Main

Arctic soils are considered to be a substantial net emission source of methane to the atmosphere. Current process-based biogeochemistry models and observation-based atmospheric inversions have estimated this source to be between 15 and 50 Tg CH4 yr−1, which accounts for 20–25% of global natural methane emissions12. Furthermore, process-based models predict that methane emissions will be two to three times greater by 21002,17,18, as warmer temperatures will increase both the rate of decomposition and availability of soil organic carbon (SOC) from permafrost-affected soils in addition to SOC from recently dead vegetation for decomposition16,21.

However, methane emissions are mainly confined to the 13% of Arctic landscapes composed of organic-rich soils where anaerobic processes dominate16. The rest are composed of mineral-rich soils, from which recent field studies have identified net annual methane sinks during growing seasons4,5,6,7. This difference may be controlled by differences in methanotroph community composition (Fig. 1)22. In wet organic soils, a fraction of methane produced by methanogenic archaea (methanogens, MGs) is oxidized by methanotrophic bacteria (methanotrophs) and the remainder is mostly emitted into the atmosphere (Fig. 1a). The methanotrophs in these wet organic soils may be low-affinity methanotrophs (LAMs) that require >600 ppm of methane (by moles) for their growth and maintenance23. But in dry mineral soils, the dominant methanotrophs are high-affinity methanotrophs (HAMs), which can survive and grow at a level of atmospheric methane abundance ([CH4]atm) of about 1.8 ppm (Fig. 1b)24.

Fig. 1: A schematic diagram of XPTEM-XHAM.
figure 1

a,b, The model simulates CH4 production by MGs and oxidation of CH4 by LAMs in wetlands (a) as well as the oxidation of [CH4]atm by HAMs in uplands (b). We used static inundation data33 to divide the Arctic landscape into wetland and upland regions but later varied the regions on the basis of time-varying inundation data34,35. Changes in MICbiomass of MGs and HAMs (grey dashed lines) depend on ε and mE, and are tracked as a function of time (t (h)). PSOC dynamics are added to account for SOC that is accessible from thawing permafrost when soil temperatures at the corresponding depths become higher than 1 °C. The dark blue arrow refers to PSOC dynamics, dark red arrows refer to microbial dynamics and grey arrows refer to processes from the original TEM.

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Quantification of the previously underestimated HAM-driven methane sink is needed to improve our understanding of Arctic methane budgets. Process-based methane models have overestimated Arctic methane emission by 5–10 Tg CH4 yr−1 when compared with observation-based atmospheric inversions11,12. Given that 87% of the Arctic is dominated by mineral-rich soils, the HAM-driven methane sink may greatly reduce current area-integrated net methane emissions. Furthermore, the positive feedbacks of methane emission that result from additional accessible permafrost soil organic carbon (PSOC) may be partially suppressed by negative feedbacks from the high activities of HAMs at future increased surface temperatures and [CH4]atm (ref. 8).

Previous studies show that simulation of explicit microbial dynamics of MGs and HAMs improve model estimates of the magnitude and seasonality of methane sources and sinks8,25. Microbial dynamics may also cause additional complexity due to different microbial physiology between MGs and HAMs19,26. Recent laboratory and field studies show that microbial communities adjust their active microbial biomass (MICbiomass) in warmer soils depending on the microbial growth efficiency (ɛ) and maintenance energy (mE)19; ɛ represents the growth efficiency of MICbiomass per unit of substrate consumed and it is a factor of ten smaller for MGs (ɛ = 0.05) than for HAMs (ɛ = 0.5)20,27; mE (that is, the rate of metabolic energy generation needed to maintain MICbiomass) increases exponentially with temperature for all microbes, including MGs and HAMs, reflecting the fast turnover associated with cell mortality (equation (16))19,28. These processes are important for current and future Arctic methane budgets; however, current process-based methane models have not considered such microbial dynamics.

First, this study estimates current pan-Arctic soil methane emissions and consumptions while accounting for microbial and PSOC dynamics; second, it evaluates the magnitude and spatial variability of those estimates; and, third, projects pan-Arctic changes in soil methane emissions and consumptions through 2100. These projections take into account enhanced methane emissions due to increased available PSOC and stimulated HAM methane consumptions, as well as the different physiological responses of MGs and HAMs at warmer temperatures.

To address these objectives, we implemented explicit microbial dynamics for MGs and HAMs into a biogeochemistry model; that is, the terrestrial ecosystem model (TEM) (Fig. 1)9,10. In a wetland system, we simulated methane oxidation by LAMs as a function of environmental parameters. We fixed LAM MICbiomass due to its limited control on Arctic wetland methane emissions (Supplementary Method 6)29,30. We thus calculated changes in MICbiomass of MGs and HAMs as a function of ɛ, mE and environmental parameters, and set mE as a constant with a temperature of 0 °C (refs. 19,28). To identify the effects of PSOC, we modified methane production to consider the amount of SOC from vegetation (net primary productivity, NPP) and thawing permafrost in wetland ecosystems. The complete model with microbial and PSOC dynamics is referred to as the explicit permafrost TEM-explicit HAM model (XPTEM-XHAM, Fig. 1; see Methods).

We conducted two additional sets of simulations for a factorial analysis to assess the effects of microbial and PSOC dynamics (Table 1). First, we developed the permafrost TEM-HAM model (PTEM-HAM), which considers HAMs and PSOC as XPTEM-XHAM does, but does not simulate the explicit microbial dynamics of MGs and HAMs. Second, we used a version of TEM that simulates the production and oxidation of methane by MGs and LAMs, respectively, but that does not consider HAMs, permafrost nor microbial dynamics (denoted TEM)9,10. For XPTEM-XHAM and PTEM-HAM, we optimized key parameters of methane production and oxidation for alpine tundra, wet tundra and boreal forest (see Methods and Supplementary Methods).

Table 1 A summary of the three models used in this study
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The three models simulated methane dynamics north of 50 °N, including low- (50–65 °N) and high- (north of 65 °N) Arctic regions at a spatial resolution of 0.5° latitude by 0.5° longitude. Gridded Climatic Research Unit (CRU) data were used as meteorological inputs for a contemporary simulation from 2000 to 201631, and inputs from IPCC representative concentration pathways (RCPs) 2.6, 4.5 and 8.5 were used for projections to 210032. For PTEM-HAM and XPTEM-XHAM, we used the Northern Circumpolar Soil Carbon Database v.2 (NCSCDv2) to estimate PSOC at different soil depths16. The simulated methane emission from wetlands and consumption from uplands were area-integrated for each grid cell on the basis of static fractional inundation data33.

For a sensitivity test of the surface area of the wetlands and uplands of XPTEM-XHAM, we used time-varying inundation data from the Satellite-driven Surface Water Microwave Product Series—Gobal Lakes and Wetlands Database (SWAMPS-GLWD) from 2000 to 201234 and transient inundation fraction simulated by Community Land Model v.5.0 from 2017 to 210035. We further conducted XPTEM-XHAM sensitivity tests of wetland emission and upland consumption to changes in meteorology and substrate inputs from 2000 to 2016. For XPTEM-XHAM from 2017–2100, we varied mE of MGs and HAMs to increase with temperature to model microbial physiological responses (equations (13C), (13D) and (16)). Finally, for RCP 8.5 of XPTEM-XHAM, we varied coenzyme Q10 for methane production and oxidation, and fixed [CH4]atm to the contemporary level (1.8 ppm) to test model sensitivity to temperature and [CH4]atm changes (see Methods and Supplementary Methods).

Our simulations from 2000 to 2016 show the effects of PSOC and microbial dynamics on wetland methane emissions (Fig. 2a, Extended Data Figs. 1–3, Supplementary Figs. 7 and 8, Supplementary Table 8). Compared with PTEM-HAM, TEM estimates larger wetland methane emissions in the low-Arctic (37.70 versus 26.83 Tg CH4 yr−1) but smaller emissions in the high-Arctic (3.73 versus 6.76 Tg CH4 yr−1). TEM simulates higher emissions in the low-Arctic as its parameterization on substrate depends only on NPP, which is higher in the low-Arctic (Extended Data Fig. 3c). For PTEM-HAM, methane emission is based on NPP and PSOC, with more prevalent PSOC in the high-Arctic (Extended Data Fig. 3d). In comparison with PTEM-HAM, XPTEM-XHAM simulates larger methane wetland emissions in the low-Arctic (32.60 Tg CH4 yr−1) due to the high MICbiomass of MGs that persists late into the growing season, extending the period of methane emissions (Extended Data Fig. 1)25.

Fig. 2: Annual estimates of the Arctic methane budget by three models for 2000–2016.
figure 2

a–c, Annual estimates of wetland methane emission (a), upland methane consumption (b) and net methane emission (c) averaged over 2000–2016 for TEM (red), PTEM-HAM (yellow) and XPTEM-XHAM (blue) for the pan-Arctic region (north of 50 °N), including the low-Arctic between 50–65 °N and high-Arctic north of 65 °N. The error bars represent 1σ of TEM, PTEM-HAM and XPTEM-XHAM, which were determined by varying the optimized parameters from ensemble simulations. The top-down inversion in c (grey) represents posterior estimates of mean and 1σ of net wetland methane fluxes by CarbonTracker-CH4 in 2000–2010 (ref. 11).

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By comparing the results from XPTEM-XHAM and TEM, we more than double the upland methane sink by including microbially dynamic HAMs (Fig. 2b). TEM estimates upland sinks of 4.16 Tg CH4 yr−1 north of 50 °N. After considering HAM and microbial dynamics, upland sinks for PTEM-HAM and XPTEM-XHAM increase to 6.15 and 9.52 Tg CH4 yr−1, respectively, which is consistent for both the low- and high-Arctic. This additional ~5.5 Tg CH4 yr−1 has not been accounted for in most current process-based methane models that do not consider microbial dynamics of HAMs1,17,18.

By integrating wetland emission and upland consumption, net Arctic methane emission of XPTEM-XHAM and PTEM-HAM are closer to posterior fluxes estimated by an observation-based inversion, CarbonTracker-CH4 (Fig. 2c)11. Starting with a previous estimate of 35 ± 10 Tg CH4 yr−1 for wetland emissions north of 50 °N, CarbonTracker-CH4 reduced net emission to 26 ± 5 Tg CH4 yr−1 during its optimization. Our estimates of increased upland methane sinks are equivalent to at least half of the difference between estimates from before and after the inversion11,12.

From 2000 to 2012, our XPTEM-XHAM sensitivity test using time-varying inundation data simulates less Arctic net methane emission due to smaller annual inundation fraction in SWAMPS-GLWD compared with the static map north of 50 °N (Extended Data Fig. 4 and Supplementary Fig. 9)33,34. Additional sensitivity tests to meteorological and substrate changes show that wetland emission is sensitive to temperature, NPP, PSOC and water table depth, whereas upland consumption is sensitive to temperature, soil moisture and [CH4]atm (Supplementary Fig. 10).

We validated the magnitude and spatial variability of the three models using site-level and regional observations (see Methods). In situ measurements from 46 flux observation sites confirm that XPTEM-XHAM reproduces both methane emission and consumption (with R2 values of 0.65 and 0.87, and r.m.s.e. values of 38.21 and 0.52 mg m−2 d−1, respectively) (Supplementary Table 5 and Extended Data Fig. 5)5,7. Compared with XPTEM-XHAM, r.m.s.e. values in PTEM-HAM and TEM were 10% and 60% larger, respectively, on average for all sites. We also compared the observed and simulated regional net methane fluxes of three regions for emission (Alaska, Hudson Bay Lowlands, West Siberian Lowlands) and two for consumption (Northeast and West Greenland) (Fig. 3a, Supplementary Fig. 8, and Supplementary Tables 6 and 7)4,6,13,14,15. XPTEM-XHAM generally matched emission estimates for the West Siberian Lowlands and consumption in upland West Greenland, whereas PTEM-XHAM and TEM agreed poorly. All three models estimate less methane emissions from Alaska than observed15, possibly because we did not consider methane emissions from aquatic sources such as thermokarst lakes36.

Fig. 3: The spatial variability of annual net methane flux north of 50 °N for XPTEM-XHAM.
figure 3

a,b, The net methane fluxes (positive for emission and negative for consumption) averaged for the contemporary period during 2000–2016 (a), as well as the difference between 2086–2100 and 2000–2016 for RCP 8.5 (b), are shown. The dotted longitudes are at 30° intervals and the dotted latitude is at 65 °N. Panel a also shows the five regions used for regional model-data comparisons (black boxes) (Supplementary Tables 6 and 7).

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Our future simulation shows that both PTEM-HAM and XPTEM-XHAM project 70 and 100% increase in wetland methane emissions by 2100 for RCP 8.5, respectively, due to increased temperature and more accessible PSOC (Figs. 3b, 4a and Supplementary Fig. 11). This increase is larger than the 59% increase predicted by TEM. However, the increase in wetland emission is mostly compensated by an increase in upland consumption by 2100 (22 and 35 Tg CH4 yr−1 for PTEM-HAM and XPTEM-XHAM, respectively) due to increased HAM activity at increased temperature and [CH4]atm (Supplementary Figs. 11–13). This leads to a reduced increase in net methane emission by 2100 for XPTEM-XHAM and PTEM-HAM (35 Tg CH4 yr−1) when compared with TEM (55 Tg CH4 yr−1) and other previous projections (40–120 Tg CH4 yr−1)2,17,18. The net methane emission increase is less for RCP 2.6 and 4.5 than for RCP 8.5 in all three models (Fig. 4a and Supplementary Fig. 11).

Fig. 4: Projected annual net Arctic methane emissions from 2017 to 2100 north of 50 °N.
figure 4

a, Annual estimates of pan-Arctic net methane emission for XPTEM-XHAM (baseline, blue), PTEM-HAM (yellow) and TEM (red). b, Annual estimates of pan-Arctic net methane emission for XPTEM-XHAM (blue) and XPTEM-XHAM with physiological responses of MG and HAM to temperature change with varying mE (green), based on RCPs 2.6 (dotted), 4.5 (dashed) and 8.5 (solid). The shaded error bars represent 1σ of TEM, PTEM-HAM and XPTEM-XHAM, and were determined by varying the optimized parameters from ensemble simulations. The mean (symbols) and 1σ (bars) in 2100 for each metric are shown to the right in both a and b. Panel a also shows mean (*) and 1σ (bars) of previous estimates of net methane emission estimated by process-based methane models2,17,18.

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Furthermore, our simulation of XPTEM-XHAM, which incorporates microbial physiology of MGs and HAMs with varying mE, shows that net Arctic methane emission can potentially decrease in the future (Fig. 4b and Supplementary Fig. 14). Increases in both methane production and oxidation are limited by decreases in MICbiomass growth for MGs and HAMs, respectively, due to an exponential increase in mE (equation (16))19,28. As mE increases with temperature, growth in MICbiomass slows more substantially for MG, because the ɛ of MGs (0.05) is a factor of ten smaller than the ɛ of HAMs (0.5)20,27. As a result, in our simulation, HAMs survive better in the warmer Arctic due to their physiological response.

Our sensitivity test of XPTEM-XHAM using time-varying inundation simulated by community land model 5.0 does not change the projection considerably as the simulated inundation fraction increases by only 5% between 2017 and 2100 (Extended Data Fig. 6)35. XPTEM-XHAM also shows a sensitivity of net methane emissions to both temperature (5 Tg CH4 yr−1) and [CH4]atm (10 Tg CH4 yr−1) by 2100 for the RCP 8.5 scenario (Supplementary Fig. 15).

Our simulation emphasizes that the current understanding of Arctic methane feedback may be incomplete (Extended Data Fig. 7)8. Previous studies predicted strong positive feedbacks between temperature and methane emission due to more accessible SOC from thawing permafrost; however, additional negative feedbacks between temperature and HAMs may suppress this feedback loop. This study also shows we need more field and laboratory experiments to understand HAM and MG physiological responses to environmental changes22,37.

Although the new model significantly revises estimates of net Arctic methane emission, there are processes that current models, including ours, have not considered. We do not capture the complex Arctic hydrological and vegetation dynamics38,39, which may influence our estimates of both methane production and consumption. We focused on terrestrial ecosystems without considering potential large methane emissions from aquatic systems, whose magnitude and spatial distribution may change36,40. We used observed wetland methane emissions to optimize methane production and oxidation where the fraction of each is uncertain25. More observations of subsurface vertical processes using isotopic labelling analysis and inhibitor techniques will better constrain future models41.

In conclusion, we show that the microbial dynamics of HAMs are an important component of the current Arctic methane budget as our estimate more than doubles that of upland sinks. We also find that our revised estimates, which incorporate microbial and PSOC dynamics, better match site-level and regional observations and observation-based inversions. This model projects a smaller increase in net methane emission by 2100 than previous models, as the increase in wetland emission (due to more accessible PSOC) is mostly offset by the increase in upland consumption by HAMs. A potential decrease in future net methane emission is projected after including the microbial physiology of HAMs and MGs. This study highlights the need to incorporate more detailed microbial dynamics into process-based methane models to better constrain the Arctic methane budget.

Methods

Model description

We incorporated explicit microbial dynamics of HAMs and MGs—including PSOC dynamics—into TEM, a process-based biogeochemistry model.

TEM

TEM is one of few biogeochemistry models that simulate net methane consumption in Arctic mineral soils, and its methane, soil thermal and hydrological dynamics have been evaluated in previous studies9,10. The methane dynamics module of TEM simulates methane production, oxidation and three transport processes between soil and atmosphere. In a wetland system, changes in methane concentrations (CMe) at depth z and time t (∂CMe(z,t)/∂t) are governed by equation (1), where Mprod(z,t), Moxid(z,t), Rpl(z,t) and Re(z,t) are methane production, oxidation, plant-mediated transport and ebullition rates, respectively, and ∂Fdiv(z,t)/∂z represents flux divergence due to gaseous and aqueous diffusion.

$$\frac{{{\it{\partial}} {{C}}_{\mathrm{Me}}\left( {z,t} \right)}}{{\partial t}} = M_{\mathrm{prod}}\left( {z,t} \right) - M_{\mathrm{oxid}}\left( {z,t} \right) - \frac{{\partial F_{\mathrm{div}}\left( {z,t} \right)}}{{\partial z}} - R_{\mathrm{pl}}\left( {z,t} \right) - R_{\mathrm{e}}\left( {z,t} \right) \ldots$$
(1)

Methane is produced in anaerobic soils by MGs and is calculated by the product of maximum potential production rate (MGO) and limiting functions of organic matter (OM) substrate, soil temperature, pH and redox potentials (SOM, Tsoil, H and X, respectively) (equation (2)). We used limiting factors of H and X to consider enzymatic activity and the relative availability of electron acceptors (for example, O2, NO3–, SO4–2, Fe+3, Mn+4) for methane production. The limiting function of substrate (f(SOM(z,t)) is mainly dependent on SOC derived from vegetation (NPP), where NPPmon is monthly NPP (gC m–2 month–1), NPPmax is ecosystem-specific maximum monthly NPP and f(CDIS(z)) describes the relative distribution of organic matter substrate at depth z (equation (3)). For the substrate availability, we calculated changes in vegetation carbon using atmospheric CO2 concentrations, transient temperature, precipitation, vapour pressure and soil texture42.

$$M_{\mathrm{prod,TEM}}\left( {z,t} \right) = {{M}}_{{\mathrm{GO}}}f\left( {{S}_{\mathrm{OM}}\left( {z,t} \right)} \right)f\left( {T_{\mathrm{soil}}\left( {z,t} \right)} \right)f\left( {H\left( {z,t} \right)} \right)f\left( {X\left( {z,t} \right)} \right) \ldots$$
(2)
$$f\left( {S_{\mathrm{OM}}\left( {z,t} \right)} \right) = \left( {1 + \frac{\mathrm{NPP}_{\mathrm{mon}}}{\mathrm{NPP}_{\mathrm{max}}}} \right)f\left( {C_{\mathrm{DIS}}\left( z \right)} \right) \ldots$$
(3)

The produced methane diffuses into aerobic soils and is oxidized by LAMs, which is calculated as the product of the maximum potential oxidation rate (Omax) and limiting functions of methane concentration, soil temperature, soil moisture, redox potential, nitrogen deposition, diffusion limited by high soil moisture and oxygen concentration (CMe, Tsoil, ESM, Rox, Ndp, DSM and \(C_{{\mathrm{O}}_{2}}\) respectively) (equation (4)). The Michaelis–Menten constant for methane oxidation was set to 5 µM (\(k_{{\mathrm{Me}},{\mathrm{LAM}}}\)) (equation (5))9,23.

$$\begin{array}{l}M_{\mathrm{oxid},{\mathrm{TEM}}}\left( {z,t} \right) = O_{\mathrm{max}}f\left( {C_{\mathrm{Me}}\left( {z,t} \right)} \right)f\left( {T_{\mathrm{soil}}\left( {z,t} \right)} \right)f\left( {E_{\mathrm{SM}}\left( {z,t} \right)} \right)\\ f\left( {R_{\mathrm{ox}}\left( {z,t} \right)} \right)f\left( {N_{\mathrm{dp}}\left( {z,t} \right)} \right)f\left( {D_{\mathrm{SM}}\left( {z,t} \right)} \right)f(C_{\mathrm{O}_{2}}\left( z \right)) \ldots \end{array}$$
(4)
$$f\left( {C_{\mathrm{Me}}\left( {z,t} \right)} \right) = \frac{{C_{\mathrm{Me}}(z,t)}}{{k_{\mathrm{Me},{\mathrm{LAM}}} + C_{\mathrm{Me}}(z,t)}} \ldots$$
(5)

The residual methane is emitted to the surface through three transport processes. First, gaseous and aqueous diffusion occur due to concentration gradients of methane (∂CMe(z,t)/∂t) following Fick’s law through soil pores (equation (6)). The molecular diffusion coefficient (D) in different soil layers was calculated based on soil texture and soil moisture. We also have a simple limitation of diffusion on temperature, that there will be no diffusion when temperature is below 0 °C. Second, ebullition occurs when methane bubble forms (that is, when CMe is greater than 500 μmol l−1 in saturated soils) \(f_{{\mathrm{e}}(C_{{\mathrm{Me}}}(z,t))};\,f_{{\mathrm{e}}(C_{{\mathrm{Me}}}(z,t))}\) is multiplied by a constant rate of 1.0 h–1 (Ke) (equation (7)).

Finally, plant-mediated transport occurs through the root systems of some plants that provide a direct conduit for methane to the atmosphere, and is a function of the rate constant of 0.01 h–1, vegetation type, root density, vegetation growth and soil methane concentrations (Kpl, Zveg, froot, fgrow and \(f_{{{\mathrm{pl}}},{C_{{\mathrm{Me}}}}}\), respectively) (equation (8))43. Rpl depends on ecosystem-specific plant functional types and increases in warmer soil due to the increase in vegetation growth. In both wetland and upland ecosystems, the 1-m soil profile was divided into 1 cm layers and the soil temperature, soil moisture and methane dynamics of TEM were simulated at daily time-steps9.

$$F_{\mathrm{div}}\left( {z,t} \right) = - D\left( z \right)\frac{{\partial {C}_{{\mathrm{Me}}}\left( {z,t} \right)}}{{\partial t}} \ldots$$
(6)
$$R_{\mathrm{e}}\left( {z,t} \right) = K_{\mathrm{e}}f_{\mathrm{e}}\left( {{C_{\mathrm{Me}}}\left( {z,t} \right)} \right) \ldots$$
(7)
$$R_{\mathrm{pl}}\left( {z,t} \right) = K_{\mathrm{pl}}Z_{\mathrm{veg}}f_{\mathrm{root}}\left( z \right)f_{\mathrm{grow}}\left( t \right)f_{\mathrm{pl,C_{\mathrm{Me}}}}\left({z,t}\right) \ldots$$
(8)

Permafrost TEM-HAM model

We first revised the TEM to consider PSOC dynamics and HAMs, but not MICbiomass changes (PTEM-HAM). We modified the Michaelis–Menten constant for methane oxidation from 5 to 0.11 µM (\({k_{\mathrm{Me,HAM}}}\)) to consider atmospheric methane oxidation by HAMs9,23 (equation (9)). We set the maximum lower boundary of the soil layer from 1 m to 3 m to account for PSOC that is accessible as the surface temperature increases and the permafrost thaws. We then added PSOC dynamics by changing the main carbon source for MGs to vegetation (NPP) and PSOC (equation (10)). PSOC(z) represents PSOC stored at depth z (g m–2) and is available when soil temperature at the corresponding depth is greater than 1 °C. We set PSOCmax as 300 kg m–2 for top 3 m soil on the basis of NCSCDv2 (ref. 16). Accordingly, methane production and oxidation equations for PTEM-HAM are similar to equations (2) and (4), but f(SOM) and f(CMe) are replaced with fnew(SOM) and fnew(CMe), respectively (equations (11) and (12)).

$$f_{\mathrm{new}}\left( {C_{\mathrm{Me}}\left( {z,t} \right)} \right) = \frac{{C_{\mathrm{Me}}(z,t)}}{{k_{{\mathrm{Me}},{\mathrm{HAM}}} + C_{\mathrm{Me}}(z,t)}} \ldots$$
(9)
$$f_{\mathrm{new}}\left( {S_{\mathrm{OM}}\left( {z,t} \right)} \right) = \left( {\left( {1 + \frac{{\mathrm{NPP}}_{\mathrm{mon}}}{{\mathrm{NPP}}_{\max}}} \right)f\left( {C_{\mathrm{DIS}}\left( z \right)} \right) + \frac{{\mathrm{PSOC}\left( z \right)}}{{\mathrm{PSOC}}_{\max}}} \right) \ldots$$
(10)
$$M_{{\mathrm{prod}},{\mathrm{PTEM}} - {\mathrm{HAM}}}\left( {z,t} \right) = M_{\mathrm{GO}}f_{\mathrm{new}}\left( {S_{\mathrm{OM}}\left( {z,t} \right)} \right)f\left( {T_{\mathrm{soil}}\left( {z,t} \right)} \right)f\left( {H\left( {z,t} \right)} \right)f\left( {X\left( {z,t} \right)} \right) \ldots$$
(11)
$$\begin{array}{l}M_{{\mathrm{oxid}},{\mathrm{PTEM}} - {\mathrm{HAM}}}\left( {z,t} \right) = O_{\mathrm{max}}f_{\mathrm{new}}\left( {C_{\mathrm{Me}}\left( {z,t} \right)} \right)f\left( {T_{\mathrm{soil}}\left( {z,t} \right)} \right)f\left( {E_{\mathrm{SM}}\left( {z,t} \right)} \right)\\ f\left( {R_{\mathrm{ox}}\left( {z,t} \right)} \right)f\left( {N_{\mathrm{dp}}\left( {z,t} \right)} \right)f\left( {D_{\mathrm{MS}}\left( {z,t} \right)} \right) \ldots \end{array}$$
(12)

XPTEM-XHAM

We further added explicit microbial dynamics of MGs and HAMs into PTEM-HAM (XPTEM-XHAM). Methane oxidation by LAM was simulated as a function of environmental parameters with fixed MICbiomass (equations (4)) due to the limited control of LAM MICbiomass on Arctic wetland methane emissions29,30. We ran additional simulations by adding microbial dynamics of LAM into XPTEM-XHAM to clarify the role of LAM microbial dynamics in wetland methane emission for both contemporary period and future projection (Supplementary Methods 6 and Supplementary Fig. 16).

Methane production by MGs (Mprod,XPTEM-XHAM) and oxidation by HAMs (Moxid, XPTEM-XHAM) are calculated by the product of MICbiomass and methane production and oxidation of PTEM-HAM (Mprod,PTEM-HAM and Moxid,PTEM-HAM), respectively (equations (13A) and (13B))8,44. Active microbial biomass changes (dMICbiomass/dt) are calculated thermodynamically by considering ɛ, mE and the Gibbs free energy (ΔG) of MGs and HAMs (equations (13C) and (13D)). Here, the maximum methane production and oxidation potentials (MGO and Omax, respectively, in equations (11) and (12)) are multiplied by a geometric parameter (γgeometric) and become \(M_{\mathrm{GO}}^ \prime\) and \(O_{\mathrm{max}}^ \prime\) (\(M_{\mathrm{GO}}^ \prime\) = MGO × γgeometric and \(O_{\mathrm{max}}^ \prime\) = Omax × γgeometric), where the units for \(M_{\mathrm{GO}}^ \prime\) and \(O_{\mathrm{max}}^ \prime\) are μMSOC μMbioC–0.66 h–1 and μMCH4 μMbioC–0.66 h–1, respectively.

$$M_{{\mathrm{prod}},{\mathrm{XPTEM}} - {\mathrm{XHAM}}} = {\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{MG}}}^{2/3} \times \gamma _{\mathrm{geometric}} \times M_{{\mathrm{prod}},{\mathrm{PTEM}} - {\mathrm{HAM}}} \ldots$$
(13A)
$$M_{{\mathrm{oxid}},{\mathrm{XPTEM}} - {\mathrm{XHAM}}} = {\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{HAM}}}^{2/3} \times \gamma _{\mathrm{geometric}} \times M_{{\mathrm{oxid}},{\mathrm{PTEM}} - {\mathrm{HAM}}} \ldots$$
(13B)
$$\begin{array}{l}\frac{{\mathrm{dMIC}}_{{\mathrm{biomass}},{\mathrm{MG}}}}{{\mathrm{d}}t} = \varepsilon _{\mathrm{MG}} \\\times \left( {0.8 \times {\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{MG}}}^{\frac{2}{3}} \times \gamma _{\mathrm{geometric}} \times M_{{\mathrm{prod}},{\mathrm{PTEM}} - {\mathrm{HAM}}} + {\mathrm{MIC}}_{{\mathrm{MG}}}\frac{{m_E}}{{\Delta G_{\mathrm{r,MG}}}}} \right) \ldots\end{array}$$
(13C)
$$\begin{array}{l}\frac{{\mathrm{dMIC}}_{{\mathrm{biomass}},{\mathrm{HAM}}}}{{\mathrm{d}}t} = \varepsilon _{\mathrm{HAM}} \\\times \left( {0.8 \times {{\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{HAM}}}^{\frac{2}{3}}} \times \gamma _{\mathrm{geometric}} \times M_{{\mathrm{oxid}},{\mathrm{PTEM}} - {\mathrm{HAM}}} + {{\mathrm{MIC}}_{\mathrm{{HAM}}}\frac{{m_E}}{\Delta G_{{\mathrm{r}},{\mathrm{HAM}}}}}} \right) \ldots\end{array}$$
(13D)

Equations for changes in MICbiomass were derived from the growth rate (ΔP)44, which is proportional to the relative magnitude in the difference between maintenance energy demand and rate of energy delivery of a metabolic redox equation in equations (13E) and (13F)), where ΔP is in \({\mathrm{kJ}} \, {\upmu}{\mathrm {mol}}_{{\mathrm {biomass}}}^{-1} \, {\mathrm{s}}^{-1}\), ΔGr is the free energy of the metabolic redox reaction (which is usually negative) at in situ temperatures, activities and fugacities in \({\mathrm{kJ}} \, {\upmu}{\mathrm {mol}}_{{\mathrm{reactant}}}^{-1}\) and mE is the maintenance energy in \({\mathrm{kJ}} \, {\upmu}{\mathrm{mol}}_{{\mathrm{biomass}}}^{-1} \, {\mathrm{h}}^{-1}\). We assumed that only 80% of the free energy is available for metabolism and the rest is lost as heat44.

$$\Delta P_{\mathrm{MG}} = - 0.8\,\Delta G_{{\mathrm{r}},{\mathrm{MG}}}{{M}}_{{\mathrm{prod}},{\mathrm{PTEM}} - {\mathrm{HAM}}} - m_E \ldots$$
(13E)
$$\Delta P_{\mathrm{HAM}} = - 0.8\,\Delta G_{r,{\mathrm{HAM}}}\,M_{{\mathrm{oxid}},{\mathrm{PTEM}} - {\mathrm{HAM}}} - m_E \ldots$$
(13F)

The rate of increase or decrease of active biomass is governed by the fraction of ΔGr that is directed to maintenance and the growth efficiency, so the active biomass increases according to equations (13G) and (13H), where MICbiomass is in µmolbiomass l–1 and ɛ is in µmolbiomass µmolsubstrate−1.

$$\frac{{\mathrm{dMIC}}_{{\mathrm{biomass}},{\mathrm{MG}}}}{{\mathrm{d}}t} = \frac{{\varepsilon _{\mathrm{MG}} \times {\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{MG}}} \times \Delta P_{\mathrm{MG}}}}{{ - \Delta G_{{\mathrm{r}},{\mathrm{MG}}}}} \ldots$$
(13G)
$$\frac{{\mathrm{dMIC}}_{{\mathrm{biomass}},{\mathrm{HAM}}}}{{\mathrm{d}}t} = \frac{{\varepsilon _{\mathrm{HAM}} \times {\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{HAM}}} \times \Delta P_{{\mathrm{HAM}}}}}{{ - \Delta G_{{\mathrm{r}},{\mathrm{HAM}}}}} \ldots$$
(13H)

Here, ΔGr is calculated using the net thermodynamic driving force (Fthermo) of the reaction in equation (14), where m is the number of moles of ATP generated per mole of reactant and ΔGphos is the free energy for the phosphorylation reaction. At the point at which the thermodynamic drive vanishes, ΔGr = –m × ΔGphos. For methanotrophs \(\Delta G_{{\mathrm{r}},{\mathrm{HAM}}}= -286 \, \times2.8 \, {\mathrm{kJ}} \, {\mathrm{mol}}_{{\mathrm{reactant}}}^{-1}=-800.8 \,{\mathrm{kJ}} \,{\mathrm{mol}}_{{\mathrm{reactant}}}^{-1}\) (ref. 45). Whereas for MGs, the free energy of the metabolic redox reaction is much smaller, ΔGr,MG = –25 kJ molreactant–1 (ref. 46).

$$F_{\mathrm{thermo}} = - {{\varDelta }}G_{\mathrm{r}} - m \times {{\varDelta }}G_{\mathrm{phos}} \ldots$$
(14)

Finally, in equations (13A–D) we added the power of two-thirds to the active biomass term to account for substrate diffusion to the cell surface. Microbes rarely exist as single microbes in isolation, but rather as aggregates47. As the availability of substrate is assumed to be positively correlated with diffusion, the rate of diffusion to the cell wall is thus determined by surface area (not cell volume). Based on this argument, as MICbiomass in equations (13C) and (13D)) does not cancel out, we calculated the theoretical MICbiomass at equilibrium, which is the maximum MICbiomass for given environmental conditions when MGs and HAMs are not limited by space (equations (15A) and (15B)).

$${\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{MG}}} = \left( {\frac{{ - 0.8 \times \gamma _{\mathrm{geometric}}\times \Delta G_{{\mathrm{r}},{\mathrm{MG}}} \times M_{{\mathrm{prod}},{\mathrm{PTEM}} - {\mathrm{HAM}}}}}{m_{E}}} \right)^3 \ldots$$
(15A)
$${\mathrm{MIC}}_{{\mathrm{biomass}},{\mathrm{HAM}}} = \left( {\frac{{ - 0.8 \times \gamma _{\mathrm{geometric}}\times \Delta G_{{\mathrm{r}},{\mathrm{HAM}}} \times M_{{\mathrm{oxid}},{\mathrm{PTEM}}-{\mathrm{HAM}}}}}{m_{E}}} \right)^3 \ldots$$
(15B)

The MICbiomass changes in equations (13C) and (13D)) are dependent on ɛ and mE. We set ɛ as 0.05 and 0.5 for MG and MT, respectively, defined from previous laboratory and experiment studies20,25,27,48. The temperature sensitivity of mE is derived from work by Tijhuis et al.28, who studied a large range of different organisms and found that maintenance energy is mainly influenced by temperature (T, in °C) with an energy of activation of 69 kJ mol–1 (equation (16)).

$$m_{{E}} = 4.5 \times {\mathrm{e}^{\left( {\frac{{ - 6.94 \times 10^4}}{R}\left( {\frac{1}{T} - \frac{1}{{298}}} \right)} \right)} \ldots}$$
(16)

The initial MICbiomass of MG and HAM is estimated from metagenomic data (0.0002 and 0.0025 μmolbiomass lsoil–1, respectively)8,45,49. We set the maximum MICbiomass of MG and HAM of each layer, as the maximum concentration of cells is 104–107 cells per gram of dry soil due to substrate availability and space lmitation50. Using conversion factors (1 cell = 8 × 10–15 mol C, 1 l soil = 1,500 g of dry soil) and the ratio of HAM and MG in the total microbial composition from Stackhouse et al.45 (maximum 1.5% of total cells), we estimated that the maximum concentrations of both MG and HAM are 50,000 nmolbiomass lsoil–1.

Model optimization

We optimized a total of five parameters for upland methane oxidation and four parameters for wetland methane production related to both PTEM-HAM and XPTEM-XHAM (Supplementary Tables 1 and 2). All other parameters were set the same as in Zhuang et al. 9 for methane production and transport processes and as in Zhuang et al. 10 for methane oxidation. We first collected observation data from six sites representing uplands and wetlands for alpine tundra, wet tundra and boreal forest ecosystems to optimize these parameters4,6,51,52,53 (data from the Greenland Ecosystem Monitoring Programme were provided by the Department of Bioscience, Aarhus University, in collaboration with the Department of Geosciences and Natural Resource Management, Copenhagen University) (Supplementary Table 1). Aside from the observed meteorology from field sites, we also used CRU time-series data version 4.01 to fill missing meteorological inputs31. We then used the Shuffled Complex Evolution Approach in R language (SCE-UA-R) to minimize the difference between simulated and observed methane emission and consumption rates54. For each site, 40 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 both XPTEM-XHAM and PTEM-HAM reasonably capture the magnitude and seasonality of observed soil methane fluxes (Supplementary Figs. 1 and 3).

Simulation for the contemporary period

Set-up

We used spatially explicit data of vegetation, soil pH and textures, meteorology and leaf area index to make spatially and temporally varying estimates of methane emission and consumption in the Arctic9. The vegetation and soil texture data sets were used to assign vegetation- and texture-specific parameters to a grid cell42,55. The soil-water pH dataset was used to estimate methane production across the study region56. Meteorological inputs were derived from historical air temperature, precipitation, vapour pressure and cloudiness from gridded CRU time-series data, v.4.01 (ref. 31). We used monthly leaf area index data derived from satellite imagery57 to prescribe leaf area index for each 0.5° latitude and longitude grid cell. Finally, for PTEM-HAM and XPTEM-XHAM, we added the NCSCDv2 to estimate PSOC16. PSOC of each 1 cm of soil layer depth was calculated using the NCSCDv2 data by dividing the PSOC data of 1 m, 2 m and 3 m depths equally into different depths.

The model was applied at the spatial resolution of 0.5° latitude by 0.5° longitude north of 50 °N for both wetland and upland ecosystems with an hourly time-step for microbial dynamics and a daily time-step for other processes and modules during 2000–2016. A year of spin up was used for methane equilibrium in soils for TEM and PTEM-HAM, and five years of spin up were used for biomass equilibrium in soils for XPTEM-XHAM. Simulated ecosystem-specific methane emission from wetlands and consumption from uplands were then area weighted for each grid cell, as defined by the static fractional inundation data33.

Model-data comparison

Site-level

We compared our model results with data from 46 in situ measurements organized by Emmerton et al. and Lau et al. (Supplementary Table 5)5,7. Specifically, Emmerton et al. summarized methane fluxes measured in high-, low- and sub-Arctic tundra for a portion of the northern growing season (May to October). Fluxes were organized by chamber and eddy covariance measurements and by terrestrial sites predominantly emitting or consuming methane. Lau et al. summarized methane emission and consumption in the northern circumpolar permafrost region, organized by soil pH, moisture, temperature, SOC and vegetation types for field measurements only. Due to a possible mismatch of soil and vegetation properties, and wetland distribution of grid cells between model and observation, we compared observed fluxes with simulated fluxes averaged over the growing season from 2000 to 2016 within two adjacent grid cells (1° × 1°) of the observation.

Regional level

We compared model simulations of three regions with methane emission (Alaska, Hudson Bay Lowlands, West Siberian Lowlands) and two regions with consumption (Northeast and West Greenland) (Supplementary Tables 6 and 7). Regional estimates of methane consumption were calculated by extrapolating the measured consumption from fields to a regional level after considering the heterogeneity of land ecosystems4,6. Regional estimates of methane emission of previous studies were calculated by combining field measurements with an atmospheric inversion13,14,15.

Pan-Arctic level

We compared the simulated net regional methane emission with results from a top-down inversion system, CarbonTracker-CH4. CarbonTracker-CH4 estimated anthropogenic and natural methane emission from 2000 through 2010 north of 50 °N (ref. 11). To produce posterior flux estimates, CarbonTracker-CH4 uses the ensemble Kalman smoother described by Peters et al.58, and the TM5 transport model with driving meteorology from the European Centre for Medium-Range Weather Forecasting59. Air samples from 88 surface flask-air methane measurements from the National Oceanic and Atmospheric Administration’s cooperative global air sampling and tall tower networks were used to constrain the flux estimates. Measurements of methane from flask-air samples collected from light aircraft were used to evaluate the inversion results.

Simulation for future projection

Set-up

From 2017 to 2100, we used the IPCC future climate scenarios from RCP climate-forcing datasets, RCP 2.6, RCP 4.5 and RCP 8.5 (Supplementary Fig. 12). RCPs 2.6, 4.5 and 8.5 are climate projections with a possible range of radiative forcing values of 2.6, 4.5 and 8.5 W m−2, respectively, in the year 210032. As RCP datasets did not provide water vapour pressure data, we used the specific humidity and sea level air pressure from the RCP data sets and elevation of surface to estimate the monthly surface vapour pressure60. Under those scenarios, the global climate was simulated with Hadley Centre Coupled Model v.3 at a 0.5° spatial resolution. Transient atmospheric methane data were obtained by linearly interpolating the decadal data for these future projections. Spatial data of vegetation, soil texture, soil pH and LAI used in the twenty-first century were the same as in the simulation for the contemporary period. Models were then applied at a spatial resolution of 0.5° latitude by 0.5° longitude north of 50 °N for both wetland and upland ecosystems from 2017 to 2100. Our simulation showed the largest increase in soil temperature and moisture for RCP 8.5 followed by RCP 4.5 and 2.6, but the soil moisture increase was not distinct (Supplementary Fig. 12).

Microbial physiology

To elucidate effects of microbial physiological responses of MG and HAM to temperature increase, we conducted sensitivity tests by setting mE as a function of temperature in equation (16).