Methane (CH4) is a powerful greenhouse gas, and its atmospheric abundance (in nmol mol−1, abbreviated ppb) has increased by about 170% since the 1750s1,2. Unlike the steady increases of atmospheric CO2 and N2O, atmospheric CH4 nearly stabilized from 1998 to 2006 and then rapidly increased with a growth rate averaging ~6 ppb yr−1 between 2007 and 2013 and ~11 ppb yr−1 between 2014 and 2021. Since 2007, CH4 has increased while its stable carbon isotopic composition (δ13C-CH4, Eq. 1) has trended to more negative values, after increasing for 200 years3,4,5. Diagnosing the mechanisms behind these changes continues to generate considerable attention and controversy6,7,8,9,10,11,12.

Measurements of atmospheric CH4 abundance and δ13C-CH4, in combination with isotopic signatures of sources and sinks, allow partitioning of CH4 budgets into different source categories. This is because isotopic signatures of source categories differ substantially, where the δ13C-CH4 of microbial sources (mean of −61.7 with variability of 6.2‰) is isotopically more depleted than fossil (mean of −44.8 with variability of 10.7‰) and biomass burning (mean of −26.2 with variability of 4.8‰) sources9,13. The destruction of CH4, primarily by reaction with hydroxyl radical (OH), isotopically enriches atmospheric CH4 relative to the emission-weighted source signature7,14,15. Due to a wide range of δ13C-CH4 in each source category13, spatial and temporal distributions must be known to reduce the uncertainty in source partitioning. Wetlands are the largest single natural CH4 source and strongly influence atmospheric δ13C-CH4 changes12, but the spatial and temporal information of wetland δ13C-CH4 is limited, and often a single uniform value is assumed15,16. Studies show that source partitioning in atmospheric modeling is highly sensitive to spatiotemporal understanding of wetland δ13C-CH49.

Observations of global wetland δ13C-CH4 show that CH4 emitted from boreal wetlands is isotopically more depleted than CH4 emitted from the tropics17,18,19; proposed causes include the abundance of C4 plants influencing the δ13C of precursor organic matter (POM) (δ13C-POM), differences in CH4-producing archaea (methanogen) communities, and different CH4 transport processes18,20,21,22. Ganesan et al.23 produced a spatially-resolved global wetland δ13C-CH4 distribution, but their study did not simulate temporal variability and did not fully represent fractionation processes that change based on meteorology, soil and vegetation properties.

Here, we incorporate a carbon isotope module into a biogeochemistry model, the Terrestrial Ecosystem Model (TEM)24,25 to simulate and mechanistically understand the global wetland δ13C-CH4 distribution. The model is evaluated using site-level and regional observations. We then use this model to understand the mechanisms behind the spatial and temporal variability of wetland δ13C-CH4, and conduct uncertainty and sensitivity tests. Finally, we investigate the effect of new wetland isotope maps on atmospheric δ13C-CH4 and global CH4 emissions by using an atmospheric model and atmospheric observations5,26.


Modeling wetland δ 13C-CH4 dynamics

TEM simulates CH4 production, oxidation, and transport between soils and the atmosphere (Eqs. 310)24,25,27,28. A carbon isotope-enabled module is incorporated into TEM, referred to as isoTEM, which explicitly considers carbon isotopic fractionation processes in wetlands (Fig. 1). The isotopic fractionation factor (α) for each process is defined in Eq. 220, where α is larger than 1 when the product is isotopically more depleted than the reactant.

Fig. 1: Schematic diagram of wetland CH4 dynamics and fractionations for isoTEM.
figure 1

The model simulates δ13C of precursor organic matter (POM) (δ13C-POM), CH4 production, oxidation, and transport to the surface. δ13C-POM is determined by global C3/C4 plant distribution and long-term trends of atmospheric δ13C-CO2. CH4 is produced by two pathways, one using H2 and CO2 and another using acetate, with fractionation factors (α) for HMs (αHM) ≈ 1.030–1.080 and for AMs (αAM) ≈ 1.000–1.040. Produced CH4 is partly oxidized by methanotrophs with a fractionation factor αMO 1.015–1.035. Residual produced CH4 is emitted to the surface via three processes, plant-mediated transport (TP), diffusion (TD), and ebullition (TE), with different fractionations, αTP 1.000–1.030, αTD 1.005, αTE 1.000, respectively (Supplementary Tables 24 and Method “Model development, Model optimization”). Bold and dashed lines in the figure refer to chemical and transport processes, respectively.

δ13C-POM is determined by the global C3 and C4 plant distribution (Supplementary Fig. 1)29, where C4 vegetation is isotopically enriched due to its photosynthetic pathway30. We incorporated observed long-term trends of atmospheric δ13C-CO2 into soil δ13C-POM (Supplementary Fig. 2)31,32,33. CH4 is produced from POM in anaerobic soils by two distinct methanogen communities: hydrogenotrophic methanogens (HMs) which use H2 and CO2 and acetoclastic methanogens (AMs) which use acetate34. The fractional contribution of these pathways is important because HMs produce isotopically more depleted CH4 compared to AMs (αHM and αAM in Eq. 12)19,35. To quantify the fractional contribution, we used in situ observations from Holmes et al.19 and conducted a regression analysis between the fractional contribution and main environmental factors, including soil pH, carbon, and latitude (Eq. 11, Supplementary Fig. 3, and Supplementary Table 1). Total produced δ13C-CH4 is then calculated using a mixing of CH4 pools from the two methanogen communities (Eqs. 1314). The CH4 produced is partly oxidized by methanotrophs in aerobic soil layers36 with 12CH4 being oxidized preferentially relative to 13CH4MO in Eq. 15). Then, the remaining CH4 is emitted to the atmosphere through three processes: plant-mediated transport, diffusion, and ebullition, with fractionation factors of αTP, αTD, and αTE, respectively (Eq. 16)20. We calculated oxidized and emitted δ13C-CH4 using the ratio of oxidation and transport processes and their fractionation factors (Eqs. 1722) (Method “Model development”).

We optimized four fractionation factors related to CH4 production, oxidation, and plant-mediated transport (αHM, αAM, αMO, αTP) using field observations in boreal (50–90°N), temperate (30–50°N/S), and tropical (<30°N/S) wetlands35,37,38 (Eqs. 12, 15, 16, Supplementary Table 24 and Supplementary Figs. 4, 5). We set αTE to 1.000 and αTD to 1.005 based on previous studies20 since ebullition and diffusion are governed by physical processes. To quantify uncertainties in model simulations, we used 20 ensemble members of optimization. We simulated global wetland CH4 fluxes and their isotopic signatures during 1984–2016 at a spatial resolution of 0.5° with a 50-year spin-up to let δ13C-CH4 of carbon pools come to a steady state (Methods “Model optimization, Simulation setup”).

Simulated wetland δ 13C-CH4 and its comparison with observations

We estimated the mean global wetland source signature to be −61.3 ± 0.7‰ during 1984–2016 (Fig. 2a). This value is more enriched than the mean wetland signature of −62.3‰ in Ganesan et al.23 but similar to the mean value of −61.5‰ reported in Sherwood et al.13 (Supplementary Figs. 8, 9). The latitudinal distribution of δ13C-CH4 ranges from a mean of −57 ± 3‰ in the tropics to −68 ± 4‰ in boreal regions (Fig. 2b). Our model simulates isotopically depleted global δ13C-CH4 during the summer due to larger emissions from boreal regions (Supplementary Fig. 10) and a long-term trend of −0.7 ± 0.1‰ during 1984–2016 (blue line in Fig. 2c) when incorporating the long-term trend in δ13C-POM (Supplementary Fig. 2)

Fig. 2: Global distribution of wetland δ13C-CH4 and its latitudinal and long-term gradients simulated by isoTEM.
figure 2

a Modeled global wetland δ13C-CH4 for wetland grid cells with static inundation data49. b Mean latitudinal distribution of δ13C of POM (yellow), produced CH4 (red), and CH4 emitted to the atmosphere for all grid cells (blue) and flux-weighted grid cells (purple). c Long-term trends of global mean wetland δ13C-CH4 with and without incorporating long-term trend in δ13C-POM (blue and purple, respectively). The shaded area in (b, c) represents one standard deviation determined from 20 ensembles of simulations where the optimized parameters were varied.

We compared the magnitude and spatial variability of the simulated wetland δ13C-CH4 with site-level observations (Method “Model-data comparison”). We used 70 in situ measurements of global wetland δ13C-CH4 from previous studies after excluding the measurements applied for optimization (Supplementary Data 1, Supplementary Fig. 11)13,19. We showed that isoTEM reduced the root mean square error (RMSE) by 40% compared to Ganesan et al.23 (2.2 vs. 3.6) (Fig. 3a, b). Compared to a static isoTEM map in July, 2016, temporally-varying isoTEM reduced the RMSE slightly (2.2 vs. 2.4) (Supplementary Fig. 12). Ganesan et al.23 prescribed maximum and minimum values as boundary conditions, resulting in unrealistic clusters of wetland δ13C-CH4 near −65‰ for boreal and −60‰ for tropical sites (Fig. 3a and Supplementary Fig. 9).

Fig. 3: Site-level and regional model-data comparison of wetland δ13C-CH4.
figure 3

a, b Site-level model-data comparison of observations with (a) Ganesan et al.23 and (b) temporally-varying isoTEM. ce Regional model-data comparison of simulated wetland δ13C-CH4 in Alaska by (c) Ganesan et al.23 and (d) isoTEM, and (e) their comparison with observation-based source signatures from NOAA aircraft measurements. The source signature is derived using Miller-Tans plots39. All observation data used for site-level comparison are listed in Supplementary Data 1. Error bars for observations in (a, b, e) represent one standard deviation of measured/inferred wetland δ13C-CH4. Error bars for isoTEM in panel e represent one standard deviation determined from 20 ensemble simulations where the optimized parameters were varied.

Furthermore, we compared the spatial variability of simulated wetland δ13C-CH4 with estimated signatures from airborne measurements for three regions in Alaska during 2012-2013 and 2015 using Miller-Tans plots (Fig. 3c–e) (Method “Model data comparison”)39. In situ flux observations collected across Alaskan wetlands show an average of −65‰, but with a large 9‰ variance40, which could be due to changes in wetland habitat including soil nutrients, pH, and vegetation distribution. The estimated signatures from observation also show that compared with δ13C-CH4 from the North Slope of Alaska (−65 ± 1‰), δ13C-CH4 from interior Alaska is more depleted (−69 ± 6) and δ13C-CH4 from southwest Alaska is more enriched (−59 ± 4‰) (Supplementary Fig. 13 and Supplementary Table 5). IsoTEM reproduces the spatial variability (−67 ± 1, −68 ± 1, and −61 ± 2‰ for North Slope, interior, and southwest Alaska, respectively), whereas Ganesan et al.23 simulated no spatial variability around −65‰ (Fig. 3e). IsoTEM simulates the spatial variability as the model optimized parameters for vegetated and non-vegetated sites separately and incorporated meteorology and soil inputs that vary spatially and temporally.

Mechanistic understanding of spatial and temporal variability of wetland δ 13C-CH4

We investigated the relative importance of the isotopic fractionation processes that affect the latitudinal gradient of wetland δ13C-CH4 (Fig. 2b and Supplementary Fig. 14). First, compared to the boreal zone, δ13C-POM is enriched in the tropics by 5 ± 2‰ as C4 plants are more prevalent (yellow line in Fig. 2b, Supplementary Figs. 1, 14a). Second, due to a larger fraction of AM in the tropics (Supplementary Fig. 3), the δ13C-CH4 produced by methanogens is enriched by 12 ± 3‰ (red line in Fig. 2b, Supplementary Fig. 14b). Third, δ13C-CH4 emitted from wetlands is 6 ± 4‰ more depleted in the tropics due to a larger proportion of plant-mediated transport causing higher effective transport fractionation (αT) (blue line in Fig. 2b, Eq. 19, Supplementary Figs. 14d, 15, 16). Thus, in our simulation, δ13C-CH4 emitted from tropical wetlands is enriched by ~11‰ compared to boreal wetlands. This difference is strengthened due to the distribution of C4 plants (+5 ± 2‰) and the fractional contribution of differing methanogen communities (+12 ± 3‰) but weakened due to plant-mediated transport (−6 ± 4‰).

The long-term decrease in wetland δ13C-CH4 simulated by isoTEM is mostly due to the decrease in atmospheric δ13C-CO232. The decreasing trend is incorporated into δ13C-POM (Supplementary Fig. 2) and causes the long-term decrease in wetland δ13C-CH4 of ~0.7‰ from 1984 to 2016 (blue line in Fig. 2c)31. We conducted a simulation without the decreasing trend in δ13C-POM, which showed that increased temperature caused plant productivity and plant-mediated transport to increase and δ13C-CH4 to decrease by ~0.1‰ during 1984–2016 (purple line in Fig. 2c and Supplementary Fig. 15). This implies that wetland δ13C-CH4 could further change in the future due to decreases in δ13C-POM and increases in plant-mediated transport.

There is no continuous long-term measurements of wetland δ13C-CH4 to verify our simulated long-term trend. Instead, we ran a regression analysis using observations collected from various wetland locations since the early 1980s (Supplementary Data 1) (Method “Uncertainty and sensitivity tests”). The results show that the representation of data increases when adding year as a parameter for the regression analysis (Supplementary Table 6), and the observed data show a long-term decreasing trend with year (~−0.1‰ year−1) (Supplementary Fig. 17). More continuous long-term observations of wetland δ13C-CH4 are necessary to further verify the simulated long-term trends in wetland δ13C-CH4.

Uncertainty and sensitivity tests

The version of TEM that we use for this study explicitly simulates soil CO2 and CH4 but not soil H2 and acetate pools27, because the spatial and temporal soil H2 and acetate pools are highly uncertain, and it is hard to verify the simulated pool changes with limited observations. On the contrary, the CH4 production, oxidation, and transport processes in TEM have been thoroughly validated for global regions from previous studies24,25,27,41,42,43,44. Therefore, instead of introducing additional uncertainty from explicitly simulating H2 and acetate pools that cannot be validated, we applied the observed fraction of different methanogen communities (fHM) based on regression to the total CH4 production rates simulated by TEM (Supplementary Fig. 3 and Supplementary Table 1). Thus, in our simulation, the fraction of HM and AM (fHM) changes spatially but not temporally.

To quantify the uncertainty of our regression analysis of fHM, we ran additional sensitivity tests by varying the fHM based on the uncertainty from Markov Chain Monte Carlo approach (Method “Uncertainty and sensitivity tests” and Supplementary Table 1)45. The results show that varying the parameters do not change the wetland δ13C-CH4 substantially (<1%) (Supplementary Table 7). We acknowledge that this simplification would cause uncertainty in our model results, and future studies should explicitly measure changes in H2 and acetate concentrations in soils to incorporate the detailed processes into the model.

The simplification of CH4 production processes may also cause uncertainty in the fractionation as we do not explicitly simulate fractionation processes from POM to CO2/acetate and from CO2/acetate to CH4. However, studies show that fractionation factors of the fermentation (POM to CO2) and syntrophy (POM to acetate) processes are minor (α ≈ 1.00)19,46,47. There may be additional CO2 produced by acetoclastic methanogenesis that have large fractionation (α ≈ 1.05), but the fraction is negligible from observations19. Thus, we believe our fractionation factors for HMs and AMs (αHM and αAM, respectively) reasonably represent the major fractionation processes of CH4 production.

Furthermore, to quantify the influence of the uncertainty of our model inputs on simulation results, we varied temperature, precipitation, net primary productivity (NPP), atmospheric CH4, and applied transient inundation maps48 (Method “Uncertainty and sensitivity tests”). The results show that meteorology and substrate inputs alter mean wetland δ13C-CH4 by ±1‰ (Supplementary Table 7). Our TEM simulations showed that CH4 fluxes are sensitive to these inputs27. However, δ13C-CH4 shows small changes because the fractionation is determined by the fraction of CH4 oxidation and transport processes (Eqs. 21, 22), that are calculated as a function of soil CH4 production and the resultant CH4 concentration changes (CM in Eqs. 610). When CH4 production increases due to input changes, CH4 oxidation and transport increase simultaneously, causing minor variation in the fraction of oxidation and transport (Supplementary Fig. 16). Inundation datasets also alter wetland δ13C-CH4 by changing the areas where wetland emissions occur (±2‰) (Supplementary Table 7 and Supplementary Figs. 6, 7).

Implication for atmospheric modeling and global CH4 budget

We constructed four scenarios with different wetland emissions and isotopic signature maps as inputs for TM5 atmospheric modeling during 1984–2016 to understand the impacts of spatially- and temporally-resolved wetland δ13C-CH4 (Table 1). Scenario A uses a globally uniform value of wetland δ13C-CH4; Scenario B uses a temporally static but spatially variable wetland isotope map from Ganesan et al.23; and Scenario C uses spatially- and temporally-resolved maps from isoTEM. We used the same wetland fluxes27 with a static inundation map49 for Scenarios A–C that applied a step increase in fluxes in 2007 and 2014 by hypothesizing that microbial wetland emissions are the dominant driver of the post-2006 atmospheric CH4 increase9,26,50 (46 Tgyr−1 increase in total 2016 emissions across the global wetlands compared to the averaged total emissions in 1999–2006) (Supplementary Fig. 19). However, since other studies have suggested an increase in fossil emission as a dominant driver for post-2006 CH4 increases12, we created scenario D that uses isoTEM wetland isotope maps with increases in both microbial and fossil emissions since 2007 (Table 1).

Table 1 Setup of TM5 atmospheric modeling for Scenarios A–D.

For Scenarios A–D, we adjusted global mean fossil and ruminant fluxes simultaneously to satisfy the long-term average mass balance of atmospheric CH4 (Fig. 4a) and δ13C-CH4 (Method “Forward modeling using TM5 atmospheric model”), as done by Lan et al.26. These adjustments bring the long-term global average δ13C-CH4 from simulation to the observed atmospheric levels without changing the post-2006 trends in simulated δ13C-CH49,26. After adjustments, global mean fossil fluxes in scenarios A–D are between 170 and 190 Tgyr−1 (Supplementary Fig. 19),within the uncertainty range in Schwietzke et al.9. For all other fluxes, their isotopic signatures, and CH4 sinks that include OH, Cl, and O(1D)14,51,52, we used the same setup in our model as in Lan et al.26 (Supplementary Table 8). We compared simulated CH4 and δ13C-CH4 with observations from NOAA/INSTAAR global flask-air measurements (Supplementary Table 10)2,5.

The atmospheric simulation showed that Scenarios A–C follow the observed δ13C-CH4 trend reasonably closely (Fig. 4b). However, Scenario D, which hypothesizes a post-2006 increase in microbial and fossil fluxes, does not follow the decreasing trend in global mean δ13C-CH4. As pointed out earlier8,9,26,50, the magnitude of the δ13C-CH4 decrease suggests that the increase in microbial emissions dominates fossil emissions in the post-2006 global CH4 increase. We also confirmed a dominant increase in post-2006 microbial emissions, even though the long-term decrease in wetland δ13C-CH4 of ~0.7‰ allow for a larger fossil emission increase. An additional simulation of Scenario C without including the long-term decrease in wetland δ13C-CH4 shows differences of ~0.1‰ in simulated atmospheric δ13C-CH4 in 2016 compared with model results with long-term wetland δ13C-CH4 trend (Supplementary Fig. 23). This difference can accommodate more post-2006 emission increases from isotopically enriched fossil sources for Scenario C.

Fig. 4: Observed and simulated atmospheric CH4 and δ13C-CH4 from TM5 atmospheric modeling.
figure 4

a, b Model-data comparison of long-term trend of (a) atmospheric CH4 from 1985 to 2016 (in ppb) and (b) δ13C-CH4 from 1999 to 2016 (in ‰) by observation (gray) and simulations from Scenario A (yellow), B (red), C (blue), and D (skyblue). c Model-data comparison of normalized north–south gradient of atmospheric δ13C-CH4 for Scenario A (yellow), B (red), and C (blue) in 2012. The north–south δ13C-CH4 was calculated by zonally-averaging the surface δ13C-CH4 and normalized based on the mean δ13C-CH4 at 60–90 °S. The normalized north–south δ13C-CH4 for other years is in Supplementary Fig. 20 and Supplementary Table 9. d Histogram of the difference between simulated and observed δ13C-CH4 for Scenario A (yellow), B (red), and C (blue) for 6 measurement sites located in the northern hemisphere. The histogram plots for all measurement sites are in Supplementary Fig. 22. Information about Scenarios A–D is in Table 1.

We differentiated Scenarios A–C by comparing their simulated latitudinal gradients of atmospheric δ13C-CH4 with observations (Fig. 4c and Supplementary Fig. 20). The observed mean latitudinal gradient during 1998–2016 shows more negative δ13C-CH4 at northern high latitudes compared to the Southern Hemisphere by 0.45 ± 0.05‰ (Supplementary Table 9), resulting from the dominance of northern emissions combined with the subsequent fractionation by reaction with OH during transport to the Southern Hemisphere17. Scenario C, which uses IsoTEM maps, best reproduces the observed north–south gradient (0.48‰); Scenarios A and B under- and over-estimate the gradient by ~0.1‰ (0.37‰, and 0.59‰, respectively). The difference is also clear when comparing simulated atmospheric δ13C-CH4 of Scenarios A–C at 10 measurement sites (Supplementary Figs. 21, 22 and Supplementary Table 10). The simulated and observed atmospheric δ13C-CH4 differ the most at Northern Hemispheric sites, where Scenario C best reproduces the atmospheric δ13C-CH4 data, but Scenario A and Scenario B simulate more negative and positive δ13C-CH4, respectively (Fig. 4d).

The difference in north–south gradient of atmospheric δ13C-CH4 between scenarios in Fig. 4c has an implication on regional partitioning of sources. Our sensitivity test of atmospheric modeling showed that all scenarios with transient inundation data48 (Scenarios E–G) underestimated the north–south δ13C-CH4 gradient (0.27 ± 0.06‰) compared with observations (0.45 ± 0.05‰) (Method “Forward modeling using TM5 atmospheric model”, Supplementary Table 11, Supplementary Figs. 2630). Thus, we ran an additional Scenario H that increased emissions from boreal wetlands by 2.5 times over the original transient data (Supplementary Fig. 26 and Supplementary Table 11), which increased the north–south gradient by ~0.1‰ and improved the match with the observed north–south δ13C-CH4 gradient (0.39‰) (Supplementary Figs. 29, 30).


The atmospheric CH4 burden has grown rapidly since 2007, and the largest annual increase since NOAA began measurements in 1983 was observed in 202153,54. Since 2019, δ13C-CH4 decreased more steeply55, suggesting a further increase in microbial emissions as this and other studies suggest8,9,26,50. The microbial sources include anthropogenic emissions from ruminants, agriculture, and waste, and natural emissions from wetlands and other aquatic ecosystems12. Our simulation with increase in wetland emissions can reproduce the observed post-2006 δ13C-CH4 decrease (Fig. 4), and our additional sensitivity test with increase in anthropogenic microbial emissions also tracks the post-2006 δ13C-CH4 decrease (Supplementary Figs. 24, 25). However, the scenario with emission increase from both microbial and fossil sources did not reproduce the decreasing trend in atmospheric δ13C-CH4 (Scenario D in Fig. 4). Other atmospheric studies that use atmospheric δ13C-CH4 observations also showed that fossil emission increase is not a dominant reason of recent CH4 increase26,56.

Atmospheric δ13C-CH4 measurements have not been widely used to inform global methane budget because of uncertainty and spatiotemporal variation in source signatures, specifically citing limitation in wetland source signatures11. In this study, we mechanistically explain the spatiotemporal variations of wetland δ13C-CH4 and validate the simulation using regional, latitudinal, and global measurements, which substantially reduce the uncertainty in δ13C-CH4 source signatures (Fig. 3). The small decreasing trend in wetland δ13C-CH4 allow for more fossil emission increase in our estimate, but cannot change the conclusion that fossil emission increases are not the dominant driver for post-2006 global CH4 increases.

This study considers wetland δ13C-CH4 during the historical period only, but the future changes in wetland δ13C-CH4 will depend on multiple factors. First, our simulation shows that changes in δ13C-POM affect wetland δ13C-CH4 as SOC is mostly derived from new carbon from vegetation. The simulated active layer depth from a previous study57 shows that the active layer depth had a minor change during our simulation period (mean of <0.1 m) (Supplementary Fig. 18). However, the usage of old stored carbon in Arctic permafrost may play an important role as a substrate for methanogens in the future58. Also, studies found the importance of microbial fossil CH4 emissions from Arctic regions in the future59,60. The emissions are partially included as geologic seep emissions in our atmospheric modeling simulation (Supplementary Fig. 19 and Supplementary Table 8), and we also considered microbial fossil emissions with depleted δ13C-CH4 in our total fossil emission estimates26. Lastly, our simulation shows that the increase in NPP cause more plant-mediated transport. This effect will be more important in the future as plant functional types and plant growth change due to temperature increase.

There are several aspects of the model that could be improved. First, our optimization of fractionation factors was based on limited observations; additional long-term measurements of wetland δ13C-CH4 would reduce the uncertainty. Second, the fractional contribution of two methanogen communities (HMs and AMs) changes spatially but not temporally in the model. We need a better understanding of temporal changes in methanogen communities especially following permafrost thaw and disturbance35, and explicitly measure changes in H2 and acetate concentrations in soils to incorporate detailed CH4 production processes into the model. Third, various vertical methanogenic and non-methanogenic processes change δ13C of CH4 and CO2, the vertical CO2/CH4 ratios, and thus δ13C-CH4 emitted from wetlands, since CO2 is a substrate for HM61,62. We need to identify detailed vertical subsurface processes by conducting manipulation experiments using isotopic labeling analysis and inhibitor techniques to include those fractionation processes in future modeling studies63. Fourth, current wetland models do not simulate large CH4 emissions and δ13C-CH4 from tropical tree stems and aquatic sources properly64,65,66. More measurements from these sources are crucial to improve the estimate of natural CH4 emission and δ13C-CH4 changes.


To the best of our knowledge, this study is the first to use a biogeochemistry model to mechanistically explain and reduce the uncertainty in global wetland δ13C-CH4. IsoTEM explains the latitudinal gradient of wetland δ13C-CH4 that is increased by the distribution of C3/C4 plants and methanogen community type but decreased by plant-mediated transport. The long-term trends of the simulated wetland δ13C-CH4 is controlled by δ13C-POM and plant-mediated transport. Our results suggest that rising microbial emissions is the dominant driver for the post-2006 global CH4 increase and the concurrent decrease in atmospheric δ13C-CH4, and the isoTEM spatial distribution of wetland δ13C-CH4 better reproduces the observed atmospheric δ13C-CH4 latitudinal gradient.


Model development

We incorporated a carbon isotope module of methane (CH4) into an existing process-based biogeochemistry model, the TEM (Fig. 1). The stable carbon isotope in delta notation (δ) describes the ratio of the heavy isotope to the light isotope in the sample (Rsam = (13C/12C)sam) relative to a known standard ratio, Rstd, which is Vienna Pee Dee Belemnite (VPDB) for carbon20 (Eq. 1). The deviation of this ratio-of-ratios from one is multiplied by 1000 to express isotope variations in parts per thousand (‰, permil). To express isotopic fractionation for the reaction A → B, we used a fractionation factor (α) defined in Eq. 220, where reactant A is in the numerator and product B is in the denominator. If α is larger than 1, the δ13C of product is isotopically more depleted in the heavy isotope than the δ13C of reactant, and if α is smaller than 1, the δ13C of product is more enriched in 13C than the δ13C of reactant.

$${\delta }^{13}C\,=\,({R}_{{sam}}{/R}_{{std}})\,-\,1$$
$$\alpha \,=\,\frac{{R}_{A}}{{R}_{B}}\,=\,\left(\frac{{\delta }^{13}{C}_{A}}{1000}\,+\,1\right)\Big/\left(\frac{{\delta }^{13}{C}_{B}}{1000}\,+\,1\right)$$

Terrestrial Ecosystem Model (TEM)

TEM is a commonly used biogeochemistry model and its CH4, soil, thermal, and hydrological dynamics have been evaluated in previous studies24,28,41,42,43,44. The CH4 dynamics module of TEM simulates CH4 production, oxidation, and three transport processes—diffusion, ebullition, and plant-mediated transport—between soil and atmosphere. Please refer to the details of TEM in Oh et al.25 and Liu et al.27.

In TEM wetland model, changes in CH4 concentrations (CM) at depth z and time t (∂CM(z,t)/∂t) are governed by Eq. 3, where Mp(z,t), Mo(z,t), Rp(z,t), and RE(z,t) are CH4 production, oxidation, plant-mediated transport, and ebullition rates, respectively, and ∂FD(z,t)/∂z represents flux divergence from gaseous and aqueous diffusion. CH4 is produced by methanogens in anaerobic soils (MP) and is calculated by multiplying maximum potential production rate (MGO) and limiting functions of substrate, soil temperature, pH, and redox potentials (SOM, MST, pH, and Rx, respectively) (Eq. 4). For this study, we assume that substrates for methanogens are mainly from soil organic carbon (SOC) derived from vegetation (Net Primary Productivity, NPP), where NPP(mon) is monthly NPP (gC m−2 month−1), NPPMAX is ecosystem-specific maximum monthly NPP, and f(CDIS(z)) describes the relative availability of organic carbon substrate at depth z (Eq. 5). The substrate availability changes depending on atmospheric CO2, meteorology, and soil properties67.

$$\frac{\partial {C}_{M}\left(z,t\right)}{\partial t}\,=\,{M}_{P}\left(z,t\right)\,-\,{M}_{O}\left(z,t\right)\,-\,\frac{\partial {F}_{D}\left(z,t\right)}{\partial z}\,-\,{R}_{P}\left(z,t\right)\,-\,{R}_{E}\left(z,t\right)$$
$$f\left({S}_{{OM}}\left(z,t\right)\right)\,=\,\left(1\,+\,\frac{{NPP}\left({mon}\right)}{{NP}{P}_{{\max }}}\right)f\left({C}_{{DIS}}\left(z\right)\right)$$

The produced CH4 is partly oxidized by methanotrophs and is calculated by the multiplying the maximum potential oxidation rate (OMAX) and limiting functions of CH4 concentration, soil temperature, soil moisture, redox potential, nitrogen deposition, diffusion limited by high soil moisture, and oxygen concentration (CM, TSOIL, ESM, ROX, NDP, DMS, and CO2 respectively) (Eq. 6). We use Michaelis-Menten kinetics with kCH4,LAM of 5 µM for the CH4 limitation (Eq. 7).


The remaining CH4 is emitted to the surface with three different transport processes. First, gaseous and aqueous diffusion (FD) occur due to concentration gradients of CH4 (∂CM(z,t)/∂t) (Eq. 8). The molecular diffusion coefficient (D) in different soil layers depends on soil texture and soil moisture. Ebullition (RE) occurs when CH4 bubble forms with CM greater than μmol L−1, and is calculated with a constant rate of Ke (1.0 h−1) (Eq. 9). Plant-mediated transport (Rp) occurs for plants that function as a direct conduit for CH4 to the atmosphere, and is functions of rate constant of 0.01 h−1, vegetation type, root density, vegetation growth, and soil CH4 concentrations (Kp, TRveg, fROOT, fGROW, and CM, respectively) (Eq. 10)68. Rp depends on ecosystem-specific plant functional types and increases in a warmer soil due to the increase in vegetation growth. In TEM model, the soil profile was divided into 1-cm layers, and soil temperature, moisture, and CH4 dynamics of TEM were simulated at an hourly time step24,27.

$${F}_{D}\left(z,t\right)\,=\,-D\left(z\right)\frac{\partial {C}_{M}\left(z,t\right)}{\partial t}$$

Methane stable carbon isotope module in TEM (isoTEM)

IsoTEM explicitly considers carbon isotopic fractionation processes for precursor organic matter (POM) and CH4 during production, oxidation, and transport process. The δ13C of POM (δ13C-POM) is determined by the global C3 and C4 vegetation distribution29 and is set to −27‰ and −13‰ for C3- and C4-only vegetation areas, respectively. The δ13C-POM for areas with mixed C3 and C4 vegetation is determined by the proportion of each type of photosynthetic pathway (Supplementary Fig. 1). We also incorporated long-term trends of atmospheric δ13C-CO2 into soil δ13C-POM changes. Atmospheric δ13C-CO2 became depleted in 13C by ≈2‰ during 1951–20165,33, and this signal is transferred to photosynthates and POM for CH4 emissions in wetlands69. We incorporated this trend with a 6-year carbon residence time between photosynthesis and CH4 emission in wetlands (Supplementary Fig. 2)31.

The CH4 is then produced in anaerobic soils by two distinct methanogen communities: hydrogenotrophic methanogens (HMs) use H2 and CO2 and acetoclastic methanogens (AMs) use acetate (CH3COO) for CH4 production34. Both mechanisms produce equimolar amounts of CO2 and CH4 from cellulose-like substrates. Using in situ observations from Holmes et al.19 the fractional contribution of the two methanogen communities is calculated based on a multiple regression analysis with the main environmental factors (Eq. 11). From the principal component analysis, Holmes et al.19 found a combination of environmental parameters including pH, vegetation type, soil organic carbon (SOC), and latitude are correlated with the dominant methanogenic pathway. The regression results show that fractional contribution of HMs (fHM) is positively correlated with latitude with a steep increase at 60°N (slope of 0.11 and 5.19 for latitudes below and above 60°N, respectively), and negatively correlated with pH (slope of −9.23) and SOC (slope of −0.7) (R2 of 0.41, p < 0.001) (Eq. 11, Supplementary Table 1, and Supplementary Fig. 3).

$${f}_{{HM}}\,=\,\left\{\begin{array}{c}{a}_{1}\times {lat}\,+\,b\times {pH}\,+\,c\times {SOC}\,+\,d\\ \,\cdots\, {for}\,{latitude} \, < \, {la}{{titude}}_{{step}}\\ {a}_{1}\times {lat}\,+\,{a}_{2}\times ({latitude}\,-\,{la}{{titude}}_{{step}})\,+\,b\times {pH}\,+\,c\times {SOC}\,+\,d\\ \cdots {for}\,{latitude} \, > \, {la}{{titude}}_{{step}}\end{array}\right.$$

The δ13C-CH4 produced by HMs and AMs more negative than the δ13C-POM, with the fractionation factors for HMs (αHM) ≈ 1.030–1.080 and for AMs (αAM) ≈ 1.000–1.040 (Eq. 12). The produced δ13C-CH4 is calculated using a binary mixing of CH4 pools from the two methanogen communities (Eqs. 13, 14).

$${\alpha }_{{HM}}\,=\,\frac{1000\,+\,{\delta }^{13}{C}_{{POM}}}{1000\,+\,{\delta }^{13}C{H}_{4,{prod},{HM}}},{\alpha }_{{AM}}\,=\,\frac{1000\,+\,{\delta }^{13}{C}_{{POM}}}{1000\,+\,{\delta }^{13}C{H}_{4,{prod},{AM}}}$$
$${\delta }^{13}C{H}_{4,{prod},{HM}}={\delta }^{13}{C}_{{POM}}-1000\times {ln}{(\alpha _{HM}}),{\delta }^{13}C{H}_{4,{prod},{AM}}={\delta }^{13}{C}_{{POM}}-1000\times {{{{{\rm{ln}}}}}}({\alpha }_{{AM}})$$
$${\delta }^{13}C{H}_{4,{prod}}\,=\,{{{{{{\rm{f}}}}}}}_{{{{{{\rm{HM}}}}}}}\,\times\, {\delta }^{13}C{H}_{4,{prod},{HM}}\,+\,(1\,-\,{{{{{{\rm{f}}}}}}}_{{{{{{\rm{HM}}}}}}})\,\times\, {\delta }^{13}C{H}_{4,{prod},{AM}}$$

The produced CH4 is partly oxidized by methanotrophs in aerobic soils, which prefer 12CH4, thus α for CH4 oxidation (αMO) ≈ 1.015–1.035 (Eq. 15). Then, the produced CH4 is transported to the atmosphere through three processes, plant-mediated transport, diffusion, and ebullition, with different fractionation factors αTP ≈ 1.000–1.030, αTD ≈ 1.000–1.010, αTE ≈ 1.000–1.005, respectively20 (Eq. 16).

$${\alpha }_{{MO}}\,=\,\frac{1000\,+\,{\delta }^{13}C{H}_{4,{prod}}}{1000\,+\,{\delta }^{13}C{H}_{4,{oxid}}}$$
$${\alpha }_{{TP}}\,=\,\frac{1000\,+\,{\delta }^{13}C{H}_{4,{prod}}}{{1000\,+\,\delta }^{13}C{H}_{4,{TP}}},{\alpha }_{{TE}}\,=\,\frac{1000\,+\,{\delta }^{13}C{H}_{4,{prod}}}{{1000\,+\,\delta }^{13}C{H}_{4,{TE}}},{\alpha }_{{TD}}\,=\,\frac{1000\,+\,{\delta }^{13}C{H}_{4,{prod}}}{{1000\,+\,\delta }^{13}C{H}_{4,{TD}}}$$

We calculated the oxidized and transported δ13C-CH4 based on “open system equations” at steady state to consider residual enriched CH4 after oxidation and transport processes70,71,72,73. We approximated that CH4 produced in the entire vertical soil column is either oxidized or transported in each hourly time step (Eq. 17). In Eqs. 17, 18, Mp(z,t), Mo(z,t), Rp(z,t), and RE(z,t) represent CH4 production, oxidation, plant-mediated transport, and ebullition rates, respectively, and ∂FD(z,t)/∂z represents flux divergence due to gaseous and aqueous diffusion for each soil layer z and time t. For simplicity, we defined effective transport fractionation, αT, by flux-weighting the proportions of fractionation factors of three transport processes in Eq. 19. The isotopic difference between oxidation and transport processes can be described by a fractionation factor, αT/MO, in Eq. 20. Given these conditions, isotopic signatures for oxidation and transport to the atmosphere (emission) can be written in Eqs. 21, 22. For more details, refer to Hayes74.

$$\mathop{\sum}\limits_{z}{M}_{P}\left(z,t\right)\,=\,\mathop{\sum}\limits_{z}{M}_{o}\left(z,t\right)\,+\,\mathop{\sum}\limits_{z}\frac{\partial {F}_{D}\left(z,t\right)}{\partial z}\,+\,\mathop{\sum}\limits_{z}{R}_{P}\left(z,t\right)\,+\,\mathop{\sum}\limits_{z}{R}_{E}\left(z,t\right)$$
$${f}_{{ox}}\,=\,\frac{\mathop{\sum}\limits_{z}{M}_{O}(z,t)}{\mathop{\sum}\limits_{z}{M}_{P}(z,t)},{f}_{{TP}}\,=\,\frac{\mathop{\sum}\limits_{z}{R}_{P}(z,t)}{\mathop{\sum}\limits_{z}{M}_{P}(z,t)},{f}_{{TE}}\,=\,\frac{\mathop{\sum}\limits_{z}{R}_{E}(z,t)}{\mathop{\sum}\limits_{z}{M}_{P}(z,t)},{f}_{{TD}}\,=\,\frac{\mathop{\sum}\limits_{z}\frac{\partial {F}_{D}\left(z,t\right)}{\partial z}}{\mathop{\sum}\limits_{z}{M}_{P}(z,t)}$$
$${\alpha }_{T}\,=\,\frac{({f}_{{TP}}{\alpha }_{{TP}}\,+\,{f}_{{TE}}{\alpha }_{{TE}}\,+\,{f}_{{TD}}{\alpha }_{{TD}})}{{f}_{{TP}}\,+\,{f}_{{TE}}\,+\,{f}_{{TD}}}$$
$${\alpha }_{T/{MO}}\,=\,\frac{{\alpha }_{{MO}}}{{\alpha }_{T}}\,=\,{\epsilon }_{T/{MO}}\,+\,1$$
$${\delta }^{13}C{H}_{4,{oxid}}\,=\,\frac{{\delta }^{13}C{H}_{4,{prod}}\,-\,\left(1\,-\,{f}_{{ox}}\right){\epsilon }_{T/{MO}}}{{\alpha }_{T/{MO}}\left(1\,-\,{f}_{{ox}}\right)\,+\,{f}_{{ox}}}$$
$${\delta }^{13}C{H}_{4,{emitted}}\,=\,\frac{{\alpha }_{T/{MO}}{\delta }^{13}C{H}_{4,{prod}}\,+\,{f}_{{ox}}{\epsilon }_{T/{MO}}}{{\alpha }_{T/{MO}}\left(1\,-\,{f}_{{ox}}\right)\,+\,{f}_{{ox}}}$$

Model optimization

We optimized 4 fractionation factors, αHM, αAM, αMO, and αTP, using in situ observations for six wetland ecosystem types (Eqs. 12, 15, 16). Since the fractionation factors for ebullition and diffusion are governed by physical processes, we set them as constants based on literature (αTE = 1.000, αTD = 1.005)20. The wetland ecosystems are divided into forested and non-forested wetlands for boreal (50–90°N), temperate (30–50°N/S), and tropical (<30°N/S) regions. To optimize parameters, we collected observation data from six sites representing each ecosystem (Supplementary Tables 24)35,37,38. For tropical wetlands, we used observation data from Burke et al.38,75. For forested wetlands, we used data from “Willow Marsh Trail” station, a swamp wetland dominated by hardwoods and Lemnaceae. For non-forested wetlands, we used data from “St. Petersburg” site where Sawgrass is the dominant vegetation. For temperate wetlands, we used data from Kelly et al.37. For forested wetlands, we used data from “S2 Bog” where is entirely forested with Picea mariana. For non-forested wetlands, we used data from “Junction Fen” where is treeless and dominated by Carex oligosperma. For Arctic wetlands, we used data from McCalley et al.35. For forested wetlands, we could not find δ13C-CH4 data from the well-drained “Palsa” occupied by woody plants, mosses, and ericaceous. Thus, we used δ13C-CH4 data from “Sphagnum” site that is in the transition between the Palsa and Eriophorum sites, and showed similar CH4 fluxes as the “Palsa” site. For non-forested wetlands, we used data from the “Eriophorum” site.

Besides the observed meteorology from field sites, we also used CRU time-series version 4.01 to fill missing meteorological inputs76. We then used the Shuffled Complex Evolution Approach in R language (SCE-UA-R) to minimize the difference between simulated and observed δ13C-CH477. For each site, 20 ensembles were run using SCE-UA-R with 10,000 maximum loops per parameter ensemble, and all of them reached steady state before the end of the loops. Our optimization results show that isoTEM captures the magnitude and seasonality of observed soil CH4 fluxes and δ13C-CH4 (Supplementary Fig. 4).

Simulation setup

To estimate spatially- and temporally-varying δ13C-CH4 from global wetlands, we used spatially explicit data of land cover, soil pH and textures, meteorology and leaf area index (LAI)24,27. Land cover, soil pH and textures were used to assign vegetation-specific and texture-specific parameters to a grid cell78,79,80. Meteorological inputs were derived from historical air temperature, precipitation, vapor pressure, and cloudiness from gridded CRU time-series version 4.0176. We used monthly LAI derived from satellite imagery81 to prescribe LAI for each 0.5° × 0.5° grid cell. All other parameters except fractionation factors were set the same as in Liu et al.27. We simulated global wetland CH4 fluxes and their isotopic ratios between 1984 and 2016 at a spatial resolution of 0.5° × 0.5° with a 50-year spin-up to let the carbon isotopic composition of carbon pools come to a steady state.

Because various wetland inundation data exist82, we first assumed that every global land grid cell can potentially be saturated, thus this product can be used with any wetland inundation data in future studies. To fill the grid cells without wetland types, we set forested and non-forested wetlands based on global vegetation types (Supplementary Fig. 5). In our analyses, simulated ecosystem-specific δ13C-CH4 from wetlands was flux weighted for each grid cell, based on CH4 emissions simulated by TEM defined over the static inundation data from Matthews and Fung (Supplementary Fig. 6a)49.

Model-data comparison

Site level

We compared our model results with previously published data from 58 in situ measurements compiled by Holmes et al.19 and 66 in situ measurements by Sherwood et al.13. Holmes et al.19 compiled latitude, fraction of HM and AM, pH, vegetation, and δ13C-CH4 to understand factors affecting the methanogenic pathway in global wetlands. The wetland database of Sherwood et al.13 includes literature reference, latitude, wetland types, and measurement methods. After combining overlapped data of Holmes et al.19 and Sherwood et al.13 and excluding data that we used for our model optimization35,37,38, 70 sites remained for site-level validation (Supplementary Fig. 11 and Supplementary Data 1). Due to a possible mismatch of soil and vegetation properties, and wetland distribution of grid cells between model and observation, we compared observed δ13C-CH4 with simulated δ13C-CH4 of the sampling year within two adjacent grid cells (1° × 1°) of the observation.

Regional level

We used aircraft air samples from 3 regions in Alaska from the Carbon in Arctic Reservoirs Vulnerability Experiment (CARVE)83,84. From 2012 to 2015, CARVE collected airborne measurements of atmospheric chemical components and relevant land surface parameters in the Alaskan Arctic to provide insights into Arctic carbon cycling. During the flights, flask-air samples were collected then sent to NOAA GML for measurements of 50 trace gases including CO2, CH4, CO, OCS, NMHCs, and then sent to INSTAAR for and the isotopic composition of CO2 and CH4. After excluding airborne data with flags, there are 1476 measurements during the sampling period.

In situ flux observations collected across Alaskan wetlands show an average of −65‰ but a large 9‰ variation, due to the complex vegetation and soil properties40. To compare the spatial variability of wetland δ13C-CH4, we divided the Alaskan continent into three regions: North Slope, interior, and southwest Alaska based on latitude (62–68 °N, 52–62 °N and 140–155 °W, and 52–62 °N and 155–170 °W for North Slope, interior, and southwest Alaska, respectively). We used Miller-Tans plots to identify the source signatures of δ13C-CH4 from wetlands using the airborne measurements39. To identify wetland isotopic signatures, we removed measurements that may have effects from fossil fuel emission (C3H8 < 300 ppt), biomass burning (CO < 300 ppb), and transport influence (Altitude < 1500 m), and we set the background altitude to >5000 m. After plotting the data, 2014 was excluded due to limited data and small R2 (Supplementary Table 5).

Uncertainty and sensitivity tests

Long-term trends in wetland δ 13C-CH4 from observations

We considered latitude, pH, and soil carbon as key parameters that determine variability of wetland δ13C-CH4 to run a linear regression using the site-level observations collected from global wetlands since the early 1980s (Supplementary Data 1). We added year as additional parameter for the linear regression and see if it improves the fit with data. The regression results show that wetland δ13C-CH4 is negatively correlated with year, latitude, and SOC (slope of −0.11, −0.10, and −0.20, respectively), and positively correlated with pH (slope of 2.21) (R2 of 0.30, p < 0.001) (Eq. 23, Supplementary Fig. 17, and Supplementary Table 6). The regression without year as a parameter showed smaller coefficient (R2 of 0.25, p < 0.001).

$${\delta }^{13}{{{{{\rm{C}}}}}}-{{{{{{\rm{CH}}}}}}}_{4}\,=\,a\times {lat}\,+\,b\times {pH}\,+\,c\times {SOC}\,+\,d\,\times\, {year}\,+\,e$$

Markov Chain Monte Carlo for the fraction of HM (fHM)

We used a Markov Chain Monte Carlo (MCMC) approach for parameter uncertainty estimation for fHM. MCMC is a method for estimating the posterior probability density function for asset of parameters, given priors on those parameters and a set of observations45. We used independent, uniform prior probability density functions for each parameter in Supplementary Table 1. Thirty-nine data points from Holmes et al.19 were used to constrain the model. Gaussian errors were assumed. We generated a Markov chain with 100,000 elements to estimate the joint posterior probability density functions. The chain converged after about 10,000 elements. We used the posterior probability density function to estimate the uncertainty of parameter (Supplementary Table 1).

Sensitivity test with meteorological and substrate inputs, fHM, and inundation

We conducted 8 sensitivity tests of meteorology and substrate inputs. Specifically, we altered air temperature by ±3 °C, precipitation by ±30%, and atmospheric CH4 abundance by ±30%, and NPP by ±30%, uniformly for each grid cell, while maintaining all other variables at their default isoTEM values. We also varied parameters for fHM based on the uncertainty range from MCMC (Supplementary Table 1). We further varied a wetland inundation using satellite-driven Surface WAter Microwave Product Series-Global Lakes and Wetlands Database (SWAMPS-GLWD)48.

Forward modeling using TM5 atmospheric model

Global mass balance for bottom-up inventory

We adjusted global long-term mean fossil fluxes to match the simulated growth rate of CH4 during 1984–2016 and the 1998–2016 mean of δ13C-CH4 with observation (Table 1 and Supplementary Table 11). Lan et al.26 showed that there is an offset of simulated global mean δ13C-CH4 when using EDGAR 4.3.2 inventory as the inventory underestimates fossil fluxes. To remove the offset and compare our scenarios fairly, we adjusted fossil fluxes between 170 and 190 TgCH4yr−1 (Supplementary Fig. 19), within the uncertainty range in Schwietzke et al.9. To satisfy the global mass balance, we ran one box model that included CH4 sources of biogenic, fossil and biomass/biofuel emissions, with corresponding isotopic signatures, and CH4 sinks due to reaction with OH, Cl, and O(1D) and soil bacteria, all with different fractionation factor. When we increased or decreased fossil fluxes, we accordingly decreased or increased ruminant flux, respectively, so the total annual CH4 fluxes followed the observed atmospheric CH4 growth rate, and the long-term mean total emission was set to 536–538 TgCH4yr−1 during 1984–2016. For more details on the setup and equations for global mass balance, refer to Lan et al.26.

Data sources for CH4 emissions and its isotopic source signatures

We used the bottom-up inventory constructed by Lan et al.26 (Supplementary Table 8). In specific, for CH4 emissions, we used GFED 4.1 s for biomass burning for 1997–201685 and annual emissions from the Reanalysis of Tropospheric chemical composition project before 1997, and the EDGAR 4.3.2 inventory for other anthropogenic emissions for 1984–201686. For emissions from geological seeps, we used gridded emission from Etiope et al.87. Emission estimates from wild animals and termites were adopted from Bergamaschi et al.88. For δ13C-CH4 source signature, fossil fuel source signature data were based on the global δ13C-CH4 source signature inventory 202089, where the data were categorized by coal gas, conventional gas, and shale gas. Biomass burning, biofuel burning, ruminant, and wild animal δ13C-CH4 data were based on the global maps of C3/C4 distribution29. The geological seeps δ13C-CH4 data were from Etiope et al.87.

TM5 atmospheric modeling of CH4 and δ 13C-CH4

Atmospheric CH4 mole fractions and δ13C-CH4 were simulated from 1984 to 2016 by coupling the surface fluxes and isotope source signatures from the bottom-up inventory with the TM5 tracer transport model driven by ECMWF ERA Interim meteorology with the 4DVAR branch of the TM5 model90,91. TM5 was run globally at 6° × 4° over 25 vertical sigma-pressure hybrid levels, for total CH4 and 13C-CH4. For each source type, 13C-CH4 fluxes were derived from total CH4 fluxes and source-specific isotope source signatures. We spun up our model during 1984–1999 and selected 2000–2016 to compare with atmospheric observations to ensure our spin-up period was sufficient for equilibration of atmospheric δ13C-CH4 inter-hemispheric gradient26,92. As per Lan et al.26 we applied tropospheric Cl sink of Hossaini et al.51 and the OH field from Spivakovsky et al.14 with a fractionation factor of −3.9‰. The CH4 sinks varied spatially and seasonally but did not change interannually. For more details on setup for TM5 modeling, refer to Lan et al.26.

Atmospheric CH4 and δ 13C-CH4 measurement

Observational data of atmospheric CH4 and δ13C-CH4 used to evaluate model results are from flask-air measurements from NOAA’s Global Greenhouse Gas Reference Network26,54. The flask-air samples was analyzed for δ13C-CH4 at the Institute of Arctic and Alpine Research (INSTAAR), University of Colorado, Boulder. Gas chromatography-Isotope-ratio mass spectrometry (GC-IRMS) is used for δ13C-CH4 analysis5. The δ13C-CH4 in air measurements are referenced against the Vienna Pee Dee Belemnite (VPDB) standard (Eq. 1). A subset of the observation sites predominantly influenced by well-mixed background air is used to construct a Marine Boundary Layer (MBL) zonally averaged surface using methods developed by Masarie and Tans (1995)93, to represent the observational-based global long-term trend and north–south gradient. This includes 31 sites with CH4 measurements during study period of 1984–2016 and 10 of which with δ13C-CH4 measurements staring in 1998 (Supplementary Fig. 21 and Supplementary Table 10). More details on the MBL data products and uncertainties can be found at For model-observation comparisons, model results from the same set of MBL sites are sampled, and the same calculation methods are applied to model results and observations for global long-term and north–south gradient. The north–south gradient was calculated as the difference of atmospheric δ13C-CH4 between 60–90 °S and 60–90 °N.

Atmospheric modeling with transient inundation data for Scenarios E-H

Since we used static wetland inundation data49 for our default Scenarios A–D, we used transient wetland inundation data from Poulter et al.48 and ran TM5 atmospheric model (Supplementary Figs. 2630 and Supplementary Table 11). Same as Scenarios A–C, we constructed Scenarios E–G with different wetland isotopic signature maps as inputs for TM5 atmospheric modeling in 1984–2016. In specific, the first uses a globally uniform wetland δ13C-CH4 of −62.3‰, the mean wetland signature from Ganesan et al.23 (referred to as Scenario E), the other uses a static wetland isotope spatial map from Ganesan et al.23 (referred to as Scenario F), and the last used spatially- and temporally-resolved maps from isoTEM (referred to as Scenario G).

The wetland fluxes for Scenarios E–G are based on Liu et al.27 and transient inundation48 but applied an increase in fluxes after 2006 by hypothesizing that the microbial wetland emission is a dominant driver of post-2006 atmospheric CH4 increase (Supplementary Fig. 26), same as Scenarios A–C. We also conducted the global mass balance by adjusting global long-term mean fossil fluxes between 160 and 180 TgCH4yr−1 for Scenarios E–G to match the simulated growth rate of CH4 during 1984–2016 and the 1998–2016 mean of annual δ13C-CH4 with observations.

Scenarios E–G reproduced the observed global CH4 growth rate during 1984–2016 and the global long-term mean δ13C-CH4 with observation during 1998–2016 (Supplementary Fig. 28), as we set the fluxes based on the mass balance. However, Scenarios E–G with transient inundation data underestimated the north–south δ13C-CH4 gradient (0.27 ± 0.06‰) compared with observations (0.45 ± 0.05‰) (Supplementary Fig. 29). Thus, we ran an additional scenario H that increased emissions from boreal wetlands by 2.5 times over the original transient data (Supplementary Fig. 26 and Supplementary Table 11), which improved the match with the observed north–south δ13C-CH4 gradient (0.39‰) (Supplementary Fig. 29). The site-level comparison with atmospheric δ13C-CH4 from 10 observation sites also confirmed that Scenario H more closely reproduced the observation (Supplementary Fig. 30). This implies that the transient inundation data from Poulter et al.48 may need more wetland emissions from boreal regions as found in static inundation data49 (Supplementary Fig. 6) and other satellite-derived inundation data94.