Delaying methane mitigation increases the risk of breaching the 2°C warming limit

5 Atmospheric methane levels are growing rapidly, raising concerns that sustained methane growth could constitute a challenge for limiting global warming to 2°C above pre-industrial levels, even under stringent CO 2 mitigation. Here we use an Earth system model to investigate the importance of immediate versus delayed methane mitigation to comply with the 2°C limit under a future scenario of low CO 2 emissions. Our results suggest that 10 methane mitigation initiated before 2030, alongside stringent CO 2 mitigation, could enable to limit global warming to well below 2°C over the next three centuries. However, delaying methane mitigation to 2040 or beyond increases the risk of breaching the 2°C limit, with every 10-year delay resulting in an additional peak warming of ~0.1°C. We find that CO 2 feedbacks amplify the peak warming level under delayed versus early methane mitigation. 15 We conclude that urgent methane mitigation is needed to increase the likelihood of achieving the 2°C goal .

2 Methane (CH4) is a potent greenhouse gas, second only to CO2 in the contribution to global temperature increase relative to pre-industrial levels 1 . Atmospheric CH4 levels have grown rapidly since the year 2007 2, 3 . The mean atmospheric CH4 concentration ([CH4]) currently exceeds 1900 parts per billion (ppb), which is more than 2.5 times larger than the pre-industrial average 4 . Recent trends of observed CH4 levels are tracking future scenarios of unmitigated emissions 5,6 . For more than three decades, global CH4 5 emissions have been dominated by anthropogenic sources mostly related to fossil fuel exploitation, livestock production, waste and agriculture 2, 3,7 . Since the 2010s, 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 economy [8][9][10] .
A salient outcome of the 2015 Paris Agreement is the international commitment to keep global 10 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 levels 11 . 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-century 12 . While the need for urgent CH4 mitigation is now recognized (e.g. the Global Methane Pledge following the recent COP26 13 ), it is necessary to assess the importance of immediate 15 versus delayed CH4 mitigation to comply with the temperature goals in the Paris Agreementparticularly taking into account potential Earth system feedbacks.
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 20 by CH4 emissions in their representation of the global CH4 cycle 14 ; and (ii) previous research applying an Earth system modelling 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 as well as potential climate-CH4 feedbacks 15 .
We use version 2.10 of the University of Victoria Earth System Climate Model (UVic ESCM) 16 , 25 into which we implemented a simplified representation of the global CH4 cyclefeaturing simulated wetland CH4 emissions (including CH4 emissions from previously frozen soil carbon upon permafrost thaw) 17  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) 18,19 : (i) 5 SSP1-2.6, a scenario featuring immediate CH4 mitigation; and (ii) SSP3-7.0, a scenario without CH4 mitigation throughout the 21 st 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 10 extension beyond the 21 st century ( Figure 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 (Table S1). By design, these idealized scenarios allow us to compare the effect of immediate versus delayed CH4 mitigation on the global climate at the end of the 21 st century and beyond. We further assume that all other future anthropogenic forcings (including CO2 emissions) evolve 15 according to SSP1-2.6, which is a scenario aimed at limiting global warming to below 2°C throughout the 21 st century 20 .

Results
Delaying CH4 mitigation results in higher peak warming

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The timing of CH4 mitigation significantly 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 ( Figure 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 25 4 in CH4 mitigation, our model simulates an additional peak warming of approximately 0.1°C (Figure 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 around the year 2100 remain high for delayed CH4 mitigation relative to early CH4 mitigation (Figure 2b) owing to a lag in CH4 sinks ( Figure S2b). 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 Supplement S4).

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The peak warming is amplified by biogeochemical feedbacks Biogeochemical feedbacks influence SAT changes in addition to the timing of CH4 mitigation. In particular, we find that climate-CO2 feedbacks contribute to increase 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 25 scenarios than for early CH4 mitigation scenarios (Figure 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 5 oceans through the solubility pump, resulting in enhanced [CO2] and an amplification of global warming 21 . Overall, we deduce that CO2 feedbacks amplify the SAT response in late versus early CH4 mitigation scenarios. However, we do not detect a significant feedback between global warming and wetland CH4 emissions in our model simulations. 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 (Figure 2a), 10 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 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  Figure 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 21 st century ( Figure 3), with longer mitigation delays implying longer overshoot periods of the 2°C threshold. As expected with SSP1-2.6, none of the CH4 mitigation scenarios considered in this study will enable to limit global warming to below 1.5°C above 1850-1900 levels ( Figure 3).

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The timing of CH4 mitigation over the next three decades has implications beyond the 21 st century. While anthropogenic CH4 emissions prescribed to our model converge by 2100 for all mitigation scenario 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 15 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 runfrom the second half of the 22 nd century onwards, after an overshoot in the first half of the 21 st century ( Figure 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 20 warming to more than 2°C above pre-industrial levels throughout the 21 st century and beyond ( Figure 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. 7

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 results 25-28 . Our study presents two additional findings: (i) the importance of biogeochemical feedbacks in the context of CH4 mitigation to achieve stringent temperature limits, and 5 (ii) long-term climate impacts of a delay or failure to mitigate CH4 in the current century. Our study shows that climate-CO2 feedbacks amplify the SAT response for delayed versus early CH4 mitigation.
However, the significance of the feedback between wetland CH4 emissions and climate change is small in the context of this study. Furthermore, 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 10 ( Figure 2d and Figure 3). Such a delayed CH4 mitigation may result in other long-term impacts such as a persistent sea-level rise over many centuries 29 . 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 (Figure 3).
While mitigation research and efforts generally focus on achieving net-zero CO2 emissions by suggests that many anthropogenic sources of CH4 can be reduced cost-efficiently 27,32,34 , 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 sectors 6,7,25-27,32 . If deployed rapidly, readily available measures for large-scale CH4 mitigation by sector can contribute to significantly slowdown global 25 warming 28 . In addition to the recent Global Methane Pledge by more than 100 countries representing 8 70% of the global economy 13 , multilateral partnerships already exist to support large-scale CH4 mitigation (e.g. the Climate and Clean Air Coalition as well as the Global Methane Initiative [35][36][37][38]. 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 security 39,40 .

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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 change 41 . 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 ESCM 17 (Table S2). Additional lifetime varies by a few months to a few years mostly due to changes in atmospheric chemistry associated with CH4 sinks 43 , and this variation in the CH4 lifetime has been invoked to explain past changes in the 20 growth rates of atmospheric CH4 levels 3,43 . Variations in the atmospheric CH4 lifetime are mainly regulated by a chemical feedback involving the oxidation of CH4 by the OH radical 3,43 , 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 25 is a potential underestimation of the [CH4] peak in delayed mitigation scenarios.
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 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 10 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

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Competing interests: The authors declare that they have no competing interests.

Data availability:
The model data that support the findings of this study will be made available on the

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Code availability: The code for the UVic ESCM version 2.10 including our representation of the global CH4 cycle will be made available on Zenodo upon publication of the manuscript.

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Correspondence and request for materials should be addressed to CMN or KZ.       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 20 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 25 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) 17 .