TROPOMI is on-board Sentinel-5 Precursor (S5P) since 2017. The radiances measured in the shortwave infrared range (SWIR, 2314–2382 nm) are used to derive methane total columns. The pixel size at nadir was about 7.2 × 7.2 km² before 2019/08/06. It was upgraded to 5.6 × 7.2 km² after a change in the instrument settings on this date. The swath is about 2600 km on ground, allowing global daily coverage. The accuracy requirements for XCH₄ total columns are 1 % bias and 1 % random error, as defined in the S5P Calibration and Validation Plan . In this study, the assimilated methane retrievals consist of three level 2 (L2) products, described in the following sections. Table  shows the number of observations available in the domain in 2019 for each of these products.

The operational TROPOMI product (v2.4), hereafter called “SRON”, is developed by the SRON Netherlands Institute for Space Research. It includes the iterative improvements of the research product , in particular better accounting for surface reflectance . In this study, we use the reprocessed albedo bias-corrected version and apply the recommended filtering criteria to ensure high-quality data (quality flag superior to 0.5). This product is retrieved from TROPOMI measurements with the RemoTeC full-physics algorithm, that retrieves both the atmospheric methane mixing ratio and the physical scattering properties of the atmosphere. A detailed description of the algorithm is given in the Algorithm Theoretical Baseline Document . A destriping procedure is applied to new XCH₄ data from 7 September 2024 (v2.07), but older orbits have not been reprocessed. This empirical approach consists in removing the CH₄ background by a median smoothing in the cross-track direction, and then computing a per orbit stripe value as a median in the flight direction, which is used for correction . However, this processing is not applied to the 2019 observations used in this study.

The BLENDED product is a corrected version of SRON: a machine learning (ML) model has been trained to predict the differences between GOSAT and TROPOMI-SRON (v2.4) observations, based on SRON data features. The GOSAT XCH₄ product uses a proxy retrieval which is less sensitive to surface and atmospheric artifacts. It is described in further detail in Sect. . The global mean bias versus TCCON data (9.2 ppb) is subtracted from all GOSAT observations . The correction is modeled on co-located observations, then applied to the whole TROPOMI-SRON record. This method aims at taking advantage of the density of TROPOMI measurements, while mitigating the effect of known biases associated to surface albedo, coarse aerosol particles and striping, thanks to the GOSAT proxy approach. We keep only the highest quality data (quality flag of 1) and filter for coastal scenes as recommended by . This quality filter is theoretically stricter than the one recommended for the SRON product, but in practice it eliminates only 12 observations over the domain in 2019. It can thus be considered that both SRON and BLENDED products share the same observation sampling (see Table ). In the BLENDED product, the observation errors, averaging kernels and prior profiles are directly taken from the SRON product (only the XCH₄ values differ between the two products).

The WFMD scientific product v1.8 , hereafter called “WFMD”, is based on the Weighting Functions Modified Differential Optical Absorption Spectroscopy (WFMD-DOAS). Quality filtering is based on a random forest (RF) classifier: data with a quality flag of 0 is selected. Post-processing includes systematic bias correction (eg. due to albedo) based on a RF regressor, as well as a destriping filter based on combined wavelet–Fourier filtering.

To separate the effect of varying coverage between products from the effect of the differences in the XCH₄ distributions, we extract a dataset of observations shared across all three products, so that they have identical spatio-temporal sampling. This “common” dataset is used for the analysis of the inter-product differences (Sect. ) and for OSSEs (Sects. , ).

In Sect. , we compare TROPOMI observations with retrievals from the University of Leicester GOSAT Proxy XCH₄ product, v9.0 . The GOSAT satellite was launched in 2009. Methane estimates are based on the CO₂ proxy method, which takes advantage of CO₂ absorption in the measured 1.65 µm band, with a finer spectral resolution than TROPOMI. This approach significantly reduces the error in the retrieval, since it cancels aerosol and surface artifact contributions that similarly affect XCO₂ and XCH₄ measurements. Only highest-quality data (quality flag of 0) is considered, yielding 12 841 observations over the domain in 2019. The global mean bias versus TCCON data is removed from the GOSAT observations shown in the following, subtracting 9.2 ppb from all retrievals, to be consistent with the dataset used by to derive the BLENDED observations (see Sect. ).

To evaluate the results of the inversions, we use independent in-situ measurements of CH₄ mixing ratios from flasks and continuous sampling sites. The 19 available surface sites for 2019 are listed in Table . The data are compiled from the ICOS atmospheric network (https://www.icos-cp.eu, last access: March 2025), the World Data Centre for Greenhouse Gases (WDCGG, https://gaw.kishou.go.jp, last access: March 2025), the NOAA ESRL discrete sampling network (https://www.esrl.noaa.gov/gmd/, last access: March 2025) and the EBAS data base. Data from sites with continuous measurements are averaged to hourly values. The evaluation consists in comparing the emissions derived from the satellite-based inversions to an inversion assimilating only these surface measurements (Sect. ). We also compare the posterior simulated concentrations at the locations of the surface stations to these independent measurements (Sect. ).

The inter-comparison of TROPOMI satellite retrievals reveals differences in coverage over Europe in 2019. The density of observations is a critical parameter for ensuring robust constraints on emissions during the inversion. Yet, substantial differences exist between SRON/BLENDED and WFMD, as shown in Table . WFMD exhibits 63 % more observations in comparison to SRON and BLENDED over Europe in 2019. This higher observation count is attributable to the different filtering approaches: as mentioned in Sect. , WFMD employs machine learning techniques to identify scenes that are poorly characterized by the retrieval algorithm ; quality control criteria for SRON and BLENDED rely on threshold-based filters for cloud fraction, solar zenith angle and other scene description variables .

The temporal coverage shows consistent variations for the three products (Fig. a): observation density is high between June and October and decreases during winter. An anomalously low density is noticeable for all products in May 2019. It is due to an increase of the Fractional Cloud Cover (CFC) over Europe during this month, as indicated by the CLARA-A3 record . Seasonal spatial variations are consistent among products, with an absence of observations at high latitudes (≳60°) during winter months (see Fig. S1 in the Supplement).

Spatial patterns of coverage differences are illustrated in Fig. b. The WFMD dataset demonstrates a higher density of observations in arid regions (e.g., over Spain and Turkey). Moreover, it includes a few observations in mountainous areas (Alps, Norway), whereas SRON and BLENDED filter out all retrievals in these regions.

The temporal and spatial XCH₄ distributions of the three products are shown in Fig. . Average observed XCH₄ in 2019 is respectively 1850, 1843 and 1856 ppb for SRON, BLENDED and WFMD (Fig. ). Part of the differences between the distributions can be explained by the differences in spatial coverage between SRON/BLENDED and WFMD. When considering only the common observations across the three datasets, the average XCH₄ are slightly closer but still differ (1851, 1844 and 1856 ppb respectively), and the analysis of space-time distributions remains similar.

The temporal variations of XCH₄ throughout the year show overall similar shapes (Fig. a). Average concentrations decrease slightly from January to May, reaching a minimum in April/May, before rising during late summer and autumn, peaking in November. The difference between BLENDED and WFMD monthly averaged values is steady over the year (-11.7±2.1 ppb). The differences between SRON and BLENDED (6.8±2.3 ppb), as well as SRON and WFMD (-5.0±2.5 ppb) depict more temporal variations: SRON observations tend to be closer to GOSAT and BLENDED in winter, but closer to WFMD in summer. Only BLENDED aligns rather well with GOSAT, due to its correction of the TROPOMI-GOSAT bias.

Overall, the spatial patterns of the distributions of CH₄ concentrations are consistent, yet with local discrepancies, e.g., in Scandinavia (higher XCH₄ than SRON for WFMD and lower for BLENDED, as seen in Fig. b). BLENDED shows lower XCH₄ over the domain, but also consistent spatial gradients with SRON and WFMD (Figs. b, S2).

To understand the drivers of the differences in XCH₄ distributions, we adopt the method outlined by . A machine learning (ML) model is trained to predict the difference in XCH₄ based on the retrieval variables. The contribution of individual features to the prediction is assessed to estimate the importance of each variable. The results and analysis of the biases are presented in Sect. . Detailed study of the differences of XCH₄ relative to TCCON is available in Appendix .

The retrieval error (in terms of uncertainty) attributed to individual observations can impact the emissions from inversions by changing their spatial and temporal variations , as well as call into question both very high and very low emission values . The definition of this error differs between the SRON/BLENDED and WFMD products. For SRON (thus also for BLENDED, for which only XCH₄ values are corrected), the reported error is defined as the standard deviation of the retrieval noise, which follows from the error covariance matrix in the retrieval inversion procedure. This error describes the effect of the noise in the measured radiances on the retrieval . For WFMD, the error is propagated in the retrieval algorithm from the noise in the measured spectra. In both cases, the characterized error σ only includes the effect of noise in the measured radiance, however the unknown noise components related to atmospheric conditions or instrumental features are not accounted for.

To avoid underestimating the observation uncertainty, the products have different error corrections, based on the validation of the satellite XCH₄ with respect to total columns observations of the ground-based TCCON stations. SRON and BLENDED provides the error σ as described before and suggest to multiply it with a factor 2 to reflect the scatter of errors in the TCCON validation . We apply this recommended correction. For WFMD, the error σ is linearly rescaled, based on a regression of the scatter relative to TCCON observations (Eq. ). The scaled error σ^ is directly provided in the product and described in the Algorithm Theoretical Baseline Document . 1σ^=4/3(σ+5ppb)

Due to this difference in error definition between SRON/BLENDED and WFMD, the errors of SRON and BLENDED (3.9 ppb in average) are smaller by a factor of 3 than those of WFMD (12.2 ppb) (Fig. b). If we try to apply the linear transformation of Eq. () to SRON/BLENDED errors, the resulting error distribution aligns more closely with WFMD: the average scaled error is 11.9 ppb for SRON and BLENDED (Fig. c). Therefore, the difference in rescaling the error based on the scatter relative to TCCON is the main source of difference in the final uncertainty provided in the products. The impact of this difference on the results of inversions is further evaluated in Sect. .

As illustrated in Fig.  (only the common observations are considered here), the column averaging kernels (AKs) and prior profiles exhibit similar shapes, characteristic of SWIR retrievals. The per level relative difference between SRON/BLENDED and WFMD vertical profiles is below 5 % for all levels. The WFMD AKs seem to be less sensitive to the layers close to the surface in comparison to SRON/BLENDED, but more sensitive to the stratosphere (pressures inferior to 200 hPa). Differences up to approximately 200 ppb occur between the prior profiles of SRON/BLENDED and WFMD, in particular for the layers close to the surface: the WFMD prior profiles are scaled to have uniform surface values of 1850 ppb, while SRON/BLENDED prior mixing ratios at the surface are between 1900 and 2000 ppb. The scaling of prior profiles for WFMD also explains the lower variability of prior mixing ratios in comparison to SRON/BLENDED, as evidenced by the narrower horizontal deviations in the right panel of Fig. . These profiles are consistent with the ones presented in , which also highlight a systemically higher prior profile for SRON in comparison to the one of WFMD. The differences in the profiles lead to differences in the simulated XCH₄ distributions, as shown in Sect. .

In the following, we use notations according to the convention defined by and . The 4D-Var inversion adjusts the control vector x, to improve the fit between observed satellite data and their simulated equivalents, by minimizing the cost function J: 2J(x)=12(x-xb)TB-1(x-xb)+12(H(x)-y0)TR-1(H(x)-y0) where xb and y0 are respectively the vector of prior information and the vector of observations, H the observation operator, B and R the covariance matrices of the control vector and observation errors. The latest combines errors in both the observation data (measurement or processing errors) and the observation operator (model error, representativity of the gridded model compared to point measurements, aggregation errors).

The control vector x contains CH₄ emissions, at a 0.5° × 0.5° horizontal resolution and a weekly temporal resolution (similar to and ). It also contains the 4D CH₄ background field used to impose the initial, lateral and top boundary conditions as well as the concentrations in the stratosphere (above 200 hPa) at the native pixel resolution of the corresponding CAMS product (3° × 2°) and 2 d temporal resolution. Indeed, the assimilated data is used by the inversion to retrieve information on emission fluxes but also on the background.

The error covariance matrix B is built by blocks, the errors on the emissions and the background being considered independent. For the CH₄ emission components, the relative error standard deviation (diagonal elements of B) are set at 100 %, similarly as . Spatial and temporal correlations are built with an e-folding decrease with correlation lengths of 150 km on land and 200 km on sea, and 2 weeks through time. For CH₄ background concentrations, we assume a 2 % relative error standard deviation for diagonal elements. The non-diagonal elements account for spatial and temporal covariances, using a similar e-folding decrease with a spatial correlation length of 200 km and a temporal correlation length of 14 d.

The matrix R is diagonal: we consider no correlation of the errors from one observation to another. The diagonal elements are the errors associated with the individual retrievals, as described in Sect. .

For the inversions, additional filters are applied to TROPOMI observations (Sect. ) to avoid large differences between observed and simulated XCH₄ caused by the model limitations. The CTM cannot capture subpixel pressure variations: to mitigate the impact of subpixel topographic variability, we remove observations with surface pressure deviating by more than 3σ from the mean pressure of the data aggregated at the scale of the CTM pixel. This filter eliminates 1.4 % of the observations for SRON and BLENDED, 1.0 % for WFMD. Data for which the difference between the observation and the simulation is more than 100 ppb are also filtered out. It impacts very few observations, removing respectively 420 observations for SRON/BLENDED and 934 for WFMD, i.e 0.009 % and 0.012 % of the data. The spatial distributions of the observations removed by these two filters are similar across the three products (Fig. ).

In this study, we perform four 4D-Var inversions assimilating real observations, using the CIF. The CIF is a modular inverse modeling platform developed as a python library , designed in the framework of European and international projects. It can drive various data assimilation schemes and can be coupled to various CTMs. Here, the cost function J is minimized using the quasi-newtonian M1QN3 algorithm . The inversion is stopped when the gradient norm reduction exceeds 95 % compared to its initial value. The first three inversions assimilate separately each one of the TROPOMI products. An additional inversion assimilating surface observations (stations listed in Table ) is performed for evaluation. These four inversions are listed in Table .

We also explore the capability of the inversion set-up to derive robust emission estimates based on the assimilation of TROPOMI products in a set of Observing System Simulation Experiments (OSSEs). The OSSE approach makes it possible to evaluate the sensitivity of the inversions to the observation coverage, the observation errors and the differences between products, comparing the results of multiple OSSE scenarios. The structure of an OSSE is described in Fig. . The general principle consists of two main parts : first, the sampling of “true” synthetic observations, given a true state defined by the prior emissions and background concentrations. Then, a Monte-Carlo ensemble of inversions with perturbed priors is performed, to evaluate the capability of the observing system to recover the true state of the emission and background estimates.

In more details, a forward run of the CHIMERE CTM produces a “true” 4D concentration field, based on the prior emissions and the prior background concentrations (called xt). Pseudo-observations y0 are sampled from this field following the specifications (date, location, averaging kernels …) of the observation dataset.

The pseudo-observations are assimilated in an ensemble of n=4 inversions using randomly perturbed priors: for each inversion member i, the priors are initially perturbed (called xib) according to the error statistics provided in B (Sect. ): 3∀i∈[1,n],xib=xt+ηi,ηi∼N(0,B) The metrics used to assess the capability of the system to improve the emission estimates (i.e. to make them closer to the truth) is the relative increment r. It compares the distance to the true initial fluxes xt of the perturbed prior xib and the posterior fluxes xia, averaged over all the members of the ensemble: 4r=1n∑iri=1n∑ixia-xtxib-xt-1 The closer r is to -100%, the more the inversion improves the fluxes. Negative values of r correspond to posterior emissions that are closer to the truth than the prior (thus “better” emissions) while positive values correspond to posterior emissions further from the truth.

We define 6 OSSE scenarios, listed in Table , using different pseudo-observation datasets. To ensure a robust comparison of the scenarios, the seed of the random perturbations is kept constant. It is important to note that since SRON and BLENDED share the same sampling and parameters (errors, vertical profiles), the pseudo-observation datasets are identical. In the following,“SB” scenarios stand for the two products. The 6 scenarios are designed to evaluate the sensitivity of the inversions to multiple parameters:

3 OSSEs are performed as reference scenarios using the pseudo-observations of the TROPOMI products: “Ref-SB” for SRON and BLENDED, “Ref-WFMD” for WFMD; a third reference OSSE (“Ref-Surf”) is performed using the pseudo-observations of the surface stations.

To evaluate the impact of the differences between products, we carry out two more inversions assimilating pseudo-observations. The method differs from previous OSSEs: in this case, synthetic observations are sampled and biased with the difference between products:

The difference WFMD-SRON (computed over the common observations) is averaged over 0.5° × 0.5° pixels and 1 h-long periods, and added to the corresponding SRON pseudo-observations. The same correction is applied to WFMD pseudo-observations with respect to SRON-WFMD difference. To evaluate the impact of the inter-product difference on the posterior increments, each “corrected” data set is assimilated (priors are not perturbed), the inversions are called “Diff-SRON” and “Diff-WFMD”.

The Ref-SB and Ref-WFMD OSSEs demonstrate a consistent capacity to constrain emission estimates. Despite the relatively low values of r (in comparison to the aim of -100 %), we focus on the relative differences of r between scenarios. The temporal (Fig. a) and spatial (Fig. b) variations of the relative increments are consistent across the three products. Monthly variations smooth the noisier weekly variations in Fig. a, but relative differences between scenarios are conserved. WFMD presents the highest performance, with a mean relative increment of -5.7 %, in comparison to -3.5 % for SRON/BLENDED, and a larger reduction in RMSE (Table ). This product thus presents a higher constraint capacity in comparison to SRON and BLENDED.

The prior temporal variations of emissions remain largely preserved through the assimilation of pseudo-observations. Consequently, the posterior time variations align closely with those of the unperturbed prior. However, the relative increment varies over the year (Fig. a). These variations are partially influenced by the observational density, with lower r (i.e. closer to -100 %) in summer, coinciding with an abundance of high-quality measurements, and higher (i.e. further from -100 %) values in January and December, when coverage decreases due to cloud filtering. A small |r| is also seen in May 2019, likely caused by the low number of observations (Fig. b).

Regions with sparse observational coverage generally exhibit worse (i.e. closer to 0) relative increments. In particular, the system fails to improve emission estimates in Scandinavia across all three configurations (Fig. b). This limitation is directly related to the sparse observation density in this region (Fig. b), with nearly no observations available during winter. Due to a sparse observation density, the system also performs poorly in the United Kingdom (Fig. b), contributing to the poor mean relative increment over Western Europe.

The system manages to make the posterior emissions closer to the truth in areas with high fluxes (northern Italy, Benelux, Romania) while struggling in areas with weaker signals, like Latvia and southern France (Fig. b). This is linked to the prior error covariance B being proportional to the emissions (see Sect. ), which limits the ability of the inversion to recover diffuse sources with low signal-to-noise ratios, as previously noted by .

These reference OSSE scenarios demonstrate the capability of all TROPOMI products to bring emission posteriors closer to the truth compared to the perturbed priors. The Ref-Surf scenario provides a better overall enhancement, with an average relative increment of -7.31 %. However, this better result on average masks a high spatial heterogeneity: the relative increments are indeed very good in Western Europe and Central Europe where a number of stations are located, but fail to provide enhancements in regions with no stations, such as Spain or Romania (Fig. b). As expected, the wider coverage of satellite observations provides the advantage of constraining the emissions on a wider area, even if there are no surface stations.

The OSSEs can also be used to estimate the uncertainty reduction (independent of the control vector) for the inversions, computing the ratio between the standard deviation of priors and the one of posterior emissions across the ensemble samples. For the total budgets, it is estimated to 78 % reduction for SRON and BLENDED, 74 % for WFMD and 51 % for surface stations. However, we do not use them for evaluating the uncertainties of our budget estimates in Sect. , because of 1) the small size of the ensemble (4 samples) and 2) the lack of proper uncertainty estimation for the prior (not provided with the emission inventories). The estimation of the uncertainty requires a deeper analysis of the propagation of errors through the system: observation errors as well as model errors due to the prior emissions and the transport .

The relationship between observation density and constraint potential is explored through the Common-SB and Common-WFMD OSSEs. As expected, the relative increments are slightly closer to zero as observation density decreases (Table ). The average difference in comparison to the reference scenario is very low (less than 0.01 gCH₄ m⁻² yr⁻¹ in RMSE) for SRON/BLENDED, with 73 % of the observations kept in Common-SB, but slightly higher (0.03 gCH₄ m⁻² yr⁻¹ in RMSE) for WFMD because the difference in observation density is larger (45 % of observations kept). The time series of Ref and Common scenarios in Fig. a illustrate that the relative increment is overall slightly deteriorated, yet not systematically, as the number of observations decreases. The observation density is thus a driver of the potential for constraining emissions through the inversion. However it only partially explains the differences of performance between the products, since Common-WFMD results in lower relative increments than Common-SB: even with the same number of observations, WFMD seems to show a better capability to bring emission closer to the truth. The key differences between these scenarios lie in the uncertainties associated with the measurements and the vertical parameters (such as pressure levels, AKs, and prior profiles) used to compute the satellite equivalents.

The linear rescaling of the error associated with individual observations, described in Eq. (), increases these individual errors in the dataset of pseudo-observations. The comparison of Err-SB scenario to Common-SB shows a slight improvement of the emissions for all months (Fig. a) and all regions (Fig. b), when rescaling these errors. The spatial distributions are similar, as shown in Fig. b, but with a slightly larger amplitude for Err-SB.

The Err-SB scenario is the closest SRON/BLENDED scenario to WFMD ones in terms of relative increment (Fig. ). The Err-SB and Common-WFMD, which share similar features in terms of coverage and errors, have the highest consistency between SRON/BLENDED and WFMD OSSEs, highlighting these features as drivers of the differences in inversion results. The remaining differences are due to the vertical parameters (pressure levels, averaging kernels, and prior profiles).

Rescaling the observation error results in an enhancement of the emissions. This counterintuitive effect is likely due to overfitting and complex indirect effects within the inversion: because of the large number of observations and the low individual observation errors, the system could struggle to overfit the observations, thus degrading the performances. At the 0.5° resolution, several observations constrain each component of the control vector, leading to overfitting of some observations if the errors are small. This effect would be mitigated in the Err-SB scenario, leading to better (i.e. more negative) r. Still, this effect is limited (r varies by a few 0.1 %) in comparison to the differences of r between products.

The scenarios Diff-SRON and Diff-WFMD provide insights into how the bias between products impacts the retrieved flux distribution. In this section, we do not focus anymore on the relative increment (fluxes are not perturbed in the Diff scenarios), but on the increments derived from the assimilation of the biased observations.

As expected, the opposite biases result in overall opposite increments. The assimilation of biased observations leads to an increase in total emissions for SRON (from 25.2 to 25.3 Tg yr⁻¹) and a decrease for WFMD (from 25.2 to 24.3 Tg yr⁻¹), consistently with the average positive difference between WFMD and SRON. However, these small differences in total emissions are the sum of large spatial variations, as shown in Fig. b. The maps highlight the contribution of the WFMD-SRON difference to the SRON increments, with negative increments in Western Europe (UK, Ireland, eastern Spain), southern Italy and Austria/Czech Republic, particularly over mountainous regions like the Pyrenees and the High Tatras in Central Europe. Positive contributions are observed across most of Eastern Europe, Benelux/Germany, central Italy and the Alps. While these contributions should be closely related to the difference of XCH₄ columns, shown in Fig. a, no clear correlation emerges between the bias in the concentrations and the corrections in the emissions: the average SRON-WFMD difference is generally negative and smooth, in contrast to the localized, strong increments in the emissions.

Yet, these two OSSE scenarios help clarify some of the patterns observed in inversions with real data. The increments of Diff-SRON (biased by the WFMD-SRON difference) and the difference of increments between inversions Inv-WFMD and Inv-SRON descrived in Sect.  are compared in Fig. c. The ratio between these two quantities show that the differences in the inversion increments can be partially explained by the difference SRON-WFMD over the sea, in Western Europe or in Romania. However, blue areas in Central Europe and Eastern Europe show opposite variations, meaning that the OSSE increments are not sufficient to explain the increments in the inversions with real data. This suggests that while XCH₄ differences provide some explanation, they do not fully account for the inversion outputs. In inversions, the CAMS background is also optimized and transport is not assumed perfect, contrary to OSSEs: it makes the tracing of the main factors impacting the increments on fluxes more complex.