We use column-averaged dry-air methane mole fractions (XCH4) from the blended GOSAT+TROPOMI satellite product (referred to as TROPOMI observations hereafter) developed by Balasus et al. (2023), which employs CO₂ proxy GOSAT methane retrievals as a reference (University of Leicester GOSAT Proxy XCH₄ dataset v9.0) (Parker and Boesch, 2020) to correct the retrieval biases of original TROPOMI data produced by Space Research Organisation Netherlands (Lorente et al., 2023). This blended TROPOMI dataset has been applied in previous studies to quantify global and regional methane emissions (Estrada et al., 2026; Pendergrass et al., 2025; Varon et al., 2026; He et al., 2026; East et al., 2025). Here we use retrievals over land from 2019 to 2023. We exclude observations poleward of 55° owing to surface snow cover, unfavorable illumination, and possible stratospheric model biases (Turner et al., 2015; Zhang et al., 2025). We feed daily grid-cell averaged XCH₄ observations, along with corresponding model values that account for each retrieval's prior vertical profile and averaging kernels (see Sect. 2.4), into the inversion. The TROPOMI observations have a spatial resolution of 7 km × 5.5 km at nadir (previously 7 km × 7 km before August 2019) and a local overpass time of approximately 13:30 local solar time (Hu et al., 2016; Veefkind et al., 2012). XCH₄ is retrieved from measurements at the SWIR (2.3 µm) band, in combination with the NIR (757–774 nm) band.

Figure 1 shows the spatial distribution of 2019–2023 annual average XCH4 concentrations and the number of observations across the study domain. On average, there are ∼ 8 × 10⁶ TROPOMI observations annually (Fig. S1 in the Supplement), with considerable spatial variability in observation density (Fig. 1). For instance, in western Europe, observation coverage is denser over Spain, Portugal, and France compared to neighboring Germany, Belgium, the Netherlands, and the United Kingdom. Satellite observations are sparse in Northern Europe but moderate in Eastern Europe. This uneven spatial coverage influences the satellite's capacity to constrain methane emissions across different regions.

We also use ground-based methane observations from the Integrated Carbon Observation System (ICOS) network across Europe (https://www.icos-cp.eu/data-products/atmosphere-release, last access: 13 October 2026; ICOS RI et al., 2025). We use hourly dry-air methane mole fraction observations from 28 ICOS atmospheric stations (Table S3), filtered for valid measurements (Flag = “O”). For 2019–2023, we compute daily daytime averages using data between 10:00 and 16:00 local time, which generally represent well-mixed boundary layer conditions. High-altitude mountain stations are excluded from the inversion due to representativeness issues associated with daytime observations at these sites (Ioannidis et al., 2026; Steiner et al., 2024) (Table S3).

Figure 2 shows the spatial distribution of the ICOS stations used in our analysis, alongside their 2019–2023 mean methane concentrations. The surface sites are predominantly clustered in western Europe, particularly in Germany, the Netherlands, and northern France (Fig. 2). Additional sites are located in the UK and Northern Europe (Fig. 2). These regions correspond to areas with sparse satellite data coverage (Fig. 1), underscoring the strong complementarity between satellite and surface observations for constraining methane emissions. Furthermore, the surface measurements reveal elevated methane concentrations in the Netherlands, northern Italy, and northwestern Germany (Fig. 2), generally consistent with the hotspots of elevated XCH₄ in satellite observations (Fig. 1).

Figure 3 shows the spatial distribution of prior emissions by sector in the inversion domain. Table S1 tabulates national totals and their sectoral breakdown. Prior anthropogenic emissions (including agriculture, fossil fuel, and waste) are taken from the Emissions Database for Global Atmospheric Research (EDGAR) v8 global emission inventory for 2019–2022 (Crippa et al., 2023). Since 2023 data are not available in EDGAR v8, the 2022 emissions are used for 2023. Prior natural emissions are compiled from multiple datasets: wetland emissions from the ensemble mean of WetCHARTs version 1.0 (Bloom et al., 2017), biomass burning emissions from the Quick Fire Emissions Dataset version 2 (QFED2), termite emissions from Fung et al. (1991), and geological methane emissions based on (Etiope, 2015; Kvenvolden and Rogers, 2005) compiled by Maasakkers et al. (2019). Prior wetland emissions are prescribed at a monthly temporal resolution, and biomass-burning emissions at a daily resolution. Freshwater (rivers and lakes) methane sources (Rocher-Ros et al., 2023; Weber et al., 2019) are not explicitly represented in the prior emissions, considering potential double counting with the wetland inventory (Saunois et al., 2020). Details of the prior emission inventories are provided in Table S2.

These prior emission inventories yield a total methane emission of 25.9 Tg yr⁻¹ for the European countries in 2019, which is mainly from anthropogenic sources (22.0 Tg yr⁻¹). The largest anthropogenic sector in Europe is livestock, distributed primarily in France, Germany, the Netherlands, and the UK (Fig. 3). By contrast, rice cultivation is a minor agricultural source, mainly located in northern Italy (Fig. 3). Oil and natural gas production are concentrated in the North Sea, while coal production is in eastern Europe such as Poland (Fig. 3). The waste sector, including wastewater and landfills, is typically associated with population-dense urban centers (Fig. 3). Natural sources are dominated by northern high-latitude wetlands (Fig. 3). The prior emission inventories indicate a steady decline in anthropogenic methane emissions from the European countries by 0.2 Tg yr⁻² (0.9 % yr⁻¹). The decrease is mainly driven by the waste sector in western Europe, the oil and gas sector in the North Sea, and the coal sector in Ukraine.

We employ the nested version of the GEOS-Chem 12.9.3 chemical transport model (https://zenodo.org/records/3974569, last access: 13 October 2026) as the forward model for the inversion, which relates atmospheric concentrations to surface emissions. The simulation has a horizontal resolution of 0.5° × 0.625° over the European domain (30–70° N, -30–50° E) with 47 vertical layers, and is driven by MERRA-2 reanalysis meteorology from the NASA Global Modeling and Assimilation Office (GMAO) (Gelaro et al., 2017). The atmospheric oxidation of methane is simulated using archived monthly OH, Cl, and stratospheric loss fields (Wecht et al., 2014).

The initial and 3 h dynamic boundary conditions for the regional simulation are taken from a 4° × 5° global GEOS-Chem simulation driven by methane emissions optimized in a global inversion (Ciais et al., 2026). We then quantify and correct residual systematic regional biases in the boundary condition, using satellite and surface observations from background grid cells near the western and northern boundaries, which are the primary inflow pathways into the European domain (Fig. S2). The derived correction, 12 ppb for the western boundary and 30 ppb for the northern boundary (Fig. S2), is applied uniformly to the entire tropospheric vertical profile at both boundaries. This correction is supported by improved agreement with independent IAGOS-CARIBIC aircraft observations (https://www.caribic-atmospheric.com/Data.php, last access: 29 July 2026) in the European free troposphere, reducing the mean bias from 14.1 to 2.9 ppb (Fig. 4). Free tropospheric methane concentrations are largely governed by boundary conditions rather than local surface emissions, making these aircraft data suitable for evaluating boundary conditions. This argument is further supported by the minimal change in simulated free tropospheric methane concentrations between the prior and posterior simulations (Fig. 4).

To compare with satellite or surface observations, we sample methane fields simulated by GEOS-Chem at the location and time of individual observations. For surface data, we compute daily daytime averages (10:00–16:00 local time) as applied to the hourly in situ measurements. For satellite data, we compute column-averaged methane mole fractions by accounting for the instrument's vertical sensitivity and the prior methane vertical profile.

We perform analytical Bayesian inversion following Zhang et al. (2022) to estimate methane emissions from Europe. The inversion, performed separately for each calendar year, optimizes a state vector x consisting of annual methane emissions from 824 spatial clusters across the study domain (819 clusters for land and 5 clusters for the North Sea, shown in Fig. 5d). We first assign the number of clusters to each country based on the country area and prior methane emissions, and then generate spatial clusters using the Gaussian Mixture Model (GMM) (Turner and Jacob, 2015) for each country.

The optimal solution of the state vector x is solved by minimizing a Bayesian cost function that incorporates both prior knowledge and observational constraints (Brasseur and Jacob, 2017): 1Jx=x-xaTSa-1x-xa+y-F(x)TSO-1y-F(x) where y is the observation vector that contains satellite and surface observations, xa denotes the prior estimate for x, Sa is the prior error covariance matrix, SO is the observing system error covariance matrix, and Fx represents the forward simulation by GEOS-Chem. We treat Sa as a diagonal matrix with a 50 % relative uncertainty assigned to annual methane emissions of each spatial cluster to be optimized. The observing system error covariance matrix, which accounts for random instrument and forward model errors, is represented by a diagonal approximation (SO) of the full matrix (SO′), which is populated with the error variance of individual observations (on average ∼ 12 ppb for satellite and ∼ 40 ppb for surface) along with spatial and temporal correlations between observations (spatial correlation length of 500 km for satellite and temporal correlation length of 2 d for both satellite and surface) derived from the error residual method (Figs. S3, S4 and Table S4). The diagonal approximation (SO) of SO′ is solved following the method of Zhang et al. (2022) and Liang et al. (2023) (see details in Sect. S1). Additionally, we perform sensitivity inversions in which the observation vector (y) contains either satellite data alone or surface data alone. This allows us to examine the consistency between the two platforms and quantify the observational constraints provided by each.

Minimizing Jx yields the analytic solutions for the optimal estimate, 2x^=xa+KTSO-1K+Sa-1-1KTSO-1y-F(xa) Linearizing the forward model Fx=Kx+c (c is a constant vector) results in the Jacobian matrix K, which represents the sensitivity of methane concentrations to emissions (∂y/∂x). The matrix K is explicitly constructed by performing GEOS-Chem model simulations with individual state vector elements perturbed.

The analytical solution also yields solutions for the posterior error covariance matrix and the averaging kernel matrix: 3S^=KTSO-1K+Sa-1-14A=∂x^∂x=I-S^Sa-1 The posterior error covariance matrix (S^) provides a quantitative measure of the uncertainty associated with the optimized emissions. The averaging kernel matrix (A) describes the sensitivity of the posterior estimate to the true state, with values ranging from 0 (no constraint) to 1 (fully constrained by observations). The trace of matrix A, known as the degrees of freedom for signal (DOFS), quantifies the number of independent pieces of information that are effectively constrained by the observing system. The analysis of A and associated DOFS allows us to quantify the information content provided by satellite and surface observations.

The optimized emissions (x^) can be projected back onto the spatial grid to obtain the distribution of methane fluxes. To assess emissions at the national scale, we further aggregate the posterior fluxes by country. This is achieved by constructing a transformation matrix W that maps the gridded flux vector (x^) to national totals. The national-level posterior flux (x^country), posterior error covariance matrix (S^country), and averaging kernel matrix (Acountry) can be calculated as: 5x^country=Wx^6S^country=WS^WT7Acountry=I-WS^WTWSaWT-1 Prior uncertainties for national estimates are aggregated following the same approach as in Eq. (6), but with the prior error covariance matrix Sa substituted in the right-hand term.

We derive sectoral methane emissions by partitioning posterior emissions in each grid cell according to prior sectoral fractions. This approach is more effective where major sectors are spatially segregated, but may misattribute emissions in regions with significant sectoral overlap (Lu et al., 2022). Although sectoral information is not directly constrained by methane observations, the sectoral estimates offer useful interpretive insights.

The joint inversion of TROPOMI and ICOS data improves the fit to both satellite and surface observations, with reduction of root-mean-square errors (RMSE) by 7.95 ppb for ICOS and by 0.84 ppb for TROPOMI (Fig. S6). Cross verification further shows that each single-dataset inversion also improves the fit to the other dataset. The TROPOMI-only inversion reduces RMSE against ICOS by 1.31 ppb, while the ICOS-only inversion reduces RMSE against TROPOMI by 0.09 ppb (Fig. S7). Although these improvements are relatively small, they confirm broad consistency between the two datasets. The posterior simulation also reproduces the observed seasonal variability in methane concentrations (Fig. S5), indicating no substantial seasonal biases in the annually optimized emissions. We further evaluate the inversion against independent ground-based column observations from the TCCON network (https://tccondata.org/, last access: 29 July 2026). Compared to the prior simulation, the posterior simulation reduces the RMSE by about 1 ppb at five of the seven TCCON sites in Europe. These sites with improved agreement are located mostly in western Europe (mainly Germany and France) where the observation constraints are strong, while the other two sites are in the UK and Cyprus where observation constraints are weak (see discussion in Sect. 3). In addition, we also evaluate the inversion against near-surface vertical gradients derived from independent IAGOS-CARIBIC aircraft observations (Fig. S8). Since most vertical profile observations are only available over Germany, where IAGOS-CARIBIC aircraft take off or land, this evaluation only provides information at local to regional scales. Compared to the prior simulation, the posterior simulation generates a sharper concentration gradient between the lower free troposphere and the surface, bringing the simulated profiles into closer agreement with the aircraft observations. The enhanced near-surface gradient reflects the upward adjustment of methane emissions over Germany inferred by the inversion (see Sect. 5.1). Overall, independent observation data remain spatially limited, preventing a systematic assessment of the inversion across the entire European domain.

We find that the inversion upward adjusts prior methane emissions from the Netherlands, northwestern Germany, and northern Italy (Fig. 8). The posterior estimates of anthropogenic emissions for these countries (Germany: 2.78 ± 0.12 Tg yr⁻¹; Netherlands: 1.15 ± 0.06 Tg yr⁻¹; Italy: 1.87 ± 0.13 Tg yr⁻¹) are 25 %–69 % higher than prior estimates (Germany: 2.23 Tg yr⁻¹; Netherlands: 0.68 Tg yr⁻¹; Italy: 1.40 Tg yr⁻¹) and 18 %–80 % higher than official reports to the UNFCCC (Germany: 1.60 Tg yr⁻¹; Netherlands: 0.64 Tg yr⁻¹; Italy: 1.58 Tg yr⁻¹) (Fig. 9). Our posterior estimates are generally comparable in magnitude with the independent country-level estimates from ITMS-D v2025 (Bruch et al., 2026) and ICOS/PARIS InTEM-NAME (Ganesan et al., 2026). The upward adjustments in these regions are derived from both of our sensitivity inversions, using either surface or satellite observations alone (Fig. S10), although the magnitudes of the adjustments differ (e.g., stronger and spatially uneven adjustment inferred by surface-only inversion than satellite-only inversion) due to varying observational constraints (Fig. 5). This general consistency in directions provides additional support that the upward adjustment is robust across different observation platforms in this region.

Based on the relative contribution of each sector in the prior inventory, we attribute most of the upward adjustment in the Netherlands, Germany, and Italy to the agriculture sector (Fig. 10). This finding is consistent with a recent satellite inversion over western and central Europe, which inferred a 17 %–29 % increase in CAMS livestock emissions (Oak et al., 2026). Our attribution to agricultural emissions also aligns with a recent local-scale survey of 51 Dutch dairy farms, which reported average whole-farm methane emissions 27 % higher than Dutch National Inventory estimates, though those local measurements carried substantial uncertainties of their own and may not fully represent national conditions (Chen et al., 2025). By contrast, urban emission measurements in several cities of these countries, including Berlin (Klausner et al., 2020), Groningen, Utrecht, Rotterdam (Tong et al., 2023), and Milan (Cristofanelli et al., 2025), have not shown significant discrepancies from EDGAR or official inventories, suggesting that the regional underestimation inferred by the inversion is unlikely to stem primarily from urban sources. Taken together, these results point to potential systematic biases in national-level livestock emission accounting, even when high-tier methodologies that incorporate detailed activity data on animal diet, milk production, and feed use are employed (Bruch et al., 2025; Steiner et al., 2024).

Despite the above evidence, our sectoral attribution is inherently limited in regions with spatial overlap among major sectors or poor prior representation of key sources. Coastal wetland and freshwater emissions, absent from our prior, may partly explain the inferred increase over the Netherlands (Buzacott et al., 2024). Geological emissions introduce major uncertainty in Italy. Etiope et al. (2019) estimated ∼ 2 Tg yr⁻¹ from geological seeps, compared to negligible amounts in our prior (∼ 0.03 Tg yr⁻¹), mirroring large discrepancy in global geological emissions using different approaches (Hmiel et al., 2020; Etiope et al., 2019). This leads to considerable uncertainties in both total emission estimation and sectoral attribution, particularly where agricultural and geological sources are spatially closely located like northern Italy. Given their important implications for distinguishing natural from anthropogenic emissions, these limitations warrant further targeted investigation. Moreover, future inversion studies could leverage observed seasonality (Ioannidis et al., 2026) and sector-specific tracers such as NH₃ (Tang et al., 2025) to enhance the ability to quantify agricultural emissions.

In addition to agriculture- and waste-related sources, the inversion analysis also revises methane emission estimates for several fossil fuel production regions, including the North Sea and southern Poland (Fig. 8). For the North Sea, posterior emissions from offshore oil and gas production are 0.28 Tg yr⁻¹, 53.4 % lower than prior estimates. This contrasts with a ship-based study (Riddick et al., 2019), which found substantial emissions from UK offshore platforms, suggesting existing inventories may underestimate. However, those measurements were limited to a short timeframe and may not reflect the variability across different phases of offshore production. This downward adjustment is mainly informed by surface observations, but both satellite- and surface-only inversions agree on its direction (Fig. S10).

Over southern Poland, the inversion reveals a revised spatial pattern of emissions within the Upper Silesian Coal Basin (Fig. 8), a major production hub accounting for the majority of the EU's hard coal output. Despite this spatial redistribution, the national estimates for anthropogenic emissions remain nearly unchanged at 1.7 Tg yr⁻¹, whereas coal mining emissions increase from 0.40 to 0.47 Tg yr⁻¹ (Fig. 9 and Table S1). The posterior coal-mining estimate is broadly consistent in magnitude with previous multi-scale observational studies conducted in the Upper Silesian Coal Basin, ranging from individual mine shafts to basin-wide assessments (Andersen et al., 2023; Fiehn et al., 2020; Luther et al., 2019, 2022; Tu et al., 2022).

Other major fossil fuel producers in Europe, such as Romania and Ukraine, show only minor emission adjustments in our atmospheric inversion (Figs. 8, 9). This is primarily due to limited capacity of the inversion system to constrain emissions in these regions, as indicated by low observational constraints (DOFS of only 0.75 for Romania and 1.38 for Ukraine). Consequently, while our posterior estimate (0.83 Tg yr⁻¹) aligns more closely with the prior EDGAR inventory, it does not conclusively rule out the plausibility of the significantly different UNFCCC value for Ukraine's oil and gas sector (1.5 Tg yr⁻¹) (Fig. 10). This limitation in observational constraint also explains why our inversion infers the relatively small adjustments for Romania (Fig. 8), though aircraft-based studies reveal that UNFCCC reports underestimate emissions from the country's southern oil fields (Maazallahi et al., 2025; Kuhlmann et al., 2025).

In Northern Europe, including wetland-rich areas (Fig. S11), posterior estimates are generally lower than the prior (Fig. 8), implying a possible overestimation of wetland and/or offshore oil and gas emissions. These regional differences reveal localized hotspots or deficits that are not fully captured in the prior inventory. While the prior emissions reproduce broad spatial patterns reasonably well, they may miss finer-scale spatial heterogeneities. However, because of the limited observational coverage, these high-latitude regions are only weakly constrained by observations, hence large uncertainties remain in observationally deriving fossil fuel and wetland emissions in Northern Europe.

The inversion also indicates moderate upward adjustments for anthropogenic emissions across France, Spain, and the terrestrial part of the United Kingdom (Figs. 8, 9). The adjustments for the UK and France are mainly driven by surface data, whereas the adjustment for Spain is driven mainly by satellite observations (Fig. S10). Posterior emissions are 2.70 ± 0.17 Tg yr⁻¹ for France and 1.74 ± 0.18 Tg yr⁻¹ for Spain, representing increases of approximately 7 % and 15 % relative to their prior estimates, respectively (Fig. 9). For the UK, the posterior anthropogenic emissions (1.58 Tg yr⁻¹) remain nearly unchanged from the prior (Fig. 9), as the increase over land is offset by decreases in offshore oil and gas emissions over the ocean. The satellite-only inversion shows little adjustment over southern UK, suggesting that the inferred increase is mainly constrained by the available surface observations, whereas offshore emissions remain weakly constrained.

Spatially, the inversion reveals concentrated upward adjustments over major urban areas such as Paris, Madrid, and London, in addition to weaker, diffuse adjustments that we attribute to agricultural sources (Fig. 8). Consistent with this finding, recent studies using ground-based (Tu et al., 2022) and satellite-based (Dogniaux et al., 2025) remote sensing have identified landfills as a major, underrepresented methane source in Madrid. Eddy covariance flux measurements in central London also show that urban methane fluxes are substantially underestimated in inventories, with contributions from both biogenic and fossil fuel sources (Helfter et al., 2016). Further attributing urban emissions to biogenic versus fossil fuel sources is challenging within our inversion framework due to spatial overlap. Inclusion of additional atmospheric tracers, such as C₂H₆ and δ13CH₄, could enhance source attribution of urban methane emissions (McKain et al., 2015; Ramsden et al., 2022; Zhao et al., 2026; Basu et al., 2022).