetland and freshwater emissions) compared to the four other sites (compare Fig. S4 to Figs. 4, S1, S10 and S18). On a yearly basis, our model overestimates δ13CCH4. The large overestimation in winter (∼ 0.2 ‰) is due to the boundary conditions that are too high in terms of total methane compared to continuous measurements (as shown in Thonat et al., 2017). Contributions of low-latitude fossil sources that are too large lead to δ13CCH4 values that are too high. Nevertheless, large spikes are simulated in winter at Barrow and Alert, some of which are attributed to ESAS emissions. Due to the low frequency of flask measurements, it is not possible to associate these simulated spikes to observed ones. Higher frequency measurements are needed to assess the reality of such spikes and their magnitudes and to allow discussion on both the magnitude of the source(s) and its/their isotopic signature(s). In summer, the model underestimates δ13CCH4 by less than 0.11 ‰ at all sites, which is in the range of the uncertainty of the measurements. However, the seasonality is only poorly captured by the model. The decrease in early summer comes too soon and so does the autumn minimum, as already noticed by Warwick et al. (2016). Thonat et al. (2017) demonstrated that this result is mostly emission driven: the seasonality of wetland emissions is not well reproduced by the various existing land surface models because wetland emissions derived from biogeochemical models occur too soon and cover too short a period during the year.

Despite their importance to assess the inter-annual variability and seasonality of δ13CCH4, the available flask measurements do not allow us to quantify the ability of the model to represent the synoptic variations. Continuous measurements of δ13CCH4, as well as δDCH4, would be necessary to evaluate the model in a more quantitative way. Even though further improvements will be necessary in the model, we assume in the following that the model performances associated with sensitivity tests using various isotopic signatures are sufficient for estimating the magnitude of the isotopic signals in δ13CCH4 originating from the various northern latitude sources.

In terms of total methane, our domain is dominated by anthropogenic sources in winter and by wetland emissions in summer. ESAS and geological sources can also have a relatively significant impact in winter in some areas, while freshwater systems are an important contributor to atmospheric methane in summer (Thonat et al., 2017). The spatial distribution of the source contribution to the δ13CCH4 value depends not only on the magnitude of the emission but also on the difference between the isotopic signature of the source and of the boundary conditions. The difference between total δ13CCH4 and the contribution of the boundary conditions (Fig. 2, black and cyan lines, respectively) represents the sum of the direct contribution from the various northern latitude sources at the measurement locations. The combination of the various signals due to northern latitude sources depends on the station, as shown in Fig. 2.

These five sites do not form a large enough sample to be representative of all northern latitude sites. Therefore, Fig. 3 shows the winter and summer means of the simulated direct contributions of the various sources to the δ13CCH4 value at the 24 sites of Fig. 1. For each site, the seasonal mean contribution of each source is plotted along a cumulative dotted line. The rightmost black point of each line represents the total contribution of all northern latitude sources, i.e. the difference between simulated total δ13CCH4 and δ13CCH4 from the boundary conditions alone. The frequency distribution of the contribution from all the Arctic sources to the signal is overplotted with an arbitrary unit, showing the range of isotopic signals covered over the season. For example, if we consider Tiksi (TIK) in winter, the direct contribution of all Arctic sources is -0.09 ‰ on average over the season. However, the frequency distribution shows that the isotopic contribution at Tiksi is mainly between 0 and -0.2 ‰ but can reach lower values up to -0.25 ‰.

On average, the contributions of northern high-latitude sources to the isotope ratio are very low in winter at all sites, between -0.65 ‰ and +0.03 ‰. The isotope ratio signal is low in winter because the largest contribution of Arctic sources to atmospheric methane in this season is due to oil and gas emissions, whose signature (-46 ‰) is very close to that of boundary conditions. One exception is YAK (see Table 1 for the definition of site abbreviations here and hereafter), where the mean winter contribution to δ13CCH4 is -0.63 ‰. This is due to large simulated mixing ratios of methane from nearby coal emissions. The daily isotope ratio signal shift due to Arctic contributions there can reach -1.75 ‰. Geological emissions have a signature close to oil and gas in our modelling framework and do not show up in the simulated signal. On the contrary, ESAS emissions have an impact on δ13CCH4 at some sites at the synoptic scale: the maximum δ13CCH4 northern high-latitude contribution at AMB and CHS in winter is ∼ -0.5 ‰ and ∼ -0.4 ‰ at TIK, which are close to the shores of ESAS. NOY is the only site with a positive mean contribution to δ13CCH4 in winter. Large enhancements of 12CH4 from oil and gas, which in NOY regularly exceeds 100 ppb in winter, succeed in making a significant difference with the δ13CCH4 value of the boundary conditions. Apart from NOY, the northern high-latitude contribution to δ13CCH4 is very rarely positive among the sites and stays low when it is positive (maximum is 0.13 ‰ at DEM).

Compared to winter, higher contributions of northern high-latitude sources to the δ13CCH4 values are found in summer at most stations because of the large magnitude of natural emissions, especially from wetlands. Wetland emissions contribute to more than two-thirds of the signal at all sites, except at BKL and CBB where the contribution of freshwater systems is also important, and at YAK (again due to coal emissions). Wetlands keep the isotope ratio quite low, with two sites having a mean δ13CCH4 contribution more negative than -1.0 ‰ (BCK and INU). Values below -2.0 ‰ are even reached on a daily basis at 15 sites; it is frequent at BCK for example, where the influence of wetlands and freshwater systems are combined. On top of wetland and freshwater influences, ESAS explains more than 10 % of the signal at TIK and AMB.

Figure 3 reveals what can be expected on a seasonal basis at the different sites, but it does not show how the various source contributions combine all along the year and how different source signatures can affect the total δ13CCH4 signal. Figures 4 and S1–S23 show the time series of the direct contribution of each source and sink to the total δ13CCH4 at the 24 northern latitude stations. A focus is put on Zeppelin station in Fig. 4 because a new Aerodyne instrument has been installed there during Summer 2018 in order to continuously measure δ13CCH4 for at least 1 year. Figure 4 illustrates the magnitude and timing of the maximum signal of each source during the year, the potential compensation between sources, and the seasonality of the various contributions.

Zeppelin is a typical example of a remote site. The δ13CCH4 values from anthropogenic emissions are very small (< 0.02 ‰, except for some particular events which concern the lightest isotopic signatures) because the source areas are far from the station and tend to be cancelled out because the signals from oil and gas, and from coal have approximately the same magnitude but opposite signs. The signal from geological sources remains negligible being 1 order of magnitude lower than anthropogenic sources. Only wetland emissions succeed to tear the signal away from the value of the boundary conditions, from June to October, with synoptic changes up to -0.2 ‰. Freshwater systems intensify the signal by 0.02 ‰ on average in summer, with maxima around 0.05 ‰ on a synoptic basis. These contributions are diminished by biomass burning (∼ +0.01 ‰) and also by the fractionating effects of the two major sinks (∼ +0.01 ‰). The simulated δ13CCH4 signal at the site is the result of these competing signals. Varying the isotopic signatures of natural sources does not change the conclusions with wetland, freshwater, and ESAS synoptic events reaching at maximum -0.3 ‰, -0.1 ‰, and -0.15 ‰, respectively . Therefore, in the case of a remote station such as ZEP, signals of individual sources remain below 0.3 ‰ at the synoptic scale, and partial compensation between sources determines the total δ13CCH4 anomaly.

Analysing other stations (Figs. S1–S23) reveals that synoptic events larger than 2 ‰ due to summer wetland emissions could happen at AMB, BCK, CHS, DEM, IGR, INU, NOY, and TIK. For freshwater emissions, events larger than 0.5 ‰ are simulated at AMB, BKL, BRW, BCK, CBB, CHL and INU. For ESAS, varying the isotopic signature induces synoptic events larger than 0.3 ‰ at some sites (AMB, BRW, CHS, and TIK). When varying the isotopic signature of anthropogenic emissions, DEM, IGR, KRS, NOY, and VGN show synoptic events due to oil and gas that are larger than 0.15 ‰, and only YAK shows synoptic events due to fugitive emissions larger than 1 ‰; these events occur mainly in winter. Biomass burning synoptic events are the largest at BCK, DEM, KRS, NOY, and YAK with events larger than 0.2 ‰.

The influence of the sinks on synoptic variations remains smaller than 0.05 ‰ at most sites. Note that the sink constituted by the reaction with Cl radicals in the marine boundary layer is not taken into account here, given its very small impact on CH4-mixing ratios in our domain (less than 1 ppb, Thonat et al., 2017), although it is highly fractionating. As aforementioned, including this sink in the regional simulation will not change significantly our conclusions on the local source detectability.

The magnitude of δ13CCH4 signals to be expected at present and potential measurement sites and the contributions of individual sources to these signals do not lead directly to quantifying the detectability of individual sources, as the latter also depends on the performances of the measuring instrument. Here we focus on a detectability definition taken from a regional inversion point of view: regional inversion systems analyse daily signals and optimize sources depending on synoptic deviations of the observed signals compared to the simulated ones. Therefore, a measuring instrument is considered to provide useful information to the inversion only if the synoptic variability of the atmospheric signal can be detected. To that end, we compute detectability capability in Fig. 5 and Table 4 as follows: (1) we compute the standard deviation over a 5 d running window of the simulated total isotopic signal; (2) for a set of instrument precision threshold (from 0.2 ‰ to 0.01 ‰, see Fig. 5 and Table 4), if the running standard deviation is higher than the corresponding threshold, the source with the higher running standard deviation for the same 5 d window is considered detected for that one day; (3) for each threshold, we count the number of days over the year that each source is detected. Although the total atmospheric signal integrates contributions from different sources with different isotopic signatures, we keep only the major source contributing to the signal as a 1st-order signal.

The range of instrument precision threshold was chosen according to present isotopic instrument systems. The flask measurements used in Sect. 3.1 (Table 1, Figs. 1 and 2) have an uncertainty of about 0.1 ‰. They were obtained using GC–IRMS (gas chromatography–isotope ratio mass spectrometry; White et al., 2018). Using continuous-flow isotope ratio mass spectrometry, Fisher et al. (2006) reached a precision of 0.05 ‰. Laser-based instruments, using cavity ring-down spectrometry or direct absorption spectrometry (Nelson et al., 2004), have been developed since 10 years for CO2 isotopes (McManus et al., 2010) and, more recently for methane (Santoni et al., 2012). The Aerodyne QCL instrument has proven to be capable of high-frequency (≥ 1 Hz) measurements of 12CH4 and 13CH4 isotopes of CH4 with in situ 1 s rms δ13CCH4 precision of 1.5 ‰ and an Allan minimum precision of 0.2 ‰ at 100 s (Santoni et al., 2012), recently improved to 0.1 ‰ through laser stability improvements. Such a small value (0.1 ‰) reaches the precisions reported for GC–IRMS (0.1 ‰). However, Aerodyne instruments face a strong drift that imposes a strict calibration protocol (every 2 h in the most recent set-ups), which dramatically reduces the daily number of available observations to typically a few tens. Depending on our capability to deploy stable and well-calibrated instruments in very remote high-latitude sites, state-of-the art isotopic instruments may provide from a few to hundreds of independent data points per day thus potentially improving the instrument precision of daily averaged observations to 0.01 ‰.

Detectability thresholds at the 24 sites of Table 1 are summarized in Table 4 and Fig. 5 when considering the mean values of the isotopic signatures of Table 2. Results for a 0.5 ‰ threshold are not shown in Fig. 5 because only the YAK station can detect sources (only the oil and gas sector) at this level of instrument precision. At ZEP, with an uncertainty higher than or equal to 0.1 ‰, no source is detected. Currently, daily flask measurements are operated at ZEP with an uncertainty of 0.05 ‰ but contamination problems occur. If such contaminations are avoided so that the measurement uncertainty reaches 0.05 ‰, some wetland events may be detected for about 10 individual days over the year. From 0.05 ‰ of measurement uncertainty, the number of events is larger and other sources (freshwater and ESAS emissions) might be detected. At only 0.01 ‰, there were about 20 d of possible detection for ESAS, a few days for freshwaters, and none for anthropogenic emissions. Looking at results for all stations, wetland emissions are the most easily detected with more than 50 d for a measurement uncertainty above 0.1 ‰ for most sites (with the exception of ALT, BKL, CHL, ICE, PAL, SUM, SUM, ZEP, and ZOT); the best scores of detection, with more than 150 d, are achieved at BCK, INU, DEM, and NOY. Freshwater emissions are easiest to detect at BKL and CBB with 100 d and 50 d above 0.1 ‰ respectively. Anthropogenic emissions are easily detected at YAK due to its close location to coal extraction sites. With a 0.05 ‰ uncertainty, most of the stations offer opportunities to detect regional sources, except remote stations and/or stations close to the boundaries of our domain (ALT, CHL, ICE, SUM, and ZEP). For ESAS emissions, the minimum detection ranges between 0.02 ‰ and 0.1 ‰ depending on stations. ESAS emissions are best detected at AMB, CHS, and TIK with more than 50 d above 0.05 ‰. A few other sites offer detectability if uncertainties are lower than 0.02 ‰ (ALT, BRW, BKL, CBB, CHL, INU, and ZOT). As already noticed, the effect of anthropogenic emissions dominates at YAK with about 100 d above 0.2 ‰ uncertainty. Other sites located in Russia are able to detect anthropogenic emissions with more than 50 d of events above 0.02 ‰ (DEM, IGR, NOY, and VGN). Excluding YAK, the minimum detection of anthropogenic emissions ranges between < 0.01 ‰ and 0.05 ‰ depending on stations. For the year 2012, YAK and KRS detected some biomass burning events with an uncertainty lower than 0.2 ‰ and 0.1 ‰ , respectively. Geological sources are detected at ZOT when the uncertainty is lower than 0.01 ‰.