Main

Methane (CH4) contributes 15–35% of the increase in radiative forcing from greenhouse gases emitted by human activities6. The atmospheric methane growth rate (MGR) has been high over the past decade, probably owing to the combined increases in fossil fuel and microbial sources7,8,9,10,11. In 2020, the MGR observed from surface sites of the NOAA Global Monitoring Laboratory (GML) network reached 15.1 ± 0.4 parts per billion per year (ppb yr−1), the highest value from 1984 to 2020 (Extended Data Fig. 1)12. The MGR was larger in the Northern than in the Southern Hemisphere, which suggests at first glance an increase of northern sources (Fig. 1). A similar, abnormally large, growth rate of 14.8 ppb yr−1 was also detected from total column concentration measurements (XCH4) by the Greenhouse Gases Observing Satellite (GOSAT; Supplementary Fig. 1). In the same year, the coronavirus pandemic led to a strong reduction of fossil fuel use, probably accompanied by a drop of CH4 emissions by 10% from oil and gas extraction, according to reports from the International Energy Agency (IEA)1 and regional estimates of emissions over extraction basins, such as the Permian Basin13. The reduced combustion of carbon fuels14 and lower fire emissions15 also caused less carbon monoxide (CO) and nitrogen oxides (NOx) to be released to the atmosphere during the first half of 202016,17. Both CO and NOx affect the atmospheric concentration of the hydroxyl radical (OH), which is the main sink of CH4. Even a small change in OH has a large impact on the MGR8. Meanwhile, the atmospheric CH4 concentration also feeds back on the OH available to remove air pollutants such as CO and NOx (refs. 18,19). Reduced CO emissions should increase the concentration of OH, whereas reduced NOx emissions should decrease OH (ref. 5), except in very polluted areas20. Thus, the net effect of COVID-19 emission changes on the MGR is uncertain. In addition, the year 2020 was exceptionally hot from early spring to late summer over northern Eurasia, a sensitive region for CH4 emissions from biogenic sources such as wetlands, permafrost slumps and arctic lakes, which are expected to emit more CH4 as the temperature increases. Determining whether the high MGR anomaly in 2020 was due to less atmospheric removal resulting from a decrease in OH or to enhanced biogenic sources is key to developing our understanding of the complex interplay of the anthropogenic and natural drivers of the methane budget required for the upcoming Global Stocktake of the Paris Agreement. Here we combined bottom-up and top-down approaches to understand the high MGR anomaly in 2020 relative to 2019 and quantified anomalies in the surface sources and in the global atmospheric OH sink.

Fig. 1: Atmospheric MGRs of four latitudinal bands.
figure 1

a–d, The annual growth rate is derived from weekly average marine surface atmospheric methane concentrations at NOAA’s surface sites in the four latitudinal bands following a previous work45. The colours correspond to the annual growth rate: warm colours for higher growth rate and cool colours for lower growth rate. The grey shaded area shows the standard deviation of the annual growth rate.

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A bottom-up view of emission anomalies

First, we estimated the change in anthropogenic CH4 emissions in 2020 from the fossil fuel, agriculture and waste sectors. To do so, we combined national greenhouse gas inventories (NGHGIs) submitted to the United Nations (UN) Framework Convention on Climate Change (UNFCCC) for Annex-I countries and the updated Emissions Database for Global Atmospheric Research (EDGAR) v6.0 inventory21 with new activity data from IEA22 and the Food and Agriculture Organization (FAO)23 of the UN for other countries (see Methods). In the category of fossil fuel extraction activities, global coal production decreased by 4.6% in 2020 compared with 2019, and global oil production and natural gas production decreased by 7.9% and 3.8%, respectively22. We inferred a decrease of CH4 emissions from oil and natural gas (−3.1 Tg CH4 yr−1) and from coal mining (−1.3 Tg CH4 yr−1). In the agricultural sector, the global rice cultivation area slightly increased according to FAO23 by 1% (+0.5 Tg CH4 yr−1), and an increase in livestock stock and slaughter numbers was reported as well (+1.6 Tg CH4 yr−1). Statistical data are not yet available for the waste sector for non-Annex-I countries, so we used the linear trends from EDGAR v6.0 for 2014–2018 to project a small global increase of +1.0 Tg CH4 yr−1 in 2020 compared with 2019. In summary, the anthropogenic CH4 emissions in 2020 decreased by 1.2 ± 0.1 Tg CH4 yr−1 (± standard deviation, hereinafter) (Extended Data Fig. 2), which at steady state would lead only to a 0.4 ± 0.0 ppb yr−1 decrease of growth in the atmosphere relative to 2019, based on the conversion factor of 2.75 Tg CH4 ppb−1 (ref. 24). This shows that the observed MGR anomaly of 5.2 ± 0.7 ppb yr−1 in 2020 compared with 2019 (15.1 ± 0.4 ppb yr−1 of MGR in 2020 relative to 9.9 ± 0.6 ppb yr−1 of MGR in 2019) must be attributed to a change of natural emissions and/or OH sink.

We then estimated biogenic and fire CH4 emissions in 2020 from bottom-up models. The year 2020 was wetter than normal in northern and tropical regions (Supplementary Fig. 2), and extremely warm in northern Eurasia from early spring to late summer25 (Extended Data Fig. 3). Two satellite-based fire emission datasets, the Global Fire Assimilation System (GFAS) and the Global Fire Emissions Database (GFED4.1s), consistently show that the global fire emissions in 2020 were lower by 6.5 ± 0.1 Tg CH4 yr−1 than in 2019 (Extended Data Fig. 4). The southern tropical regions (30° S–0°) dominated the 2020 decrease in fire emissions in both datasets, although in the USA there were fewer fires in the first half of the year but more in the second half of the year26. The GFAS data show that eastern Siberia had higher fire emissions in 2020 compared with 2019, by 0.4 Tg CH4 yr−1. This anomaly is related to the heatwave in the region (Extended Data Fig. 3)25, where the fire season advanced by two months in 2020 and began in May27. Globally, fire emissions appear to have dropped in 2020 compared with 2019, implying other processes must explain the large positive MGR anomaly in 2020.

We found that most wetland areas of the world were exposed to warmer and wetter conditions in 2020 than normal years (Fig. 2 and Extended Data Fig. 3). Northern wetlands were exposed to warmer temperatures (+0.43–0.58 °C) relative to 2019 as shown in Fig. 2 (Supplementary Table 1). Precipitation over global wetlands28 had a 2–11% annual increase relative to 2019, mainly in the northern high latitudes and in the tropics (Supplementary Table 1). With increased precipitation, an expansion of wetland area and more shallow water tables promoting emissions are expected. In addition, the earlier soil thaw and later soil freeze in 2020 resulted in a longer emission season in the high northern wetlands (Supplementary Fig. 3), and possibly in increased emissions from permafrost and thermokarst lakes. To quantify wetland emissions from 2000 to 2020, we used two process-based wetland emission models (WEMs) forced by different climate datasets (see Methods). These models show that wetland emissions significantly and positively correlate with precipitation in the tropics (30° S–30° N)29 and in the southern extra-tropics (90° S–30° S) and with both temperature and precipitation in northern wetlands (30° N–90° N) (Fig. 2). Warmer and wetter wetlands over the Northern Hemisphere in 2020 (Supplementary Table 1) increased emissions by 6.0 ± 2.5 Tg CH4 yr−1 relative to 2019, dominating the net increase in global wetland emissions (6.0 ± 2.3 Tg CH4 yr−1) in 2020 (Extended Data Fig. 5). The spread in the estimates of WEMs is mainly due to differences in wetland area related to differences in the precipitation forcing (Supplementary Fig. 2), and partly to model structure, even though the two models have similarities in parameterizations. With a 4% increase in precipitation over wetlands from the Multi-Source Weighted-Ensemble Precipitation (MSWEP) precipitation field, which merges gauge, satellite, and reanalysis data to obtain accurate precipitation estimates30,31, wetland emissions increased by 5.8 ± 1.5 Tg CH4 yr−1. Using root-zone soil moisture from Global Land Evaporation Amsterdam Model (GLEAM) v3.5a32 as a proxy to calculate the expansion of wetland areas in 2020 (see Methods), we found a larger wetland emission increase of 7.4–9.3 Tg CH4 yr−1, mainly in the Northern Hemisphere (Extended Data Fig. 5). Observed land liquid water mass change from the GRACE-FO satellite33 confirms that wetlands water storage increased in the Northern Hemisphere. The increase in soil moisture over wetlands in the Northern Hemisphere simulated by the two WEMs is less than the liquid mass change observed from GRACE-FO, especially north of 30° N (Supplementary Figs. 4 and 5), suggesting that the expansion of Northern Hemisphere wetlands or the water table levels—and thus emissions in 2020—may be underestimated by WEMs. Overall, it is probable that wetland emissions made a dominant contribution to the soaring level of atmospheric methane in 2020, although there is uncertainty regarding the magnitude of the contribution, mainly owing to uncertainty in the precipitation data.

Fig. 2: Wetland methane emissions and temperature and precipitation in the four latitudinal bands during the period 2000–2020.
figure 2

a–d, The black lines show the anomalies of average wetland emissions simulated from the two WEMs with four climate forcing. The temperature anomalies over wetlands, from CRU TSv4.05, ERA5 and MERRA2, and the precipitation anomalies over wetlands, from these three datasets and MSWEP, are shown in red and blue, respectively. The shaded area shows the standard deviation of 12 simulations for wetland emissions (eight from ORCHIDEE-MICT and four from LPJ-wsl, see Methods). The correlation coefficients between wetland emissions and temperature (red) and precipitation (blue) are also marked in the upper left of each panel, with *** for P < 0.001, ** for P < 0.01 and ns for not significant. The vertical dashed line marks the year of 2019 for reference.

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According to our ensemble of bottom-up estimates, an increase in wetland emissions (6.0 ± 2.3 Tg CH4 yr−1) does not fully explain the increased methane emissions (14.4 ± 2.0 Tg CH4 yr−1) inferred from the MGR anomaly (5.2 ± 0.7 ppb yr−1) between 2020 and 2019 under the assumption that the sink remains unchanged. Considering a decrease in anthropogenic emissions of 1.2 Tg CH4 yr−1 and fire emissions of 6.5 Tg CH4 yr−1, even with our largest estimate of wetland emissions (9.4 Tg CH4 yr−1), the bottom-up budget is still not closed, revealing a missing source anomaly of more than 12.7 Tg CH4 yr−1, which must be attributed to a decrease in the atmospheric CH4 sink, to additional sources such as lakes or permafrost or to extra-wetland emissions that were missed by the WEMs.

Atmospheric constraints in 2020

The increase in wetland emissions is mainly located in the Northern Hemisphere, whereas the decrease in fire emissions is mainly in southern tropical regions, and so we expect that the MGR in the Northern Hemisphere should be higher than the MGR in the Southern Hemisphere. Indeed, the latitudinal averaged growth rate of methane observed from the surface sites confirms that the Northern Hemisphere had a higher growth rate than the Southern Hemisphere in 2020 (Supplementary Fig. 6). The GOSAT data, which provide an MGR integrated over the whole column, and are thus much less sensitive to changes in the depth of the boundary layer at continental stations, also show a similar latitudinal pattern to the data from the surface sites, with a peak in the column growth rate at 10° N–50° N (Supplementary Fig. 7).

To quantify the spatial and temporal distribution of emission anomalies in 2020 from atmospheric observations, we used a three-dimensional (3D) atmospheric inversion assimilating surface CH4 observations from a total of 103 stations (see Methods). Inversions have the advantage over bottom-up methods to match the observed MGR and gradients between all stations. We performed a 3Datmospheric inversion (INV) that prescribes changes in the OH concentration field, as simulated by a full chemistry transport model (LMDZ-INCA)34,35 with realistic CO, hydrocarbons and NOx anthropogenic emissions derived from gridded near-real-time fossil fuel combustion data that include lockdown-induced reductions in 202036,37. The chemistry transport model is driven by meteorology from ECMWF ERA5 data38 and biomass burning emissions from GFED4.1s15. Figure 3 shows a decrease in NOx emissions by 6% in 2020 relative to 2019, which is particularly apparent in the spring (March, April and May) when COVID-19 lockdown measures were imposed in many Northern Hemisphere countries (Extended Data Fig. 6). The decrease in global NOx emissions in 2020 relative to 2019 was seven times larger than the decreasing trend from 2005 to 2019 (Supplementary Figs. 8 and 9). Both the global NOx emissions and satellite-derived tropospheric NO2 concentration from Ozone Monitoring Instrument (OMI) in 2020 were the lowest during the period 2005–2020 (Supplementary Fig. 9). Our chemistry transport model LMDZ-INCA produced a globally averaged 1.6% decrease in annual tropospheric OH concentration in 2020 relative to 2019. The decrease in monthly tropospheric OH reached as high as 6% in April, May and June (Fig. 3d) over the Northern Hemisphere (0°–60° N; Extended Data Fig. 7), suggesting that the drop of NOx emissions in 2020 outweighedthe effects of a decrease in anthropogenic and fire CO emissions (Supplementary Fig. 10) and made OH lower. To independently verify this modelled decrease of global OH in 2020, we used a 12-box model to infer changes in OH9,39 by simultaneously optimizing OH concentration and the emissions of two HFC and one HCFC species (HCFC-141b, HFC-32 and HFC-134a) using atmospheric observations of these three species from the NOAA and AGAGE networks including the latest data for 2020. This diagnostic of OH is based on the premise that errors in the prior emissions should be largely independent between the three gases, but errors in OH will be correlated for all of them (see Methods). The box model shows a net decrease in OH of 1.6–1.8% in 2020 relative to 2019 after the optimization. This estimate of the OH decrease in 2020 is independent and consistent with the full chemistry model simulation.

Fig. 3: Anomaly of NOx emissions and tropospheric hydroxyl radical (OH) in 2020 relative to 2019.
figure 3

a,c, Spatial patterns of NOx emissions anomaly (ΔNOx emissions; a) and OH anomaly (ΔOH; c) in 2020 relative to 2019. b,d, Difference in monthly global NOx emissions (b) and monthly tropospheric OH (d) between 2020 and 2019. The NOx emissions data are from the Community Emissions Data System dataset36.

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Prescribed with the decrease of OH and its spatial pattern from the chemistry transport model, the INV gives a global increase of 6.9 ± 2.1 Tg CH4 yr−1 for surface emissions and a decrease of 7.5 ± 0.8 Tg CH4 yr−1 for the weaker atmospheric CH4 sink. Considering the uncertainty of the decrease in OH and of the observed MGR12, the global increase in surface emissions and decrease in the atmospheric CH4 sink contributed, respectively, 47 ± 16% and 53 ± 10% of the total positive MGR anomaly in 2020 relative to 2019 (Fig. 4). The global increase of surface emissions is decomposed into an increase in the Northern Hemisphere of 14.3 Tg CH4 yr−1, partly offset by a decrease in the Southern Hemisphere of 7.4 Tg CH4 yr−1 (Fig. 4a). The spatial pattern of emission anomalies produced by INV confirms enhanced emissions in northern North America, and western and eastern Siberia hinted by the bottom-up wetland models. In the Northern Hemisphere, our maximum bottom-up estimate of the increase in wetland emissions (11.2 Tg CH4 yr−1) is, however, smaller than the solution of INV. This suggests that either wetland models underestimated emissions, possibly because of underestimated soil water content (see above), too deep water table, missed emissions from small wetlands and/or other sources spatially collocated with northern wetlands such as lake and pond emissions40, aquaculture emissions41 and thawing permafrost slump emissions42. The largest temperature anomaly of the past two decades was also indeed found over permafrost regions in 2020, particularly in Russia (Extended Data Fig. 3a and Supplementary Fig. 11), which could have increased methane emissions from upland permafrost soils43 and lakes, including thermokarst lakes44. Estimation of changes in emissions from lakes (including reservoirs) and permafrost shows limited contributions from these two sources (<0.1 Tg CH4 yr−1) to fill the gap in the emission changes between bottom-up and top-down approaches, although with large uncertainties (Supplementary Information). We note that owing to the sparse atmospheric networks in Central and South Asia, Middle East, Africa and tropical South America (Supplementary Fig. 12), the inferred fluxes and therefore flux changes in these regions may have large uncertainties. The evaluations against independent observations revealed that emission changes over large latitudinal bands or at hemispheric scales are robustly constrained (Supplementary Figs. 13–18). In addition, an extension of our 3D inversion and analyses to cover the period 2015–2020 also showed similar attribution of the MGR anomaly in 2020 (Supplementary Fig. 19).

Fig. 4: Methane emissions and sink anomaly in 2020 relative to 2019.
figure 4

a, Methane emissions anomaly of four latitudinal bands derived from atmospheric 3D inversions with OH field from LMDZ-INCA simulations (INV), wetland emissions anomaly from two WEMs, fire emissions anomaly from GFED4.1s and GFAS, and anthropogenic (Anthro.) emissions anomaly. The black dots show the net changes in global CH4 emissions between 2020 and 2019. The sink anomaly is calculated by a 1.6 ± 0.2% decrease in OH in INV. The observed MGR anomaly (14.4 ± 2.0 Tg CH4 yr−1) from surface sites is defined as the difference in MGR between 2020 (15.1 ± 0.4 ppb yr−1) and 2019 (9.9 ± 0.6 ppb yr−1) with a conversion factor of 2.75 Tg CH4 ppb−1. The error bars represent one standard deviation. b, Spatial pattern of emissions anomaly from top-down INV. c, Spatial distribution of contribution sources (wetlands, fire and anthropogenic) to change in emissions derived from bottom-up estimates. d, Spatial pattern of emissions anomaly from bottom-up estimates including wetland, fire and anthropogenic emissions.

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In summary, our results show that an increase in wetland emissions, owing to warmer and wetter conditions over wetlands, along with decreased OH, contributed to the soaring methane concentration in 2020. The large positive MGR anomaly in 2020, partly due to wetland and other natural emissions, reminds us that the sensitivity of these emissions to interannual variation in climate has had a key role in the renewed growth of methane in the atmosphere since 2006. The wetland methane–climate feedback is poorly understood, and this study shows a high interannual sensitivity that should provide a benchmark for future coupled CH4 emissions–climate models. We also show that the decrease in atmospheric CH4 sinks, which resulted from a reduction of tropospheric OH owing to less NOx emissions during the lockdowns, contributed 53 ± 10% of the MGR anomaly in 2020 relative to 2019. Therefore, the unprecedentedly high methane growth rate in 2020 was a compound event with both a reduction in the atmospheric CH4 sink and an increase in Northern Hemisphere natural sources. With emission recovery to pre-pandemic levels in 2021, there could be less reduction in OH. The persistent high MGR anomaly in 2021 hints at mechanisms that differ from those responsible for 2020, and thus awaits an explanation. Our study highlights that future improvements in air quality with reduced NOx emissions may increase the lifetime of methane in the atmosphere5, and therefore would require more reduction of methane emissions to achieve the target of Paris Agreement.

Methods

Atmospheric methane growth rate (MGR)

We used the monthly time series of globally averaged marine surface atmospheric methane concentration covering the period July 1983–Dec 2020 from NOAA’s Global Monitoring Laboratory (NOAA/GML)12,45. After the seasonal cycle of atmospheric methane is removed by the CCGvu programme46, the smoothed annual MGR shown in Fig. 1a is the MGR calculated for each specific month (for example, 1 March in that year to 1 March of the next year). The annual MGR in a given year is the increase in its abundance (mole fraction) from 1 January in that year to 1 January of the next year12. The MGR anomaly in 2020 relative to 2019 is defined as the difference in MGR between 2020 (15.1 ± 0.4 ppb yr−1) and 2019 (9.9 ± 0.6 ppb yr−1).

Anthropogenic methane emissions

For Annex-I countries that reported their national greenhouse gas inventories (NGHGIs) to UNFCCC and updated to 2020, we used the reported anthropogenic emissions (coal mining, oil and gas production, agriculture and waste) of these 41 countries (https://unfccc.int/ghg-inventories-annex-i-parties/2022). For other countries, emissions from coal mining, oil and gas production, agriculture and waste from 2000 to 2018 were from EDGAR v6.021. We collected updated activity data from IEA22 and FAO23 for 2019 and 2020, and used the same emission factors as 2018 from EDGAR v6.0 to estimate methane emissions from coal mining, oil and gas production and agriculture sources in 2019 and 2020. For oil and gas production and combustion, we collected data from IEA22. For coal production, we collected coal production data from IEA22 and corrected China’s production using data from the statistical yearbook for China47. For agricultural activity data, we used livestock data and rice cultivation area from FAO23. As waste activity data are not yet available for these countries, we used the linear trends of waste sector from EDGAR v6.0 for 2014–2018 to project the change in 2020 relative to 2019.

Global fire methane emissions

Both the Global Fire Emissions Database version 4.1 including small fire burned area (GFED4.1s)15 and the Global Fire Assimilation System (GFAS, https://atmosphere.copernicus.eu/global-fire-monitoring) from Copernicus Atmosphere Monitoring Service (CAMS) are used to derive monthly global fire methane emissions. GFED4.1s combines satellite information on fire activity and vegetation productivity to estimate the gridded monthly burned area and fire emissions, and has a spatial resolution of 0.25° × 0.25° (ref. 15). Note that GFED4.1s fire emissions in 2017 and 2020 are from the beta version. The GFAS assimilates fire radiative power (FRP) observations from satellites to produce daily estimates of biomass burning emissions. We aggregated the GFAS daily fire emissions into monthly emissions.

Wetland CH4 emissions simulated by models

We used two process-based WEMs to simulate global wetland CH4 emissions: ORCHIDEE-MICT48 and LPJ-wsl4. These two WEMs simulate methane production and transport to the atmosphere through diffusion, ebullition and plant transportation based on a previously published framework49. To estimate the uncertainty of the change in wetland emissions in 2020, four climate forcing datasets were used to drive the two WEMs. First, we downloaded two reanalysis climate datasets: hourly ERA5 with a spatial resolution of 0.25° × 0.25° from 1979 to 202038 and hourly MERRA2 with a spatial resolution of 0.5° × 0.625° from 1980 to 202050. We resampled these two reanalysis datasets (air temperature, precipitation, humidity, downward shortwave and longwave radiation, surface air pressure and wind speed) into 1° × 1° and 0.5° × 0.5° resolutions to drive ORCHIDEE-MICT and LPJ-wsl, respectively. These different climate datasets had large differences in the change of precipitation in 2020 (Supplementary Fig. 2), so we also used monthly temperature and precipitation data from CRU TS v4.0551 and monthly precipitation from MSWEP v2.830,31 to calibrate the ERA5 climate forcing. For the CRU data, we added the difference in monthly temperature between CRU and ERA5 into the hourly ERA5 temperature field, and scaled the ratio of monthly precipitation between CRU and ERA5 into hourly ERA5 precipitation from 1979 to 2020. These scaled data, along with the other unchanged ERA5 fields, were used to drive the models. For the MSWEP precipitation data, we only scaled the ratio of monthly precipitation between MSWEP and ERA5 into hourly ERA5 precipitation, and these data along with the other ERA5 fields was used to drive the models. The wetland area dynamics were simulated by a TOPMODEL-based diagnostic model that has successfully predicted the spatial distribution and seasonality of natural wetlands extents (dynamics by ORCHIDEE-MICT52 and dynamics by LPJ-wsl53 are described previously). For wetland dynamics simulated in ORCHIDEE-MICT, two wetland maps were used to calibrate the parameters, one is the Regularly Flooded Wetlands static map (RFW)28 recording the long-term maximum wetland area used to calibrate the long-term maximum wetland extent for each grid cell, and the other is the satellite-based global inundation product GIEMS-2 (Global Inundation Estimate from Multiple Satellites version 2)54 used to calibrate the yearly maximum wetland extent for each grid cell. Details of wetland dynamics and the parameter calibration can be found in earlier works52,55. Thus, for wetland emissions simulated by ORCHIDEE-MICT, we obtained two sets of wetland dynamics for each climate forcing: in total, eight simulations with four climate forcing and two sets of calibrated parameters from RFW and GIEMS2. In addition, we also used monthly root zone soil moisture from GLEAM v3.5a products32 with TOPMODEL to calculate wetland area dynamics, and with wetland emission density per wetland area from ORCHIDEE-MICT plus ERA5 climate forcing, we derived an additional estimate of the change in wetland emissions in 2020.

AGAGE 12-box model and inversions

This model has four equal area boxes in the latitudinal direction (90° N–30° N, 30° N–0°, 0°–30° S, 30° S–90° S) and three boxes in the vertical representing the lower and upper troposphere, and stratosphere, and has been used extensively in atmospheric chemistry and lifetime studies39,56,57. Horizontal and vertical mixing rates between the boxes are provided monthly and are based on a climatology of empirical values. The model was integrated in two-day time steps using the fourth-order vectorized Runge–Kutta algorithm. Atmospheric chemistry is calculated at each time step using Arrhenius equations and includes OH reactions. Atmospheric inversions were performed using the adjoint of the AGAGE 12-box model and a quasi-Newton algorithm to find the best linear unbiased estimate (for details see a previous work)9.

OH was optimized by simultaneously solving for an annual scalar of OH concentration and the monthly emissions of two HFC species (HFC-134a and HFC-32) and HCFC-141b, on the basis of the premise that errors in the prior emissions of these species are probably not strongly correlated, whereas the impact of errors in the prior OH on the atmospheric concentrations of all three species will be fully correlated. The three species were chosen because they all are principally lost by oxidation by OH, have relatively short atmospheric lifetimes (14, 5.4 and 9.4 years for HFC-134a, HFC-32 and HCFC-141b, respectively) and have had substantial emissions over the past decade58. Observations were used from the NOAA GML discrete sampling network, which has 12 sites globally with observation uncertainties of 0.2 ppt, 0.2 ppt and 0.1 ppt for the mean concentrations in the four latitudinal boxes for HFC-134a, HFC-32 and HCFC-141b, respectively. Prior emissions of HFC-134a and HFC-32 were based on UNFCCC reports and published data59 for China with seasonality based on ref. 60. Prior emissions of HCFC-141b were from ref. 58. Uncertainties of the two HFC species were based on previous estimates59 and for HCFC-141b an uncertainty of 50% was assumed. Prior OH concentrations were obtained from the Copernicus reanalysis product EAC461. With the prior emission uncertainties described above and 10% prior uncertainty for OH concentration, the decrease in OH in 2020 relative to 2019 was 1.8%, and the posterior uncertainty of OH decreased by 55% compared with the prior uncertainty. We ran another sensitivity test using 10% prior uncertainty for OH and 25% uncertainty in the prior emissions of all species, and found a 1.6% decrease in OH in 2020. An additional sensitivity test was run using a 5% prior uncertainty for the OH concentration, although it is too optimistic, and we found 0.6% decrease in OH in 2020. The inversed magnitude of change in OH partly depends on the prior uncertainties of OH and F gases, but still offers OH change signal from independent F-gases observations. The posterior uncertainty in OH was estimated as the 1 standard deviation (1σ) of the results from a Monte Carlo ensemble of 100 inversions, with random errors added to the prior emissions and observations for each member of the ensemble.

OH concentrations simulated from a full chemistry transport model LMDZ-INCA

Global gridded OH concentrations were simulated by the full chemistry transport model LMDZ-INCA34,35. The anthropogenic emissions were derived from the Community Emissions Data System (CEDS) emission inventory up to 201936 and were further updated to 2020 on the basis of the sectoral CO2 emission changes estimated by Carbon Monitor37 to reflect the influence of COVID-19 on emission changes. The emissions data revealed the decline and rebound in anthropogenic emissions of NOx, the key precursor of OH, during and after the COVID-19 lockdowns around the world, which are broadly consistent with different bottom-up and top-down estimates17,62,63. For the baseline simulations, each year, we used the monthly anthropogenic emissions compiled previously64. These emissions include the different sectors: energy, industrial, residential, transportation and waste. The agricultural soil emissions for NOx and NH3 are also included, and no natural soil emissions are added in complement to those emissions. The biomass burning emissions are from GFED4.1s15. The ORCHIDEE vegetation model is used to calculate offline the biogenic surface fluxes of isoprene, terpenes, acetone and methanol as described previously65. Natural emissions of dust and sea salt are computed using the 10-m wind components from ECMWF ERA5 reanalysis. The lightning NOx emissions are parameterized in the model on the basis of convective cloud heights as described in an earlier work66. On the basis of this parameterization, the total lightning NOx emissions for the baseline simulation are 5.5 Tg N yr−1. The meteorological fields used to drive the LMDZ-INCA model simulations were derived from the ECMWF ERA5 reanalysis dataset38. Our LMDZ-INCA simulations reproduced the monthly changes in mid-troposphere ozone and tropospheric NO2 columns during the last decade up to 2020 (Supplementary Figs. 20 and 21). Given that ozone and NOx have important roles in OH sources and sinks, the agreement of our LMDZ-INCA simulations with their observed values suggests that the simulations are representative of the global atmospheric chemical state including the variations of OH.

Atmospheric 3D inversion

A variational Bayesian inversion system, PYVAR-LMDZ-SACS, was used to infer weekly CH4 fluxes at a spatial resolution of 1.9° (in latitude) by 3.75° (in longitude) between July 2018 and May 2021. The system combines a variational data assimilation system Python Variational (PYVAR)67, an atmospheric transport model Laboratoire de Météorologie Dynamique with zooming capability (LMDZ)68, and a Simplified Atmospheric Chemistry System (SACS)69. It has been widely applied to optimize sources and sinks of reactive atmospheric tracers such as CH4 and CO11,70,71,72,73, and has contributed to top-down inversions of the global CH4 budgets74,75. Technically, the inversion system finds the optimal state vector that statistically best fits both the observations y and a prior state vector xb weighted by their respective uncertainties (defined as the covariance matrices B and R), through iteratively minimizing a cost function J defined as follows:

$$J({\bf{x}})={0.5({\bf{x}}-{{\bf{x}}}^{{\rm{b}}})}^{{\rm{T}}}{B}^{-1}({\bf{x}}-{{\bf{x}}}^{{\rm{b}}})+{0.5(H({\bf{x}})-{\bf{y}})}^{{\rm{T}}}{R}^{-1}(H({\bf{x}})-{\bf{y}})$$
(1)

where x is the state vector that contains the variables to be optimized, including (1) the time series of grid-point-based eight-day mean surface emission fluxes of CH4, and (2) grid-point-based scaling factors for the initial column-mean concentrations of CH4. H represents the observation operator that projects the state vector into the observation space, and includes the chemistry-transport model (CTM) plus the convolution operation. Here, the CTM is composed of the atmospheric transport model LMDZ68 coupled with the SACS module69 that accounts for the chemical interactions between CH4 and OH. The transport model was nudged towards reanalysed horizontal wind fields from ERA5, and run in an offline mode with precomputed three-hourly transport mass fluxes. The minimization of the cost function is solved iteratively until a reduction of 99% in the gradient of the cost function is achieved.

The prior CH4 fluxes were compiled from existing bottom-up inventories for different sectors. Detailed information is given in Supplementary Table 2. The dataset incorporates recent development of emission inventories and current understanding of various CH4 sources and sinks, and has therefore been proposed for use as the priors for top-down CH4 inversions contributing to the next phase of the global methane budget assessment. The OH and O(1D) fields were prescribed from model outputs of the chemistry–climate model LMDZ-INCA with a full tropospheric photochemistry scheme34,76 (see Methods section ‘OH concentrations simulated from a full chemistry transport model LMDZ-INCA’). The definition of prior errors (the B matrix) follows previous schemes11,70,71, that is, 70% for gridded CH4 emissions.

Observations of CH4 concentrations were obtained from ground-based greenhouse gas monitoring networks. For the set-up of observation constraints, surface in situ and flask–air CH4 observations from a total of 103 stations were assimilated, including 71 stations with their records extending to late 2020 or early 2021, mostly from the NOAA and ICOS networks (Supplementary Fig. 12). All these observations have been reported on, or linked to, the WMOX2004 calibration scale. With respect to continuous CH4 measurements, daily afternoon means (12:00–16:00 lst; lst, local sidereal time) were assimilated for stations below 1,000 m above sea level (a.s.l.) and morning means (0:00–4:00 lst) for those above 1,000 m a.s.l., owing to uncertainties in the model’s representation of boundary layer mixing and complex terrain mesoscale circulations77,78. The observation errors (the R matrix) combine measurement errors, representation errors and transport model errors that contribute to model–observation misfits. For surface CH4 observations, the synoptic variability at each station was used as a proxy for representation errors and transport model errors70,71, and was calculated as the residual standard deviation (RSD) of the de-trended and de-seasonalized observations. For the effect of OH variations on derived emission anomalies, we took the OH field simulated by a full chemistry transport model LMDZ-INCA (see Methods section ‘OH concentrations simulated from a full chemistry transport model LMDZ-INCA’). Note that, to ensure the assumption of OH changes from LMDZ-INCA, the OH fields were not adjusted in 3D inversions.

To validate the robustness of our 3D CH4 inversion, we compared the prior and posterior model states with independent observations from multiple platforms (Supplementary Fig. 13), including the XCH4 observations from the Total Carbon Column Observing Network (TCCON; Supplementary Figs. 14 and 15) and the CH4 vertical profiles from aircraft samplings (Supplementary Fig. 16) and AirCore campaigns (Supplementary Figs. 17 and 18). The evaluation demonstrates the overall good performance of our 3D inversion in separating latitudinal emissions and representing large-scale atmospheric mixing (horizontally and vertically). The underestimation of XCH4 increases in northern TCCON sites (Supplementary Figs. 14 and 15), as well as biases in the vertical CH4 difference within northern low-to-mid latitudes (Supplementary Fig. 16), may suggest uncertainties in flux inversion in the Northern Hemisphere, including those related to sparse data coverage (as shown in Supplementary Fig. 12 for certain regions) and inherent transport model errors (for example, biases in representing stratospheric processes) that are not resolved yet by the current model community.

Reporting summary

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