Introduction

Methane (CH4) is a potent greenhouse gas, second only to CO2 in the contribution to global temperature increase relative to pre-industrial levels1. Atmospheric CH4 levels have grown rapidly since the year 20072,3. The mean atmospheric CH4 concentration ([CH4]) currently exceeds 1900 parts per billion (ppb), which is >2.5 times larger than the pre-industrial average4. Recent trends of observed CH4 levels are tracking future scenarios of unmitigated emissions5,6. For more than three decades, global CH4 emissions have been dominated by anthropogenic sources mostly related to fossil fuel exploitation, livestock production, waste and agriculture2,3,7. Several studies have highlighted the importance of CH4 mitigation for tackling climate change in the current century, in parallel with efforts to decarbonize the world economy8,9,10.

A salient outcome of the 2015 Paris Agreement is the international commitment to keep global warming to well below 2 °C above pre-industrial levels, and pursue efforts to limit the mean global temperature increase to 1.5 °C above pre-industrial levels11. Achieving these temperate goals will require reaching net-zero CO2 emissions alongside deep reductions in CH4 and other non-CO2 emissions by or around mid-century12. While the need for urgent CH4 mitigation is now recognized (e.g. the Global Methane Pledge following COP2613), it is necessary to assess the importance of immediate versus delayed CH4 mitigation to comply with the temperature goals in the Paris Agreement—particularly taking into account potential Earth system feedbacks. There is still limited knowledge about (i) the importance of biogeochemical feedbacks14,15 in the context of CH4 mitigation for achieving the Paris temperature goals16,17, and (ii) long-term (i.e. multi-century) climate impacts of delaying or failing to mitigate CH4 in the current century18,19.

In this study, we use an Earth system model with an interactive CH4 cycle to investigate the importance of immediate versus delayed CH4 mitigation to comply with stringent warming limits in the Paris Agreement. It is important to note that: (i) currently, there are very few Earth system models driven by CH4 emissions in their representation of the global CH4 cycle17,20; and (ii) previous research applying an Earth system modeling approach to investigate CH4 mitigation and its implication for meeting stringent temperature goals have relied on scenarios of prescribed [CH4] without considering explicit changes in anthropogenic CH4 emissions, potential climate-CH4 feedbacks, and climate impacts of CH4 mitigation beyond the 21st century16. We use version 2.10 of the University of Victoria Earth System Climate Model (UVic ESCM)21, into which we implemented a simplified representation of the global CH4 cycle—featuring simulated wetland CH4 emissions (including CH4 emissions from previously frozen soil carbon upon permafrost thaw)22 and atmospheric CH4 decay (See Methods). We validate the model against historical [CH4] data and estimations of the global CH4 budget in recent decades (See Supplementary Notes 1 & 2).

To assess the importance of timing for CH4 mitigation to achieve the 2 °C temperature goal, we prescribe anthropogenic CH4 emissions according to two Shared Socioeconomic Pathways (SSPs)23,24: (i) SSP1-2.6, a scenario featuring immediate CH4 mitigation; and (ii) SSP3-7.0, a scenario without CH4 mitigation throughout the 21st century. We design four additional scenarios of anthropogenic CH4 emissions by assuming different initiation of CH4 mitigation over the next few decades. These scenarios follow the SSP3-7.0 trajectory up to a specific year (2020, 2030, 2040 and 2050) and decline linearly to reach the same amount of CH4 emissions as SSP1-2.6 in 2100, and then evolve according to the SSP1-2.6 extension beyond the 21st century (Fig. 1). These mitigation scenarios assume deep reductions in anthropogenic CH4 emissions, corresponding to 69–78% of emission reductions between the year of peak emissions and the year 2100 (Supplementary Table 1). CH4 mitigation approaches that are currently achievable with existing strategies and technologies (i.e. technically feasible solutions) could ̶ once deployed ̶ lead to the elimination of >50% of global anthropogenic CH4 emissions by the year 2050, with large contributions from cutting fossil fuel and solid waste emissions25. By design, our idealized mitigation scenarios allow us to compare the effect of immediate versus delayed CH4 mitigation on the global climate at the end of the 21st century and beyond. We further assume that all other future anthropogenic forcings (including CO2 emissions) evolve according to SSP1-2.6, which is a scenario aimed at limiting global warming to below 2 °C throughout the 21st century26.

Fig. 1: Anthropogenic CH4 emissions prescribed to the UVic ESCM in this study.
figure 1

Emissions in the early mitigation scenario (“Early Mitig”) correspond to SSP1-2.6, whereas emissions without mitigation (“No Mitig”) correspond to SSP3-7.0. Immediate and delayed mitigation scenarios follow the SSP3-7.0 CH4 emission trajectory to the specified point in time and decline linearly to reach the same amount of CH4 emissions as SSP1-2.6 in 2100, and evolve according to the SSP1-2.6 extension beyond the 21st century.

Full size image

Results

Delaying CH4 mitigation results in higher peak warming

The timing of CH4 mitigation affects peak levels of [CH4], [CO2], and surface air temperature (SAT) in the future. According to our model, every 10-year delay in CH4 mitigation increases the [CH4] peak by 150-180 ppb (Fig. 2b). As such, delaying CH4 mitigation to the 2040-2050 decade will increase the [CH4] peak by 450–540 ppb relative to CH4 mitigation initiated at or around 2020. The [CH4] increase has a direct effect on global mean surface air temperature (SAT). For every 10-year delay in CH4 mitigation, our model simulates an additional peak warming of ~0.1 °C (Fig. 2d). Delaying CH4 mitigation to or around mid-century will increase the peak warming by 0.2–0.3 °C relative to a CH4 mitigation initiated at present-day. Through feedback mechanisms operating in the Earth system (discussed below), one indirect effect of delaying CH4 mitigation manifests with atmospheric CO2 concentration ([CO2]). Our model suggests that every 10-year delay in CH4 mitigation implies an increase in the [CO2] peak by 2-3 ppm (Fig. 2c). Consequently, delaying CH4 mitigation to the 2040-2050 decade will increase the [CO2] peak by 6-9 ppm relative to CH4 mitigation at present-day. Relative to the early mitigation scenario (SSP1-2.6), delaying CH4 mitigation to the 2040-2050 decade implies more [CH4] (~200 ppb) and warming (~0.2 °C) at the year 2100 (Fig. 2b, d and Supplementary Note 3).

Fig. 2: Projected changes in atmospheric composition and temperature relative to present-day conditions under the mitigation scenarios explored in this study.
figure 2

Changes are shown for (a) global wetland CH4 emissions, (b) atmospheric CH4 concentration, (c) atmospheric CO2 concentration, and (d) surface air temperature (SAT) relative to 2006-2015 for different initiation of CH4 mitigation under the assumption that all non-CH4 forcing agents (including CO2) from anthropogenic sources evolve according to SSP1-2.6. The variability in the SAT curves is associated with the solar cycle.

Full size image

The decline in [CH4] in response to CH4 mitigation depends on the balance between CH4 sources and sinks (Supplementary Fig. 1). CH4 sources are dominated by anthropogenic CH4 emissions (Fig. 1 and S1a), whereas CH4 sinks in our model are proportional to the atmospheric CH4 burden (Methods and Supplementary Fig. 1b, c). A delayed CH4 mitigation results in a higher atmospheric CH4 burden and [CH4] than for an early mitigation, which implies a lag in the decline of CH4 sinks and [CH4] for the delayed mitigation in comparison to the early mitigation. Implications of this lag are most noticeable towards the end of the 21st century: while total CH4 emissions converge in 2100 for all mitigation scenarios, the atmospheric CH4 burden around the year 2100 remains high for delayed CH4 mitigation relative to early CH4 mitigation owing to a lag in CH4 sinks (Supplementary Fig. 2). Overall, relative to the early CH4 mitigation (SSP1-2.6), simulated CH4 sinks in 2100 are ~65 Tg CH4 yr−1 higher for CH4 mitigation delayed to 2040-2050 (See Supplementary Note 4).

The peak warming is amplified by biogeochemical feedbacks

In our model simulations, SAT changes are influenced by biogeochemical feedbacks in addition to the timing of CH4 mitigation. In particular, we find that the feedback of SAT changes on the atmospheric CO2 concentration (referred to as the carbon-climate feedback) contributes to increasing peak SAT differences between early and delayed CH4 mitigation. While we prescribe the same anthropogenic CO2 emissions in all our model simulations (See Methods), atmospheric CO2 levels are projected to be higher for delayed CH4 mitigation scenarios than for early CH4 mitigation scenarios (Fig. 2c). In comparison to early CH4 mitigation, delayed CH4 mitigation results in high [CH4] levels that lead to high SAT levels. Enhanced global warming results in high [CO2] levels, which in turn contribute to increase the SAT differences between early and delayed CH4 mitigation scenarios. Such feedbacks between SAT and [CO2] involve the response of natural CO2 sinks to global warming and climate change. For instance, increased SAT enhances the release of CO2 through soil respiration and weakens the uptake of atmospheric CO2 by oceans through the solubility pump, resulting in enhanced [CO2] and an amplification of global warming14. Overall, we deduce that the carbon-climate feedback amplifies the SAT response in late versus early CH4 mitigation scenarios (Fig. 2d and Fig. 3). To quantify the contribution of the carbon-climate feedback to additional peak warming from delayed CH4 mitigation, we performed additional model simulations with prescribed CO2 concentration from the early mitigation scenario (i.e. Early CH4 Mitig SSP1-2.6). These model simulations suppress the warming signal from delayed CH4 mitigation that is due to the carbon-climate feedback, and their difference with our standard model simulations allows to quantify the magnitude of the feedback. According to our results, the contribution of the carbon-climate feedback to the peak warming increases for every 10-year delay in CH4 mitigation (Fig. 3). The peak warming attributable to the feedback ranges from ~0.03 °C for CH4 mitigation initiated in 2020 to ~0.06 °C for CH4 mitigation initiated in 2050 (Fig. 3).

Fig. 3: Projected changes in air temperature relative to the pre-industrial era under the mitigation scenarios explored in this study.
figure 3

Changes are shown for global mean surface air temperature (SAT) relative to 1850–1900 for different initiation of CH4 mitigation under the assumption that non-CH4 forcing agents evolve according to SSP1-2.6. An estimate of 0.97 °C is considered for the global warming level in the 2006-2015 decade relative to the 1850–1900 period29. The variability in the SAT curves is associated with the solar cycle. Given that the observed historical warming level for the 2006-2015 decade relative to the 1850–1900 period is associated with an uncertainty of ±0.12 °C29, we provide a version of this figure with the uncertainty range in the supplementary information (Supplementary Fig. 5). The dashed lines correspond to model simulations with prescribed CO2 concentration from the Early CH4 Mitig (SSP1-2.6) scenario, which imply climate projections without the carbon-climate feedback. The difference between dashed and continuous lines of the same color illustrates the magnitude of the carbon-climate feedback.

Full size image

In contrast, we do not detect a strong feedback between global warming and wetland CH4 emissions in our model simulations ̶ despite changes in precipitation patterns and wetland areal extents between the different mitigation scenarios explored in this study (Supplementary Fig. 3). Differences in projected wetland CH4 emissions between early and delayed CH4 mitigation scenarios do not exceed 1 Tg CH4 yr−1 for more than two centuries (Fig. 2a), which translates into a negligible fraction of [CH4] and SAT differences between these mitigation scenarios. We conclude that the importance of the feedback between wetland CH4 emissions and climate change is small under the low CO2 emission scenarios explored in this study.

Timing of CH4 mitigation and stringent warming limits

Determining the historical warming level is a critical aspect for assessing the implications of future climate projections on global warming limits in the Paris Agreement27,28. Our model simulates a global warming level of 1.1 °C for the 2006-2015 decade relative to the 1850–1900 period, whereas the recent Sixth Assessment Report (AR6) by the IPCC provides an estimate of 0.97 °C for the global warming level over the same decade relative to the same baseline period29. Hence, for this study, we adopt the above IPCC estimate to project future global warming levels associated with different scenarios of CH4 mitigation (Fig. 3).

According to our model simulations, the 2 °C temperature goal can be achieved through rapid and deep cuts in anthropogenic CH4 emissions along with stringent CO2 mitigation. Our results suggest that global warming relative to the pre-industrial period (1850–1900) could be limited to well below 2 °C throughout the 21st century if global-scale CH4 mitigation is initiated before 2030 while all other anthropogenic emissions evolve according to SSP1-2.6 (Fig. 3). However, if CH4 mitigation is delayed to 2040, our results suggest that the 2 °C warming target will be overshot for at least two decades in the 21st century (Fig. 3), with longer mitigation delays implying longer overshoot periods of the 2 °C threshold. As expected with SSP1-2.6, all our considered CH4 mitigation scenarios imply a breaching of the 1.5 °C limit relative to the 1850–1900 levels (Fig. 3).

Timing of CH4 mitigation and its implications beyond the 21st century

The timing of CH4 mitigation over the next three decades has implications beyond the 21st century. While anthropogenic CH4 emissions prescribed to our model converge by the year 2100 for all considered scenarios other than SSP3-7.0 (Fig. 1), atmospheric [CH4] levels for delayed and early CH4 mitigation scenarios converge in the first half of the 22nd century (Fig. 2b). However, SAT differences between our mitigation scenarios persist for more than two centuries in the future (Fig. 2d), owing partly to the carbon-climate feedback (Fig. 2c and Fig. 3) as well as inertia in the climate system. These results suggest that, although CH4 stays in the atmosphere for only about a decade, delaying CH4 mitigation by 10–30 years will have an impact on global warming over many centuries.

The timing of CH4 mitigation has long-term implications for achieving the temperature goals in the Paris Agreement. When implemented alongside CO2 mitigation, rapid and deep reductions in CH4 emissions will provide long-term benefits with regards to lowering global warming levels. According to our model simulations, initiating CH4 mitigation before 2050 will increase the likelihood of limiting global warming to 1.5 °C in the long run—from the second half of the 22nd century onwards, after an overshoot in the first half of the 21st century (Fig. 3). However, even under the assumption of net-zero CO2 emissions by mid-century, an eventual failure to mitigate CH4 in the current century will raise global warming to >2 °C above pre-industrial levels throughout the 21st century and beyond (Fig. 3). We conclude that rapid CH4 mitigation efforts will provide a long-term safeguard for the temperature goals in the Paris Agreement, whereas a failure to mitigate CH4 within the next few decades will constitute a serious challenge for achieving the 2 °C warming limit.

Discussion

Previous studies have demonstrated that deep reductions in CH4 emissions alongside stringent CO2 mitigation by mid-century are needed to limit global warming to below 2 °C above pre-industrial levels, in agreement with our results18,19,30,31. Our study presents two additional findings: (i) the importance of biogeochemical feedbacks in the context of CH4 mitigation to achieve stringent temperature limits, and (ii) long-term climate impacts of a delay or failure to mitigate CH4 in the current century. Our study shows that the carbon-climate feedback amplifies the SAT response for delayed versus early CH4 mitigation. In particular, our results suggest that the strength of the carbon-climate feedback increases for every 10-year delay in CH4 mitigation (Fig. 3). The simulated contribution from the carbon-climate feedback to the peak warming ranges from ~0.03 °C to ~0.06 °C for CH4 mitigation initiated in 2020 and 2050, respectively. Given that the UVic ESCM has a relatively high carbon-climate feedback parameter compared to most other ESMs32 and a TCRE (transient climate response to cumulative emissions) value close to the CMIP6 ensemble mean14,21, we infer that our estimated warming from the carbon-climate feedback lies in the upper 50-percentile of what the CMIP6 ESM ensemble would simulate in the context of this study. With regards to climate-CH4 feedbacks, our model simulations suggest a negligible contribution from wetland CH4 emissions to temperature change for every 10-year delay CH4 mitigation in a low CO2 emission scenario. However, we do not rule out the potential for a strong climate-CH4 feedback involving wetlands, wildfires, and atmospheric CH4 oxidation15—which would imply a potential underestimation of the contribution from the climate-CH4 feedback to the additional peak warming under delayed CH4 mitigation.

Despite that CH4 stays in the atmosphere for only about 10 years, delaying CH4 mitigation by 2-3 decades will have an impact on global warming over many centuries (Fig. 2d and Fig. 3). Such a delayed CH4 mitigation may result in other long-term impacts such as a persistent sea-level rise over many centuries33. On the contrary, early CH4 mitigation reduces the risk of losing the summer sea-ice across the Arctic Ocean34. A failure to mitigate CH4 in the current century implies a high risk for global warming to exceed the 2 °C warming limit for more than two centuries even under net-zero CO2 emissions by 2050 (Fig. 3). Such an overshoot of the 2 °C threshold has the potential to increase the risk for record-breaking climate extremes35 and tipping elements in the Earth’s climate system such as the dieback of the Amazon rainforest as well as the melting of the Greenland and West Antarctic Ice Sheets36.

While mitigation research and efforts generally focus on achieving net-zero CO2 emissions by 205012,19, it is becoming more clear that rapid reductions of both CO2 and CH4 emissions are crucial for holding global warming to well below 2 °C above pre-industrial levels37. To pave the way for CH4 mitigation in the context of meeting the temperature goals in the Paris Agreement, there is a growing number of studies on: (i) understanding processes and reasons behind changes in [CH4] trends in recent decades2,5, (ii) constraining the global CH4 budget2,38, and (iii) developing strategies for reducing anthropogenic CH4 emissions39 as well as technologies for atmospheric CH4 removal40. Research suggests that many anthropogenic sources of CH4 can be reduced cost-efficiently19,25,39,41, and that the priority for deep emission cuts should be in the energy, industry and transport sectors without neglecting the high potential from the waste and agricultural sectors6,7,19,30,31,39. If deployed rapidly, readily available measures for large-scale CH4 mitigation by sector can contribute to slowdown global warming18. In addition to the Global Methane Pledge by >100 countries representing 70% of the global economy13, multilateral partnerships already exist to support large-scale CH4 mitigation (e.g. the Climate and Clean Air Coalition as well as the Global Methane Initiative42,43,44,45). Given that atmospheric CH4 is a precursor to ground-level ozone (O3)—an air pollutant with negative impacts on human health and crop yields, CH4 mitigation offers the opportunity of simultaneously tackling climate change and improving air quality, global health, as well as food security17,46,47.

Limitations of this study include uncertainties in the areal extent and dynamics of natural wetlands, as well as in the wide array of physical, biological, and chemical controls on CH4 production and oxidation which determine the response of wetland CH4 emissions to climate change48. Despite its simplicity, our wetland CH4 model is capable of reproducing present-day wetland CH4 emissions based on soil moisture, carbon, and temperature simulated by the UVic ESCM22 (Supplementary Table 2). Additional limitations of this study are associated with: (i) static CH4 emissions from non-wetland natural sources, and (ii) a constant lifetime for atmospheric CH4 as part of the parameterization for atmospheric CH4 decay. Natural CH4 emissions from non-wetland sources (such as termites, lakes, wildfires, geologic seeps, marine hydrates) are not represented in the UVic ESCM and are held fixed in our model simulations (See Methods). Processes governing the future evolution of these natural CH4 sources are poorly understood2,49.

The consideration of a constant lifetime for atmospheric CH4 is a simplified assumption made in this study as part of initial steps to represent the atmospheric CH4 decay and the global CH4 cycle in the UVic ESCM (See Methods and Supplementary Note 5). In reality, the atmospheric CH4 lifetime varies by a few months to a few years mostly due to changes in atmospheric chemistry associated with CH4 sinks50, and this variation in the CH4 lifetime has been invoked to explain past changes in the growth rates of atmospheric CH4 levels3,50. Variations in the atmospheric CH4 lifetime are mainly regulated by a chemical feedback involving the oxidation of CH4 by the OH radical3,50, a process not simulated by our model. This feedback mechanism is such that increasing [CH4] (e.g. under delayed CH4 mitigation) reduces the abundance of the OH radical, which further increases [CH4] and raises the global warming level. Therefore, one consequence of our assumption of a constant lifetime for atmospheric CH4 is a potential underestimation of the [CH4] peak in delayed mitigation scenarios. However, our main result that delaying CH4 mitigation increases the risk of breaching the 2 °C warming limit is not considerably affected by the use of different values for the atmospheric CH4 lifetime in the range of published estimates (i.e. 7–11 years)2 (Supplementary Fig. 4).

By design, this study makes a fundamental assumption with regards to future emission scenarios: effective mitigation of CO2, other non-CH4 greenhouse gases (GHGs), as well as aerosols, except for CH4. This assumption is such that future emissions of non-CH4 GHGs (including CO2) and aerosols decline by mid-century according to a scenario consistent with limiting global warming to 2 °C by 2100 (i.e. SSP1-2.6), while anthropogenic CH4 emissions continue to increase throughout the next three decades and beyond (i.e. SSP3-7.0). While we acknowledge the importance of aerosols and other non-CO2 forcing agents in the context of climate mitigation to achieve the temperature goals in the Paris Agreement16,51, our future scenarios focus on CH4 mitigation to investigate recent concerns raised about sustained [CH4] growth since 2007 and the associated potential challenge for achieving the 2 °C warming limit even under stringent CO2 mitigation by mid-century5,38.

Our study suggests that aggressive reductions of anthropogenic CO2 emissions without CH4 mitigation could push the Earth system beyond the 2 °C warming limit above pre-industrial levels for more than two centuries in the future. Initiating large-scale CH4 mitigation in the current decade, along with stringent CO2 mitigation, can allow to achieve the temperature goals in the Paris Agreement. However, delaying CH4 mitigation to the next decade or beyond will increase the risk of breaching the 2 °C warming limit. According to our model simulations, every 10-year delay in CH4 mitigation will result in an additional peak warming of about 0.1 °C. Consequences of such an increased peak warming over time and breaching the 2 °C warming limit are widespread, including an increased risk for an Arctic Ocean without sea ice in the summer34, record-breaking climate extremes35, the dieback of the Amazon rainforest36, the disintegration of major ice sheets36, persistent sea-level rise over multiple centuries33, and several other global and regional impacts of increasing global warming levels on natural and socio-economic systems52,53. Considering that [CH4] has been rising steadily since 2007 in line with unmitigated emission scenarios5,6, we highlight the importance of immediate cuts in anthropogenic CH4 emissions globally, along with stringent CO2 mitigation, in order to increase the likelihood of keeping global warming to well below 2 °C above pre-industrial levels. Actions associated with the Global Methane Pledge13 launched at COP26 in November 2021 should not be delayed, because every year of delayed CH4 mitigation implies additional global warming.

Methods

Model description

We use the University of Victoria Earth System Climate (UVic ESCM) for our simulations. The UVic ESCM consists of a 2-D (vertically-integrated) energy-moisture balance model for the atmosphere coupled to a comprehensive 3-D ocean general circulation model (OGCM) with marine biogeochemistry, a thermodynamic sea ice model, and a land surface model with dynamic vegetation as well terrestrial carbon fluxes (in the form of CO2)54,55. In this study, we use a version of the EMIC based on UVic ESCM 2.1021 which features a multi-layer ground structure (i.e. 14 ground layers of unequal thicknesses extending down to a depth of 250 m) that is capable of simulating permafrost freeze-thaw processes as well as permafrost CO2 fluxes (i.e. CO2 release and uptake)56. Furthermore, the version of the UVic ESCM used in this study simulates the spatial and temporal dynamics of wetlands57. In particular, sub-grid scale wetlands are identified in the EMIC following a TOPMODEL approach for global models58. The areal extent of wetlands varies in response to changes in soil hydrology (soil moisture content, runoff, surface inundation, etc.), which is affected by changes in precipitation, evapo-transpiration, temperature, vegetation—among many other atmospheric and terrestrial processes. In this study, we use a modified version of UVic ESCM 2.10 into which we incorporated a simplified representation of the global CH4 cycle (See next sections).

Wetland CH4 emissions

Wetland CH4 emissions are simulated in the UVic ESCM following a recent model development22. Wetland CH4 emissions are calculated as the balance between microbial production and oxidation of CH4 in the soil column. CH4 production is calculated in each soil layer as a function of moisture content, carbon content, temperature, and the relative depth from the soil surface. In this approach, soil moisture (i.e. water saturation) represents potential anoxic conditions. Soil carbon represents organic matter that may be accessed by methanogens. Soil temperature allows to estimate potential changes in methanogenic activity, whereas the relative depth from the soil surface allows to represent the net effect of depth-dependent controls on CH4 production that are unresolved by the UVic ESCM (e.g. the quality of organic matter and the distribution of methanogens in the soil). CH4 production is assumed to not take place in dry soil layers (i.e soil layers unsaturated with water) as well as in frozen soil layers. CH4 oxidation is calculated for the entire soil column as a fraction of the amount of CH4 produced in the soil column. The oxidized CH4 fraction is determined based on an estimated oxic zone depth, which represents the prevalence of methanotrophs in the soil. This fraction increases as the oxic zone deepens. By design, our model simulates wetland CH4 emissions associated with CH4 production across the globe (including CH4 emissions from previously frozen soil carbon upon permafrost thaw)22.

Atmospheric CH4 and associated radiative forcing

A simple one-box model is used to simulate the evolution of the atmospheric CH4 burden (B) with time as the balance between total CH4 emissions (E) and total CH4 sinks (S). The box model is defined as \(\frac{{{{{{\rm{dB}}}}}}}{{{{{{\rm{dt}}}}}}}\,=\left({{{{{\rm{E}}}}}}-{{{{{\rm{S}}}}}}\right)\), where \({{{{{\rm{E}}}}}}={{{{{{\rm{E}}}}}}}_{a}+\,{{{{{{\rm{E}}}}}}}_{w}+\,{{{{{{\rm{E}}}}}}}_{n}\) represents the sum of prescribed anthropogenic CH4 emissions (\({{{{{{\rm{E}}}}}}}_{a}\)), simulated wetland CH4 emissions (\({{{{{{\rm{E}}}}}}}_{w}\)), as well as natural CH4 emissions from non-wetland sources (\({{{{{{\rm{E}}}}}}}_{n}\)) such as termites, wild ruminants, wildfires, lakes, rivers, geologic seeps, and marine hydrates. Given that the UVic ESCM does not incorporate these non-wetland natural sources and in the absence of dataset for CH4 emissions from these sources, we assume that non-wetland natural CH4 emissions remain constant in time at 45 Tg C yr−1 (equivalent to 60 Tg CH4 yr−1). This value is in the range of estimated total CH4 emissions from non-wetland natural sources over the last four decades2,3 as well as pre-industrial periods59. Sinks of atmospheric CH4 are aggregated into a single term (\({{{{{\rm{S}}}}}}\)) calculated as \({{{{{\rm{S}}}}}}={{{{{\rm{B}}}}}}\,(1-{{\exp }}(-\frac{1}{{\tau }_{{{{{{\rm{CH}}}}}}4}}))\), where \({\tau }_{{{{{{\rm{CH}}}}}}4}\) is the atmospheric CH4 lifetime assumed to be 9.3 years2. Similar estimates for the atmospheric CH4 lifetime have been reported for the pre-industrial era (9.5 ± 1.3 years) and present-day (9.1 ± 0.9 years)60. At each time step, [CH4] is determined based on the atmospheric CH4 burden (B) by using a factor equivalent to ~2.8 Tg CH4/ppb. Radiative forcing associated with changes in [CH4] is calculated using the formulation in ref. 61 and is accounted separately from the aggregated forcing of other non-CO2 GHGs that is prescribed to the UVic ESCM in its standard configuration21.

Non-CH4 radiative forcing agents

To drive the UVic ESCM over the 1850–2300 period (1850–2014 for the historical simulation and 2015-2300 for future projections), we use CMIP6 data for non-CH4 natural and anthropogenic radiative forcing agents23,62,63,64. For natural forcing agents (volcanic and solar), we use volcanic radiative forcing anomalies spanning the historical period (1850–2014)64 and solar constant data prescribed to 230063. For anthropogenic forcing agents, we (i) use CMIP6 data for the historical simulation, and (ii) assume that all non-CH4 GHGs (including CO2) as well as aerosols evolve according to a scenario consistent with limiting global warming to 2 °C throughout the future (i.e. SSP1-2.6). Specifically, we prescribe CO2 emissions from fossil fuels as defined in the SSP1-2.6 scenario and their long-term extension23,24. The SSP1-2.6 scenario features strong reductions in CO2 emissions as well as negative CO2 emissions (i.e. artificial removal of atmospheric CO2) in the second half of the 21st century65. Furthermore, we prescribe gridded land-use change (LUC) data according to SSP1-2.666 and the UVic ESCM internally calculates corresponding LUC CO2 emissions. The radiative forcing of CO2 is calculated within the UVic ESCM following the formulation from ref. 61. Radiative forcing values of other non-CH4 GHGs are calculated externally using concentration data and their extension23, which are then summed up into an aggregated forcing that is prescribed to the UVic ESCM. For anthropogenic sulfate aerosols, we prescribe SSP1-2.6 gridded aerosol optical depth (AOD) data to the UVic ESCM67,68 and the model uses this data to internally calculate the associated radiative forcing. While forcing data for CO2 and other non-CH4 GHGs extend to 230023, forcing data for LUC and sulfate aerosols are prescribed to 2100 and their radiative forcing are held fixed at their 2100 values in our climate simulations.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.