Atmospheric methane underestimated in future climate projections

Methane (CH4) is the second most important naturally occurring greenhouse gas (GHG) after carbon dioxide (Myhre G et al 2013 Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge: Cambridge University Press) pp 659–740). For both GHGs, the present-day budget is dominated by anthropogenic emissions (Friedlingstein P et al 2019 Earth Syst. Sci. Data 11 1783–838; Saunois M et al 2020 Earth Syst. Sci. Data 12 1561–623). For CO2 it is well established that the projected future rise in atmospheric concentration is near exclusively determined by anthropogenic emissions (Ciais P et al 2013 Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Inter-governmental Panel on Climate Change (Cambridge: Cambridge University Press) pp 465–570). For methane, this appears to be the common assumption, too, but whether this assumption is true has never been shown conclusively. Here, we investigate the evolution of atmospheric methane until 3000 CE under five Shared Socioeconomic Pathway (SSP) scenarios, for the first time using a methane-enabled state-of-the-art Earth System Model (ESM). We find that natural methane emissions, i.e. methane emissions from the biosphere, rise strongly as a reaction to climate warming, thus leading to atmospheric methane concentrations substantially higher than assumed in the scenarios used for CMIP6. We also find that the natural emissions become larger than the anthropogenic ones in most scenarios, showing that natural emissions cannot be neglected.


Introduction
Projections of future climate are strongly dependent on the assumed concentrations of greenhouse gases (GHG). The GHG concentration scenarios used in Phase 6 of the Coupled Model Intercomparison Project (CMIP6) (O'Neill et al 2016) were derived using the reduced-complexity carbon cycle climate model MAGICC (Meinshausen et al 2011). One of the assumptions going into the determination of future methane concentrations is that the natural CH 4 emissions can be derived by closing the methane budget over a part of the historical period, in the case of the CMIP6 scenarios over the period 1994-2004(Meinshausen et al 2020. These natural emissions are then assumed to remain constant over the future period investigated. The approach thus relies on the assumption that changes in the natural emissions of methane are substantially less important than the anthropogenic emissions, an assumption that generally holds for carbon dioxide and was reasonable to make considering the published literature on future methane emissions at the time the MAGICC model was first published. In the light of the experiments presented here, however, this assumption will need to be reconsidered.
In the present-day top-down methane budget (Saunois et al 2020), about 40% of the methane emissions are attributed to natural sources, with wetland emissions being by far the largest component of the natural emissions. Measurements indicate that CH 4 emissions may increase under future climatic conditions, from soils (van Groenigen et al 2011) as well as from several other natural methane sources (Dean et al 2018). Using a data-driven modelling approach, Koffi et al (2020) thus find an increase in natural emissions by 50%-80% by 2100. However, the future natural emissions of methane have only rarely been investigated in scenario experiments with ESMs to this date, likely because methane emissions are not yet a standard output of ESMs and require dedicated submodels. Shindell et al (2013) investigated future methane with a focus on atmospheric chemistry and found an increase of wetland emissions by 20% under RCP 8.5 until 2100. Denisov et al (2013), on the other hand, see an increase by 47% in natural emissions by 2100under RCP 8.5. Finally, Zhang et al (2017, using a stand-alone land model, driven by climate scenarios from several climate models, find increases by up to 97% in wetland emissions. So far, no ESM study investigated future CH 4 concentrations beyond 2100 CE, although it is clear that future warming will persist for far longer, especially in the case of scenarios with high radiative forcing. Furthermore, previous studies mainly focused on single forcing factors. Thus the objective of this study is twofold. First, we aim to extend the assessment of the consequences of future warming for the methane cycle beyond the time horizon investigated in previous studies, 2100 CE, using a state-of-the-art ESM, the Max Planck Institute for Meteorology Earth System Model (Mauritsen et al 2019) (MPI-ESM). Second, we assess the entirety of methane emission fluxes in a full methane cycle representation in order to determine the relative importance of both natural and anthropogenic forcings under five different climate change scenarios.

Methane emissions in MPI-ESM
We use MPI-ESM, the Max Planck Institute for Meteorology Earth System Model (Mikolajewicz et al 2018, Mauritsen et al 2019, consisting of the atmospheric general circulation model ECHAM6, the ocean general circulation model MPIOM, and the land surface model JSBACH in coarse resolution (T31GR30 ≈ 3.75 • × 3.75 • ) to investigate the future evolution of the climate system and methane cycle for the next millennium. We have developed a methaneenabled version of MPI-ESM for paleoclimate applications. As described in Kleinen et al (2020), we use a TOPMODEL (Beven and Kirkby 1979) approach to determine inundated areas, in which we determine wetland methane emissions based on Riley et al (2011). Methane emissions from wildfires and biomass burning are determined from the SPITFIRE fire model (Lasslop et al 2014), using emission factors from Kaiser et al (2012). Termite methane emissions are determined using the approach from Kirschke et al (2013) and Saunois et al (2016).
In the TOPMODEL approach, the soil water content determined in the MPI-ESM land surface model JSBACH is combined with sub-gridscale topographic information, the Compound Topographic Index (CTI), in order to determine the variation of the water table in each model grid cell. We then use this to determine inundation fraction, the fraction of each grid cell where the water table is at or above the surface. In Kleinen et al (2020) we have evaluated the model for present-day climatic conditions against remote-sensing data of inundation (Prigent et al 2012) and found a reasonable agreement between model and data, considering the limitations of both model and remote-sensing data. Total extent and seasonality are rather similar for the NH extratropics, while the model slightly overestimates the extent for tropical wetlands.
We assume that soil carbon decomposition, described in JSBACH by the YASSO model (Goll et al 2015), occurs anaerobically in inundated areas, with YASSO rate constants reduced to 35% of the standard (aerobic) decomposition rates (Wania et al 2010). The anaerobically decomposed carbon results in production of CO 2 and CH 4 , with a temperaturedependent partitioning of the anaerobic decomposition product into CO 2 and CH 4 , as described by Riley et al (2011). Soil transport of O 2 , CO 2 and CH 4 is determined in an emission model based on Riley et al (2011), which explicitly simulates methane transport via the pathways diffusion, ebullition, and plant aerenchyma, as well as the oxidation of CH 4 , if sufficient oxygen is present. As CH 4 also diffuses into the soil in dry areas, where it is oxidised, the model also determines the soil sink of methane. We do not model the CH 4 emissions from inland waters (lakes) explicitly, but rather assume that their emissions are implicitly contained in the wetland emission flux. This is a simplification made for practical reasons, as no appropriate model exists in the literature at present. We assume, however, that the error introduced by this simplification is relatively small on the scales the model was designed for (∼350+ km spatial resolution, decadal to centennial temporal scale). This assumption is based on two factors: the surface water extent data used to calibrate the wetland model also contains inland water bodies, and we assume that the changes in methane fluxes from inland waters on these scales will be driven by the same factors that drive the changes in wetland emissions, i.e. carbon, temperature, and precipitation. On shorter time (monthly to annual) and spatial (10s of kilometers) scales, the errors introduced through this simplification may be substantial, though.
Methane emissions from wildfires and biomass burning (with the sum subsequently called the 'fire' emissions) are determined from the SPITFIRE fire model (Lasslop et al 2014), using emission factors from Kaiser et al (2012). The SPITFIRE fire model determines the spread of fires using the fire ignition probability, a function of lightning frequency and population density, and flammability (higher under dryer/warmer conditions), as well as the amount of biomass available for burning. The methane emissions are then determined from the burned biomass using emission factors. Termite methane emissions are determined using the approach from Kirschke et al (2013) and Saunois et al (2016), which determines termite mass from gross primary productivity in tropical areas and assumes a constant emission factor to determine the final methane emissions. Geological emissions are prescribed with a spatial distribution from Etiope (2015), but scaled to give a total of 5 TgCH 4 yr −1 , based on Hmiel et al (2020).

Atmospheric methane sink
The spatiotemporal evolution of methane abundance is simulated using a methane tracer undergoing transport, emission and chemical destruction in the atmospheric model ECHAM6. The CH 4 atmospheric sink is calculated using a zonally averaged methane reactivity field obtained from the comprehensive ECHAM/MESSy Atmospheric Chemistry Model (EMAC) (Joeckel et al 2010). The tropospheric reactivity contribution is parameterised to account for changes in atmospheric oxidative capacity as follows (Gromov et al 2018): with LN being the global lightning nitrogen oxides (NO X ) emission, simulated interactively according to Grewe et al (2001), M the CH 4 atmospheric burden, RN and RC the terrestrial (surface) emissions of reactive nitrogen and carbon compounds. All terms are given in TgC or TgN, respectively, per yr for the emission fluxes. Fit parameters (α = 2.74, p = 0.36, q =−0.48, k N = 0.18, k C = 3.10) are obtained from an ensemble of EMAC simulations covering a wide range of RN, RC, LN and M values probed in last glacial maximum (LGM) and present-day conditions. The fitted r CH4 value is accurate within (1.6-5.5)% at 95% CI. In the MPI-ESM experiments, the natural emission components of RN and RC are obtained from the MEGAN model (Guenther et al 2012) for the biogenic sources and from the SPITFIRE model (Lasslop et al 2014) with emission factors from Kaiser et al (2012) for biomass burning. We are using NO X emissions (scaled by a factor of 2.5 to account for other N-containing compounds) as a proxy for the total natural RN term. For the RC term, CO and isoprene (C 5 H 8 ), scaled by a factor of 1.4 to account for secondary biogenic co-emitted compounds, are used as proxies for the RC term. These scaling factors were derived by comparing the PD emissions of NO X as well as CO and C 5 H 8 with present-day RN and RC emissions. Where available, anthropogenic emissions of RC and RN are considered, as detailed below.

Model forcing
The model is forced with prescribed CO 2 and N 2 O concentrations, as well as anthropogenic emissions of methane, NO X , CO, and volatile organic compounds (VOC). We prescribed CO 2 concentrations from Meinshausen et al (2020) until 2500 (Meinshausen and Vogel 2016, Meinshausen and Nicholls 2018a, 2018b, 2018c, 2018d. For the years 2501-3000 CE, CO 2 was calculated by the climate-carbon cycle model of intermediate complexity CLIMBER-2, used for glacial and interglacial simulations (Brovkin et al 2012, Kleinen et al 2016, assuming no additional anthropogenic CO 2 emissions or land use change. CLIMBER-2 accounts for the biogeochemical processes essential on multi-centennial timescales in the ocean (carbonate sedimentation) and on land (weathering, vegetation dynamics). N 2 O concentrations were prescribed from Meinshausen et al (2020) until 2500 (Meinshausen and Vogel 2016, Meinshausen and Nicholls 2018a, 2018b, 2018c, 2018d and kept constant for 2501-3000 CE. The atmospheric CH 4 concentration was not prescribed, but rather modelled interactively from the methane sources and sinks calculated by MPI-ESM as described above. Anthropogenic methane emissions for the historical period are available from Hoesly et al (2017aHoesly et al ( , 2018. While the data for 1970-2014 are part of the released input files for CMIP6, emissions for 1850-1969 are only available as supplementary data with higher uncertainty (Hoesly et al 2017b), and no anthropogenic CH 4 emissions for the time before 1850 have been published that are compatible with the Hoesly et al (2018) data set. The emissions before 1850, used in the model spinup, were thus interpolated linearly between 1770 and 1849, assuming zero anthropogenic emissions in 1770. This latter assumption is known to be wrong-agricultural emissions were certainly larger than zero before 1850-but as the atmospheric lifetime of methane is of the order of a decade, we assume that this slight underestimate is not relevant for later times.
Anthropogenic CH 4 emissions for 2015-2100 were prescribed from Gidden et al (2019) for the SSP scenarios (Gidden et al 2018a(Gidden et al , 2018b(Gidden et al , 2018c(Gidden et al , 2018d. For the time after 2100 we use the same approach as Meinshausen et al (2020): we assume that anthropogenic emissions from non-agricultural sources decline to zero over 150 years, while agricultural emissions stay constant at the 2100 CE level (figure 3). Similarly, anthropogenic emissions of NO X , CO, and volatile organic compounds (VOC) were obtained from Hoesly et al (2017aHoesly et al ( , 2018 for the historical period, and from Gidden et al (2018aGidden et al ( , 2018bGidden et al ( , 2018cGidden et al ( , 2018dGidden et al ( , 2018e, 2019 for the SSP scenarios. These were interpolated linearly between 1650 and 1750, as well as between 2100 and 2250, assuming zero emissions in 1650 and 2250. We prescribed these as the anthropogenic shares of RC and RN emissions, with RC given by the sum of CO and VOC emissions, and RN given by the NO X emissions, again scaled to match RN inventories.
Due to the nature of the model set-up, intended for paleoclimate simulations, we neglect two shortterm climate forcings: anthropogenic emissions of aerosols and anthropogenic land use changes. The result of the former is that the model does not reflect the slight cooling trend, relative to the GHGinduced warming, induced by the aerosol loading during the 20th century. The effect of the latter is that the biogeophysical feedbacks between land surface and atmosphere are biased towards a natural system, i.e. high latitude temperatures are slightly warmer than they would be with land use, while tropical temperatures are slightly cooler. We judge the effect of this omission on CH 4 emissions to be minor. The primary effects of land-use on greenhouse gases are considered by prescribing atmospheric CO 2 concentrations, as well as anthropogenic CH 4 emissions, which contain the agricultural fluxes.

Model experiments
We conduct a set of 5 model experiments, following the SSP scenarios 1-1.9, 1-2.6, 2-4.5, 3-7.0 and 5-8.5. All experiments are initialised for the year 1850 CE from an identical model state, and forcings for historical and future climate states are prescribed as described above.
We obtained the initial model state from a transient model experiment from the last glacial maximum (LGM) to the present, to be described in detail in a subsequent publication. Briefly, the transient experiment consisted of a spinup phase for several millennia at 26 ka BP boundary conditions, followed by a transient model integration for 26 000 model years. The model was forced by orbital changes from Berger (1978), atmospheric greenhouse gas concentrations from Köhler et al (2017), and the GLAC-1D ice sheet reconstruction (Tarasov et al 2012, Briggs et al 2014, Ivanovic et al 2016. We branched from this model experiment in the model year corresponding to 1550 CE, running it to 1850 CE with the full set of anthropogenic forcings as described above.

Atmospheric CH 4 concentration in response to natural CH 4 emissions
In all scenarios investigated, the atmospheric global mean near-surface CH 4 concentrations in the model experiments (figure 1) are higher than in the published CMIP6 scenarios (Meinshausen et al 2020). In the case of the low radiative forcing scenarios SSP1-1.9 and SSP1-2.6, the concentration maximum occurs at the end of the historical period and does not differ significantly between our experiments and the published scenarios. The concentration decline after that maximum, however, occurs much more slowly in our experiments, leading to higher atmospheric methane concentrations than in the published scenarios. For the moderate to high warming scenarios SSP2-4.5, SSP3-7.0 and SSP5-8.5, however, the evolution of atmospheric methane is much more dramatic. Here, maximum atmospheric concentrations become substantially higher than in the published scenarios and stay at a very high level until the end of the experiments in 3000 CE. For SSP2-4.5, the maximum in CH 4 is 50% higher than published previously, for SSP3-7.0 it is 131% higher and for SSP5-8.5 it is 130% higher. The maxima also occur substantially later, ∼200 years in the case of SSPs 3-7.0 and 5-8.5, while it is 450 years in the case of SSP 2-4.5. Furthermore, the atmospheric concentrations given for the CMIP6 scenarios decrease relatively quickly after reaching their maxima, stabilising in 2250 CE, when the non-agricultural emissions cease in the Meinshausen et al (2020) scenarios. In our experiments, however, they remain high and decline much slower. This is due to the fact that the natural emissions increase with warming in our model, while Meinshausen et al assume constant PD emissions. As a consequence, radiative forcing by methane also increases. Following Etminan et al (2016), the methane radiative forcing change from preindustrial is 0.64 Wm −2 for 2010 CE. Assuming SSP 3-7.0, it increases to 1.31 Wm −2 in 2110 when following the GHG scenario from Meinshausen et al (2020). Using our model results, however, it peaks at 2.37 Wm −2 in 2377 to −81% larger than following the published scenario ( figure A3).
The reason for these high concentrations of atmospheric methane is that the natural emissions of CH 4 are substantially higher than assumed previously. While Meinshausen et al (2020) assumed that the natural emissions would stay constant, they rise roughly proportionally to temperature change in our model experiments (figure 2).
Mean natural net CH 4 emissions, i.e. the sum of emissions from wetlands, termites, fires, and the soil methane uptake, for 2000-2009 are 220 TgCH 4 yr −1 , and emissions increase by between 22% and 149% in 2100 CE (table 1)   beyond 2100 CE in the scenarios with a radiative forcing larger than 2.6 Wm −2 . In these scenario experiments, with the exception of SSP3-7.0, the natural emissions also become larger than the anthropogenic emissions (figure 3) and stay higher than at present for far longer than the anthropogenic emissions assumed in the scenarios (Gidden et al 2019, Meinshausen et al 2020. As a result, the atmospheric CH 4 concentrations will be higher-in the case of the large radiative forcing scenarios substantially higher-than in the published scenarios. In the SSP3-7.0, as an example of a high radiative forcing scenario, global mean temperature increases rapidly by 6.8 K between 2010 CE and 2200 CE (figure A2), with the rate of increase diminishing after 2200 and temperature stabilising at a global mean warming of about 8.5 K after 2500 CE. The natural net methane emissions (figure 2) increase rapidly by 221% until 2200 CE, reach a maximum of 719 TgCH 4 yr −1 (+226%) in the 2310s, and decrease slowly thereafter, with emissions in 3000 CE still 2.6 times as large as in 2010. Anthropogenic emissions, for comparison, increase to 715 TgCH 4 yr −1 in 2100 CE and decline quickly thereafter (figure 3), until stabilising at 379 TgCH 4 yr −1 in 2250, as only agricultural emissions are assumed for anthropogenic emissions after this time. Spatially, the bulk of the increase in natural emissions (shown for 2300 CE) occurs in tropical regions (figure 4), with NH high latitudes also showing significant increases, while net emissions from dryland regions decrease due to increasing soil uptake of CH 4 . The developments in methane fluxes described for SSP3-7.0 are similar in the other two high radiative forcing scenarios, though with lower or higher absolute values for SSP2-4.5 and SSP5-8.5, respectively.
The other two scenarios, SSP1-1.9 and SSP1-2.6, are characterised by CO 2 concentrations which quickly decline after an initial peak (figure A1), leading to a substantially faster temperature decrease than in the other scenarios, with temperatures stabilising in the 22nd century. In SSP1-2.6, as an example of a low radiative forcing scenario, net CH 4 emissions increase to 299 TgCH 4 yr −1 (+36% from 2010 CE) in the 2070s, then rapidly decline to 274 TgCH 4 yr −1 in 2200 CE, followed by a gradual decrease to 256 TgCH 4 yr −1 in 3000 CE. Being much smaller than the increase in the high warming scenarios, this nevertheless implies that natural methane emissions will exceed present-day fluxes by 15% or more throughout the next millennium and longer.
Concentrating on the time frame until 2200 CE, the phase of rapid increases in global mean temperature, the rise in natural net methane emissions is directly proportional to the change in global mean temperature with an emission increase by 75 TgCH 4 yr −1 per K temperature increase (figure A4), independent of the chosen scenario. This temperature sensitivity of the natural net methane emissions leads to a sensitivity of the radiative forcing from methane of 0.1 Wm −2 K −1 , based on Etminan et al (2016).

Wetland emissions
Wetland emissions are by far the largest component of the natural methane emissions in the present-day budget (Saunois et al 2020), with all other natural fluxes being of secondary importance. The bulk of wetland emissions (62%-77%) originates in the latitudes between 30 • S and 30 • N, while a much smaller part (20%-33%) is emitted from high latitudes (Bousquet et al 2011). These relations do not change substantially under the SSP scenarios, with between 60% and 78% of the wetland emissions coming from low latitudes. For the wetland CH 4 emission change between last glacial maximum and preindustrial, we were able to show that the change can be explained by changes in atmospheric CO 2 concentration and soil carbon stocks, both contributing about 40% to the change, and the remaining 20% can be explained by further climate changes, with temperature and precipitation changes being most important (Kleinen et al 2020). We have no reason to assume that this relationship will not hold in future climate states, although the percentage shares of the contributions will likely be different. Looking at the high radiative forcing scenarios, a significant part of the emission increase in the low latitudes stems from expansion of wetland areas. This is different in high latitude areas, where winter freezing becomes less important as climate warms. As a result, the seasonality of inundation changes, although the annual maximum inundation does not change. Thus expanding wetland areas play a significant role in the low latitudes, but not in the boreal regions. However, the model version employed in our experiments does not explicitly consider permafrost and may therefore underestimate hydrological changes in present-day permafrost areas.
In the SSP3-7.0, wetland CH 4 emissions (figure A5) increase from 212 TgCH 4 yr −1 in 2010 CE to 674 TgCH 4 yr −1 in 2200 CE, reach a maximum of 699 TgCH 4 yr −1 in the 2310s and slowly decrease afterwards, with emissions of 569 TgCH 4 yr −1 in 3000 CE. The initial surging of wetland emissions is driven by a combination of an increase in vegetation productivity due to warming and CO 2 growth, warming-induced increase in soil carbon turnover, as well as an expansion of tropical wetland areas due to intensified precipitation. High latitude wetland areas, on the other hand, do not change in their maximum extent, although warmer winter conditions lead to larger effective (unfrozen) wetland areas in the winter season. The slow decrease in emissions after 2330 CE, on the other hand, is caused by a slow decline in the carbon available for anaerobic decomposition, as the enhanced turnover caused by warmer condition leads to a decline in the litter and soil carbon stocks. While wetland CH 4 emissions change in a very similar way in SSP2-4.5, the evolution in SSP5-8.5 is slightly different. Here, tropical wetland emissions decline more quickly for the first 150 years after the emission peak in the 2200s, due to a shift in precipitation patterns, leading to a drying in subtropical Africa and South-East Asia.

Other natural CH 4 sources and sinks
CH 4 emissions from termites in SSP3-7.0 increase from 11 TgCH 4 yr −1 in 2010 CE to 88 TgCH 4 yr −1 in 2200 CE, reach their maximum of 95 TgCH 4 yr −1 in the 2280s, and slowly decrease to 74 TgCH 4 yr −1 in Figure 5. Composition of gross methane emissions, i.e. all emissions except the methane uptake by soils, for SSPs 1-2.6, 2-4.5, 3-7.0 and 5-8.5 for the 2010s, 2100s, 2300s, and 3000s. 3000 CE. The initial rapid increase in termite methane emissions is very well correlated with the growth of CO 2 in the atmosphere, as tropical gross primary production (GPP) is the main driver of termite emissions in the model employed (Kirschke et al 2013, Saunois et al 2016, which is strongly influenced by atmospheric CO 2 . Termite emissions become even larger in SSP5-8.5, where they increase to about 125 TgCH 4 yr −1 in 2200 CE. As this flux appears to be rather large, we assume that the climate forcing in SSPs 3-7.0 and 5-8.5 exceeds the range of applicability of the model of termite emissions we are using (Kirschke et al 2013, Saunois et al 2016. However, we are not aware of any better approach to determine future termite methane emissions. Methane emissions from fires (figure A7) in SSP3-7.0 increase from 14 TgCH 4 yr −1 in 2010 CE to 33 TgCH 4 yr −1 in 2200 CE, peaking at 35 TgCH 4 yr −1 in the 2310s and decline to 27 TgCH 4 yr −1 in 3000 CE. Even larger emissions (40 TgCH 4 yr −1 ) are reached in SSP5-8.5, but nonetheless fires remain a small source of methane to the atmosphere.
Methane uptake in upland soils (figure A8) increases in SSP3-7.0 from 18 TgCH 4 yr −1 in 2010 CE to 87 TgCH 4 yr −1 in 2200 CE, peaking at 111 TgCH 4 yr −1 in the 2360s. In our model this flux is largely determined by the gradient between the CH 4 concentrations in the atmosphere and in the soil, as all methane transported into upland soils is oxidised eventually, making the diffusive transport into the soil the limitation on the oxidation rate.
Climate warming will thus lead to a change in the composition of the gross methane emissions (figure 5): at present, anthropogenic emissions make up more than half the gross emission flux, but climate change will lead to a strong warming-induced increase in the natural emissions, which will eventually surpass the anthropogenic emissions. As a result, the anthropogenic emissions are only at present larger than the gross (i.e. without uptake) natural methane emissions. For the future, only the high anthropogenic methane emission scenario SSP3-7.0 shows larger anthropogenic than natural emissions for 2100, while all other scenarios show that future natural emissions are larger than the anthropogenic ones.

Study limitations
Uncertainties in our study are high, and the exact numbers from our experiments will therefore have to be interpreted with caution. The experimental setup was not optimised for short-term climate change simulations over the historical  and near future (2016-2100) period, some of the rapidly changing forcings, such as land-use changes and aerosol emissions, were not taken into account. Historical (1850-2015) climate therefore is not reproduced as well as in some CMIP6 experiments. Qualitatively, however, we consider our experiment outcomes to be reliable: Our model shows strong increases in wetland methane emissions in comparison to the historical period, which are well explained by the combination of warming, CO 2 increase and increase in vegetation productivity.
Our modelled changes in wetland methane emissions show reasonable estimates for the LGM and PD states (Kleinen et al 2020). However, the modelled carbon cycle changes are dependent on both temperature and CO 2 changes. If the CO 2 -fertilisation, the enhancement of vegetation productivity with rising CO 2 , is overestimated in our model, this would also result in an overestimate of wetland CH 4 emission changes.
Termites and fires contribute substantially less to the natural methane emissions. Nonetheless the performance of the fire model has been validated for both historical and near future climate conditions (Lasslop et al 2014), giving confidence in those results. The strong increase in CH 4 emissions from termites displayed by our model for the high warming scenarios likely is an overestimate, however.
The atmospheric sink in our model was calibrated to consistently reproduce the observed LGM and present-day concentrations of methane, which also resulted in moderate variations in its atmospheric lifetime, in line with the recent findings on the present and glacial methane cycle (Naik et al 2013, Murray et al 2014, Hopcroft et al 2017. Larger future changes in methane lifetime could affect the sensitivity of methane emissions to temperature in experiments similar to the ones shown here. However, the well-buffered atmospheric oxidative capacity, sustained to a large extent by compounds emitted from anthropogenic sources (foremost nitrogen oxides), renders such conditions unlikely until at least 2100 CE (Voulgarakis et al 2013, Lelieveld et al 2016). While we use a rather rigorous atmospheric CH 4 reactivity parameterisation, errors of up to 20% in the simulated CH 4 sink are admissible due to propagation of the uncertainties associated with the input parameters, viz. emissions of trace gases (such as NO X and VOCs). The latter typically reach 50% even for the present-day conditions (Gromov et al 2017) and thus are the current limiting factor for CH 4 sink estimates. As a result, we are more confident in the simulated changes in natural methane emissions than in the projected atmospheric methane concentration.
We assume that ice sheets will not change under future climatic conditions. This assumption may be justified for the low warming scenarios, but it is clearly not justified for the high warming scenarios. It is highly unlikely that the Greenland ice sheet will remain unchanged for the next 1000 years if global mean temperature increases by 12 K. However, we do not have an interactive ice sheet model available at this time, and thus cannot evaluate the climatic consequences of the eventual waning of the Greenland (and likely West Antarctic) ice sheets.
Finally, the anthropogenic emission scenarios we are comparing to have only been published for the years until 2100 CE (Gidden et al 2019), and we are making the same assumptions as Meinshausen et al (2020) for the years beyond this time: we assume that agricultural emissions stay constant, and that the non-agricultural emissions decrease linearly until they reach zero in 2250 CE. This is an obvious simplification. However, no other extensions to the scenarios have been published yet, making it impossible for us to rely on other sources. Since all scenarios but SSP3-7.0 already have declining emissions in 2100 CE, we assume the error we are introducing for the non-agricultural emissions is not large. With regard to the agricultural emissions, it appears unlikely that they will stay constant indefinitely, and as population is declining by 2100 CE in all scenarios but SSP3-7.0 (KC and Lutz 2017), a decrease in agricultural emissions might be considered more logical. The anthropogenic emissions we are assuming for the years beyond 2100 CE therefore likely are an upper bound for all scenarios but SSP3-7.0.

Conclusions
Our results show that the natural CH 4 emissions will increase dramatically in high warming scenarios, compared to the late historical period. This increase is predominantly driven by the increase in emissions from wetlands, caused by the combination of warmer temperatures, higher CO 2 concentrations leading to increased vegetation productivity, and changes in wetland seasonality or area. Furthermore, CH 4 emissions will remain larger than in the historical period for a long time, likely for as long as CO 2 and temperatures remain above present levels. As a result, atmospheric concentrations of methane are likely to be significantly higher than those obtained for CMIP6 with an assumption of constant natural emissions. The direct consequence is that radiative forcing from methane will be higher than assumed in the scenarios used in CMIP6-by 80% in the case of SSP3-7.0. This is a significant increase, although the forcing by methane is yet dwarfed by the forcing from CO 2 .
Our results also bear on the recent discussion of the positive effects of short-term reductions in anthropogenic methane emissions (Ocko et al 2021): while a reduction in anthropogenic methane emissions will clearly be beneficial in reducing short-term climate warming, our results show that this effect will be short-lived, if CO 2 emissions are allowed to continue rising. In that case the natural methane emissions will increase in response to the warming and negate any positive effects of the reduction in anthropogenic methane emissions. A further consequence of the increased atmospheric methane concentration is a reduction of the atmospheric selfcleansing capacity via OH radicals, as additional OH is used up in the oxidation of methane. The resulting effects will impact removal of pollutants from the atmosphere, exacerbating negative health consequences and mortality, and increasing economic costs for air pollution control measures (Lelieveld et al 2015).
While the above-mentioned factors lead to some uncertainty about the exact increase in emissions (and atmospheric concentration) of CH 4 , our main conclusions are robust, underlined by the fact that our model is able to reproduce methane changes from last glacial maximum to the present (Kleinen et al 2020). We thus conclude that the natural emissions of methane will increase much more strongly in response to warming than was assumed previously, becoming larger than the anthropogenic emissions in all scenarios investigated, with the exception of SSP3-7.0. This change needs to be taken into account when assessing future changes in atmospheric methane and radiative forcing.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://cera-www.dkrz.de/WDCC/ui/cerasearch/ entry?acronym=DKRZ_LTA_060_ds00007.