All GOSAT-derived emissions and corresponding inputs/algorithms are available at 10.5281/zenodo.15786798 (Worden and Pandey, 2025).

Jupyter/python code at 10.5281/zenodo.16921536 (Pandey and Worden, 2025) shows how to compare these GOSAT derived emissions to inventories.

Methane is a potent greenhouse gas that plays a significant role in atmospheric warming (Saunois et al., 2020). Methane is emitted from multiple anthropogenic sources including livestock, oil and gas exploitation, manure, rice cultivation, wastewater, solid waste, and coal mining, and from natural sources, particularly wetlands. Methane is also the main component of natural gas, a valuable global commodity that can pose safety risks when it leaks. Accurate and verifiable estimates of its emissions are essential for tracking progress and guiding effective mitigation strategies, and for accounting for the economic value of energy waste (IEA, 2025; World Bank, 2025). Gridded methane emission inventories, such as the gridded United States Environmental Protection Agency's Greenhouse Gas Inventory (EPA GHGI), the Emissions Database for Global Atmospheric Research 2024 release (EDGAR 2024), and the National Oceanic and Atmospheric Administration's Fuel-based Oil and Gas inventory (NOAA FOG), are widely used for comparing sectoral emissions, primarily at the regional scale, to atmospheric data (EPA, 2023; Maasakkers et al., 2023; Crippa et al., 2020, 2024a, b; Francoeur et al., 2021; Kruskamp et al., 2025). However, discrepancies in how the inventories are generated, e.g. from emission factor assumptions, activity data, and/or spatial proxies and resolution can result in substantial variation in both the magnitude and sectoral attribution of emissions (Hristov et al., 2017; Alvarez et al., 2018; Maasakkers et al., 2021; Petrescu et al., 2024; Gordon 2025). In some cases, differences between inventories can be as large as the emissions themselves (Fig. 1), complicating the evaluation of national and regional emission trends. Verification of their underlying parameterizations is often limited by spatiotemporal mismatches between empirical measurements and inventory assumptions. Moreover, differences between activity-based emissions and flux estimates based on observations combined with atmospheric modeling (e.g., top-down atmospheric inversions) can far exceed the changes inferred from the observed growth in atmospheric methane concentrations (Nisbet et al., 2019; Worden et al., 2022). As a result, tracking mitigation progress using bottom-up inventories alone could be unreliable without independent observational constraints. In addition to these uncertainties, emissions missing in the inventories pose another significant challenge. For instance, sporadic high emitters in both fossil fuel production and waste management, often caused by mechanical failures, may not be captured in traditional inventories (Cusworth et al., 2020; 2024; Sherwin et al., 2024); consequently, the magnitude of these emissions remains poorly understood.

To evaluate potential uncertainties in bottom-up inventories, top-down emissions estimates derived from satellite observations, such as those from the Greenhouse Gases Observing Satellite (GOSAT), provide a valuable, independent constraint. These atmospheric measurements inherently capture all emissions influencing methane concentrations, including unreported or underestimated sources, and therefore offer a more comprehensive view of total methane emissions. However, the resulting estimates and their information content (spatial resolution + uncertainties) depend strongly on the observational sampling, sensitivity of the observation to the emissions, choice of a priori fluxes, and the inversion regularization. Consequently, over regions with limited sampling, e.g., due to clouds or low sunlight, top-down analyses have greatly reduced sensitivity to nearby emissions, so the estimates there simply reflect the a priori. In contrast, emissions inferred for regions with ample sampling are more likely to accurately represent local sources. The focus of this paper is to demonstrate how this GOSAT-based benchmark can be used to evaluate alternative gridded inventories while accounting for its variable information content as discussed next.

Accounting for choice of a priori and inversion regularization. Comparisons between satellite-based top-down fluxes and activity-based inventories must account for the variation in sensitivity of the data to emissions and choice of a priori, otherwise substantial uncertainty (also known as smoothing error) is introduced into the comparison (Rodgers, 2000; Worden et al., 2022, 2023). Smoothing error in this context can be mitigated for these comparisons by at least three ways: (1) by using the inventory as the a priori in the inversion or (2) by applying an inversion operator to the inventory being compared (the inversion operator depends on the inversion a priori and what is called the averaging kernel matrix, Appendix B) or (3) by adjusting the GOSAT based estimate using the gridded inventory and the averaging kernel matrix to replace the effect of the original prior (also known as prior swapping).

In the first scenario, recalculating the inversion and subsequently comparing to the a priori is computationally expensive (e.g., Nesser et al., 2024 and references therein) as it involves minimizing a cost function of gridded emissions vector (e.g. z) that typically has the following form: 1C=||y-F(zA)||Sn-12+||z-zA||SA-12 where y is a state vector representing concentrations (e.g. total column methane or XCH4), the forward model F(zA) in this case is the Goddard Earth Observing System – Chemistry model (GEOS-Chem) driven by a distribution of a priori emissions (zA). The matrix Sn represents the measurement error covariance for the total column data and the matrix SA represents the uncertainty (or covariance) in our a priori emissions. For the benchmark described in this paper, the vector z represents the spatial distribution of anthropogenic emissions by sector, in this case livestock, waste, coal, rice, oil and gas. Wetlands and fire emissions are also estimated with the GOSAT data and the effect of jointly estimating these emissions are included in the posterior covariance and uncertainties of the anthropogenic emissions estimate (Worden et al., 2022, 2023).

The estimate for the converged solution, z^, can be related to the “true distribution” of the emissions (z) with the following (e.g. Rodgers, 2000). 2z^=zA+A(z-zA) where for clarity we have not included the uncertainty terms (see Appendix B). The averaging kernel matrix A is a function of the a priori and posterior covariance, Z^ and ZA (see Appendix B for a description of uncertainties and prior covariances) and describes the sensitivity of the distribution of estimated emissions to the true state (A=∂z^∂z ). Approach #2, which is to apply an inversion operator to the inventory, is equivalent to replacing z, or the “true distribution” of emissions, with the alternative inventory, zI in Eq. (1); this approach is commonly used for data assimilation or for comparing atmospheric trace gas profiles from models or in situ measurements to remotely sensed measurements (e.g. Wecht et al., 2014; Herman et al., 2014). This revised estimate can be compared to z^ while accounting for the a priori and regularization choices made in the inversion described by Eq. (1). Approach #3 (or prior swapping) instead involves replacing zA with the alternative inventory (e.g. Rodgers and Connor, 2003) 3z^new=z^-(I-A)zA+(I-A)zI And is equivalent to re-running the inversion described by Eq. (1) with this alternative a priori.

As approaches 2 and 3 are linear operations, they result in equivalent comparative differences as shown in Appendix B. In this manuscript we use the inversion operator approach (Eq. 2) for consistency with previous publications (e.g. Worden et al., 2022, 2023).

Sector Based Attribution. We use estimates of gridded integrated fluxes from a GEOS-Chem based inversion using GOSAT XCH4 data as described in Qu et al. (2022, 2024). We use a Bayesian-based sectoral partitioning approach (Appendix A, Worden et al., 2022, 2023) to project these top-down integrated fluxes to emissions by sector at a 1° × 1° resolution. This approach characterizes the inversion solution by providing a posterior covariance for the solution and provides the “inversion operator” (Eq. 2) that, when applied to a gridded inventory, enables the comparison to inversion results by capturing the influence of the inversion's prior emissions and the sensitivity of the satellite observations to those emissions (Rodgers, 2000).

Inventories. (See Appendix C for more detail.) The inventories we compare include EDGAR 2024 (Crippa et al., 2024a, b), the gridded U.S. EPA GHG inventory (GHGI) (Maasakkers et al., 2023), and NOAA FOG (Francoeur et al., 2021). The EDGAR and GHGI inventories provide information about methane emissions across multiple sectors (e.g., livestock, waste, oil and gas, coal, rice). The approaches estimating these emissions vary, with EDGAR down-scaling national totals to finer scales using spatial information about the sources using global datasets while the GHGI gridded inventory reflects emission factors and activity data used in the EPA US Greenhouse Gas Inventory. In contrast, NOAA FOG focuses specifically on fossil methane emissions and is a hybrid inventory that integrates atmospheric CH4 and NO2 observations with activity-based NO2 metrics (Francoeur et al., 2021). While these inventories show considerable overlap in the location of emissions, differences can be large, even when aggregating from the original 0.1° grid of the inventories to the 1° grid shown for Fig. 1.

As stated previously, our goal for this study is to demonstrate a benchmark for US methane emission gridded inventories and their changes from 2012 to 2020. These comparisons are documented and publicly accessible at Zenodo (see data availability); Jupyter notebooks are provided here that demonstrate how to compare gridded inventories to GOSAT-based emissions. These benchmarks will be updated as newer datasets, such as inverse analyses using Sentinel-5P TROPOMI (Tropospheric Ozone Monitoring Instrument) observations, become available (e.g., Nesser et al., 2024; Hancock et al., 2025). Readers unfamiliar with the Bayesian attribution framework, the GOSAT inversion, or the specific inventories compared are encouraged to consult the appendices, where these methods are summarized, or our previously published work on the subject (Cusworth et al., 2021; Worden et al., 2022, 2023).

Table 1 summarizes US methane emissions by sector for 2015, based on the GOSAT data and the sectoral attribution approach described in this study (Appendix A). The error characterization (Appendix B) includes uncertainties from the a priori as well as measurement and model systematic error. The prior emissions are taken from Worden et al. (2023). Table 1 also shows a quantity called the Degrees of Freedom for Signal (DOFS), which is given by the trace of the averaging-kernel matrix for the corresponding state-vector elements in z. The DOFS describe the extent to which the estimate is informed by observations rather than prior assumptions (Appendix B), as well as the spatial information content. For example, from Eq. (2), if A≈0 (equivalent to DOFS = 0), observations say essentially nothing about the emissions and the estimate reduces to the prior. If A is the identity matrix, then the DOFS equals the number of state-vector elements and the estimate exactly reflects the true distribution, modified by the expected uncertainties (Appendix B). The DOFS reported in Table 1 refer to the spatially distributed estimate, not for the total emissions value. Hence, DOFS > 1 means there is at least some spatial information for that sector's estimate.

For this GOSAT-based benchmark, the highest information content is available for total, livestock, and oil and gas (O&G) emissions, while waste emissions estimates are only moderately constrained by the data, and rice and coal emissions have limited observational information. This variability in information content underscores the need for careful interpretation of top-down estimates, particularly when examining spatial and sectoral patterns or trends.

Table 2 compares our emissions to previous inversions using atmospheric data and to the inventories discussed in this paper (Appendix C). As can be seen in Table 2, our atmospheric-based emissions are generally consistent with other studies, typically within 1–2 standard deviations of the reported uncertainties, even though each study uses different priors, has different systematic errors, and has different sensitivity to the underlying emissions. These comparisons also show that total emissions from atmospheric-based inversions are typically larger than activity-based estimates, with the livestock and oil and gas sectors responsible for most of the discrepancy.

Top-down methane emissions estimates vary in their information content depending on the emission sector and observing system. For these GOSAT based emissions estimates, information content is greatest for oil and gas and livestock, so these sectors are best suited for inventory evaluation using the results shown here. Waste, coal, and rice exhibit lower information content in this analysis because GOSAT does not adequately sample methane variability attributable to those sources. Even so, our information-content-based comparison identifies where additional measurements would yield the largest uncertainty reductions in gridded inventories.

In particular, our results highlight the need for targeted measurement campaigns, especially in the Texas, Oklahoma, and Louisiana drilling basins, where additional data can most effectively reduce inventory uncertainties. For the livestock sector, California and Northern Texas stands out as key regions where improved activity based and atmospheric methane observation can have the highest impact. These findings underscore the importance of prioritizing high-emitting or uncertain regions to refine national methane budgets.

Beyond regional targeting, improving inversion resolution is also key. Higher-resolution flux estimates, whether through satellites like TROPOMI or plume-resolving instruments (e.g., Jacob et al., 2022; Pandey et al., 2025 and refs therein), are particularly needed for sectors such as waste, coal, and oil and gas, where coarse-resolution inversions struggle to isolate source signals. In particular, integrating plume-resolving and area-flux estimates enhances the sectoral attribution of emissions and improves the information content for inventory evaluation (Pandey et al., 2025).

(Trends) Inversions conducted using GOSAT data and GEOS-Chem (see references in Table 2), show no discernible trend over the analysis period, which is consistent with all three gridded inventories discussed in this manuscript. However, the fact that other inversions show different trends highlights the importance of benchmarking approaches (Janardanan et al., 2024), not only for validating inventories but also for identifying uncertainties in inversion outputs themselves. These differences matter for informing effective remediation strategies and setting realistic expectations for emission reductions.

As satellite constellations improve in spatial resolution, sampling, and accuracy, top-down flux estimates become more accurate at higher spatial resolution (e.g., Jacob et al., 2022). Using TROPOMI, Nesser et al. (2024) produced a 2019 North American emissions map with a degree of freedom for signal (DOFS) of ∼ 772, more than two orders of magnitude higher than in our GOSAT record, driven by a similar increase in observations. This resolution enables explicit estimation of many large sources, including landfills. East et al. (2025) extended this approach to global coverage at similar ∼ 25 km gridding. Building a benchmark from the combined record will help evaluate how countries have managed emissions before and after the Global Methane Pledge, which targets a 30 % reduction from 2020 to 2030. Our approach shows how inventories can be benchmarked against these improved flux estimates to reduce uncertainty, especially smoothing error, without re-running inversions with inventory priors. Combining high-resolution, independent datasets will support more accurate methane inventories, clarify source trends, and inform effective mitigation strategies.