TROPOMI is onboard the polar sun-synchronous Sentinel-5 Precursor satellite with a ∼ 13:30 local overpass time. The instrument observes methane columns by solar backscatter in the 2.3 µm absorption band with near-uniform sensitivity down to the surface. The column-averaged dry-air methane mixing ratio (XCH4) is retrieved with a full-physics algorithm (Butz et al., 2011) together with surface and atmospheric scattering properties. We use the recently updated TROPOMI version 2.02 retrieval from the Netherlands Institute for Space Research (Lorente et al., 2021; http://www.tropomi.eu/data-products/methane, last access: 10 October 2021), filtering out low-quality retrievals (“qa_value” < 0.5) and surfaces above 2 km where the stratospheric contribution to the column is large (Shen et al., 2022). We further adopt the “blended albedo” filter suggested in Lorente et al. (2021) to remove snow- or ice-covered scenes identified by blended albedo exceeding 0.8 from October to April.

Global mean bias in the TROPOMI observations is inconsequential for regional inversions because it can be incorporated in the boundary conditions (defined as the edges of the study domain), and random error (precision) is effectively reduced through the large number of observations (Fig. 1). More problematic is spatially variable bias, which corrupts the information on methane concentration gradients used to optimize emissions in the inversion. This variable bias typically arises from aliasing of surface spectral features into the XCH4 retrieval. Lorente et al. (2021) estimated a variable bias of 5.6 ppb for the TROPOMI XCH4 full-physics retrieval as the spatial standard deviation of the mean difference with ground-based methane observations from the Total Carbon Column Observing Network (TCCON; Wunch et al., 2011). This is below the threshold requirement of 10  ppb recommended by Buchwitz et al. (2015) for use of satellite data in regional inversions. However, the TCCON network is sparse and includes no sites in China.

Qu et al. (2021) conducted a more thorough worldwide analysis of variable bias in the TROPOMI version 1.03 data (Hu et al., 2018) by using the GOSAT observations as reference on a 4∘×5∘ grid. GOSAT is much less subject to retrieval artifacts because of its higher spectral resolution and its use of the CO2 proxy retrieval method in the 1.65 µm absorption band (Parker et al., 2020). Qu et al. (2021) found TROPOMI variable biases typically in the range of 9–13 ppb but exceeding 20 ppb for some regions. Repeating this analysis for our East Asia domain with TROPOMI version 2.02 (Lorente et al., 2021) on the 0.25∘×0.3125∘ grid, we find a mean TROPOMI–GOSAT difference of -9.9±17.6 ppb (Fig. 2a). The mean difference is largely driven by TROPOMI values below 1830 ppb at high latitudes (Fig. 1), likely reflecting snow-covered surfaces that are not successfully removed by the blended albedo filter. The standard deviation of the difference (measure of variable bias) is relatively high in part due to the high spatial resolution in our analysis, which also means that a higher bias threshold is acceptable because methane enhancements are larger. Here we exclude TROPOMI observations that show discrepancies larger than 20 ppb compared with GOSAT. The mean TROPOMI–GOSAT difference after these outlying data have been excluded is -3.6±9.1 ppb with no evident regional structure (Fig. 2b).

Figure 1 shows the mean TROPOMI observations for 2019 retained in our analysis on the 0.25∘×0.3125∘ grid, along with the number of observations in each grid cell. We assimilate m=5907939 TROPOMI retrievals over the inversion domain. There are few observations in western China and no observations at all in Tibet because we have excluded locations with surface altitude above 2 km following Shen et al. (2022).

Figure 3 shows the prior estimates of emissions from different sectors over the inversion domain and Table 1 gives national totals for China. Anthropogenic emissions for China are from the latest 2014 national governmental report to the UNFCCC (UNFCCC, 2020). Emissions from coal and oil/gas exploitation are spatially allocated to the 0.25∘×0.3125∘ GEOS-Chem grid using infrastructure information compiled by the Global Fuel Exploitation Inventory (GFEI v2; Scarpelli et al., 2022). This includes bottom-up information from Sheng et al. (2019) for the distribution of China's coal emissions. Other anthropogenic sources are spatially allocated using the EDGAR v4.3.2 inventory. Anthropogenic emissions outside of China are from GFEI v2 for fuel exploitation and from EDGAR v4.3.2 for other sectors. Wolf et al. (2017) produced an alternative global gridded inventory for livestock emissions, but we find that it is too uniform over China, as Scarpelli et al. (2020a) previously found over Mexico, because they use livestock numbers resolved only by province and distribute them over all grasslands and shrublands. All anthropogenic emissions are assumed to be aseasonal, except for manure management for which we apply temperature-dependent corrections following Maasakkers et al. (2016) and rice paddies for which we apply seasonal corrections derived from a biogeochemical model (Zhang et al., 2016).

Wetland emissions are monthly means for 2019 on a 0.5∘×0.5∘ grid from the nine-member high-performance subset of the WetCHARTs v1.3.1 inventory ensemble that best fits global GOSAT inversions (Ma et al., 2021). Other natural sources include daily open-fire emissions from the Global Fire Emissions Database version 4s (GFED4s; van der Werf et al., 2017), termite emissions from Fung et al. (1991), and geological seepage emissions from Etiope et al. (2019) scaled to a global magnitude of 2 Tg a-1 following Hmiel et al. (2020).

A nested version of the GEOS-Chem chemical transport model (13.0.0; 10.5281/zenodo.4618180) is used as the forward model in the inversion to relate methane emissions to atmospheric observations. The model is driven by GEOS-FP reanalysis meteorological fields with 0.25∘×0.3125∘ spatial resolution and 3 h temporal resolution (1 h for mixing depths and surface fields) from the NASA Global Modeling and Assimilation Office (Lucchesi, 2013). We conduct GEOS-Chem model simulations at 0.25∘×0.3125∘ resolution over the study domain of Fig. 1 for 2019. The nested version of GEOS-Chem is similar to that used in previous regional inversions of TROPOMI observations (Zhang et al., 2020; Shen et al., 2021) and uses 3 h dynamic boundary conditions from the global GEOS-Chem simulated vertical profiles at 2∘×2.5∘ resolution for 2019 with posterior methane emissions optimized by TROPOMI observations (Qu et al., 2021). The global simulation includes methane sinks from atmospheric oxidation and uptake by soils, but these are inconsequential in the nested version because the ventilation time scale for the nested domain is much shorter than the methane lifetime. We convolve the GEOS-Chem vertical profiles of methane dry mixing ratios with the TROPOMI averaging kernel vectors and prior vertical profiles (Varon et al., 2022) to obtain the model simulation of XCH4 for comparison with the TROPOMI observations in the inversion.

Bias in boundary conditions is critical to avoid as it would propagate to biases in the inversion. The boundary condition vertical profiles obtained from Qu et al. (2021) avoid systematic drift of the simulation from the TROPOMI observations, but some bias could remain because Qu et al. (2021) used an earlier version (1.03) of the TROPOMI data and the data would not be expected to perfectly correct the model anyway. We therefore further correct the boundary conditions on each side of our domain (north, south, west, and east) and for each season as part of the inversion (Table S1 in the Supplement). Initial conditions on 1 January 2019 are also from the GEOS-Chem simulations by Qu et al. (2021) and uniformly scaled to match the mean column mixing ratios retrieved from TROPOMI.

The state vector x to be optimized in the inversion includes spatially resolved emissions within the inversion domain and seasonal boundary conditions. We could technically carry out the inversion on the 0.25∘×0.3125∘ model grid, but satellite observations do not have sufficient information to constrain emissions in such detail everywhere; attempting to do so would introduce large smoothing errors (Wecht et al., 2014; Turner and Jacob, 2015). Here we use the Gaussian mixture model (GMM) of Turner and Jacob (2015) to define emission patterns that can be effectively constrained by the TROPOMI observations as informed by the prior estimates. The GMM functions are selected with the goal of retaining native resolution for strong localized source features while merging weak source regions as given by the prior emission field. Specifically, we project methane emissions at 0.25∘×0.3125∘ resolution onto K-dimensional Gaussian functions where K is the number of similarity criteria, in this case 14 similarity factors on the 0.25∘×0.3125∘ grid including longitude and latitude (spatial proximity), and the prior emission patterns by sector (Sect. 2.2). Each multivariate Gaussian is hence built to characterize the location (determined by longitude and latitude), emission magnitude, and distribution from different sectors (Turner and Jacob, 2015). The parameters of the Gaussians are estimated using an expectation-maximization algorithm (Dempster et al., 1977) to find the maximum likelihood. We choose to use 600 Gaussian functions, based on previous experience in inversions for North America (Turner and Jacob, 2015; Maasakkers et al., 2022). The inversion optimizes the amplitudes for each Gaussian. We also optimize 16 boundary condition (four seasons × four boundaries) for a total of 616 state vector elements. Construction of the GMM does not include information from the observations and therefore might not resolve hotspots in the observations that are not present in the prior emission patterns. Nesser et al. (2021) proposed an alternative approach where information from the observations is integrated into the emission patterns to be optimized.

We perform the inversion with log-normal error probability density functions (PDFs) for prior emissions (Maasakkers et al., 2019; Lu et al., 2022). Specifically we optimize ln⁡(x) instead of x, with the prior errors on ln⁡(x) (referred to hereafter as x′) following a Gaussian distribution. This enforces positivity of the solution and better captures the high tail of the frequency distribution of emissions than a normal error PDF. High-tailed emissions have been observed for all sectors including oil/gas (Yuan et al., 2015; Zavala-Araiza et al., 2015; Lyon et al., 2015; Alvarez et al., 2018), coal (Sadavarte et al., 2021), waste (Maasakkers et al., 2022), and livestock (Duren et al., 2019).

Bayesian inference of the maximum a posteriori (MAP) estimate for the state vector x assuming normal error PDFs involves minimization of the cost function J(x) (Brasseur and Jacob, 2017): 1J(x′)=x′-xa′TSa′-1x′-xa′+γ(y-K′x′)TSo-1(y-K′x′), where x′=ln⁡(x) and xa′=ln⁡(xa), xa(n×1) is the prior emission estimate (Sect. 2.2), and y(m×1) is the m-dimensional vector of TROPOMI observations (m=5907939). Sa′(n×n) is the prior error covariance matrix in log space and So(m×m) is the observational error covariance matrix. K′=∂y/∂x′(m×n) is the Jacobian matrix that describes the sensitivity of observations y to x′, and K′x′=Kx where K=∂y/∂x is the sensitivity of y to x, which can be readily represented by the GEOS-Chem forward model (Jacob et al., 2016). The relationship between methane emissions and concentrations (or more precisely, concentration enhancement above background mixing ratios) in the nested GEOS-Chem simulation is linear (omitting the minimal effect of potential errors in initial conditions), so that K defines the forward model for the purpose of the inversion. We hence derive Ki,j′=∂yi∂ln⁡(xj)=xj∂yi∂xj=xjKi,j, where i and j represent the indices of the observation and the state vector elements. γ is a regularization factor to avoid over- or underfit to observations. γ is needed because the prior and observational error covariance matrices can only be roughly estimated and is assumed here to be diagonal for lack of better information and convenience of computation.

We assume a geometric standard deviation factor (σg) of 2 for the log-normally distributed errors in x and construct the Sa′ matrix (with diagonal elements sa′) following sa′=ln⁡(σg) (Kirkwood, 1979; Limpert et al., 2001). Observational error standard deviations (square roots of diagonal terms of So) include contributions from instrument error, retrieval error, representation error, and forward model error. We calculate the sum of these errors using the residual error method (Heald et al., 2004) on the basis of the XCH4 differences Δ=y-yGEOS-Chem,prior for individual 0.25∘×0.3125∘ grid cells between individual TROPOMI observations and the GEOS-Chem simulation with prior emissions. The temporal mean 2019 difference Δ‾=y-yGEOS-Chem,prior‾ for each grid cell is to be corrected in the inversion while the standard deviation of the residual difference Δ–Δ‾ is taken as the observational error standard deviation, adjusted up to a minimum value of 10 ppb following Maasakkers et al. (2019) if necessary (10.4 % of the retrievals). The resulting observational error standard deviation averages 13.4 ppb, which agrees closely with previous TROPOMI inverse analyses and is mostly due to retrieval error (Shen et al., 2021; Qu et al., 2021). Sparse matrix algebra is applied wherever possible in matrix calculations, making use of the diagonal structure of the error covariance matrices Sa′ and So.

As mentioned earlier, the Jacobian matrix K′ is nonlinear and can be immediately transformed following Ki,j′=xjKi,j. Here we construct K column by column, by perturbing individual elements xi of the state vector independently and running GEOS-Chem forward model simulations to obtain the columns ∂y/∂xi. These simulations are readily achievable with massively parallel computing.

The optimization problem is nonlinear and needs to be solved iteratively. We approach the solution using the Levenberg–Marquardt method (Rodgers, 2000): 2xN+1′=xN′+γKN′TSo-1KN′+(1+k)Sa′-1-1γKN′TSo-1y-KxN-Sa′-1xN′-xa′. k is a coefficient for the iterative approach, and we tested three methods to set κ:

κ is set to 100 to start and is gradually decreased as the solution is approached, i.e., κ=101-max(N,101) where N is the iteration index;

It is of critical importance to discuss if the Gaussian transformation in Eq. (1) could arrive at a best linear unbiased estimator (BLUE) solution (Cohn, 1997). As x′-xa′∼N(0,Sa′) and y-K′x′=y-Kx∼N(0,So) (Fig. S1 in the Supplement), both the prior and observational errors are Gaussian with zero mean; there is a nonlinearity relationship between x′ and y that are linked by K′. Our analytical transformation thus conforms to the case of a “Gaussian anamorphosis” defined by Bocquet et al. (2010), for which a BLUE solution can be properly carried out. A weak point is that the Jacobian matrix may be nonlinear, which is, however, sometimes the case in particular if the original Jacobian matrix is linear. Previous studies have applied this approach to transform non-Gaussian problems (Fletcher, 2010; Brioude et al., 2011; Saide et al., 2015; Cui et al., 2019). We acknowledge that those studies assumed non-Gaussian errors for both the prior information and the observations, while our work only assumes log-normally distributed errors on the prior state vector.

Rodgers (2000) indicated that the solution of a nonlinear problem using the Levenberg–Marquardt method can be applied to obtain the posterior error covariance matrix S′^: 3S′^=γK′TSo-1K′+Sa′-1-1, with the averaging kernel matrix A quantifying the sensitivity of the solution to the true value: 4A=∂x′^∂x′=In-S^′Sa′-1, where In is the identity matrix. The trace of A measures the number of independent pieces of information on x′ obtained from the observations, and is often referred to as the degrees of freedom for signal (DOFS). The diagonal terms of A define the averaging kernel sensitivities, which quantify the extent to which the solution is informed by the observations within the inversion framework. They measure the actual error reduction if the inversion framework is correct, but errors in inversion parameters, such as prior emission distributions, can affect this interpretation (Yu et al., 2021). An alternative and better way to estimate posterior errors is to generate an ensemble of sensitivity inversions (Sect. 2.6).

The optimal value of γ can be determined following X. Lu et al. (2021) so that the sum of state vector terms in the posterior estimate of the cost function, Jax′^=(x′^-xa′)TSa′-1(x′^-xa′) has value of ∼n±2n, which is the expected value (±1  standard deviation) from the Chi-square distribution with n degrees of freedom. We find in this manner an optimal γ value of 0.015 as the best fit for our TROPOMI inversion. This is smaller than a previous regional TROPOMI inversion at 0.25∘×0.3125∘ resolution (γ=0.25 in Shen et al., 2021) because of the much larger number of observations per state vector element (m/n) in our work. We also conducted sensitivity inversions using γ=0.005 and 0.03 ns as described in Sect. 2.6.

The MAP estimate in log space is for the median of emission but not for the mean; mean emissions are, however, necessary for spatial aggregation and sectoral attribution purposes. Here we make use of the posterior error covariance matrix from Eq. (3) to infer the mean emissions from the median following the log-normal distribution statistics xmean=xmedianexp⁡s′^2, and the corresponding analytical posterior error covariance S^ (with diagonal elements s^=xmean2exp⁡(s′^-1)), where s′^ is the diagonal element of the posterior error covariance matrix in log space corresponding to that state vector element. We still use the normal error assumption for the boundary condition elements of the state vector, with a prior error standard deviation of 10 ppb.

The posterior estimate of methane emissions for the GMM state vector can be readily mapped on the 0.25∘×0.3125∘ grid by summation of the GMM elements, but it is also of interest to aggregate it spatially for inferring national totals including by source sector. This reduction in state vector dimension is readily done while preserving the information from the posterior error covariance matrix by using a summation matrix W to represent the linear transformation from the full state vector (n×1) to the reduced state vector. Here we use the reduction of the state vector to 12 sectors (Sect. 2.2) of aggregated emissions as an example to illustrate the construction of W. The GMM approach derives the relative weighting of each Gaussian on the p native-resolution grid W1(p×n); W1 thus allows the spatial allocation of the posterior state vector to the individual 0.25∘×0.3125∘ grid cell (Fig. 4c and d). W1 is further multiplied by W2(12×p), the fractional contribution of individual sectors to total grid cell emissions, to obtain the summation matrix W=W2W1 (12×n in this example).

The posterior estimate of the reduced state vector (xred) is computed as 5x^red=Wx^ and the posterior error covariance and averaging kernel matrices are then given by 6S^red=WS^WT7Ared=WAW*, where W*=(WTW)-1WT is the Moore–Penrose pseudo inverse (Calisesi et al., 2005).

The sections above describe our base inversion with the solution defined by (x^, S^). By using the regularization factor γ, we prevent overfit to the observations and therefore S^ is a fair representation of the uncertainty within our choice of inversion parameters. However, there is uncertainty in these parameters, and we therefore perform an ensemble of sensitivity inversions with different choices. The sensitivity inversions include (1) using ln⁡(1.5) and ln⁡(2.5) for the prior error standard deviations instead of ln⁡(2); (2) using 0.005 and 0.03 for the regularization factor γ instead of 0.015; and (3) using 5 and 20 ppb for the prior error standard deviation in the boundary condition elements of the state vector instead of 10 ppb. We also perform sensitivity inversions assuming normally distributed errors with prior error standard deviation sa=50 %. Combination of these perturbations to our inversion framework generates 36 members in the inversion ensemble. The uncertainty in posterior estimates reported here is taken as the greater of the range of solutions given by the inversion ensemble and the 2σ error inferred from the diagonal of S^, and is generally determined by the ensemble (Fig. S2).

Figure 4 compares the prior and posterior estimates of emissions mapped on the 0.25∘×0.3125∘ grid. It also shows the averaging kernel sensitivities (diagonal terms of the averaging kernel matrix), which measure the ability of TROPOMI observations to determine the posterior solution independently of the prior estimate (0 = not at all; 1 = perfectly). High averaging kernel sensitivities reflect a combination of high observation density and large prior emissions. We achieve high sensitivities to observations in major source regions, with 167 independent pieces of information (DOFS) out of the 600 Gaussian state vector elements.

Comparison of GEOS-Chem simulations using posterior versus prior emissions indicates an improved ability of the posterior emissions to fit the TROPOMI observations (Fig. 1). The mean bias over the inversion domain decreases from 7.8 to 0.4 ppb while the RMSE decreases from 16.8 to 13.6 ppb. The inversion effectively corrects the mean bias from using the prior emissions. The ability to decrease the RMSE is limited by the retrieval error on individual observations.

We independently evaluate the posterior estimate by comparison to in situ surface observations from the GLOBALVIEWplus CH4 ObsPack v4.0 database compiled by the National Oceanic and Atmospheric Administration (NOAA) Global Monitoring Laboratory (Schuldt et al., 2021). There are five sites in East Asia in 2019, all in relatively remote locations and with near-weekly sampling schedule (Fig. 5 and Table S2). The GEOS-Chem model bias for 2019 annual mean concentrations across the five sites is -4.1±9.5 ppb using prior emissions and -3.8±4.7 ppb using posterior emissions. There is little decrease in the mean bias, which is consistent with the mean bias of -3.4 ppb for TROPOMI relative to TCCON (Lorente et al., 2021) and implies that both the prior and posterior simulations are effectively unbiased in the mean. The factor of 2 lower standard deviation in the posterior simulation indicates a better fit to observations. The RMSE for individual observations decreases only slightly from 23.7 to 20.8 ppb because it is limited by the forward model transport error, previously estimated by X. Lu et al. (2021) at 20 ppb for the GLOBALVIEWplus CH4 ObsPack database using the residual error method. The model transport error is larger for surface than satellite observations because the amplitude of variability is larger and includes uncertainties in boundary layer vertical mixing.

Qu et al. (2021) previously reported overcorrections and inconsistencies with respect to GOSAT in their global TROPOMI inversion results over southeastern China. They attributed the problem to spatial overlap of coal and rice emissions, and to seasonal cloudiness correlated with the peak in rice emissions. We have more confidence in our results for several reasons. First, our higher spatial resolution compared with the 2∘×2.5∘ of Qu et al. (2021) allows better separation of coal and rice emissions. Second, we use an improved spatial distribution of coal emissions (Sheng et al., 2019) compared with the EDGAR v4.3.2 inventory in Qu et al. (2021). Third, we use version 2.02 of the TROPOMI retrieval with additional filters, and exclude data inconsistent with GOSAT (Fig. 2), whereas Qu et al. (2021) used TROPOMI v1.03 data with quality flags but no other filtering. Our results show higher averaging kernel sensitivities over southeastern China than those of Qu at al. (2021) and no overcorrections (Fig. 1).

Table 1 compiles the total national and sectoral posterior emissions for China. Sectoral attribution assumes that the posterior/prior emission ratios for a given 0.25∘×0.3125∘ grid cell (Fig. 4c) apply equally to all prior emission sectors within that grid cell, so that the combination of Figs. 4c and 3 gives the spatial distribution of the change in emission by sector. Posterior estimates of total, anthropogenic, and natural emissions for China are 70.0 (61.6–79.9), 65.0 (57.7–68.4), and 5.0 (3.9–11.6) Tg a-1, respectively, where the parentheses indicate the uncertainty range in the inversion solution as described in Sect. 2.6. The averaging kernel sensitivities for the national total and anthropogenic posterior emission estimates are 0.91, indicating that these estimates are largely determined by the TROPOMI observations with little influence from the prior estimate. Our best posterior estimate of 65 Tg a-1 for Chinese anthropogenic emissions is 21 % higher than the 2014 value of 53.6 Tg a-1 reported by the Chinese government to the UNFCCC, and the range of our inversion results gives us high confidence that the reported emissions are too low.

Our ability to separate the contributions from different sectors to the posterior emission estimates for China can be evaluated by examining the error correlations in the reduced posterior error covariance matrix (Sect. 2.5), as shown in Fig. 6. We find that landfills and wastewater treatment cannot be effectively separated in the posterior solution (posterior error correlation coefficient r=0.95), because they have similar spatial distributions associated with population (Fig. 3), and we thus group them as a single waste sector for further analysis. The “Other” sector, which is mostly associated with urban emissions, also has strong error correlations with waste (r=0.66–0.75). Other sectors can be successfully separated, as shown by the posterior error correlations in Fig. 6. We find that most of the posterior error correlation coefficients between sectors are lower than 0.2. For example, there is little error correlation (r=-0.2–0.1) between coal and other sectors. The global TROPOMI inversion by Qu et al. (2021) found it difficult to separate emissions between coal and rice paddies, but here we find a low error correlation of –0.04 that reflects our much higher spatial resolution. The main natural emission sector is wetlands, which is effectively separated from all other sectors except rice (r=0.29).

We can now attribute the 21 % underestimate of anthropogenic emissions in the Chinese government report to the UNFCCC, as given in Table 1. We find large upward corrections in emissions from oil (+147 %), gas (+61 %), livestock (+37 %), rice paddies (+34 %), and waste (+41 %), but a downward correction in coal emissions (-15 %). Averaging kernel sensitivities for all anthropogenic sectors are high (0.71–0.91), indicating strong constraints from the observations. An exception is the gas sector (0.31), for which emissions are relatively small. The uncertainty ranges of the inversion results for the different sectors are small, indicating an insensitivity to different inversion assumptions and high confidence in the posterior sectoral emissions in the base inversion.

The inversion returns a larger estimate of 5.0 (3.9–11.6) Tg a-1 for natural sources relative to 3.2 Tg a-1 in the prior estimate, mainly driven by increased contributions from wetlands (+1.1 Tg a-1) and termites (+0.5 Tg a-1). Averaging kernel sensitivity for wetlands is moderately high (0.61) but low for the other small natural sources.

The base inversion assuming a log-normal error distribution for prior emissions returns larger posterior Chinese emissions from all sectors relative to a normal error assumption, as would be expected from the asymmetry of the log-normal function. The largest differences are for the oil and gas sectors, where the sensitivity inversion, assuming a normal error distribution, yields posterior estimates respectively 22 % and 21 % lower than the base inversion. The oil and gas sectors are particularly high-tailed in their frequency distributions of emissions (Zavala-Araiza et al., 2015; Lyon et al., 2015; Brandt et al., 2016; Alvarez et al., 2018).

Our downward correction of coal emissions compared with the UNFCCC report is driven by both Shanxi province and southwestern China, which are the two largest coal producing regions in China (Zhu et al., 2017). This could reflect (1) overestimate of EFs in the UNFCCC report, (2) under-accounting of surface mines, and (3) increasing coal methane utilization. With regard to (1), many high-methane-content coal mines with inefficient coal production have been closed in the past decade (Wang et al., 2020). Coal production has shifted from southern and eastern China to northwestern China (including Shanxi) with abundant coal reserves and where methane content is relatively low (Gao et al., 2021; Liu et al., 2021). With regard to (2), a previous study (Gao et al., 2021) indicated an underestimated share of surface mining in the UNFCCC report for China. The methane emission intensity of surface mining is 10 times lower than underground mining (Palmer et al., 2021). With regard to (3), coal mine methane (CMM) utilization in China has greatly increased in the past decade (Y. Y. Lu et al., 2021).

However, uncertainty in the spatial distribution of coal emissions remains a major obstacle for top-down studies. Different bottom-up inventories are inconsistent in their estimates of the number of mines in China (e.g., 324 in EDGAR v4.2, 4243 in EDGAR v4.3.2, and 10 963 in Sheng et al., 2019). Mine closures and regional shifts in coal production may also be difficult to track (Gao et al., 2021). New satellite observations of methane plumes from individual point sources could provide important new information for geolocation and quantification of emissions from coal mines, as shown for the Shanxi province by Guanter et al. (2021) and Sánchez-García et al. (2022).

Our posterior estimate of oil/gas emissions is higher than the UNFCCC report and Peng et al. (2016), but lower than EDGAR v4.3.2 and v6. The previous top-down estimates in Fig. 7 range from 0.7 Tg a-1 by X. Lu et al. (2021) to 5.5 Tg a-1 by Miller et al. (2019), and our estimate is in mid-range. Scarpelli et al. (2022) found that the oil/gas emissions from X. Lu et al. (2021) were heavily influenced by the low GFEI v1 inventory (Scarpelli et al., 2020b) used as their prior estimate. The high emissions in Miller et al. (2019) could reflect their use of the EDGAR v4.2 inventory as prior estimate with spuriously high emissions from pipelines (Scarpelli et al., 2020b).

We find that the oil sector has the largest relative upward correction to the UNFCCC inventory (+147 %) among all sectors. The correction might be attributed to methane leakage from oil extraction not fully accounted for in the UNFCCC report (Rutherford et al., 2021; Deng et al., 2022). Lauvaux et al. (2022) used 2019–2020 TROPOMI observations to identify a number of ultra-emitters (>25 t h-1 on the 5.5×7 km2 grid) from oil production fields; their identified ultra-emitters in China are consistent with the locations where we find large oil upward adjustments.

Gas emissions for China in the UNFCCC report (0.18 Tg a-1) are dominated by distribution (0.125 Tg a-1) with only small contributions from production (0.03 Tg a-1) and transmission (0.025 Tg a-1). This is in part because of low EFs from production, and in part because a large fraction of the gas used in China is imported. The assumed EF for gas production in the UNFCCC report is 1.3×10-10 Gg m-3 of gas production, much lower than in the IPCC (2006) EF guidelines (lower-end value of 3.8×10-10 Gg m-3 of gas production for developed countries). Of the gas used in China in 2019, 42 % was imported (EIA, 2020).

Our inversion returns a posterior emission for the gas sector of 0.29 Tg a-1 including 0.16 Tg a-1 from distribution, 0.07 Tg a-1 from production, and 0.06 Tg a-1 from transmission. However, the averaging kernel sensitivity is low (0.3) and the distribution subsector is difficult to disentangle from the waste sector because it is mostly urban. Alvarez et al. (2012) suggested that the life-cycle loss rate from gas production should be less than 3.2 % for a coal-to-gas transition to be of climate benefit. Our posterior estimate indicates a loss rate of 1.7 % (1.3 %–1.9 %) for China, assuming 92 % methane gas by volume (Scarpelli et al., 2022).

China's gas industry has entered a rapid development stage driven by the domestic coal-to-gas transition policy (Qin et al., 2018); China's gas production in 2019 was 42 % higher than in the 2014 year of the UNFCCC inventory (EIA, 2020). The small loss rate suggests that the transition will be beneficial for climate but is somewhat misleading because of the large fraction of imported gas. Of that imported gas, 25 % is from Turkmenistan (EIA, 2020), where emissions from gas production are exceedingly high (Varon et al., 2019; Irakulis-Loitxate et al., 2022; Lauvaux et al., 2022). A more complete accounting of the loss rate in China from gas production would factor in the effect of international trade.

Our estimate of Chinese livestock emissions is higher than that of any previous study (Fig. 7). This is because our inversion corrects livestock emissions upward in northwestern and northeastern China, where existing bottom-up inventories show weak emissions (Lin et al., 2021). Previous GOSAT inversions had poor observational coverage over these regions (Fig. 5 in Qu et al., 2021), and their inversion solutions hence cannot depart sufficiently from the low bottom-up inventories used as prior estimates. However, TROPOMI observations provide strong constraints as illustrated by the high averaging kernel values (Fig. 3).

We estimate higher waste emissions than the 2010 Peng et al. (2016) inventory and the 2014 UNFCCC report, and we attribute this in part to the rapid development of wastewater treatment in China. China has enacted major policies on water pollution prevention since 2014 (Xu et al., 2020), including new standards for sewage discharge (Han et al., 2016). The number of wastewater treatment plants increased by 44 % from 2014 to 2019 (Xu et al., 2020). Solid waste generation has also increased in the past decade (Sheng et al., 2021), but an increasing percentage is incinerated rather than landfilled (Liu et al., 2021).