The observation vector for the inversion (y) consists of column-averaged dry-air methane mole fractions during 2010–2018 observed by the TANSO-FTS instrument on board the Greenhouse Gases Observing Satellite (GOSAT) (Kuze et al., 2009). The satellite is in polar sun-synchronous low-Earth orbit and observes methane by nadir solar backscatter in the 1.65 µm shortwave infrared absorption band. Observations are made at around 13:00 local solar time. We use the University of Leicester version 9 CO2 proxy retrieval (Parker et al., 2020a). The retrieval has been extensively validated against ground-based column observations from the Total Carbon Column Observing Network (Wunch et al., 2011). Validation has also been performed for the model XCO2 used in the CO2 proxy retrieval (Parker et al., 2015) and for a specific region (i.e., the Amazon) against aircraft profile observations (Webb et al., 2016). Overall, the retrieval has a single-observation precision of 13.7 ppb and a regional bias of 4 ppbv (Parker et al., 2020a), which is sufficient for a successful methane inversion (Buchwitz et al., 2015). The inversion ingests a total of 1.5 million successful GOSAT retrievals. Previous inversions of GOSAT data often excluded high-latitude observations because of seasonal bias, large retrieval errors at low solar elevations, and forward model errors for the stratosphere (Bergamaschi et al., 2013; Turner et al., 2015; Z. Wang et al., 2017; Maasakkers et al., 2019). The exclusion of high-latitude observations limited the capability of the inversions to resolve emissions at high latitudes such as from boreal wetlands and oil and gas activity in Russia (Maasakkers et al., 2019). Here we use an improved model bias correction scheme (Sect. 2.5) and include these high-latitude observations in the inversion.

The state vector (x) is the ensemble of variables that we seek to optimize in the inversion. In this work, the state vector includes (1) mean 2010–2018 methane emissions from non-wetland sources (all anthropogenic and natural emissions excluding wetlands) on a global 4∘×5∘ grid (1009 elements), (2) linear trends of non-wetland emissions on that same grid (1009 elements), (3) wetland emissions from 14 subcontinental regions for individual months (1512 elements) (Fig. 1), and (4) annual mean tropospheric OH concentrations in the Northern and Southern Hemisphere (18 elements). The reason to treat wetland and non-wetland emissions separately is that wetland emissions have large seasonal and interannual uncertainties (compared to anthropogenic emissions); coarsening the spatial resolution when optimizing wetland emissions allows us to estimate monthly values for individual years (Bloom et al., 2017). This is a significant improvement over the inverse analysis of Maasakkers et al. (2019), wherein interannual and seasonal errors in prior wetland emissions were not addressed by the inversion.

Another improvement in the state vector definition relative to Maasakkers et al. (2019) is to optimize annual mean OH concentrations in each hemisphere rather than just globally. Y. Zhang et al. (2018) previously found with an observing system simulation experiment that it should be possible to constrain annual mean hemispheric OH concentrations from satellite methane observations. Patra et al. (2014) suggested that global chemical transport models (CTMs) are often biased in their inter-hemispheric OH gradient relative to methyl chloroform observations, and such bias, if not corrected, would propagate to the solution for methane emissions.

Prior estimates for methane sources and sinks (xa) are compiled from an ensemble of bottom-up studies. Figure 1 shows the spatial distribution of prior emission estimates. For gridded 4∘×5∘ anthropogenic emissions, we use as default the EDGAR v4.3.2 global emission inventory for 2012 (https://edgar.jrc.ec.europa.eu/, last access: 1 December 2017) (Janssens-Maenhout et al., 2017). We supersede it for the US with the gridded version of the Environmental Protection Agency greenhouse gas emission inventory for 2012 (Maasakkers et al., 2016). We further supersede it globally for fuel (oil, gas, and coal) exploitation with the inventory of Scarpelli et al. (2020) for 2012, which spatially disaggregates the national emissions reported to the United Nations Framework Convention on Climate Change (UNFCCC) (https://di.unfccc.int/, last access: 22 June 2020). All anthropogenic emissions are assumed to be aseasonal, except manure management for which we apply local temperature-dependent corrections (Maasakkers et al., 2016) and rice cultivation for which we apply gridded seasonal scaling factors from B. Zhang et al. (2016).

For the prior estimates of natural emissions, we take monthly wetland emissions during 2010–2018 from the WetCHARTS v1.0 extended ensemble mean (Bloom et al., 2017) for each subcontinental domain in Fig. 1. To test the impact of wetland spatial distribution within the subcontinental domains on inversion results, we performed a sensitivity inversion in which prior WetCHARTS emissions in Africa (regions 10 and 13 in Fig. 1) are increased by a factor of 3 in the Sudd wetland of South Sudan and decreased by a factor of 2.5 in the Congo Basin, following Lunt et al. (2019) and as shown in Fig. S1. Daily global emissions from open fires are taken from GFEDv4s (van der Werf et al., 2017), which accounts for high methane emissions from peatland fires (Liu et al., 2020). For geological sources, we scale the spatial distribution from Etiope et al. (2019) to a global total of 2 Tg a-1 inferred from preindustrial-era ice core 14CH4 data (Hmiel et al., 2020). Termite emissions are from Fung et al. (1991), totalling 12 Tg a-1.

The prior estimates for 2010–2018 trends in non-wetland emissions are specified as zero on the 4∘×5∘ grid, except for interannual variability in fire emissions given by GFEDv4s. In this manner, all information on the posterior estimate of anthropogenic emission trends is from the GOSAT observations.

The prior estimates for the hemispheric tropospheric OH concentrations are based on a GEOS-Chem full chemistry simulation (Wecht et al., 2014). The monthly 3-D OH concentration fields from this full chemistry simulation are also used in the forward model. We optimize hemispheric OH concentrations as the methane loss frequency [s-1] due to oxidation by tropospheric OH (ki) in the Northern and Southern Hemisphere (i= north or south): 1ki=∫troposphere,ik′TOHnCH4dv∫atmospherenCH4dv, where nCH4 is methane number density [molec. cm-3], v is volume, and k′(T)=2.45×10-12e-1775/T cm3 molec.-1 s-1 is the temperature-dependent oxidation rate constant (Burkholder et al., 2015). In this definition, the denominator of Eq. (1) integrates over the entire atmosphere, and the numerator integrates over the hemispheric troposphere. Hence, global methane loss frequency (or inverse lifetime; k) due to oxidation by tropospheric OH can be expressed as the sum of hemispheric values (k=1/τ=knorth+ksouth, where τ is the global lifetime due to oxidation by tropospheric OH). Our prior estimates from Wecht et al. (2014) are 0.050 a-1 for knorth and 0.043 a-1 for ksouth, which translates to a τ of 10.7 years and a north-to-south inter-hemispheric OH ratio of 1.16. In comparison, the methyl chloroform proxy infers τ of 11.2±1.3 years (Prather et al., 2012) and an inter-hemispheric ratio in the range 0.85–0.98 (Montzka et al., 2000; Prinn et al., 2001; Krol and Lelieveld, 2003; Bousquet et al., 2005; Patra et al., 2014), while the ACCMIP model ensemble yields a τ of 9.7±1.5 years and an inter-hemispheric ratio of 1.28±0.10 (Naik et al., 2013).

The Bayesian inversion requires error statistics for the prior estimates. The prior error covariance matrix (Sa) is constructed as follows. For mean non-wetland emissions, we assume 50 % error standard deviation for individual grid cells and 20 % for each source category when aggregated globally. For linear trends in non-wetland emissions, we specify an absolute error standard deviation of 5 % a-1 for individual grid cells. For wetland emissions, we take the full error covariance structure (including spatial and temporal error covariance) derived from the WetCHARTs ensemble members for the 14 subcontinental regions (Bloom et al., 2017). For annual hemispheric OH concentrations, we assign 5 % independent errors for individual years on top of a 10 % error for the 2010–2018 mean.

We use the GEOS-Chem CTM v11.02 as a forward model (F) for the inversion (Wecht et al., 2014; Turner et al., 2015; Maasakkers et al., 2019) that relates atmospheric methane observations (y) to the state vector to be optimized (x) as y=F(x). The simulation is conducted at 4∘×5∘ horizontal resolution with 47 vertical layers (∼30 layers in the troposphere) and is driven by 2009–2018 MERRA-2 meteorological fields (Gelaro et al., 2017) from the NASA Global Modeling and Assimilation Office (GMAO). The prior simulation is conducted from 2010 to 2018. The initial conditions are from Turner et al. (2015) with an additional 1-year spin-up starting from January 2009 to establish methane gradients driven by synoptic-scale transport (Turner et al., 2015). We further set the initial conditions on 1 January 2010 to be unbiased by removing the zonal mean biases relative to GOSAT observations. Thus, we attribute any model departures from observations over the 2010–2018 period in the inversion to errors in sources and sinks over that period.

We use archived 3-D monthly fields of OH concentrations from a GEOS-Chem full chemistry simulation (Wecht et al., 2014) to compute the removal of methane from oxidation by tropospheric OH. Other minor loss terms include stratospheric oxidation computed with archived monthly loss frequencies from the NASA Global Modeling Initiative model (Murray et al., 2012), tropospheric oxidation by Cl atoms computed with archived Cl concentration fields from X. Wang et al. (2019b), and monthly soil uptake fields from Murguia-Flores et al. (2018). The inversion does not optimize these minor sinks. The loss from oxidation by Cl is 5.5 Tg a-1, accounting for ∼1 % of methane loss. It is lower than the previous estimate of 9 Tg a-1 (Sherwen et al., 2016) used by Maasakkers et al. (2019) but is consistent with a recent analysis of methane and CO isotopic signatures (Gromov et al., 2018). Use of monthly soil uptake fields from the Murguia-Flores et al. (2018) climatology of 2000–2009 data is another update relative to Maasakkers et al. (2019) and yields a global soil sink of 34 Tg a-1.

The GEOS-Chem-simulated methane columns have a latitude-dependent background bias relative to the GOSAT data (Turner et al., 2015). This is thought to result from excessive meridional transport in the stratosphere, a common problem in global models (Patra et al., 2011). In particular, coarse-resolution global models have difficulty resolving polar vortex dynamics that control the distribution of stratospheric methane in the winter–spring hemisphere (Stanevich et al., 2020). The GEOS-Chem model evaluation with stratospheric sub-columns derived from ground-based TCCON measurements shows that the stratospheric bias varies seasonally (Saad et al., 2016). Previous GEOS-Chem-based inversions of GOSAT data (Turner et al., 2015; Maasakkers et al., 2019) developed correction schemes by fitting differences between the prior model simulation and background GOSAT observations as a second-order polynomial function of latitude. However, these correction schemes did not consider the seasonal variation of the stratospheric biases. Moreover, they could falsely attribute high-latitude model–GOSAT differences to stratospheric model bias rather than to errors in prior emissions. Therefore, previous studies excluded high-latitude observations from their analyses (Turner et al., 2015; Maasakkers et al., 2019).

Here we improve the stratospheric bias correction by using satellite observations from ACE-FTS v3.6 (Waymark et al., 2014; Koo et al., 2017). ACE-FTS is a solar occultation instrument launched in 2003 that measures vertical profiles of stratospheric methane (Bernath et al., 2005). We compute correction factors to GEOS-Chem stratospheric methane sub-columns as a function of season and equivalent latitude based on the ratios of stratospheric methane sub-columns between the ACE-FTS and GEOS-Chem prior simulation for 2010–2015 (Fig. 2). A global scaling factor (1.06) is applied to these correction factors to enforce mass conservation for methane in the stratosphere so that the correction does not introduce a spurious stratospheric source and sink in the model simulation. We use equivalent latitude, computed on the 450 K isentropic surface from MERRA-2 reanalysis fields, as one of the predictors for parameterization. The equivalent latitude is a coordinate based on potential vorticity (PV) that maps PV to latitude based on areas enclosed by PV isopleths (Butchart and Remsberg, 1986), and it is often used to represent the influence of high-altitude dynamics (e.g., polar vortex) on chemical tracers (Engel et al., 2006; Hegglin et al., 2006; Strahan et al., 2007). We use the same stratospheric bias correction for all years because the correction does not vary significantly for individual years (Fig. S2). Figure 2 shows that GEOS-Chem model biases are largely confined to high latitudes of the winter–spring hemisphere. By having our correction factors be dependent on equivalent latitude and season, we specifically account for the overly weak polar vortex dynamical barrier in the model as the cause of the stratospheric bias (Stanevich et al., 2020).

We perform the inversion by minimizing the Bayesian cost function (Brasseur and Jacob, 2017): 2Jx=x-xaTSa-1x-xa+γy-KxTSO-1y-Kx. Here, the Jacobian matrix K(=∂y∂x) is a linearized description of the forward model (F) that relates y (observations) to x (state vector). We explicitly compute the Jacobian matrix by perturbing each individual element of x independently in GEOS-Chem simulations and calculating the sensitivity of y to that perturbation. xa is the prior estimate for x and Sa is the prior error covariance matrix (Sect. 2.3). SO is the observation error covariance matrix including contributions from the instrument error and the forward model error. We take SO to be diagonal and compute the variance terms from the statistics of the residual error (εO=y-Fxa-y-F(xa)‾, where the overbar denotes annual averages in a 4∘×5∘ grid cell) that represents the random component of model–observation differences (Heald et al., 2004). This method of constructing SO has been previously applied to GOSAT observations by Turner et al. (2015) and Maasakkers et al. (2019). The observational error standard deviation derived in this manner averages 13 ppbv. γ is the regularization parameter taken to be 0.05 following Y. Zhang (2018) and Maasakkers et al. (2019) to account for missing error covariance structure in SO.

Minimizing J(x) (Eq. 2) by solving dJ/dx=0 analytically (Rodgers, 2000; Brasseur and Jacob, 2017) yields a best posterior estimate of the state vector (x^) and the associated posterior error covariance matrix (S^) characterizing the error statistics of x^: 3x^=xa+γKTSO-1K+Sa-1-1γKTSO-1y-Kxa,4S^=γKTSO-1K+Sa-1-1.

From there we derive the averaging kernel matrix A=∂x^/∂x describing the sensitivity of the solution to the true state: 5A=I-S^Sa-1. The trace of the averaging kernel matrix is referred to as the degrees of freedom for signal (DOFS) (Rodgers, 2000) and represents the number of independent pieces of information on the state vector that are constrained by the inversion. We refer to the diagonal terms of A as averaging kernel sensitivities, which measure the ability of the observations to quantify the individual elements of the state vector (Sheng et al., 2018c; Maasakkers et al., 2019).

The posterior solution is often presented in reduced dimensionality. For example, spatially resolved emission and trend estimates on the 4∘×5∘ grid can be aggregated to countries, regions, or global and/or regional emissions from individual source sectors (oil and gas, livestock, etc.). Let W be a matrix that represents the linear transformation from the full state vector to a reduced state vector. The posterior estimation of the reduced state vector (x^red) is computed as 6x^red=Wx^, with posterior error covariance matrix 7S^red=WS^WT and averaging kernel matrix 8Ared=WAW*, where W*=WT(WWT)-1 is the pseudo-inverse of W. The regional and global budget terms and their error covariance structures obtained by using this approach are consistent with the full inversion. In the case of aggregation by sectors, we construct W on the basis of the relative contribution of the sector to the prior emissions in each 4∘×5∘ grid cell. This does not assume that the prior distribution of sectoral emissions is correct, only that the relative allocation within a given 4∘×5∘ grid cell is correct.

Figure 7 shows the correction factors from the inversion to 2010–2018 mean non-wetland emissions (posterior-to-prior ratios) along with the associated averaging kernel sensitivities (corresponding diagonal terms of the averaging kernel matrix). We achieve 179 independent pieces of information (DOFS) for constraining the emissions on the 4∘×5∘ grid. The spatial distribution of averaging kernel sensitivities largely follows the pattern of prior emissions (right panel of Fig. 5). The inversion provides strong constraints in major anthropogenic source regions such as East Asia, South Asia, and South America. The constraints are generally weaker over North America, Europe, and Africa, indicating that the inversion provides more diffuse spatial information in these regions.

We find that the prior emission inventory significantly overestimates anthropogenic emissions in eastern China (Fig. 7). The posterior estimate of Chinese anthropogenic emissions (47±1 Tg a-1) is 30 % lower than the prior estimate (67 Tg a-1) and is also lower than the latest national report from China to the UNFCCC of 55 Tg a-1 for 2014 (Fig. 8). Based on the relative contribution of each sector in the prior inventory, we attribute ∼60 % of this downward correction to coal mining. The overestimation of anthropogenic emissions from China has been reported by previous global and regional GOSAT inversion studies using different EDGAR inventory versions as prior estimates (Monteil et al., 2013; Thompson et al., 2015; Turner et al., 2015; Maasakkers et al., 2019; Miller et al., 2019).

Another major downward correction is for the oil- and gas-producing regions in Russia. We estimate Russia's anthropogenic emissions to be 20±1 Tg a-1 as opposed to the prior estimate of 34 Tg a-1 (Fig. 8), and the difference is mainly attributable to the oil and gas sector (posterior: 15 Tg a-1; prior: 27 Tg a-1). This finding is consistent with Maasakkers et al. (2019), though they used a different oil and gas emission inventory. Russia has been revising downwards its national emission estimates submitted to the UNFCCC, and our posterior estimate of total anthropogenic emissions is closer to the country's latest submission to the UNFCCC for 2010–2018 (16 Tg a-1; Fig. 8). The new submission revises oil and gas methane emissions downward by a factor of 3 relative to the previous submission used as a prior estimate in our inversion (Scarpelli et al., 2020).

We find large upward corrections to the prior inventory over East Africa (Mozambique, Zambia, Tanzania, Ethiopia, Uganda, Kenya, and Madagascar) and over South America (Brazil). A previous inversion suggested that corrections for these regions may be due to an underestimation of prior wetland emissions (Maasakkers et al., 2019). Our inversion, which optimizes wetland and anthropogenic emissions separately, attributes the underestimation to anthropogenic emissions (see also Sect. 4.3 for wetland results), though there is some error aliasing between them (r=-0.5 for sub-Saharan Africa, -0.4 for southern Africa; Fig. 6). We find that the upward correction over eastern Africa generally remains robust in a sensitivity inversion whereby prior wetland emissions in a neighboring region (Sudd in South Sudan) are increased by a factor of 3 (Figs. S4 and 8). Based on prior sectoral information, these underestimations are most likely due to livestock emissions, whose bottom-up estimates have large uncertainties in these developing regions (Herrero et al., 2013).

Another upward correction pattern in South America is located near Venezuela, a major oil-producing country in the region. The large correction in Venezuela likely reflects underestimation of fossil fuel emissions by the national estimates for 2010 reported to the UNFCCC. Upward corrections are also seen in central Asia (Iran, Turkmenistan), where the regional posterior estimates (10.1±0.9 Tg a-1) are 49 % higher than the prior (6.8 Tg a-1), with adjustments mainly attributed to the oil and gas sector. This region has previously been identified by satellite observations as a methane emission hot spot (Buchwitz et al., 2017; Varon et al., 2019; Schneising et al., 2020).

The inversion finds small upward corrections over the US (prior: 28 Tg a-1; posterior: 33±1 Tg a-1) (Fig. 8), resulting mainly from underestimation of emissions from the oil and gas sector in the western and south-central US (Fig. 7). This result is consistent with a high-resolution inversion over the US using the 2010–2015 GOSAT data, which spatially allocates the correction more specifically to oil and gas basins (Maasakkers et al., 2020). A number of previous studies have found that emissions from oil and gas production are underestimated in the national US inventory (e.g., Kort et al., 2014; Smith et al., 2017; Peischl et al., 2018; Alvarez et al., 2018; Y. Zhang et al., 2020; Gorchov Negron et al., 2020).

Small downward corrections with a diffuse pattern are found over Europe. The posterior estimate of anthropogenic emissions for the European Union (including the UK) is 16±0.7 Tg a-1, slightly lower than the prior estimate (21 Tg a-1) and the UNFCCC national reports (19 Tg a-1 for 2014) (Fig. 8). Source sector attribution is difficult in this case because of spatial overlap between emission sectors. The inversion finds only small adjustments to prior emissions for India (prior: 32 Tg a-1; posterior: 33±0.6 Tg a-1) even though the information content is relatively large, confirming the prior inventory used in the inversion. Our estimate, however, is much higher than a previous inversion study for India (Ganesan et al., 2017) (22 Tg a-1), the results of which are in agreement with India's UNFCCC report (20 Tg a-1 for 2010) (Fig. 8). Our inversion attributes the discrepancy with the UNFCCC submission mainly to the livestock sector.

Figure 9 shows the spatial distribution of 2010–2018 trends for anthropogenic emissions inferred from GOSAT observations, along with the associated averaging kernel matrix sensitivities. The GOSAT observations provide 42 pieces of information to constrain the spatial distribution of anthropogenic emission trends, suggesting that, compared to mean emissions, the inversion is only able to constrain more diffuse spatial patterns for emission trends. These constraints are strongest in China and India, but there is also fairly strong information aggregated over other continental regions. The prior estimate assumed zero anthropogenic trends anywhere; therefore, the posterior trends are driven solely by the GOSAT information.

Significant positive trends of anthropogenic emissions are found in South Asia (0.58±0.16 Tg a-1 a-1 or 1.4±0.4 % a-1; Pakistan and India), East Africa (0.22±0.10 Tg a-1 a-1 or 1.4±0.6 % a-1; Ethiopia, Tanzania, Uganda, Kenya, and Sudan), West Africa (0.28±0.10 Tg a-1 a-1 or 4.4±1.4 % a-1; Nigeria, Niger, Ghana, Côte d'Ivoire, Mali, Benin, Burkina Faso),and Brazil (0.19±0.15 Tg a-1 a-1 or 0.8±0.6 % a-1). Based on prior sectoral fractions in each 4∘×5∘ grid cell, we attribute these positive trends mostly to the livestock sector (0.31 Tg a-1 a-1 in South Asia, 0.13 Tg a-1 a-1 in East Africa, 0.09 Tg a-1 a-1 in West Africa, and 0.17 Tg a-1 a-1 in Brazil). Indeed, according to the United Nations Food and Agriculture Office (UNFAO) statistics (http://www.fao.org/faostat, last access: 22 June 2020), all these regions have had rapid increases in livestock population. The fastest-growing cattle populations in the world reported by the UNFAO over the 2010–2016 period were in Pakistan (1.4×106 heads a-1), Ethiopia (1.2×106 heads a-1), Tanzania (1.1×106 heads a-1), and Brazil (0.9×106 heads a-1). Moreover, our inversion results for these regional trends in livestock emissions are generally consistent in magnitude with the trends from bottom-up livestock emission inventories (FAOSTAT, IPCC tier I method; EDGAR v4.3.2 and v5, hybrid tier I method; Chang et al., 2019, IPCC tier II method) (Fig. 10). Because our inversion assumes zero prior trends in anthropogenic emissions, the inferred trends are solely informed by satellite observations and are independent of the bottom-up trends in Fig. 10.

A positive trend in anthropogenic emissions (0.39±0.27 Tg a-1 a-1 or 0.8±0.6 % a-1) is found over China driven by coal mining (northern China) and rice (southern China), but the magnitude of the trend is smaller than previous inverse analyses of satellite and surface observations for time horizons before 2015 (Bergamaschi et al., 2013; Thompson et al., 2015; Patra et al., 2016; Saunois et al., 2017; Miller et al., 2019; Maasakkers et al., 2019). We infer a much stronger trend (0.72±0.39 Tg a-1 a-1 or 1.6±0.9 % a-1) for China if we restrict the GOSAT record to 2010–2016. Our results thus suggest that anthropogenic emission trends in China peaked midway within the 2010–2018 record. Indeed, coal production in China peaked in 2013 (Sheng et al., 2019).

The inversion does not find significant 2010–2018 trends in anthropogenic emissions over the US (-0.06±0.21 Tg a-1 a-1, -0.2±0.6 % a-1). This is generally consistent with the lack of a trend in US emissions over 2000–2014 in inversions collected by the Global Carbon Project (Bruhwiler et al., 2017) and over 2010–2015 in a North America regional inversion using GOSAT data (Maasakkers et al., 2020). It contradicts the 2 % a-1–3 % a-1 positive trend inferred from direct analysis of GOSAT enhancements (Turner et al., 2016; Sheng et al., 2018a) and the inference of large positive trends based on increasing concentrations of ethane and propane (Franco et al., 2016; Hausmann et al., 2016; Helmig et al., 2016). Bruhwiler et al. (2017) pointed out that the inference of methane emission trends from a simple analysis of GOSAT data could be subject to various biases including variability in background and seasonal sampling, which would be accounted for in an inversion. Increasing ethane-to-methane and propane-to-methane emission ratios over years may confound the inference of methane emission trends from ethane and propane records (Lan et al., 2019).

Small negative trends are found in central Asia (Uzbekistan, Kazakhstan, Turkmenistan, Afghanistan; -0.17±0.16 Tg a-1 a-1), Europe (-0.19±0.15 Tg a-1 a-1), and Australia (-0.12±0.07 Tg a-1 a-1). The decrease in central Asia is attributed mainly to oil and gas, and the decrease in Australia is attributed to coal mining and livestock. Trends over Europe and Russia are too diffuse to be separated by sectors. No significant trend is found in Russia (-0.01±0.25 Tg a-1 a-1).

From the inversion we infer wetland emissions for 14 subcontinental regions (Fig. 1) and for individual months from 2010 to 2018, thus allowing seasonal and interannual variability to be optimized. This achieves 167 independent pieces of information (DOFS) for wetland emissions. The results are presented as mean seasonal cycles (Fig. 11) and time series of annual means (Fig. 12). Recent studies have found that the mean WetCHARTs inventory used here as a prior estimate is too high in the Congo Basin and too low in the Sudd region (Lunt et al., 2019; Parker et al., 2020b; Pandey et al., 2021). Our inversion is unable to resolve this subregional spatial correction pattern because of coarse resolution in the wetland state vector (Fig. 1). We therefore perform a sensitivity inversion with modified prior estimates following Lunt et al (2019) (Fig. S1), which finds a 20 % (3 Tg a-1) increase in estimates of the 2010–2018 average for sub-Saharan Africa and a 7 % (0.6 Tg a-1) increase for southern Africa relative to the base inversion (Fig. S5). Interannual trends and seasonal cycles are almost unchanged between the two inversions (Fig. S5).

As shown in Figs. 11 and 12, our results find lower wetland emissions than the mean of the WetCHARTs ensemble (prior estimate) over the Amazon, temperate North America (the US), and eastern Canada. The previous inversion of GOSAT data by Maasakkers et al. (2019) also found overestimation of emissions by WetCHARTs in the coastal US and Canadian wetlands but did not have significant corrections over the Amazon. The overestimation of wetland emissions in the US and eastern Canada is also reported in analyses of aircraft measurements in the southeastern US (Sheng et al., 2018b) and surface observations in Canada (Baray et al., 2021), both of which used WetCHARTs v1.0 as prior information. The downward correction of North American emissions is consistent with recent WetCHARTs updates (v1.2.1) that substantially reduce methane emissions across regions categorized as partial wetland complexes (Lehner and Döll, 2004; Bloom et al., 2017).

The seasonal cycles inferred from the inversion are in general consistent with prior information (Fig. 11), although averaging kernel sensitivities indicate that we only have limited constraints on the seasonality, particularly for high-latitude regions in Northern Hemisphere winter. This was generally expected given the limited GOSAT observational coverage at high latitudes during winter months. The inversion infers a sharp and late (May–June) onset of methane emissions across boreal wetlands, in contrast to an early and gradual increase starting from March predicted by the prior inventory. This feature in posterior estimates appears to be consistent with aircraft and surface observations over Canada's Hudson Bay Lowlands (Pickett-Heaps et al., 2011) and eddy flux measurements over Alaskan Arctic tundra (Zona et al., 2016), while the gradual onset in the prior inventory agrees with aircraft observations over Alaska by Miller et al. (2016). The negative fluxes right before the onset may reflect strong soil sinks during spring thaw over these high-latitude regions (Jørgensen et al., 2015). The inversion also indicates stronger seasonal cycles than the prior inventory in sub-Saharan Africa and tropical South Asia, which suggests that WetCHARTs may underestimate the sensitivity of wetland emissions to precipitation but overestimate their sensitivity to temperature.

Our posterior estimates of 2010–2018 trends in wetland emissions vary greatly by region and are generally larger than the prior estimates from WetCHARTs (Fig. 12). Large positive trends are found in the tropics (Amazon: +1.0 Tg a-1 a-1; sub-Saharan Africa: +0.6 Tg a-1 a-1; southern Africa: +0.4 Tg a-1 a-1) and high latitudes (Siberia: +0.4 Tg a-1 a-1). Increasing Amazonian wetland emissions may have been driven by intensification of flooding (Barichivich et al., 2018) or increasing temperature (Tunnicliffe et al., 2020) in the region over the past decades. Our result of increasing tropical Africa wetland emissions is consistent with a previous regional analysis of GOSAT data, which found a positive trend of 1.5–2.1 Tg a-1 a-1 in the region for 2010–2016 attributed mainly to wetlands, particularly the Sudd in South Sudan (Lunt et al., 2019). Compared to steady and linear increases in the tropics, boreal Siberia and northern Europe show abrupt increases in 2016–2018 for reasons that are unclear (Fig. 12). Decreasing but weaker trends are found in tropical Southeast Asia (-0.2 Tg a-1 a-1) and Australia (-0.1 Tg a-1 a-1).

Figure 14 shows the 2010–2018 annual methane growth rates inferred from NOAA background surface measurements (Dlugokencky, 2020) and from our inversion of GOSAT data. There is general consistency between the two, with both showing the highest growth rates in 2014–2015 and a general acceleration after 2014. Our inversion achieves a much better match to the interannual variability of the NOAA record than the previous work of Maasakkers et al. (2019), in large part because of our optimization of the interannual variability of wetland emissions.

The bottom panel of Fig. 14 attributes the interannual variability in the methane growth rate to individual processes as determined by the inversion. The growth rate Gj=[dm/dt]j in year j (where m is the global methane mass) is determined by the balance between sources and sinks: 9Gj=Ej-kjmj-Lj.

Here, Ej denotes the global emissions in year j, for which the inversion provides further sectoral breakdown, kj is the loss frequency against oxidation by tropospheric OH (Eq. 1), mj is the total methane mass, and Lj represents the minor sinks not optimized by the inversion. Let ΔEj=Ej-Eo, Δkj=kj-ko, and Δmj=mj-mo represent the changes relative to 2010 conditions (Eo, ko, mo) taken as a reference. We can then write 10Gj=Eo+ΔEj-ko+Δkjmo+Δmj-(Lo+ΔLj)≈Eo-komo-Lo-koΔmj+ΔEj-moΔkj, where we have neglected the minor terms ΔkjΔmj and ΔLj. Here, the growth rate Gj in year j is decomposed into three terms: (1) a relaxation to steady state based on 2010 conditions (Eo-komo-Lo-koΔmj), (2) a perturbation to emissions (ΔEj) that can be further disaggregated by sectors, and (3) a perturbation to OH concentrations (moΔkj).

We see from the bottom panel of Fig. 14 that the legacy of the 2010 imbalance sustains a positive growth rate throughout the 2010–2018 period, but this influence diminishes towards the end of the record. The 2010–2018 trend in anthropogenic emissions is linear by design of the inversion and sustains a steady growth rate over the 2010–2018 period as the legacy of the 2010 imbalance declines. Figure 15 shows the sectoral breakdown of the anthropogenic trend. The increase in global anthropogenic emissions totalling 1.9±0.8 Tg a-1 a-1 is driven by livestock (0.70±0.36 Tg a-1 a-1; South Asia, tropical Africa, Brazil), rice (0.44±0.18 Tg a-1 a-1; East Asia), and wastewater treatment (0.33±0.13 Tg a-1 a-1; Asia). We find an insignificant positive global trend in emissions from fuel exploitation (oil, gas, and coal) (0.18±0.4 Tg a-1 a-1) (Fig. 15).

The bottom panel of Fig. 14 also shows that the spike in the methane growth rate in 2014–2015 is attributed to an anomalously low OH concentration in 2014 (5 % lower than 2010–2018 average; Fig. 13), partly offset by low wetland emissions and anomalously high fire emissions in 2015, mostly from Indonesia peatlands (Worden et al., 2017). Smoldering peatland fires are particularly large sources of methane (Liu et al., 2020). The large fire emissions are informed by the GFED inventory because the interannual variability of fire emissions is not optimized in our inversion. Despite their small magnitude relative to wetland and anthropogenic emissions globally, anomalous fire emissions can be an important contributor to methane interannual variability (Worden et al., 2017; Pandey et al., 2017b) both directly by releasing methane and indirectly by decreasing OH concentrations through CO emissions.

In addition to the 2014–2015 extremum, the NOAA surface observations show an acceleration of methane growth during the latter part of the 2010–2018 record (Nisbet et al., 2019), and this is reproduced in our inversion (Fig. 14). This accelerating growth is driven by strong wetland emissions, particularly in 2016–2018, on top of increasing anthropogenic emissions (Fig. 14). Our inversion infers a relatively steady 2010–2018 increase from tropical wetlands (in particular the Amazon and tropical Africa) and a 2016–2018 surge from extratropical wetlands (in particular boreal Eurasia) (Fig. 12). More work is needed to understand the drivers of changes in wetland emissions.

We estimate from the inversion global mean methane emissions for 2010–2018 of 512±4 Tg a-1 (wetlands: 145 Tg a-1; anthropogenic: 336 Tg a-1) and a sink of 489±4 Tg a-1. This posterior global emission is lower than the prior estimate (538 Tg a-1) and the 538–593 Tg a-1 range reported by the Global Carbon Project for 2008–2017 (Saunois et al., 2020). Compared to prior emissions, we estimate lower emissions for wetlands and fossil fuel and higher emissions for livestock and rice (Figs. 12 and 15). Meanwhile, we estimate a methane lifetime against tropospheric OH oxidation of 12.4±0.3 years, which is at the high end of 11.2±1.3 years based on the methyl chloroform proxy (Prather et al., 2012), though strong error correlations between wetland emissions and methane lifetime suggest that our inversion has limited ability to constrain both independently (Fig. 5).