Anthropogenic emission is the main contributor to the rise of atmospheric methane during 1993–2017

Abstract Atmospheric methane (CH4) concentrations have shown a puzzling resumption in growth since 2007 following a period of stabilization from 2000 to 2006. Multiple hypotheses have been proposed to explain the temporal variations in CH4 growth, and attribute the rise of atmospheric CH4 either to increases in emissions from fossil fuel activities, agriculture and natural wetlands, or to a decrease in the atmospheric chemical sink. Here, we use a comprehensive ensemble of CH4 source estimates and isotopic δ13C-CH4 source signature data to show that the resumption of CH4 growth is most likely due to increased anthropogenic emissions. Our emission scenarios that have the fewest biases with respect to isotopic composition suggest that the agriculture, landfill and waste sectors were responsible for 53 ± 13% of the renewed growth over the period 2007–2017 compared to 2000–2006; industrial fossil fuel sources explained an additional 34 ± 24%, and wetland sources contributed the least at 13 ± 9%. The hypothesis that a large increase in emissions from natural wetlands drove the decrease in atmospheric δ13C-CH4 values cannot be reconciled with current process-based wetland CH4 models. This finding suggests the need for increased wetland measurements to better understand the contemporary and future role of wetlands in the rise of atmospheric methane and climate feedback. Our findings highlight the predominant role of anthropogenic activities in driving the growth of atmospheric CH4 concentrations.

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INTRODUCTION
Stabilizing atmospheric methane (CH 4 ) emissions from anthropogenic activities is a critical component of climate change mitigation [1]. The atmospheric CH 4 concentration has increased ∼2.5-fold from 731 ppb (parts per billion) in 1750 (preindustrial reference year [2]) to 1890 ppb in 2020 [3]. Meanwhile, over the past century, atmospheric δ 13 C-CH 4 values increased from ∼−49.0 in 1912 to −47.2 in 2007 due to increasing emissions of isotopically 13 C-enriched (i.e. isotopically heavy) fossil fuels [4]. Despite the importance of under-standing the temporal changes in atmospheric CH 4 , the drivers of changes in the growth rate of atmospheric CH 4 over recent decades remain poorly understood [5]. The increase in atmospheric CH 4 slowed in the early 1990s and was followed by a so-called stabilization period during 2000-2006 [6]. Since 2007, global atmospheric CH 4 concentrations have begun to rise again, accompanied by a decline in δ 13 C-CH 4 values from −47.2 in 2007 to −47.4 in 2017 [3]. The cause of this change has been studied recently using atmospheric inversion models [7][8][9][10], atmospheric box models [11][12][13][14][15] and of CH 4 from fossil fuels, agriculture, wetlands and/or decreased hydroxyl radicals (OH) as main drivers due to different measurements, methodologies and time periods considered (see Materials and Methods). Such discrepancies highlight the need to reconcile our understanding of the drivers of growth in atmospheric CH 4 in order to design mitigation policies [18].
Sources of the global CH 4 budget are mainly determined by three broadly defined groups: (i) thermogenic sources from industrial fossil fuel (e.g. coal, oil and natural gas; IFF CH4 ) and geological sources (GEO CH4 ); (ii) biogenic sources from livestock, rice agriculture, landfills and waste (AGW CH4 ), and natural wetlands (WET CH4 ); and (iii) pyrogenic sources from wildfires and biomass burning (BB CH4 ). The primary sink for CH 4 is reactions with tropospheric OH, soil microbial uptake and a small contribution from tropospheric chlorine reactions, which affect the isotopic compositions. The shift of the trend in atmospheric δ 13 C-CH 4 values towards more 13 C-depleted (i.e. isotopically light) compositions suggests a higher dominance of isotopically light biogenic emissions in the global CH 4 budget [11,19]. This hypothesis has been supported by recent process-based and inversion modeling, which points to either a systematic underestimation of AGW CH4 [20] or a large increase in WET CH4 [8,10,21,22]. In contrast, there are large differences in the rate of change across inventorybased estimates of industrial fossil fuel source activity IFF CH4 [23,24], as well as substantial underestimates in some regions and overestimates in other regions [12,25,26]. Globally, studies suggest that BB CH4 has been declining, with fire CH 4 emissions associated with an isotopically enriched signature, thus providing room in the isotopic budget for an increase in fossil fuel sources [13]. GEO CH4 , which is often co-located with the fossil fuel industry, is suggested to be largely overestimated by recent studies [27,28], indicating a potentially larger role of IFF CH4 in affecting the global CH 4 budget given its underestimated share of the total CH 4 source [12,29].
OH oxidation in the troposphere is the main CH 4 sink, and reactions with chlorine (Cl), stratospheric sinks and soil removal are small-magnitude sinks. Substantial difficulties remain in quantifying CH 4 sinks, especially the main chemical sink for CH 4 , tropospheric OH [5]. OH plays a significant but ambiguous role in driving the observed atmospheric trend; it is difficult to estimate due to its complicated chemistry, i.e. non-linear chemical feedback and short lifetime [30,31]. For example, estimates of interannual variability (IAV) in global mean OH are significantly higher in the empirical box-model estimates that use CO and methylchloroform (MCF) constraints [32] than estimates based on chemical transport models (Fig. S1). Although there are debates on the potential biases in the box-modelbased OH due to ignorance of complex spatial heterogeneity in OH and transport [33,34], the uncertainties in OH trends and variability are likely large enough to explain any potential CH 4 growth scenarios [14,15,35]. In addition, the trends in OH exert isotopic leverage on atmospheric δ 13 C-CH 4 values via the kinetic fractionation effect, such that increasing OH increases the atmospheric δ 13 C-CH 4 value by OH reacting with more 12 CH 4 . Therefore, it is of interest to investigate hypotheses regarding CH 4 sources with atmospheric δ 13 C-CH 4 observations while assuming that these sources can reproduce the atmospheric records with varying OH.
A thorough investigation of these hypotheses in a clearly defined framework is essential to help resolve the unexplained change in the growth rate of atmospheric CH 4 . Here, we use an isotopic mass balance approach to attribute drivers of the growth rate of atmospheric CH 4 using a large ensemble of scenarios to represent different combinations of emission hypotheses (denoted emission scenarios, see Materials and Methods) from a comprehensive set of updated bottom-up estimates representing anthropogenic emission inventories and spatially explicit signatures for major CH 4 sources. Each emission scenario is composed of a time series of sectoral CH 4 fluxes and their hemispheric emission-weighted δ 13 C-CH 4 values. A globally representative database and spatially resolved distributions of δ 13 C-CH 4 values for the major CH 4 sources [36][37][38] were used to evaluate the temporal and regional variability in observed δ 13 C-CH 4 values. Monte Carlo techniques were applied to explore the uncertainty in δ 13 C-CH 4 estimates with full consideration of the spatial heterogeneity in CH 4 sources and their δ 13 C-CH 4 signatures. Scenario-specific parameters for the time series of the CH 4 removal rate driven by OH variations and run-specific 13 CH 4 fractionation factors were derived by inverting an atmospheric two-box model (see Methods and Supplementary Data). We then evaluated the emission scenarios against observed δ 13 C-CH 4 values for 1993-2017 by running the two-box model in the forward mode. To test the hypothesis of a large increase from wetland CH 4 emissions, the idealized wetland scenarios (i.e. without process-based constraint) were then calculated to reproduce the temporal pattern of δ 13 C-CH 4. The comparison against atmospheric isotopic observations allowed us to select the most likely set of emission scenarios, which are defined as the first percentile cut-off of the lowest mean squared difference (MSD) in simulated δ 13

Temporal variations in the atmospheric CH 4 concentration and its δ 13 C-CH 4 value
The ensemble simulations for the 96 emission scenarios (4 IFF CH4 × 3 AGW CH4 × 2 WET CH4 × 2 BB CH4 × 2 GEO CH4 ) reproduced the observed atmospheric CH 4 concentration (Fig. 1A) using the corresponding optimized time series of OH derived from running the box model in inverse mode (Fig. S1). We accounted for the uncertainty in source signatures of δ 13 C-CH 4 by resampling 1000 sets of δ 13 C-CH 4 signature time series for each emission scenario (n = 96 × 1000), which resulted in a wide range of modeled atmospheric δ 13 C-CH 4 values with some closely reproducing the observations. However, most emission scenarios tended to generate more enriched δ 13 C-CH 4 trends for 1993-2017, suggesting that existing bottom-up inventories overestimate the increase in IFF CH4 during the study period, especially during slowdown and stagnation periods (Fig. 1B). Furthermore, to balance the rise in CH 4 sources, the increases in OH levels also led to positive trends in atmospheric δ 13 C-CH 4 values during these two periods (Fig.  S1). Note that the large increase in coal-related emissions since 2003 has increased the δ 13 C-CH 4 values of the sources, which contribute to the divergence between the model and observations. The timing of this divergence is consistent with a rapid increase in methane emissions from China (mainly coal emissions) as reported by the inventories [23] and inversions [39]. For most of the emission scenarios, the estimated temporal variations in  OH for 1993-2017 fall within the 1-σ range of the Bayesian inversion from Ref. [14] and are in good agreement with Ref. [35] for the post-2000 period. The EDGARv4.2-based emission scenarios have the largest mismatch with the inversionbased OH anomaly (relative to a global mean concentration of 1e 6 molecules (molec)/cm 3 ), confirming the known higher bias in EDGARv4.2 than in other inventories (Fig. S2). The time series of CH 4 sources for 1993-2017 ( Fig. 1C) suggests that decadal-scale variations in atmospheric CH 4 are dominated by anthropogenic emissions from both agricultural and fossil fuel activities. However, there is high uncertainty across IFF CH4 inventories, with a sizable (>40 Tg CH 4 yr -1 ) difference in magnitude and a large difference in temporal trends between inventories (i.e. EDGARv4.2, EDGARv4.3.2 and GAINS) and an atmospheric-observation-constrained approach (i.e. SCH150, which hypothesizes that IFF CH4 is underestimated but does not increase over time). The temporal variation in AGW CH4 exhibits a lower discrepancy than IFF CH4 in the inventories, whereas WET CH4 and BB CH4 are more constrained. The IAV and magnitude of our estimates for WET CH4 , calculated using the process-based model LPJ-wsl, are comparable to the ensemble mean of multiple wetland models [40] and a global wetland CH 4 emission model ensemble for use in atmospheric chemi-cal transport models (WetCHARTs) [41]. The wetland CH 4 estimates derived from driving the wetland model with a ground-measurementbased meteorological dataset from the Climate Research Unit (CRU) yield a small increase (<1 Tg CH 4 yr -1 ), whereas the same model with climate reanalysis (REN) has an ∼7.3 Tg CH 4 step increase from tropical wetlands between 2000-2006 and 2007-2017 [22]. Figure 2A shows the distribution of residual bias in the individual box model simulations in terms of how they reproduce the observed δ 13 C-CH 4 values. In the Taylor diagram [42] the global average δ 13 C-CH 4 values of the sources before fractionation by chemical sinks range from −53 to −55 over 1993-2017, and a correlation coefficient lower than 0.6 is obtained for all of the simulations for 1993-2017. The low agreement suggests that the biases in the inventories and the wetland models contribute to the discrepancies in reproducing the δ 13 C-CH 4 , which is likely due to the overestimated increase in inventories, especially the coal emission that has a relatively heavy isotopic signature, as found by previous atmospheric inversion studies [16]. In addition, some of the simulations can reproduce similar IAV in atmospheric δ 13 C-CH 4 values with root mean square errors (RMSEs) from 0.05 to 0.5 , but ∼85% of simulations tend to produce higher IAV than observed. Although the global average δ 13 C-CH 4 value was regarded as observational 'truth', this reference has an uncertainty of 0.04 , attributed to variability in measurements across all the stations and uncertainty from scale conversions between networks [43].

Evaluations of proposed CH 4 hypotheses using emission scenarios
The density distributions of RMSEs grouped by different bottom-up CH 4 estimates show the divergent performance of emission scenarios in reproducing observed atmospheric δ 13 C-CH 4 values (Fig. 2B). Among the four IFF CH4 inventories, 80% of the simulations using EDGARv4.2 generated more positive trends of δ 13 C-CH 4 values than the other three inventories, with no EDGARv4.2based runs located in the most likely set of emission scenarios (Fig. S3). This result corroborates previous studies that also suggest that EDGARv4.2 tends to overestimate fossil fuel growth [44]. The more recent EDGARv4.3.2 has been improved, with 95% of the simulations located within the RMSE range from 0.1 to 0.3 , mainly due to improved emission factors and revised statistics of CH 4 sectors [23]. SCH150 produces lower agreement than EDGARv4.3.2 partly due to the low IAV of SCH150, as SCH150 focuses on the long-term trends in IFF CH4 . The GAINS inventories generated better performance: 78% of the simulations in the first percentile of MSD are based on GAINS IFF CH4 . Note that this does not rule out the IFF CH4 scenarios that have flat or insignificant trends (e.g. SCH150), as 13 C-enriched BB CH4 estimates in this study show declining trends over recent years, which would allow for compensation by increasing emissions from IFF CH4 to meet the decreasing atmospheric δ 13 C-CH 4 values. Generally, IFF CH4 has a more pronounced impact in determining the past trends in δ 13 C-CH 4 changes than the other major CH 4 sources.
The contribution of combined agriculture, landfills and waste included in AGW CH4 , which together represent 50%-62% of all anthropogenic sources, again reveals a higher bias of EDGARv4.2based simulations compared to the other two inventories (Fig. 2B). Agricultural emissions dominate AGW CH4 , with an average contribution of 77.5% to the total AGW CH4 over the study period. The lower MSD scores using EDGARv4.3.2 and WOLF2017 emission scenarios show improved reconciliation of estimates for the AGW CH4 source relative to the isotopic budget. This result supports the hypothesis that the global livestock estimates based on the 2006 IPCC Tier 1 guidelines underestimate livestock CH 4 emissions at the national or state level [45], which is potentially attributable to outdated information used to develop the emission factors. However, there is no clear signal to distinguish whether EDGARv4.3.2 or WOLF2017 has a lower a priori bias, suggesting the need for further regional and global assessments by spatially explicit 4-D atmospheric models.
Our calculations suggest that, in contrast to anthropogenic sources, wetland CH 4 emissions play a limited role in reproducing the decadal trend in atmospheric δ 13 C-CH 4 (Figs 1 and 2B). Both REN and CRU demonstrate that wetland CH 4 emissions appear to have contributed little to the renewed growth in atmospheric CH 4 . However, wetland emissions help explain the IAV in the atmospheric CH 4 growth rate via its pulsed responses to climate dynamics, such as the El Niño-Southern Oscillation [46]. The latitudinal gradient of the growth rate for CH 4 sources (Fig. S4) suggests that WET CH4 in the tropics has an important impact on the IAV of the CH 4 growth rate, albeit the current limited understanding of WET CH4 is due to a significant deficiency in WET CH4 measurements in the tropics, especially for Africa [21].
The density distribution of RMSE grouped by BB CH4 and GEO CH4 (Fig. 2B) suggests that the recent hypotheses regarding a larger decrease [13] in BB CH4 and overestimated contemporary GEO CH4 [27,28] have a good agreement with the isotopic budget. The lower RMSE of Worden (2017)-based scenarios supports the hypothesis of a decreasing trend in BB CH4 during the post-2007 period, as suggested by inversion modeling based on satellite measurements of carbon monoxide [47]. The low GEO CH4 scenarios, which assume a geological source of 15 Tg CH 4 yr -1 with upward-revised IFF CH4 (see Methods and Supplementary Data), yield lower RMSEs than the conventional high-GEO CH4 scenarios in which GEO CH4 was set to 52 Tg CH 4 yr -1 . These findings support the hypothesis that the current bottom-up estimates of anthropogenic fossil fuel CH 4 emissions are underestimated and that geological emissions are overestimated.

Changes in the trends of δ 13 C-CH 4 source signatures
A change in source signature (Fig. 3A) suggests varying global-emission-weighted average sources driven by the change in spatiotemporal distribution of CH 4 source estimates for the four major CH 4 categories. When considering spatial heterogeneity in the source signature, the globally representative δ 13 C-CH 4 values tend to suggest a larger variation than previous assumptions that use globally uniform values [7,13]. The IFF CH4  Note that the effect of the decreasing trend of atmospheric δ 13 C-CO 2 values on the C 3 -C 4 diet composition of domestic ruminants in recent decades was not taken into account in this study; consideration of this factor would yield a slight decrease in the AGW CH4 signature [48]. Wetland δ 13 C-CH 4 values increased slightly from −59.7 to −59.5 from the stabilization period to the renewed-growth period, mainly attributable to increased tropical wetland CH 4 emissions since 2007. Tropical wetlands tend to have a more enriched signature (mean −56.7 ) than northern high-latitude peatland-based wetlands (mean −67.8 ) (Fig. S5), as supported by a few site-level measurements [36,38,49]. The possible signature enrichment from wetlands is another line of evidence for a weak wetland CH 4 emission response [22,40], while there is no evidence of a signif-icant change in wetland CH 4 from high latitudes in either model [16,44] or by direct atmospheric measurement [50], where the rise of WET CH4 may possibly be counteracted by increased soil uptake [51]. However, it is difficult to distinguish CH 4 from wetlands and livestock, as the signatures of the two sectors are similar and the spatial distributions are possibly co-located [3], suggesting a critical need for more measurements to provide better constraints on δ 13 C-CH 4 values in the tropics.
The change in the δ 13 C-CH 4 contribution from individual sources does not necessarily imply the same trend in the global average signature. Theoretically, even if the tropical wetland signature becomes more positive, the increased proportion of wetland-contributed 13 CH 4 mass to the total 13 CH 4 mass can still result in a shift towards a more negative global signal, as the biogenic signature is considerably lighter than the global atmospheric δ 13 C-CH 4 value [36] (∼−53.6 ) before fractionation. This is the case in some paleoclimate studies [52] where tropical wetlands and other natural sources (e.g. biomass burning) dominated the annual CH 4 budget. However, the role of human activities has Natl Sci Rev, 2022, Vol. 9, nwab200 become dominant in the annual CH 4 and isotope budgets since AD 1750, and the relative importance of wetlands has lessened. Figure 3B also shows the probability distribution of the relative contribution of 13 CH 4 mass to the annual total 13

Idealized wetland emission scenarios that reproduce the decrease in atmospheric δ 13 C-CH 4 values
Beyond our wetland-model ensemble, we created scenarios to investigate the possible involvement of rising WET CH4 in the decrease of atmospheric δ 13 (Fig. 4A). Note that all the idealized WET CH4 scenarios are higher than the two WET CH4 scenarios in this study (i.e. CRU and REN) or WetCHARTs, a wetland CH 4 product that is based on satellitederived surface water extent and precipitation reanalysis and an ensemble of ecosystem respiration estimates. One process-based WET CH4 that overlaps the increases in idealized wetland scenarios is the ensemble mean of LPJ-wsl simulations for a future projection under the climate scenario RCP8.5 [53] (denoted Zhang2017). RCP8.5 is considered the upper bound of wetland CH 4 feedback to rising temperature in LPJ-wsl because the strong and steady increase in temperature in RCP8.5 is higher than that determined from actual observations. Note that this scenario would occur only in combination with the hypothesis that IFF CH4 has had no significant trends in recent years. The comparison of 2000-2017 trends in WET CH4 (Fig. 4B) suggests that to reproduce the magnitude of the observed decrease in atmospheric δ 13 C-CH 4 values, the required emission increase from natural wetlands would need to be much higher than the current estimates from process-based wetland models. The trend of CRU is consistent with the ensemble estimate of global wetland model simulations [5,40], while that of REN is at the higher end of the trends that consider the potential inundation increase due to enhanced tropical precipitation [22]. Note that the range of idealized increases in WET CH4 is in line with two recent inversion studies [8,10] based on GOSAT CH 4 measurements, which suggests a positive wetland trend of 2-3 Tg CH 4 yr -1 yr -1 for 2010-2018. However, to produce such a significant trend, the Q10 parameter (temperature sensitivity of CH 4 emissions) in the wetland models would need to be much higher than the range of 2-3 from LPJ-wsl and WetCHARTs or the measurement-based average of 2.57 from FLUXNET-CH4 [54]. In addition, a recent multi-model ensemble inversion study [55] suggests that the observation-constrained wetland CH 4 feedback to rising temperature is lower than that of Zhang 2017. Despite this, there are considerable uncertainties in modeled WET CH4 due to scarcity of measurements for the tropics [40]. We conclude that the hypothesis that a large increase in natural wetlands drives the decrease in atmospheric δ 13 C-CH 4 values cannot be reconciled with process-based wetland CH 4 models. The higher IAV of BB CH4 than the uncertainty range is due to the spikes during some extreme El Niño years, which are one order of magnitude higher than that of most years.

Attributions of the CH 4 rise based on the most likely scenarios
Our Monte Carlo estimation (Table 1) suggests that the largest uncertainties in global representative source δ 13 C-CH 4 values are in industrial fossil fuel activities, providing clues for future studies.
Our estimated global representative values for total CH 4 source signatures are within the uncertainty of recently compiled databases [12,36] but are lower than the value used in previous inverse studies (see Fig. S6 for references). Among the major CH 4 emis- sion sectors, the global average emission-weighted δ 13 C-CH 4 signature for coal has the highest IAV, which is mainly due to the large deviation in countrylevel data in coal emissions [39] and the heterogeneous distribution of different coal ranks [56]. Note that the low-rank coals tend to produce isotopically lighter CH 4 [36] with a potentially biogenic origin [57], indicating that the proportion of consumption of different coal types may have a significant impact on atmospheric δ 13 C-CH 4 values. We calculate the most likely scenarios based on the agreement of bottom-up estimates with isotopic observations (Fig. 5). The results suggest that the agricultural, landfill and waste sectors account for 53 ± 13% (21.0 ± 0.8 Tg CH 4 yr -1 ; 1-σ ) of renewed growth over the period of 2007-2017 compared to 2000-2006, with industrial fossil fuel sources and wetland sources contributing 34 ± 24% (13.7 ± 8.8 Tg CH 4 yr -1 ) and 13 ± 9% (5.3 ± 3.5 Tg CH 4 yr -1 ), respectively. The decreasing emissions from fossil fuel sectors in 1993-1999 compared to 2000-2006, combined with the increasing OH anomaly (Fig. S8), may have contributed to the CH 4 stabilization period ( Fig. 5 and Fig. S7). The increases in methane emissions (mainly from the fossil fuel, agriculture and waste sectors) combined with a step increase from wetland CH 4 and small decreases in OH levels led to renewed growth in methane during 2007-2012. Moreover, the higher CH 4 emissions from mainly anthropogenic activities, i.e. coal, oil, gas, livestock, landfill and waste sectors, drove the accelerated increase in atmospheric CH 4 during 2013-2017. These sectoral emission increases are consistent with economic activity data (Table S2;  Table S3) showing that, in the past decade, coal production has increased by 41.7% globally (International Energy Agency, https://www.iea.org/ topics/coal/statistics/) and that the populations of major livestock species (e.g. swine, chickens and ruminant animals) have increased by 22.5% (FAO-STAT, http://www.fao.org/faostat/). Although coal production exhibited a temporary decline during 2014-2016 (Statistical Review of World Energy 2020, https://www.bp.com/content/ dam/bp/business-sites/en/global/corporate/pdfs/ energy-economics/statistical-review/bp-stats-review-2020-full-report.pdf), average coal emissions during 2013-2017 were higher than those during 2007-2012, indicating that coal mining emissions continued to grow, with a higher contribution to the increase in atmospheric CH 4 .

CONCLUSIONS
Our analysis shows that a comprehensive evaluation of hypotheses regarding the attribution of rising atmospheric CH 4 based on a combination of bottom-up approaches and isotopic values can reconcile multiple lines of evidence into a robust global CH 4 budget. However, we acknowledge that there are some biases and uncertainties in the bottom-up estimates and that our exploration of possible emission scenarios does not cover all potential scenarios. This study clearly suggests that the proposed hypotheses are influenced by the choice of a priori estimates, indicating that the high-bias a priori estimates of trends applied in some earlier studies have led to equally biased conclusions regarding the attribution of atmospheric methane rise. Our results suggest that decreasing emissions from coal, oil and gas from 1993-1999 to 2000-2006, combined with the increasing OH anomaly, likely contributed to the methane stabilization period. Anthropogenic sources were the most likely major contributor to the renewed growth in CH 4 after 2006. Moreover, the good agreement of low present-day geological source estimates with observations supports the hypothesis that the IFF CH4 in recent decades has been largely underestimated. However, our understanding of the role of livestock and wetlands, particularly in tropical regions, is more limited [58,59]. Aircraft measurements in these regions may help address the lack of data and improve our understanding of WET CH4 . This study highlights the dominant role of anthropogenic emissions from fossil fuels, agriculture, landfills and waste in driving the recent rising trend in atmospheric CH 4 . Our findings improve our understanding of the causes of changes in atmospheric CH 4 over the past 25 years, enabling the development of more targeted mitigation strategies and policies to stabilize and ultimately reduce key contributing emission sectors.

Model descriptions
The model was developed from previous studies [15,60,61] and consists of two perfectly mixed boxes representing the troposphere in the northern and southern hemispheres. The changes in CH 4 concentration are calculated using the following equations: 12 CH S 4 (t + t) = 12 CH S 4 (t) where 12 CH 4 is approximated by CH 4 and 12 S N i (t) and 12 S S i (t) represent the annual source strength of the source in the northern hemisphere and southern hemisphere, respectively. k 12 is the first-order removal rate coefficient for the sinks. The interhemispheric exchange time τ is set to a constant value of 1 yr given that the overall methane CH 4 concentration and OH anomalies are largely unaffected by the interhemispheric exchanges [15].
The δ 13 C-CH 4 isotopic signatures of the different source categories i and the kinetic isotope effect (KIE) in the individual sink reactions j are used to calculate the sources ( 13 S i ) and removal rate coefficients ( 13 k j ) for δ 13 C-CH 4 values.
These terms are then used to derive the mixing ratio changes in 13 C-CH 4 : 13 CH S 4 (t + t) = 13 CH S 4 (t) The mixing ratios of the individual isotopologues are converted to δ values as follows: where 13 R std = 1.12372% is the 13 C/ 12 C ratio of the international reference material Vienna Pee Dee Belemnite (VPDB). The soil sink is considered to have a low IAV, as suggested by biogeochemical models [62,63], despite a recent study [64] based on a few site-level measurements suggesting a decline in the soil sink in temperate forests in recent decades. For soil CH 4 uptake, we use climatology from a process-based model [63] in the calculation of the hemispheric net CH 4 source (see equation 6 in Materials and Methods). The contributions of Cl sink and stratospheric loss to the removal of CH 4 in the troposphere are highly uncertain and not well constrained by direct observations, but have a strong kinetic isotope effect on 13 CH 4 . Given the large uncertainty in Cl and stratospheric sinks and the lack of available datasets, the magnitudes of these two sinks were not explicitly considered in the calculation of the hemispheric CH 4 budget. We assume that the annual methane removal rate is driven solely by OH variability, while other minor sinks are kept constant over the study period. Because sensitivity tests [65] suggest that the uncertain magnitude of Cl fields leads to a wide range of simulated δ 13 C-CH 4 values given its strong 'isotope leverage' effect [66] (−60 ± 1 ) on total ε, the sink-weighted average fractionation factor ε is highly uncertain. The approach in this study is to estimate the total ε value for each box model run that optimizes the match between atmospheric observations and simulation at the onset of the study period. The optimized ε values were derived from running the box model in inverse mode by matching the observed global average [11]. This allows us to explore the uncertainty in ε based on bottom-up source aggregation and the uncertainty in δ 13 C-CH 4 values. Figure S6 shows that the estimated fractionation factors for the full ensemble and first percentile ensemble are broadly in agreement with previous studies [11][12][13]60,[66][67][68][69][70]. The distribution of the mean methane lifetime (Fig. S9) over the study period is slightly lower than the estimated 9.1 ± 0.9 yr from Ref. [71] and is comparable in magnitude to that between atmospheric chemistry-transport models in the recent model intercomparison [31,32,72]. Here, we evaluate the global results from the box model, instead of hemispheric results, to minimize the potential influence of uncertainty in IAV from interhemispheric transport on box model performance, as suggested by a recent study [73]. See Supplementary Data for details about the model strategy.

CH 4 source estimates
To test all the proposed competing hypotheses, we carried out simulation experiments using box modeling for different emission scenarios based on a suite of bottom-up datasets. We first list all the possible options for the CH 4 inventories by five CH 4 source categories (i.e. IFF CH4 , AGW CH4 , WET CH4 , BB CH4 and GEO CH4 ) and then generate emission scenarios with combinations of CH 4 inventories. The assignment of the inventory (i.e. EDGAR)-specific sectors into the main categories IFF CH4 , AGW CH4 and BB CH4 follows the criteria from Supplementary Table S4 in Ref. [5]. Anthropogenic CH 4 emissions related to fossil fuels from exploitation, transportation and usage of coal, oil and natural gas are defined as IFF CH4 . For methane sectors related to enteric fermentation and manure, landfills, waste and rice agriculture are defined as AGW CH4 .

Spatially resolved δ 13 C-CH 4 and uncertainty estimation
Spatially resolved distributions of δ 13 C-CH 4 source signatures for the following major methane categories were applied in this study: coal, natural gas/oil, livestock, wetlands and biomass burning. For the other sources, including agricultural waste, rice, geological sources, termites, freshwater systems and wild animals, we use a globally averaged value (Table S4) from a global inventory database that collected isotopic source signatures based on literature values [36,66,68].

Emission scenarios
An emission scenario is a combination of the individual CH 4 source estimates listed in Table S1. Annual total net CH 4 sources can be expressed as follows: S tot = S IFF + S AGW + S WET + S BB + S GEO , where S represents the individual CH 4 source from Table S1 and S soil is a constant soil sink. The total number of emission scenarios is 96, calculated as 4 IFF CH4 × 3 AWG CH4 × 2 WET CH4 × 2 BB CH4 × 2 GEO CH4 . For each emission scenario, we use Monte Carlo techniques to estimate the uncertainty in the source signature propagated from bottom-up estimates and the spatial variability of the source signature. A set of 1000 random maps of δ 13 C-CH 4 values for each major CH 4 source (Table 1) were generated based on the uncertainty maps in this study assuming a Gaussian distribution. For CH 4 sources that are not spatially resolved, 1000 samples of the global-representative signature values are calculated with mean and 1-standard deviation defined by observations from the compiled databases (Table S4). One thousand sets of emission-weighted hemispheric time series of δ 13 C-CH 4 , which were calculated with bottom-up estimates depending on emission scenarios, were used as inputs for the box model. For each emission scenario, the simulated time series of δ 13 C-CH 4 values covers the uncertainty range of spatial variability in the isotopic signatures of major CH 4 categories.

DATA AVAILABILITY
All data needed to evaluate the conclusions in this paper are present in the paper and/or the Supplementary Data. Additional ancillary data are available from the corresponding author upon request.