Methane (CH4) abatement has emerged as a top priority for addressing climate change in the short term; a reduction of 40–45% in CH4 emissions by 2030 could prevent nearly 0.3 °C of global warming by the 2040s1. Recognizing this, 110 countries have recently committed to reduce global anthropogenic CH4 emissions by 30% from 2020 levels by 2030 through the “Global Methane Pledge” initiative, launched at the United Nations Climate Change Conference, COP26 in Glasgow. This pledge aims to support the Paris Agreement’s goal of limiting global warming to below 2 °C, preferably 1.5 °C, above the pre-industrial average. Developing effective strategies to mitigate CH4 emission necessitates a meticulous understanding of the magnitude and spatiotemporal variability of source sectors.

CH4 emission studies employ bottom-up and top-down approaches. While bottom-up approaches provide detailed insights into specific CH4 sources (Figs. 1, S1) by accounting activity data and emission factors for anthropogenic sectors (e.g., oil and Gas (ONG), coal, landfills, enteric fermentation and manure management (ENF-MNM) etc.)2,3,4 and utilizing environmental factors in process-based models for natural emission sectors (e.g., wetlands, termites etc.)5, discrepancies often arise when comparing total emissions (sum of all sectors) to atmospheric observations6,7,8. This incongruence can arise from imprecise emission factors and activity data (e.g., fugitive fossil fuel sector2,3,9), or by process-based models that perform poorly due to a host of environment factors (e.g., wetland models rely on wetland inundation maps, biogeochemical process parameterizations and knowledge of carbon availability6). Top-down methods use inversion techniques to refine total bottom-up estimates (sum of all emission sector contributions) by aligning them with observations of the atmospheric growth rate and latitudinal gradient10,11,12,13,14,15,16,17. However, these methods lack granularity and have limited ability to distinguish between individual CH4 sources, resulting in multiple plausible emission scenarios. Although advancements in satellite observations refined point sources detection capability18, in addition to improved inversion techniques19,20,21,22, discerning individual CH4 source contributions using only atmospheric CH4 observations remains a challenge8.

Fig. 1: CH4 emission distributions across various source sectors.
figure 1

Temporal (a), latitudinal (b), and spatial (ce) variation in CH4 emissions for different sectors used to prepare the baseline scenario (E0; details in Table S1). The solid lines and shaded areas in the latitudinal plot (b) represent the mean and ±1σ (standard deviations) for 1970–2020. The symbols in maps represent observation locations operated by INSTAAR/NOAA (square for CH489 and plus for δ13C-CH490) and Tohoku University (TU) / National Institute of Polar Research (NIPR) (green circles for both CH4 and δ13C-CH491). The observation sites falling in the three latitude bands (as shown in Figs. 2, 4), separated by lines on the maps, were used to calculate the mean CH4 and δ13C-CH4 time series in respective latitudinal bands.

The isotopic composition of CH4 offers insights into atmospheric CH4 origins since different sources emit CH4 with characteristic stable carbon and hydrogen isotopic ratios (δ13C = ([(13C/12C)sample / (13C/12C)standard] −1; hydrogen isotopic ratio (δD) is likewise defined)23,24,25). The global mean atmospheric δ13C source value ranges between −54‰ and −52‰, and turns approximately −47‰ with effects of chemical sink corrected25. The δ13C-CH4 signatures of microbial sources (−55‰ to −70‰), for example, are lower than the atmospheric δ13C value (approximately −47‰), while thermogenic sources have higher δ13C-CH4 values (−35‰ to −45‰)24,25,26. Previous 3D inversion13,14,27 and box model28,29,30,31,32,33 studies have incorporated measurements of atmospheric δ13C-CH4 as an additional constraint for better source attribution of the global CH4 emissions. Yet, they suggest diverse conclusions about the cause of the observed CH4 growth rate change10,13,14,16,26,27,28,29,30,31,32,34,35,36,37,38,39,40. Some emphasize increased emissions from microbial sources13,28,29,35,41, while others suggest competing contributions from both microbial and fossil fuel sources10,14,30. The studies that emphasize large contributions from microbial sources typically conclude that there has not been a rise in fugitive fossil fuel emissions in the past two decades. Yet, the steady upward trends in fossil fuel emissions are reported in emission inventories, caused by the rise in the unconventional gas production since 2006, coal mining resurgence, and growth of the Asian economies2,3,42,43.

The discrepancies in previous conclusions may have arisen due to various factors. For instance, the results from simplified box models could be influenced by potential biases stemming from factors such as overlooked spatial emissions, uncertain δ13C-CH4 source signature information, and the absence of  real atmospheric 3D transport and chemical processes. Additionally, the current sampling networks might introduce biases to the hemispheric averages44. Furthermore, δ13C source signatures and kinetic isotope effects (KIEs) of chemical sinks are associated with considerable uncertainties45,46,47. When these uncertain parameters are integrated in a complex 3D inversion and box modeling system, they can interact and impact the simulated composition of the atmospheric CH4 in very complex ways. Importantly, when δ13C-CH4 observations are incorporated into 3D inversions (as opposed to box-model studies), the spatio-temporal CH4 constraint greatly outweighs the information from the relatively sparse δ13C-CH4 observations, leading to varying results based on modeling choice (e.g., Basu et al.13 choose to optimize emission sectors, while Thanwerdas et al.14 optimize δ13C source signatures).

As a complementary effort to δ13C-CH4 inversions, this study examines forward simulations to assess the current understanding of the CH4 budget. We use the MIROC (version 4)-based atmospheric chemistry-transport model (MIROC4-ACTM)48 for simulating the history of δ13C-CH4 and δD-CH4 alongside CH4 from 1970 to 2020. The simulations integrate diverse data sources, including emission inventories, KIE values, chlorine fields, and region-specific source signatures (detailed in the Methods section and Table 1, S1). Analyzing extensive sets of simulations, we propose sector-specific emission changes that align best with observations. Specifically, the simulation results are compared to balloon-based vertical measurements up to the stratosphere and to surface observations covering latitudes and past decades. The simulations are tested rigorously against various benchmarks (e.g., choice of initial atmospheric CH4 and δ13C-CH4 values (Fig. S4) and drift in tracer mass conservation in simulating δ13C-CH4 (Fig. S5)), which are detailed in the Methods section. While δD-CH4 simulations are valuable for assessing vertical profiles and broadly global trend (Fig. S6), they are excluded from sub-hemispheric analyses (Fig. 2) due to limited coverage of observation and source signatures data.

Table 1 Details of sensitivity simulations (shown in Figs. 2 and 4) using different combinations of emission sectors from various inventories and isotopic source signatures
Fig. 2: Evaluating the simulations of long-term atmospheric CH4 and δ13C-CH4 trend.
figure 2

Model (solid lines) and observation (symbol) comparison of long-term trend and growth rates (± standard error) (bars) of atmospheric CH4 (in ppbv) from 1985 to 2020 (ac) and δ13C-CH4 (in ‰) from 1998 to 2020 (df). The growth rates were calculated as the time derivative of long-term trends (detail in Chandra et al.10) and averaged for different periods (defined in the top of panels in “a” for CH4 and in “d” for δ13C-CH4). The time series are based on an average of atmospheric CH4 and δ13C-CH4 measurements and corresponding simulations from multiple stations in the marine boundary layer of three respective latitude bands shown in Fig. 1. Individual site comparisons for CH4 and δ13C-CH4 are presented in Figs. S7, S8. The root-mean-square error (in ‰) and correlation coefficients (obs vs model) for different simulation cases are shown for δ13C-CH4 in legends.


Decadal trends of atmospheric CH4 and its stable isotopic composition

The observations showed a decline in the CH4 growth rate and an increase in δ13C-CH4 during the 1990s, followed by a plateau until 2006 (Fig. 2). However, since 2007, there has been a substantial increase in atmospheric CH4 levels, while δ13C-CH4 turned its trend to negative (i.e., a decrease in δ13C). The base simulations, based on emission scenario E0 that uses increasing fossil fuel and microbial emissions from EDGARv6 and the VISIT model2,5 (details in Table 1 and “Method” Section), reproduces the observed CH4 growth rate well (represented by bars in Fig. 2) in 1985–1989 and to some extent in 1990–1999 (bars agree within the error bars). However, after 2000, the E0 simulation overestimates the observed growth rate, particularly in the NHL and TrP regions, due to a rapid increase in input emissions (Fig. 1a). Additionally, the δ13C-CH4 simulations based on the same E0 scenario shows a sustained increase from 2000 to 2020, contradicting the observed trend of an initial steady state followed by a decrease in the mid-2000s and 2010s (r < 0.4), respectively. These discrepancies suggest gaps in our understanding of the total and sectorial emissions used in the E0 scenario (Fig. 2). Previous studies adjusted bottom-up CH4 emissions to match global atmospheric CH4 increases and to satisfy global mass balance of δ13C-CH4 using the mass-balance equation13,16,35. However, such adjustment implicitly assumes that CH4 emissions from bottom-up estimates are more uncertain than source signature estimates and KIE values. In reality, each term of the isotopic mass balance of CH4 includes notable uncertainties. In this study, we used several bottom-up CH4 estimates from different inventories, which are more realistic based on varying statistics but suffer from observation-based validation4.

The joint comparison of observed CH4 and δ13C-CH4 and baseline simulations trend in Fig. 2 hints at the most plausible potential emission sector that need to be changed in the E0 scenario. Reducing emissions from microbial (MiB) sectors (e.g., wetlands, landfills, ENF&MNM, etc.) could help to reduce the overestimation of CH4 in the E0 emission scenario. However, this would not reverse the rising δ13C-CH4 trend in E0, as decreasing isotopically light MiB emissions would shift the global δ13C-CH4 signal towards even higher values. Although emissions from biomass burning (BB) are strongly enriched in 13CH4 (δ13C-CH4 ~ −26‰) compared to other sources, these emissions are relatively small globally (~34 Tg-CH4 yr−1 for 1990–2020: Table S1), and thus adjusting them would have a little effect on the modeled CH4 growth rate but largely impact δ13C-CH4 trend32,49,50. Conversely, reducing proportions of 13CH4-enriched fugitive fossil fuel (FF) sector (coal, ONG, and geological), the second-largest contributor in the E0 (Fig. 1 and Table S1), is likely the most plausible way to align with both CH4 and δ13C-CH4 observations simultaneously, especially given the substantial uncertainties in the EDGARv6 inventory for major emitters9.

Balancing the CH4 and 13CH4 budget by revising fugitive fossil fuel emissions

Fugitive fossil fuel emissions from the ONG sector are highly uncertain and exhibit noteworthy discrepancies between the EDGARv6 and GAINSv4 inventories regarding their magnitude (exceeding 35 Tg CH4 yr−1) and trend (Fig. 3a)4. These discrepancies arise from variations in emission factors associated with the venting and flaring of associated gas during ONG extraction, which differs across various ONG fields worldwide (further details are provided in the Methods section). Meanwhile, trend in microbial emission sources, such as ENF-MNM, landfills, wetlands, show smaller discrepancies among different inventories and process-based models than fossil fuel emissions2,4, offering less scope for change. To address the model-data discrepancy, we prepared an ensemble of emission scenarios based on GAINSv4 fossil fuel estimates and other suggested estimates in the literature (details provided in the Method Section). In these scenarios, we assumed that microbial/biomass burning (BB) emissions, depleted/enriched in 13CH4, align with the inventories.

Fig. 3: Global CH4 emissions change under different emission scenarios.
figure 3

Panel (a) displays global coal and ONG emissions used for sensitivity and baseline (E0; EDGARv6) simulations. Sensitivity simulations include total ONG emissions from GAINSv4 (E1; ONG_total4), ONG emissions from GAINSv4 after excluding unconventional emissions from the USA (ONG_wUnc), and scaled China coal emissions (Scaled_coal) from 2000–2020 based previous inversion study10 (E2; ONG_wUnc + Scaled_coal), as well as reduced geological emissions (E3) (detailed in Table 1). In (b), we compare the most plausible total fugitive fossil fuel and microbial emissions of this study, which are able to reproduce atmospheric CH4 and δ13C-CH4 history, with independent studies using a box model by Schwietzke et al.29. Panel (c) compares global total CH4 emissions used for baseline (E0) and sensitivity simulations (E1, E2, E3 shown in Fig. 2) with the independent inversion-estimated global total emission10.

The E1 scenario replaces ONG emissions trend in the E0 scenario with the GAINSv4 inventory estimates (shown as “ONG_total” in Fig. 3a). Though the E1 simulation replicates the CH4 growth rate shifts over the first decades, it overestimates the post-2000 growth rate and fails to match the δ13C-CH4 trend during the 2010s. The divergence (r < 0.4) likely results from overestimated emissions after 2000, tied to overestimated coal emissions in China after 200010,42,43 and unconventional shale gas extraction primarily driven by hydraulic fracturing and horizontal drilling in the USA since around 2005. Several studies have indicated that the rates of these emission increases are highly uncertain across inventories and inconsistent with atmospheric observations and regional inversions10,11,15,42,51,52,53. Additionally, the higher CH4 increase rates simulated at the sites close to the USA (a downwind area for Bermuda) and China (source area for Mongolia) also support higher emission increase rates in E1 scenario over these regions (Fig. S9).

To reconcile observed discrepancies, we designed the E2 scenario, excluding 15Tg emission increase (representing an extreme case) from unconventional US gas extraction since 2006 (Fig. S10b), as this rise is not evident in satellite and surface observations20,51,54. The uncertainty in leakage rate55,56,57,58 used for calculating the emissions from shale gas production, could skew the estimation by inventory. The E2 scenario also aligns China’s coal emissions with regional trends from a previous MIROC4-ACTM inversion study10. The simulations using the E2 scenario align well with both the CH4 and δ13C-CH4 trends (R > 0.85 for CH4 and R > 0.7 for δ13C-CH4). However, a noticeable consistent bias remains between simulated and observed CH4, indicating that adjusting emissions from any time-invariant source might reduce this systematic offset without altering the overall trend. The global emission strength of geological CH4 remain uncertain, with estimates varying from 2 TgCH4-yr−1 to 76 TgCH4-yr−1 based on various measurements and estimates7,59,60,61. As there is no discernible trend in these emissions on the timescale of our simulation, which is relatively short from the perspective of geologic processes59, we have revised the global geological emissions down to 19 TgCH4-yr−1 in scenario E3. The simulations based on this scenario aligns closely with the observed CH4 magnitude and trend across all latitudinal bands.

We also validate the total CH4 emissions from the E3 scenario using inversion estimates (“Inv”; black line in Fig. 3c) based on observed atmospheric CH4 growth as discussed in Chandra et al.10. While the decadal mean of E3 emissions aligns with the inversion estimates, slight discrepancies appear in the early 2000s growth rate, which was also evident in the E3-based simulated growth rate for that period (Fig. 2). The high emission growth in E3 emission scenario between 2000 and 2006 as compared to inversion estimates, indicates some emission sectors (e.g., coal mines, landfills, etc.) could still have high growth during this period. It is noteworthy that our results arise solely from forward simulations, and further improvement in emission inventories could help to refine the remaining changes in emissions. Although the E3 scenario closely matches the observed CH4 and δ13C-CH4 trend, the δ13C-CH4 absolute value is more negative than the observations. We undertook additional sensitivity analysis to address the source of δ13C-CH4 simulation bias.

Uncertainty in δ 13C-CH4 simulations due to the representation of atmospheric chemistry

The mean atmospheric δ13C-CH4 represents a flux-weighted average of all emissions, as well as isotopic fractionation due to sinks of CH4. The bias in simulated δ13C-CH4 values could therefore be attributable to the representation of atmospheric chemistry and different specifications of δ13C-CH4 source signatures. In this section, we focus on uncertainty due to atmospheric chemistry, specifically the role of the Cl sinks and isotopic fractionation or KIE for OH (KIEOH) in the troposphere (mainly).

The role of the active Cl sink in the troposphere is poorly constrained due to a lack of consensus on the strength and distribution of the tropospheric Cl sink and trend62,63,64,65,66. Including extra tropospheric Cl via a recently proposed photocatalytic mechanism on mineral dust-sea spray aerosols could help to reduce the negative bias in δ13C-CH4 simulations66. To assess the effect of the Cl sink on modeled CH4 and δ13C-CH4, we ran simulations using the cyclostationary Cl field from Wang et al.65 (Cl_wang) in addition to a control Cl field (Cl_ctrl; Takigawa et al.67). The Cl_ctrl field has higher stratospheric concentrations than the Cl_wang field, with a mean value of 2.1 × 105 molec. cm−3. The primary difference in both fields is the representation of tropospheric reactive chlorine chemistry through the treatment of sea salt aerosol and its chloride mobilization. The Cl_wang field includes this representation, but Cl_ctrl does not. Simulations with the Cl_wang fields increased the offset in δ13C-CH4 simulations by 0.6‰ compared to Cl_ctrl-based simulations, but the trends remained unchanged (Fig. S11). These sensitivity tests had a negligible impact on CH4 simulations. The Cl_ctrl field does not include a parameterization for atomic Cl production in marine environments, as the spatial distribution and interannual variability of marine Cl are highly uncertain, which is an interesting target for future study.

OH oxidation is the dominant sink for atmospheric CH4 (~90%). Consequently, KIEOH values could greatly influence the δ13C-CH4 simulations. The literature suggests notably different values for KIEOH; Saueressig et al.45 reported a low KIEOH value (L-KIEOH: 1.0039) compared to Cantrell et al.46 (H-KIEOH: 1.0054) and recently Whitehill et al.47 (1.0061). Previous studies have adopted either values (L-KIEOH vs H-KIEOH) based on their preference14,16,28,29,32,34,35,36,39,49,50,64. Since we cannot determine the relative merits of the reported OH fractionation, we tested both (L-KIEOH, H-KIEOH) values in the sensitivity simulations. Simulations with H-KIEOH and L-KIEOH differed by approximately 1.2‰, however the impact on the temporal δ13C-CH4 trend was negligible (Fig. S12).

Improving the δ 13C-CH4 bias and trend using varying source signatures

Our knowledge of δ13C-CH4 signatures is incomplete because of the sample biases (including over- and under-representation of source regions) and limited δ13C databases for specific source categories24,29,68. Along with this, the globally uniform δ13C-CH4 source signature used in simulations (shown in Fig. 2 and “E3_const” scenario in Fig. 4) does not account for regional/geographical variations in CH4 sources (as depicted in Fig. S13). For example, the wetland isotope signature varies with temperature, resulting in a latitude gradient36,69. Ruminant emissions and biomass burning signatures also depend on factors like the diet (C3 or C4) and burning material types (C3 or C4)24,35. To assess the overall uncertainty in modeled δ13C-CH4, we ran simulations using 32 ensemble scenarios based on the common E3 emission scenario and Cl_ctrl field, as well as different combinations of δ13C-CH4 source signatures and two KIEOH values (Tables 1 and S2). The δ13C signature maps for coal and ONG were derived from country-specific values, while those for ruminants and biomass burning were based on regional C3/C4 fraction maps35. The wetland signature was determined considering different wetland subtypes (e.g., bog, fen, and mineral wetlands with C3/C4 pathways)36. With the MIROC4-ACTM simulations, we have quantified the contribution from globally invariant vs. geographically varying signatures of individual sectors to the simulated δ13C-CH4 value and trend (Figs. 4, S14, S15).

Fig. 4: Evolution of δ13C-CH4 simulations under different scenarios based on isotopic signatures and KIEOH.
figure 4

All sensitivity runs use the most likely emission scenarios (“E3”), but different combinations of source signatures and KIEs. The simulations presented in the left column (ac) and right column (df) correspond to H-KIEOH (1.0054: Cantrell et al.46) and L-KIEOH (1.0039: Saueressig et al.45), respectively. This sensitivity run proceeds to improve the growth rate and difference between modeled and observed δ13C-CH4. The numbers root-mean-square error (RMSE) and correlations (R) between observed and δ13C-CH4 simulations are shown in the legends. See Fig. S8 for the comparison of individual sites used for preparing the mean.

The global mean source signature of CH4 varies temporally due to regional isotopic variations in CH4 sources (Fig. S14g). The ENF&MNM source signature, for example, has become less negative from −66.4‰ in 1990 to −66‰ in 2020 because of expanded agriculture in tropical regions like India, South America, and Tropical Asia24; the prevalent C4 vegetation diet at lower latitudes would result in higher δ13C-CH4 signature of the ENF&MNM source (Fig. S14d). When these variations are incorporated in simulations (MENF), δ13C-CH4 values reduced by about −0.2‰ compared to E3_const, while the growth rate remains relatively stable (Fig. S15). Biomass burning and wetland signatures show yearly variability (IAV) without a clear trend (Fig. S13d, f). Incorporating the ~10‰ latitudinal difference between the NHL (mean −67.8‰) and tropical (mean –56.7‰) wetland signature, using a spatial map of isotope signatures, improves the latitudinal gradient and seasonal cycle (obs: model; r = 0.85) and growth rate as compared to scenario E3_const (Fig. 4). Still, the model underestimates the seasonal amplitude, which could be enhanced by incorporating a seasonal variation in the wetland signature36,69. Updated biomass burning signatures (based on a map) increased δ13C-CH4 values by 0.1‰ compared to E3_const but had no effect on the trend.

With spatially varying source signature, global coal emissions signature transitioned from less negative value in 1970 to more negative post-2011 (Fig. S14a). The shifts are primarily due to changes in China’s coal emissions42, whose δ13C-CH4 signature is relatively high (−36‰) compared to the global average (−44.6‰). Accounting for these signatures, simulation led to more negative trend compared to the E3_const simulations and slight improved growth rate, while the inter-annual variability remained unchanged (Mcoal in Fig. S15). Yet, this experiment underscores the significance of China coal emission and its δ13C-CH4 signature in shaping the global δ13C-CH4 trend, albeit not clearly quantified in previous studies due to competing contributions of different sources.

Employing all available source signature maps in the M-all scenario notably improves the seasonal cycle and interannual variability (IAV) (r > 0.85) in the NHL (Fig. 4). The observed δ13C-CH4 growth rate change during 2010s across latitudinal bands was also closely replicated (Fig. 4). However, discrepancies remain between simulated and observed atmospheric δ13C-CH4 (1.4‰ in L-KIEOH, and 0.5‰ in H-KIEOH). By adjusting ONG and geological signatures to less negative (−40‰) as suggested in previous studies34,49,70, the discrepancies were reduced from 0.5‰ in M-all (using H-KIEOH) to within ±0.2‰ (M2_Hgeol-ong: +0.2‰, M3_Hgeol-ong: −0.2‰), falling well within the uncertainty range of the observed data (Fig. 4a–c). Importantly, these sensitivity experiments suggest that the geographical variations in wetland, biomass burning, and coal signatures are crucial in simulating the IAV, seasonal cycle, and latitudinal gradient of δ13C-CH4 (Fig. 4).

Evaluating the vertical and geographical distribution of CH4 and δ 13C-CH4 simulations

Before attributing emission changes to observed CH4 and δ13C-CH4, it is essential to evaluate the model’s dynamical and chemical processes. We use simulated vertical profiles as indicators of the model’s proficiency in capturing intricate processes, such as stratospheric chemistry and vertical transport (stratosphere – troposphere exchange)71. Consequently, beyond analyzing long-term trends, we assessed model’s efficacy in representing stratosphere-troposphere exchange by comparing simulated and vertical profile observations of CH4, δ13C-CH4, and δD-CH4 distributions from balloon flights over the Kiruna, Sweden (polar region) and Hyderabad, India (subtropical region)71.

Simulations under the E3 emission scenario, M2_Hgeol-ong signature, Cl_ctrl field, and H-KIEOH (most plausible to reproduce CH4 and δ13C-CH4 long-term trend in Figs. 2, 4) demonstrated excellent agreement (r > 0.9) with observed profiles, indicating the model’s capability in representing complex processes like chemical loss and transport (Fig. 5). The comparison suggests that while the KIEOH introduces offsets (seen from Cl_ctrl_H-KIEOH and Cl_ctrl_L-KIEOH in Fig. 5), the primary influencer of the vertical gradient is the Cl distributions (seen from Cl_ctrl_H-KIEOH and Cl_wang_H-KIEOH in Fig. 5). Cl_ctrl simulations depict a pronounced vertical gradient above 25 km due to higher Cl concentrations, corroborated by observed δ13C-CH4 and δD-CH4 gradients from the tropical site Hyderabad. Conversely, a reduced vertical gradient observed over the polar site Kiruna aligns with the Cl_Wang field. It is important to note that the Cl fields cannot be validated solely based on these limited observations, but they provide insights into the associated uncertainty.

Fig. 5: Validating model results (transport and chemistry) using balloon-borne measurements.
figure 5

Comparisons of CH4, δ13C-CH4, and δD-CH4 simulations (lines) with balloon measurements (filled circles) over Kiruna (ac) and Hyderabad (df)55. Model simulations are sampled at the date and time of the observations. The model simulations are shown for two different Cl (Cl_Ctrl67; and Cl_Wang65;) fields using the E3 emission scenario and M2_Hgeol-ong source signature scenario. The sensitivity simulations based on different KIEOH (H-KIEOH46, L-KIEOH45) values are additionally shown for δ13C-CH4. The δD-CH4 simulations are adjusted by a constant offset of 15‰ to focus on the gradient.

We further evaluated our δ13C-CH4 based emission attribution by comparing the observed and simulated latitudinal gradient (Fig. 6) and the north-south gradient (expressed as “N-S gradient”; the difference between NHL and SHL: Fig. S16)10. Among the scenarios, E3 consistently matched the observed CH4 latitudinal distribution (Fig. 6a, d, g). The observed N-S gradient of CH4 decreased from 1985–1989 to the 1990s (1990–1999) and stabilized afterward (Fig. S16a) due to a southward emission shift10. Yet, E0 (total FF emission 142 ± 15 TgCH4 yr−1 for 1990–2020) showed an inconsistent increase in this gradient, primarily driven by rising fossil fuel emissions in the NHL. Whereas the E3 scenario, which included a flat fossil fuel emission trend (by reducing coal emission growth rate over China and excluded rapidly increasing unconventional gas emissions after 2006 from the USA) and reduced geological emissions, mirrored the observed changes in the N-S gradient with a slight overestimation in magnitude. Comparing ONG estimates, GAINSv4 showed higher emissions than EDGARv6 in the NHL (Fig. S17). To address this slight overestimation, we introduced E4 scenario, where the EDGARv6 ONG map was scaled to GAINSv4 global total estimate. Although both scenarios had the same global emissions, E4 reduced the overestimation of the observed N-S CH4 gradient by 10% compared to E3, indicating better agreement with EDGARv6 emission spatial patterns in the Northern high latitude regions (Fig. S16). Additionally, E4 aligned well with the long-term variation of CH4 in the NHL (Fig. S18a).

Fig. 6: Evaluating geographical CH4 emissions and δ13C-CH4 source signatures.
figure 6

Comparison of the observed and modeled latitudinal gradient of CH4 (a, d, e) and δ13C-CH4 using different emission scenarios and KIEOH (H-KIEOH: b, e, h; L-KIEOH: c, f, i) values for three periods. Only a few cases are shown for clarity. All simulations are adjusted to the SPO observation to highlight the latitudinal gradient. All the δ13C-CH4 simulations use common E3 emissions but different combinations of source signatures, shown in Fig. 4 (detailed in Table 1). Please note that here the number of sites is different from sites used for the long-term trend shown in Figs. 2, 5. Also, the total number of sites for CH4 and δ13C-CH4 are different (side codes used for δ13C-CH4 plot are shown below y-axis in the bottom panel).

During 1998–2020, the latitudinal distribution of δ13C-CH4 showed more negative values in the NHL compared to the SHL. This was primarily due to the prevalence of emissions in the north and subsequent fractionation through reaction with OH during transport to the Southern Hemisphere. The E3_const scenario (Fig. 6b–i), which used globally uniform source signatures, reasonably captured the observed δ13C-CH4 gradients south of 30°N but overestimated them in the north (>30°N). Incorporating geographically varying δ13C-CH4 source signatures, especially from boreal wetlands with lower δ13C-CH4 signatures, improved the simulated gradient in the north. Notably, the choice of KIEOH values also influenced the latitudinal δ13C-CH4 gradient (Fig. S16b, c), suggesting uncertainty ties to both KIEOH values and source signature and the best different combinations may yield to similar model results. For example, M-all scenario in the case of L-KIEOH values, as well as “M2_Hgeol-ong” and “M3_Hgeol-ong” scenarios in the case of H-KIEOH values reproduce the observed N-S gradient (Fig. 6). Recently, Whitehill et al.47 even reported a higher KIEOH value of 1.0061, near to H-KIEOH value used in this study that align well with observed variation, supporting our findings that a greater KIEOH value is a possibility to reproduce the observed long-term trends, vertical distributions, and north-south gradients. Overall, the simulated and observed global N-S gradients of CH4 and δ13C-CH4 at remote background sites add a spatial source attribution constraint. On the basis of simulated scenarios, we find that. the E3 emission scenario combined with M2_Hgeol-ong source signatures is consistent with the observed global N-S gradient.

Discussion and conclusions

Reconciling the global CH4 budget remains an under-constrained problem with multiple sources of uncertainty from sectoral emission sources (both anthropogenic and natural), loss mechanisms (e.g., OH, Cl etc.), isotope signatures, KIE values, and limited global CH4 and δ13C-CH4 observations. These uncertainties have complicated modeling of the atmospheric CH4 changes and resulted in diverse conclusions. Our study refines the understanding of atmospheric CH4 drivers by uniquely leveraging diverse inventory estimates, accounting the impact of isotope parameter (KIE values and source signature) uncertainties, and incorporating balloon and surface observations within a 3D ACTM forward modeling approach.

Instead of hypothetically adjusting bottom-up emissions to fit global CH4 increments and to satisfy the global mass balance of δ13C-CH4, we prioritized use of emission estimates from different inventories to check their alignment with long-term and vertical observations using MIROC4-ACTM. Our primary focus was on fugitive fossil fuel sectors (notably ONG and coal) due to substantial uncertainties in their reported trends across inventories like EDGARv6 and GAINSv4. The distinction between conventional and unconventional ONG emissions in GAINSv4 was pivotal in analyzing unconventional ONG emission trends in the USA, which is one of the most conflicting and debated topics and important for the policy measures. Although wetland emission estimates can be contentious, the utilized VISIT wetland trends align with most of other process-based model estimates and hence do not alter our primary conclusion on long-term CH4 growth rate change drivers. However, we recognize the presence of wetland magnitude uncertainties in the relative contribution of mean emissions to the total CH4, which will be explored in future studies.

Additionally, this study utilized diverse isotope signatures from the literatures and experimentally distinct KIE values to quantify their influence on simulated δ13C-CH4 values and trends. Our finding indicates that the choice of the KIE values has notable impact on both the simulated magnitude and latitudinal gradient of δ13C-CH4, but not on the long-term δ13C-CH4 trend (Figs. 4, 6). Notably, changes in the latitudinal signature of sources, such as wetlands, could improve the mismatch between simulated and observed latitudinal gradient without requiring emission modifications as widely done by inverse modeling (Fig. 6). These experiments underscore the importance of correct KIE and source signature values when trying to distinguish relative contribution of sources (e.g., Fossil fuel, Microbial, Biomass Burning) in total emissions. Such knowledge is crucial when correcting emissions using inverse modeling of δ13C-CH4.

In summary, consistent increases in microbial and fossil fuel emissions, as indicated by the EDGARv6 inventory (E0 emission scenario in Table 1 and Fig. 1), did not align with observed atmospheric CH4 and δ13C-CH4 trends during 1985–2020. However, the GAINSv4 inventory, which showed declining fossil fuel emissions from 1990–2004 and stability thereafter (after removing unconventional emissions from 2006) (E3 emission scenario; Fig. 3b), successfully replicated observed trends and latitudinal/vertical distribution of atmospheric CH4 and δ13C-CH4 (Figs. 57). Although some studies13,16,29,35 have suggested stable fossil fuel emissions in recent decades, our study further elucidates potential underlying causes in the fossil fuel sector. Specifically, the decline in emissions from the ONG sector during 2000–2010, combined with the rise and subsequent fall in coal emissions during 2000–2012, contributed to the stable fugitive fossil fuel trend (Fig. 3b). Our ONG estimates for the USA (~7Tg for 2018–2020), after removing unconventional emissions, is very close to an independent estimate by the GFEIv2 inventory (8.1 Tg) based on UNFCCC data72, but slightly lower than the result of an inversion study (12.6 Tg) based on the TROPOMI data19. In addition to this, the global coal estimate from this study (~30 Tg) closely matches with the TROPOMI data-based inversion estimate (~32 Tg) and UNFCCC data (32.8 Tg) during 2018–202072. While the total fossil fuel emission trend in E3 seems reasonable in reproducing observed CH4 and δ13C-CH4 trend, this study does not assess the validity of zero unconventional emissions (an extreme case considered in E3 scenario). Nevertheless, our assessment is constrained by the application of a uniform source signature for both conventional and unconventional emissions, which presents limitations in distinguishing their respective contributions to the observed δ13C trend. So, instead, it quantifies the change in the overall ONG, coal, and total fossil fuel emissions required to match the observed CH4 and δ13C-CH4 trends. It is plausible that some unconventional shale gas emissions exist, but other ONG emissions might have decreased further to compensate for fracking emissions. Furthermore, it is possible that any reduction in CH4 emissions resulting from improvements in the natural gas industry’s management practices and equipment replacement could be offset by increased natural gas production20,73.

Fig. 7: Attributing the drivers for global CH4 and δ13C-CH4 trends.
figure 7

The emissions are plotted for three subcategories i.e., Microbial, Fossil Fuel and Biomass burning based on the most plausible E3 emission scenario. The budget imbalance is determined from total sources minus total loss due to reactions with OH, atomic Cl, excited oxygen O(1D), and oxidation by bacteria in aerobic soils. The monthly mean CH4 (circle for observations and line for model simulations based on most plausible scenario E3) values represent the Southern Hemisphere, as shown in Fig. 2c. For δ13C-CH4, we have plotted observations and the “M2_Hgeol-ong” case based on H-KIEOH for northern and southern surface baseline stations, Ny‐Ålesund, Svalbard and Syowa, Antarctica, operated by Tohoku University (TU) and National Institute of Polar Research (NIPR)91.

The total CH4 emissions from fossil fuels (FF) in the most plausible E3 scenario decreased by about 6 TgCH4 yr−1 (from 129 ± 7 TgCH4 yr−1 (mean ±1σ stdev) in the 1990s to 123 ± 4 Tg-CH4 yr−1 in the 2000s) due to decline in ONG emissions, while concurrently microbial and biomass burning emissions are increased by roughly 17 TgCH4 yr−1 and 4 TgCH4 yr−1, respectively (Figs. 3, 7). The reduction in ONG emissions is attributed to decreased oil production after the Soviet Union’s collapse in the 1990s3,4, and reduced oil extraction emissions resulting from efficiency improvements, such as increased recovery rates and decreased venting of associated petroleum gas, mainly in Russia and parts of Africa3. These factors contributed to the slowdown in atmospheric CH4 growth from 1990 to 2005. Previous studies based on δ13C-CH4 observations provided conflicting results on changes in FF emissions27,49, with only Bousquet et al.27 suggesting FF emission reductions for 1988–2002. In our study, between 2000s and 2010s, CH4 emissions from FF and biomass burning remained relatively stable at around 124 TgCH4 yr−1 and 33 TgCH4 yr−1 (Figs. 1, 3), respectively. This stable fossil fuel emission trend is consistent with previous studies, however the magnitude differs13,28,29,35. Meanwhile, microbial emissions increased by about 27 TgCH4 yr−1 during the same period due to expanding cattle rearing in Latin America and increased waste emissions in developing regions like China, India, Southeast Asia, Latin America, and Africa (Figs. 7, S19, S20). The wetland accounted for approximately 16% of the total increase in microbial emissions from 1990s to 2010s. The decadal mean of E3 emissions aligns with the inversion estimates using surface observations10 (Fig. 3c), which indirectly validate the most plausible emission scenario (E3) from this study.

This study acknowledges certain limitations, particularly in systematically exploring the uncertainties of individual components of CH4 budget because the number of uncertain parameters (e.g., emission sectors such as wetland, fossil fuel, KIE, OH trend, Cl sink, etc.) outweigh the available constrains (CH4 and δ13C-CH4 measurements). For microbial emission trends, we rely on the agreement between multiple data sources, including inventories and process-based models. Uncertainty in magnitude of microbial emissions, like wetlands, could influence the selection of our optimal KIE value, source signatures and relative contribution of fossil fuel emissions to balance the δ13C mean value. The magnitude of wetland emissions estimated by VISIT is close to the ensemble mean of the Global Carbon Project’s (GCP) wetland models, showing consistent variability and trends (e.g., recent study for northern high latitude regions74). Therefore, integrating results from alternative wetland models will likely lead to similar results, in contrast to the different fossil fuel scenarios that we have used. If a more robust estimation of KIE becomes available, it could resolve part of the uncertainties in assigned values, allowing for more definitive conclusions about the relative magnitude of fossil fuel and microbial emissions, but again a change in the absolute value of the KIE will not affect the temporal trends (Fig. S12). Further, due to lack of consensuses on atmospheric OH trend from global models constrained by emissions75 versus observationally constrained inversion methods17,76,77 over 1990–2018, as detailed in the recent IPCC-AR6 report78, this study presumes no long-term changes in atmospheric OH sink, in line with methyl chloroform gradient and concentration76,79. Yet, we recognize that short-term interannual OH variabilities76,77 can influence on atmospheric CH4 growth rate80. While we have primarily examined the impact of Cl uncertainty in δ13C-CH4 simulations, we plan to address emerging evidence of additional tropospheric sources66 in future studies. In conclusion, the findings of this study suggest that the increase in microbial emissions, primarily agriculture and landfills, has substantially contributed to the atmospheric CH4 trend over the past three decades. These findings enhance the global effort to reduce methane emissions by offering a clearer understanding of historical emission trends, which is crucial for developing effective future reduction strategies.

Materials and methods

Atmospheric chemistry transport model

Atmospheric CH4 mole fractions, δ13C-CH4, and δD-CH4 were simulated from January 1, 1970, to December 31, 2020, using the JAMSTEC’s Model for Interdisciplinary Research on Climate, version 4, based Atmospheric Chemistry Transport Model (MIROC4-ACTM)10,48. We ran the model globally at a resolution of approximately 2.8125° × 2.8125° over 67 hybrid vertical pressure levels extending from the Earth’s surface to 0.0128 hPa (~80 km). The MIROC4-ACTM simulated horizontal winds (u and v) and temperature (T) are nudged to the Japan Meteorological Agency reanalysis fields81 at 2–61 vertical levels for better representation of synoptic-scale transport features. The model’s interhemispheric and vertical transport is validated using SF6 simulations in the troposphere and the CO2-derived age of air in the troposphere and stratosphere10,48.

CH4 emission sources and scenarios

Methane (CH4) emissions can be broadly classified into three categories: fossil fuel exploitation (FF), microbial processes (MiB), and biofuel and biomass burning (BB). The FF category includes emissions from industrial sources (IFF) (such as coal, oil, and natural gas (ONG)), and natural geological sources. The IFF mainly emits CH4 through extraction, transport, and use, while natural FF sources release CH4 through terrestrial and marine seeps, mud volcanoes, and other geological processes. The MiB category includes emissions from wetlands, rice paddies, enteric fermentation, and manure management (ENF&MNM), and waste/landfills (LDF). CH4-generating microbes (methanogens) in anaerobic environments produce these emissions. BB emissions result from the incomplete combustion of biomass and soil carbon during wildfires and biofuel burning.

We prepared four different CH4 emission scenarios, based on bottom-up emission estimates (Tables 1, S1). These scenarios are further evaluated using the long-term trends and latitudinal gradients of CH4 and δ13C-CH4.

Baseline scenario (E0)

We obtained emissions data from various sources to create the baseline scenario (E0). For estimates of emissions from IFF sources, we used data from the Emissions Database for Global Atmospheric Research (EDGARv6.0)2. EDGARv6 provides yearly/monthly emissions at a resolution of 0.1° × 0.1° for the period of 1970–2018. We extrapolated the emissions for the years 2018–2020 by calculating the rate of change in previous years. For emissions from natural geological sources, we used gridded data from Etiope et al.59. We used the same geological emissions for each year by assuming no IAV during our study period, as suggested by previous studies59. For MiB emissions, we used data from the process-based model VISIT(based on Cao scheme)5 for wetlands and rice paddies, and from EDGARv6 for ENF&MNM and LDF emissions. For emissions from biomass burning (BB), we used inter-annually varying emissions from the Global Fire Database (GFEDv4s) for the period of 1999–202082. For residential burning (RCO), we used data from EDGARv6. We used annually repeating emissions from the Goddard Institute for Space Studies (GISS) scaled by ×0.315, as an estimation of biofuel burning. For the period of 1970–1998, we obtained inter-annually varying fire emissions data from the Mac-City inventory83. To maintain the same spatial distribution, we used GFEDv4s seasonal climatology for the period of 1999–2020 and scaled the annual emissions to the Mac-City inventory estimate for the period of 1970–1998. We used monthly GFEDv4s emissions from 1998 to 2020. For emissions from ocean and termites, we used data from Weber et al.84 and Saunois et al.8, respectively.

E1 emission scenario

To prepare the E1 scenario, the ONG emission in the E0 scenario was replaced with estimates from the GAINSv4 model4. The GAINS model, developed by the International Institute for Applied Systems Analysis (IIASA), is a multipollutant emission estimation model that uses bottom-up emissions estimates and future mitigation potentials based on any externally given energy sector scenario.

EDGARv6 and GAINSv4 provide different estimates of ONG emissions, with a difference of over 35 TgCH4 yr−1, and also show discrepancies in emission trends from 1990–2018 (Fig. 3a). EDGARv6 suggests a consistent increase in ONG emissions during 1990–2018, while GAINSv4 suggests a decline from 1990–2006 and a slight increase afterward. These differences arise from varying emission factors related to the venting and flaring of associated gas during ONG extraction, which vary across different ONG fields worldwide. GAINSv4 uses country-specific information on associated petroleum gas generation, recovery, and venting/flaring rates, calibrated to satellite image estimates of volumes of gas flared. By combining information on the associated gas flow from published sources with inter-annual variations in observed flaring of associated gas from the Visible Infrared Imaging Radiometer Suite (VIRS) satellite-based nighttime fire imagery3, GAINSv4 estimates country-specific annual CH4 emissions from flows of associated gas. On the other hand, EDGARv6 estimates emissions from venting based on national GHG inventories reported to the UNFCCC. However, it is unclear how the latter is reflected in emission estimates. National GHG inventories reported to the UNFCCC typically apply close to constant default emission factors across historical years, making production quantities the main driver for emissions. This may explain the relatively stable emission factors reflected over time in EDGARv6. The GAINSv4 estimates of ONG emissions are available for 1990–2020, and for 1970–1989, the scaled EDGAR emissions were used at the annual global total of GAINS estimates in 1991.

E2 emission scenario

Based on the GAINSv4 estimate, CH4 emissions from the oil production sector have shown a consistent decline (Fig. S10). However, this decline is offset by a substantial increase (~19 Tg) in emissions from unconventional gas, mainly shale gas, in the USA from 2006 to 2020 (Fig. S10b). The substantial increase in emissions from the unconventional gas sector over the USA is highly debatable and atmospheric observations of CH4 around the USA contradict these findings51,54. Despite the increase in CH4 production over the USA, a recent study did not support a large ONG emissions72 as well as concomitant large increase in total ONG emissions (including shale gas) because of the decrease in CH4 intensity (emissions per unit CH4 gas production) from 2010 to 201920. Furthermore, the estimates of coal emissions in China provided by EDGAR (used in E0 and E1) are subject to debate, as regional bottom-up estimates and inversions suggest varying rates of increase after 200010,11,42,43,53. Therefore, in the E2 emission scenario, we have revised the estimates of ONG and coal emissions and other sectors are the same as in the E1 scenario. Specifically, we have excluded unconventional gas emissions from the total ONG emissions of USA and adjusted the coal emission growth in China based on regional emission trends from a MIROC4-ACTM inversion study10.

E3 emission scenario

We conducted a study to test two hypotheses related to geological CH4 emissions. These hypotheses were based on recent debates in the scientific literature regarding the total magnitude of geological CH4 emissions59,60,61. Some of the studies suggests that natural geological sources contribute largely to the atmospheric CH4 budget59, while others argue that contemporary natural geological emissions have been overestimated based on paleo-radiocarbon estimates60,61. The previous scenarios (E0, E1, and E2) used the global geological estimates 37 TgCH4 yr−1. Additionally, we considered scenario E3 in which global geological emissions in E2 were reduced to the value of 19 TgCH4 yr−1. This allowed us to prepare a consistent CH4 budget and test the impact of different geological emission scenarios on the overall budget that was consistent with observed CH4 and δ13C-CH4 trend and growth rates, simultaneously.

Methane loss processes and fractionation in MIROC4-ACTM

Atmospheric CH4 has four loss mechanisms: atmospheric oxidation by hydroxyl radicals (OH) and chlorine (Cl) throughout the atmosphere, destruction by electronically excited atomic oxygen (O(1D)) in the stratosphere and consumption by microbes in upland soils (Table S1). The CH4 consumption by bacteria in soils, taken from the process-based terrestrial ecosystem model, VISIT5, is modeled as a negative flux at the surface. The loss by chemical reactions is calculated online in the model using the following equations.

$$C{H}_{4}+{OH} \longrightarrow C{H}_{3}+{H}_{2}O\,({k}_{{OH}}=2.45 \times 1{0}^{-12} \exp (-1775/T))$$
$$C{H}_{4}+{Cl} \longrightarrow C{H}_{3}+{HCl}\,({k}_{{Cl}}=7.3 \times 1{0}^{-12} \exp (-1280/T))$$
$$C{H}_{4}+{O}({\,\!}^{1}D) \longrightarrow {Products} \,({k}_{{O}({\,\!}^{1}D)}=1.5 \times 1{0}^{-10})$$

The temperature-dependent reaction rates (k; units: cm3 molecule−1 s−1) were taken from the JPL synthesis of chemical kinetics, also used in the TransCom-CH4 intercomparison experiment85. The reaction rates differed between the CH4, 13CH4, and CH3D which is characterized by a distinct kinetic isotope effect (KIE). KIE is quantified using the ratio of reaction rate constants for the light and heavy isotopologue of a certain species, e.g., 13CKIEj = kj(12CH4)/kj(13CH4); j = OH, Cl, O1D (Table S1). The loss of the heavier methane isotopologues (e.g., 13CH4, and CH3D) is slower than the destruction of 12CH4, which is quantified by a kinetic fractionation factor. Each loss process has a different KIE (summarized in Table S1). CH4 losses due to reactions with Cl and O(1D) are small compared to the total loss, but the strong isotopic fractionations (Table S1) in these reactions greatly impact the isotopic budget45,86.

Methane loss fields and lifetime

The inter-annually varying soil sink of CH4 is used from the process-based VISIT model. The climatological monthly variations of stratospheric OH and the tropospheric and stratospheric control Cl (Cl_ctrl) fields are used from an output of the ACTM’s stratospheric model run, and O(1D) is calculated online based on a climatological O3 field67. The monthly mean three-dimensional tropospheric OH field is provided here for online calculation in the model from Spivakovsky et al87 after scaling by 0.92 to match the decay rate of methyl chloroform (CH3CCl3: MCF) in the Earth’s atmosphere79. This study did not consider the long-term trend in OH as previous research has ruled out an OH-driven explanation for the growth in CH410,13,76,77,88.

The chemical lifetime of CH4 is calculated by τ = Burden / Total chemical loss. Despite the climatological OH, Cl, and O(1D) fields, the modeled chemical lifetime of CH4 shows a decreasing trend (~1% - decade−1). The decreasing trend could be due to inter-annually varying temperatures, as CH4 loss due to OH and Cl increases as temperature increases (Eqs. R1, R2). The average CH4 chemical lifetime during 1985–2020 is 9.59 ± 0.04 years, with a total lifetime of 8.98 ± 0.06 years including the soil sink. These estimations agree with the recent IPCC AR6 estimation.

Model’s spin-up and mass conservation

Modeling δ13C-CH4 and CH4 mole fractions are highly sensitive to the initial condition. We used the initial CH4 distributions from a 32-year simulation (1985–2016) based on a previous study by Chandra et al.6 to obtain the initial distributions of CH4 on January 1, 1970, for this study. To obtain the initial distributions of CH4 on 01 January 1970 for this study, the ratio of observed atmospheric CH4 values from ice core data and simulations at Syowa (a clean representative site of global air mass) were calculated. Then the three-dimensional (3-D) distribution in January 1970 was derived by globally multiplying the distributions in Jan 2016 by the ratio. To derive the initial 3-D δ13C-CH4, we applied Rayleigh fractionation equations16,39 to the 3-D total CH4 distributions in January 1970. Since we start from atmospheric CH4 and δ13C-CH4 fields based on observations, the time required to relax to a steady state will not be more than a few CH4 lifetimes. We spun up our model for 15 years (1970–1984) and selected 1985–2020 for the CH4 analysis. For δ13C-CH4, we used 25 years (1970–1994) as the spin-up period and used 1995–2020 for the analysis.

To validate our initialization approach, we conducted multiple simulations with fixed emissions, but different initial CH4 mixing ratios ranging from 1100 ppbv to 1500 ppbv and δ13C-CH4 ranging from −48.5‰ to −50‰ (Fig. S4). The CH4 simulations converged to less than a 5% difference from its initial values, while δ13C-CH4 simulations converged at ~0.02‰ difference, which is small enough to have a negligible impact on their long-term trend analysis. We conducted an additional evaluation to assess the tracer mass conservation capability of MIROC4-ACTM in simulating δ13C-CH4. To accomplish this, we disabled fractionation (i.e., KIE = 1) and emissions on January 1, 2000. The results reveal a consistent δ13C-CH4 value after disabling the sink fractionation and emissions (Fig. S5). This indicates that the drift in tracer mass is inconsequential when simulating δ13C-CH4 in MIROC4-ACTM for the trend analysis.

Atmospheric measurements

We evaluated the performance of model simulations using observations from background stations in the NOAA Global Greenhouse Gas Reference Network / Institute for Arctic and Alpine Research (INSTAAR) and two sites of Tohoku University (TU)/National Institute of Polar Research (NIPR) located in the northern and southern polar regions (as shown in Fig. 1). The NOAA observed molar fraction values were reported on the WMO-X2004A scale89. The INSTAAR δ13C-CH4 data were measured in a subset of air samples collected from NOAA’s Global Greenhouse Gas Reference Network90. TU/NIPR measurements of CH4 mole fractions and δ13C-CH4 were taken at Ny-Ålesund (NAL; since August 1991 for CH4, since March 1996 for δ13C-CH4), and Syowa (SYO; since 1983 for CH4, since March 1995 for δ13C-CH4). Details of these measurements are described in previous studies16,91.

We used the measurements from all available sites to prepare the latitudinal profile of CH4 and δ13C-CH4 for evaluating the latitudinal distribution of emissions, as shown in Fig. 4. In addition, we used vertical observations of CH4, δ13C-CH4, and δD-CH4 from balloon flights over the polar region (Kiruna, Sweden) and the subtropical region (Hyderabad, India)71. The balloon observations were used to validate the model’s ability to accurately simulate the troposphere-stratosphere exchange of these species, which are affected by different factors in different atmospheric layers.

It is worth noting that δ13C-CH4 measurements at different laboratories showed systematic offsets due to variations in instrument settings, correction methods, and traceability to reference materials92. For this reason, the δ13C-CH4 values measured by NOAA/INSTAAR and TU/NIPR have offsets that impede direct combination for model evaluations. To address this, the time series was harmonized with the TU scale by applying an offset of −0.20‰ to the NOAA/INSTAAR measurements92. This offset was determined based on measurements of cylinders, flasks filled from cylinders, and co-located sample data92.

Data processing

The model simulations are sampled at the time of the observations and at the nearest grid point to the measurement locations. To analyze the long-term trend, we fitted the measured and simulated daily/weekly time series at each station using digital filter techniques93. We used six harmonics to extract the sinusoidal component (i.e., seasonal cycle) and applied a Butterworth digital filter with a cut-off length of 24 months to determine the long-term trends. The growth rate is calculated by taking the time derivative of the long-term trend, expressed in units of ppb yr−1 for CH4 and ‰ yr−1 for δ13C-CH4.

Our primary interest is in the multi-year trends on a large scale, so we selected only a subset of the global network sampling sites (as shown in the spatial maps in Fig. 1) that are predominantly influenced by well-mixed background air. These sites were used to construct representative mean time series and growth rates for sub-hemispheric latitudinal bands, as shown in Fig. 1. We only used sites (a total of 11 for δ13C-CH4 and 18 for CH4) that had full-time series available. The number of sites used for the CH4 and δ13C-CH4 hemispheric averages are different. However, the latitudinal profile uses observations from 50 sites for CH4 and 23 sites for δ13C-CH4 (Fig. 6).