Methane emissions decreased in fossil fuel exploitation and sustainably increased in microbial source sectors during 1990–2020

Abstract

Methane (CH₄) emission reduction to limit warming to 1.5 °C can be tracked by analyzing CH₄ concentration and its isotopic composition (δ¹³C, δD) simultaneously. Based on reconstructions of the temporal trends, latitudinal, and vertical gradient of CH₄ and δ¹³C from 1985 to 2020 using an atmospheric chemistry transport model, we show (1) emission reductions from oil and gas exploitation (ONG) since the 1990s stabilized the atmospheric CH₄ growth rate in the late 1990s and early 2000s, and (2) emissions from farmed animals, waste management, and coal mining contributed to the increase in CH₄ since 2006. Our findings support neither the increasing ONG emissions reported by the EDGARv6 inventory during 1990–2020 nor the large unconventional emissions increase reported by the GAINSv4 inventory since 2006. Total fossil fuel emissions remained stable from 2000 to 2020, most likely because the decrease in ONG emissions in some regions offset the increase in coal mining emissions in China.

Introduction

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 observations^6,7,8. This incongruence can arise from imprecise emission factors and activity data (e.g., fugitive fossil fuel sector^2,3,9), 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 gradient^{10,11,12,13,14,15,16,17}. 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 techniques^19,20,21,22, discerning individual CH₄ source contributions using only atmospheric CH₄ observations remains a challenge⁸.

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

Temporal (a), latitudinal (b), and spatial (c–e) 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 inversion^13,14,27 and box model^{28,29,30,31,32,33} 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 change^{10,13,14,16,26,27,28,29,30,31,32,34,35,36,37,38,39,40}. Some emphasize increased emissions from microbial sources^{13,28,29,35,41}, while others suggest competing contributions from both microbial and fossil fuel sources^10,14,30. 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 economies^2,3,42,43.

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 uncertainties^45,46,47. 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.

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 (a–c) and δ¹³C-CH₄ (in ‰) from 1998 to 2020 (d–f). 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.

Results

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 model^2,5 (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 equation^13,16,35. 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 trend^32,49,50. 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 emissions^2,4, 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.

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 2000^10,42,43 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 inversions^{10,11,15,42,51,52,53}. 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 observations^20,51,54. The uncertainty in leakage rate^55,56,57,58 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 estimates^7,59,60,61. 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 (KIE_OH) 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 trend^{62,63,64,65,66}. 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, KIE_OH values could greatly influence the δ¹³C-CH₄ simulations. The literature suggests notably different values for KIE_OH; Saueressig et al.⁴⁵ reported a low KIE_OH value (L-KIE_OH: 1.0039) compared to Cantrell et al.⁴⁶ (H-KIE_OH: 1.0054) and recently Whitehill et al.⁴⁷ (1.0061). Previous studies have adopted either values (L-KIE_OH vs H-KIE_OH) based on their preference^{14,16,28,29,32,34,35,36,39,49,50,64}. Since we cannot determine the relative merits of the reported OH fractionation, we tested both (L-KIE_OH, H-KIE_OH) values in the sensitivity simulations. Simulations with H-KIE_OH and L-KIE_OH 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 categories^24,29,68. 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 gradient^36,69. 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 KIE_OH 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 KIE_OH.

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 (a–c) and right column (d–f) correspond to H-KIE_OH (1.0054: Cantrell et al.⁴⁶) and L-KIE_OH (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 (M_ENF), 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 signature^36,69. 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-KIE_OH, and 0.5‰ in H-KIE_OH). By adjusting ONG and geological signatures to less negative (−40‰) as suggested in previous studies^34,49,70, the discrepancies were reduced from 0.5‰ in M-all (using H-KIE_OH) 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-KIE_OH (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 KIE_OH introduces offsets (seen from Cl_ctrl_H-KIE_OH and Cl_ctrl_L-KIE_OH in Fig. 5), the primary influencer of the vertical gradient is the Cl distributions (seen from Cl_ctrl_H-KIE_OH and Cl_wang_H-KIE_OH 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.

Comparisons of CH₄, δ¹³C-CH₄, and δD-CH₄ simulations (lines) with balloon measurements (filled circles) over Kiruna (a–c) and Hyderabad (d–f)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 KIE_OH (H-KIE_OH⁴⁶, L-KIE_OH⁴⁵) 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.

Comparison of the observed and modeled latitudinal gradient of CH₄ (a, d, e) and δ¹³C-CH₄ using different emission scenarios and KIE_OH (H-KIE_OH: b, e, h; L-KIE_OH: 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 KIE_OH values also influenced the latitudinal δ¹³C-CH₄ gradient (Fig. S16b, c), suggesting uncertainty ties to both KIE_OH 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-KIE_OH values, as well as “M2_Hgeol-ong” and “M3_Hgeol-ong” scenarios in the case of H-KIE_OH values reproduce the observed N-S gradient (Fig. 6). Recently, Whitehill et al.⁴⁷ even reported a higher KIE_OH value of 1.0061, near to H-KIE_OH value used in this study that align well with observed variation, supporting our findings that a greater KIE_OH 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. 5–7). Although some studies^13,16,29,35 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 production^20,73.

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

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-KIE_OH 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 1990s^3,4, 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 emissions^27,49, 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 differs^13,28,29,35. 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 methods^17,76,77 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 concentration^76,79. Yet, we recognize that short-term interannual OH variabilities^76,77 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 stratosphere^10,48.

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 findings^51,54. 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 2000^{10,11,42,43,53}. 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 emissions^59,60,61. 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 estimates^60,61. The previous scenarios (E_0, 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.

$$C{H}_{4}+{OH} \longrightarrow C{H}_{3}+{H}_{2}O\,({k}_{{OH}}=2.45 \times 1{0}^{-12} \exp (-1775/T))$$

(R1)

$$C{H}_{4}+{Cl} \longrightarrow C{H}_{3}+{HCl}\,({k}_{{Cl}}=7.3 \times 1{0}^{-12} \exp (-1280/T))$$

(R2)

$$C{H}_{4}+{O}({\,\!}^{1}D) \longrightarrow {Products} \,({k}_{{O}({\,\!}^{1}D)}=1.5 \times 1{0}^{-10})$$

(R3)

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., ^13CKIE_j = k_j(¹²CH₄)/k_j(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 budget^45,86.

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 CH₄^{10,13,76,77,88}.

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 equations^16,39 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 studies^16,91.

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).