The pixel size (in terms of ground footprint) during each TROPOMI orbit are different, resulting from changing viewing angles across the swath, and Earth's curvature. In order to map Level-2 pixels to Level-3 grids as a temporal average for use in this work, such that a source region is based on a city boundary shapefile, and directly comparable to gridded bottom-up inventories, we use remapping to generate a regularized grid. Here, we remapped the methane column mixing ratios retrieved from TROPOMI that passed the filters described in Sect.  to a resolution of 0.1°×0.1° for each orbit. Remapping makes use of shifting pixel locations and sizes in daily observations to achieve spatial resolutions finer than the original pixel size. The remapping method treats satellite observation pixels as surface polygons and calculates the fractional area of each grid cell covered by individual pixel polygons. The calculation of this overlapping area requires filling the irregular pixels with regular grid cells, also known as “tessellation”, which is well-described by . In , day-to-day observations from multiple overpasses were utilized to oversample satellite column data to increase spatial resolution through temporal averaging. In contrast, in our study, valid pixels from each individual overpass are remapped onto a regular grid to enable orbit-level methane emission estimates. The remapping method is described by the following relationship: 1Ω‾(i)=∑p=1N(i)A(p,i)S(p)σ(p)Ω(p)∑p=1N(i)A(p,i)S(p)σ(p) Where A(p,i) is the overlap area between the pixel p and remapping grid cell i. S(p) is the pixel area. σ(p) denotes the absolute error standard deviation of the satellite observation data as reported in the retrieval products. Ω(p) represents the corrected average total column mixing ratio of methane. Through this remapping method, the area-weighted and error-weighted average column for each 0.1°×0.1° grid cell is then derived. In order to fit to the re-gridded resolution, all variables of TROPOMI retrieval products included in this study were calculated using the same remapping method.

To quantify emissions for each city, the source pixel method that was first introduced by is applied here, which was further developed and fully modeled by . This fast data-driven method is derived from the concept of mass balance, and designed to calculate methane surface emissions of areas showing elevated atmospheric concentrations relative to their surrounding areas from satellite retrieval XCH₄ maps. An elegant advantage of the method is that emissions can be inferred solely from methane enhancements (e.g., source minus background value) in the source pixels, along with knowledge of a representative advective flow vector (i.e. mean wind). Source pixel methods usually apply to time-averaged satellite-derived XCH₄ data sets. Despite large systematic emission uncertainties (typically of the order tens of percent), emission uncertainty can be reduced when the signal (over a city) is proportionately larger than the surrounding background area (and when the background is less variable). The source pixel method was used by to derive urban emissions with magnitudes of several Mt CH₄ yr⁻¹. Here, we propose an improved source pixel method that integrates detailed wind vector information to better represent ventilation over the source region and methane enhancement relative to the upwind background, thereby improving the quantification of city-scale methane emissions.

Detailed application of this improved method in this work is as follows: we first re-grid TROPOMI Level-2 retrieval products using a regular latitude-longitude grid (here: 0.1°×0.1° resolution following remapping as described in Sect. ). The second step defines a source region (SR) and background region (BR) aligned to the mean PBL wind as described in Sect. . Previous applications of the source pixel method assume that the observed methane enhancement in the source area is associated with the source region alone (with no account for the true upwind background) and that any possible enhancement in the background area caused by outflow of the source region can be neglected . This could bias the estimated methane enhancements and inferred emissions if substantial emissions occur around the source region. Debates remain on the choice of the background domain due to different research scales and locations, including (1) expanding the coordinates of the source region to a size defined by the maximum extents in the meridional and zonal directions , (2) using a large background region to decrease the impacts on emissions estimates from any potential emissions in the background region , (3) proposing a land cover weighting method to estimate the background XCH₄ . An alternative approach to defining a background concentration is to characterize adjacent up-wind regions, though insufficient observations in this region may be caused by clouds, oceans, and other factors affecting retrieval quality can limit the number of days available for emissions analysis. In our variation of the source pixel method, emissions in the background region are implicitly accounted for and subtracted such that the new method does not necessitate the background region to be completely free of methane emission sources. In this work, the background region is defined as an equal area region located upwind of the source region. We chose this novel up-wind method to define the background region located immediately-adjacent and in the upwind direction as defined by PBL-pressure-weighted mean wind as described in Sect. . It is oriented such that two sides of the box (e.g., source region and background region) are perpendicular to the pressure-weighted PBL wind direction, and the full width of the emitted urban plume is observable over the city. The third step calculated the methane enhancement (e.g. ΔXCH4) for each overpass over the source region compared with its adjacent up-wind background region. This methane enhancement is computed by subtracting the mean retrieved XCH₄ in the background region from the mean over the source region. To minimize potential bias from the statistics of small sampling (and therefore potential bias from outlier pixels remaining after data-filtering), we defined two further thresholds in data coverage that must be met in order for emissions for a city from a single orbit to be considered meaningful, as follows: the source region must be at least 25 % populated with valid data after filtering (Fig. ). and the background region must have at least 10 observations. This resulted in the loss of the majority of city overpasses (due predominantly to cloudy scenes, in addition to surrounding coasts). We assert that this is an important and necessary loss of data to preserve emissions accuracy. We noted that emissions calculated where we attempted to relax these constraints further, resulted in wildly different and simply impossible results.

Finally, combined with additional TROPOMI retrieval products, the elements extracted above provide all inputs necessary to implement the improved source pixel method and estimate urban methane emission rates: 2E=MCH4Mair(SRCH4-BGCH4)UPWg where E is the emission rate of the source region with unit t h⁻¹, MCH4 denotes the molecular mass of CH₄, with a constant factor of 0.016 kg mol⁻¹, Mair is the molecular mass of dry air, 0.029 kg mol⁻¹. Methane enhancement ΔXCH4, computed from the (SRCH4-BGCH4), is observed from a source relative to the upwind background. U is the mean PBL wind speed of the source box in km h⁻¹, P refers to the atmospheric surface air pressure, provided with the retrieval product, W is the length of side of the square source box (unit: km), g is the acceleration of gravity (9.8 m s⁻²).

An illustrative example of the improved source pixel method used in this study is shown in Fig.  for London, demonstrating how the retrieved methane enhancement over the source region (ΔXCH4) is defined and oriented to the ERA5 wind direction and the corresponding location of the up-wind background region. To compute the PBL wind speed and direction, ERA5 hourly wind products are gridded onto the same spatial grid as TROPOMI data (Fig. b). After calculating the pressure-weighted average wind vector in the PBL over source region, the location of the up-wind background is obtained, as shown in Fig. c. Using this method, the valid orbits that pass through the satellite configuration filters, coverage threshold and uncertainty threshold, vary significantly across years and in different months. In Fig. d, the lowest observation is in New York city in 2021, with only 5 valid orbits that overpass the urban domain. Coverage increases to 8 and 25 overpass in 2022 and 2023, but the month-to-month variation is notable with most of the orbits observed in spring and winter seasons. Los Angeles has the largest coverage, nearly 100 total single orbits are usable in the method from 2021 to 2023. The number of annual valid satellite overpass over London urban area are between 10 and 25 orbits, and mostly are observed in spring, summer and winter seasons (as might be expected due to autumn storms and cloud). Clearly, such seasonality and inter-year variability in the number of valid scenes can be expected to lead to bias. This would be expected to be a limitation inherent to any application of the source pixel method using TROPOMI, even without the additional filtering we have applied here to reduce potential bias associated with cloudy scenes. We highlight this problem here as an honest appraisal of the challenges and limitations of using satellite data for urban emissions quantification. Put simply, biases implicit to sampling may remain, despite any attempt to minimize their presence. Therefore, when comparing annualized emissions by the improved method in this study (or any other) with inventories, it is important to be cognizant of how such biases may manifest; for example in the context of which periods of a given year may be poorly sampled compared to others and whether this may expected to manifest as a low or high bias overall versus perfect year-round sampling.

To estimate the uncertainty of urban emission rates, we assess the influence of uncertainties in ΔXCH4 and U, which can be derived statistically from TROPOMI and ERA5 data products. This procedure captures the potential sensitivity of systematic errors in the retrieved column mixing ratio over source pixels and uncertainty in the background estimate used to define methane enhancements. Also, the simulation of the constant wind within source region can result in large uncertainty because of changes in wind direction over the course of a typical day .

When assessing the ΔXCH4 uncertainty, the satellite retrieval measurements of atmospheric albedo and aerosol in SWIR band are involved. They may cause an overestimate or underestimate of the average column dry air mixing ratio relative to its real abundance through lengthening or shortening the light path . To calculate the error of methane enhancement results from the albedo and aerosol difference in the source region and background region, we use a linear fitting method to simulate the relationship between the column methane XCH₄ and the factors of albedo and aerosol within the source or background regions. The uncertainty of wind speed is estimated from the standard deviation of wind speed over the source region in a period of four consecutive hours around the TROPOMI local overpass time. Then, a representative statistical confidence error of emission rates σE for a single scene is computed as the sum in quadrature of 1σ of methane enhancement and wind speed. 3y=ax+b

4σΔXCH4=aalb(xSR,alb-xBR,alb)2+aaer(xSR,aer-xBR,aer)25σE=E⋅σΔXCH4ΔXCH42+σUU2 Here, aalb and aaer denote the slopes of the linear regression (Eq. ) obtained by regressing XCH₄ against surface albedo and aerosol optical thickness, respectively, within the study domain. xSR and xBR refer to the mean value of albedo or aerosol in the source region and background region.

For urban areas that have multiple valid overpasses (i.e. days), the emission rates and uncertainties need to be averaged to generate total urban estimates at the desired timescale (e.g. monthly or yearly). To ensure the quality of results, we only include orbits with uncertainties of less than 100 %. Most previous studies using the source pixel method have analyzed aggregated emissions at monthly or yearly timescales from orbit-level estimates by assigning equal weight to each overpass, regardless of whether the overpass has limited or full valid data coverage over the source region. In this study, we use spatial coverage (in %) of valid observations in the source region to weight each overpass during averaging, in an effort to reduce spatial bias arising from potential heterogeneity in methane mixing ratios. Note that potential surface emission transfer among different pixels is not considered. Finally, the uncertainty in the temporally-averaged estimates is calculated as the root mean square error (RMSE), in Eq. (). 6RMSE(%)=1N∑i=1N(σEi)21N∑i=1NEi×100 Where σEi refers to the uncertainty of emission rate for orbit i (Eq. ), and Ei denotes the calculated emission rate of orbit i, N is the valid overpass of TROPOMI for a given urban domain that restricted by cloud, water, and oceans, etc.

The urban domain used to implement the improved source pixel method of this work is defined over London, a source region that has been the topic of numerous methane emission studies . The results for 2021–2023 are summarized in Fig. . Figure a presents the spatial distribution of mean XCH₄ levels over London urban area for the study period. The urban enhancement relative to the surrounding background is generally modest, with no persistently strong hotspot visible within the defined source region. The relatively weak spatial contrast implies that the calculated ΔXCH4 is sensitive to background variability (As shown in Fig. ). In particular, when the upwind sector (e.g. background XCH₄) contains elevated methane from other nearby source regions, the derived ΔXCH4 over the study area can be substantially reduced and may occasionally become negative (see Sect. ). This result is consistent with previous aircraft-based and dispersion modeling analyses over London , which also reported relatively small urban-scale enhancements. The corresponding monthly time series of ΔXCH4 of London urban area is shown in Fig. c. The annual mean enhancement increased from 1.47±0.76 ppb in 2021 to 1.98±1.38 ppb in 2022, before slightly declining to 1.70±0.83 ppb in 2023. A clear seasonal cycle is observed in the monthly average ΔXCH4, with larger enhancements during winter months. This seasonality likely reflects a combination of increased emissions and more stable atmospheric conditions. It should also be noted that data coverage is uneven throughout the year due to cloud contamination, which reduces the number of valid TROPOMI overpasses in certain months. Figure b presents estimated methane emission rates for London from 2021 to 2023, derived using the method outlined in Sect.  . The 3-year mean emission rate is 7.78±4.84 t h⁻¹, where the long-term uncertainty is estimated from multiple satellite overpasses following Eq. (). The annual mean emissions are 5.99±3.25 t h⁻¹ (2021), 11.90±8.56 t h⁻¹ (2022), and 7.25±4.64 t h⁻¹ (2023). The relatively low estimate in 2021 is primarily driven by an anomalously low value in October, when background XCH₄ exceeded concentrations within the urban domain, resulting in near-zero or negative ΔXCH4. If this month is excluded as a statistical outlier, the 2021 annual emission increases to 10.11±6.28 t h⁻¹, highlighting the sensitivity of the method to background characterization under weak enhancement conditions. The mean wind speed over the urban domain during 2021 to 2023 is 5.15±0.55 m s⁻¹, with pronounced seasonal variability (Fig. d). Comparison of Fig. b–d indicates that temporal variations in emission estimates are primarily controlled by variability in ΔXCH4 rather than wind speed. Uncertainty propagation analysis attributes approximately 80 % of the total emission uncertainty to variability in the methane enhancement, whereas wind-related uncertainty only accounts for about 20 %. This result underscores that, for weakly enhanced urban regions (such as London), accurate background determination and robust enhancement retrievals are the dominant factors governing emission estimate reliability.

The bottom-up methane emissions for the London urban area, as reported by the EDGAR inventory, are shown in Fig. a. To ensure direct comparability with top-down estimates in this work, the gridded EDGAR emissions were extracted and summed over the same source box defined in Sect. . In this way, both bottom-up and satellite-based emissions refer to an identical spatial domain. The EDGAR-derived emissions are significantly lower than the satellite-based emission rates estimated using the improved source pixel method. Over the same spatial domain and time period, the top-town emission estimates in this work are approximately 2.1 times higher than the EDGAR inventory values. According to EDGAR, the dominant methane source in London during 2021–2023 is waste management, contributing on average approximately 63 % of the total emissions (Fig. a). Fossil fuel-related emissions (e.g. leakage from natural gas transmission and distribution systems) represent the second largest source, accounting for about 32 %, followed by agriculture activities (nearly 5 % of total emission). Other sectors (e.g., wetlands and other anthropogenic sources) contribute comparatively smaller fractions.

Methane emissions over the Los Angeles urban area for the period 2021–2023 were estimated using the same improved source pixel method. The results are summarized in Fig. , along with the mask that delineates the source region. The spatial distribution of TROPOMI-derived XCH₄ in Los Angeles city (Fig. a) reveals a pronounced methane hotspot over the defined urban domain, with clearly elevated concentrations relative to the surrounding background. In contrast to London, the methane enhancement over Los Angeles is spatially coherent and persistent, indicating a strong urban emission signal detectable from space. The 3-year average emission estimate from 2021 to 2023 is 47.19 t h⁻¹, with a 1σ uncertainty range spanning from 13.51 to 80.87 t h⁻¹. As shown in Fig.  b, the annual mean methane emissions increase from 26.21±23.03 t h⁻¹ in 2021 to 50.18±36.55 t h⁻¹ in 2022 and further to 62.77±35.95 t h⁻¹ in 2023, indicating a substantial interannual growth over the study period. Although this apparent increase is inconsistent with the decreasing trends reported in previous studies , the large uncertainties in the annual estimates and their substantial overlap indicate that a decreasing trend similar to those reported previously cannot be ruled out. A clear seasonal pattern is apparent, with higher emission estimates generally occurring during winter and early spring. Notably, little to no valid emission estimates are available during the summer months, particularly in 2021 and 2023, likely due to persistent marine boundary layer clouds and coastal meteorological conditions that substantially reduce the number of usable satellite overpasses (e.g. insufficient valid pixels are available within either the source region or the upwind background region to satisfy the data quality thresholds defined in Sect.  and ). Figure c and d show that the average methane enhancement ΔXCH4 over the study period is 10.66±5.87 ppb, while the mean wind speed is 2.96±1.10 m s⁻¹. Although the seasonal variation of emission rate broadly follows that of ΔXCH4, uncertainty analysis indicates that more than half of the total emission uncertainty is attributable to wind variability. This reflects the sensitivity of the emission rates calculation to wind speed during the satellite overpass window (19:00, 20:00, 21:00, 22:00 UTC), when coastal circulations and ocean–land breeze dynamics can induce substantial short-term wind fluctuations over the Los Angeles basin.

The spatial distribution of methane emissions from the EDGAR inventory for 2021–2023 is shown in Fig. b. When aggregated over the identical source domain used in the this work, the mean EDGAR emission for Los Angeles urban area is 20.07 t h⁻¹, which is notably lower than the satellite-derived estimate of 47.19±33.68 t h⁻¹. Sectoral attribution (see Fig. b) indicates that Los Angeles is dominated by waste-related emissions, primarily from landfills, which account for more than 90 % of the total methane emissions in each study year. Fossil fuel-related sources represent a much smaller contribution, approximately 9 % of the total.

New York serves as the third case study for evaluating the improved source pixel method. The corresponding results for 2021–2023 are summarized in Fig. . The TROPOMI-derived XCH₄ fields (Fig. a) exhibit a discernible enhancement over the defined urban domain, particularly in 2022 and 2023, indicating a persistent methane signal relative to the surrounding background. However, the geographic setting of New York – located at the confluence of major waterways and influenced by frequent cloud cover – limits the number of valid satellite retrievals in certain months, especially during the 2021 and 2022. The temporal evolution of the derived methane emission rate is shown in Fig. b. The three-year mean emission is 42.94 t h⁻¹ with a standard deviation of 24.69 t h⁻¹. Among the individual year, 2023 exhibits the highest annual mean emission rate (44.77±25.03 t h⁻¹), whereas 2022 shows the lowest (30.85±21.50 t h⁻¹). Monthly variability reveals a recurring seasonal structure, with relatively elevated emissions during early autumn, particularly in September. In contrast to the other two years, 2023 provides more continuous data coverage, with valid emission estimates available for most non-summer months. However, June–August remain largely data-limited, and intermittent gaps are still evident due to cloud contamination and quality-control filtering of satellite retrievals. Figure c and d indicate a mean methane enhancement of 9.15±5.72 ppb and an average wind speed of 5.43±0.91 m s⁻¹ over the study period. Although seasonal variations in emission rates are primarily driven by changes in methane enhancement within the source region relative to the background, wind variability plays a non-negligible role in modulating the magnitude of the calculated emissions. The relatively strong and seasonally variable winds over New York introduce additional variability during the satellite overpass window. Uncertainty analysis shows that methane enhancement accounts for approximately 60 % of the total emission uncertainty, while wind contributes the remaining 40 %, indicating a more balanced uncertainty structure compared to Los Angeles.

The spatial distribution of EDGAR gridded methane emissions for New York city is shown in Fig. c. Emissions within the urban area are relatively weak and spatially diffuse, with only a few grid cells exhibiting moderate emission values. When aggregated over the identical source box used in this work (red box), the annual mean methane emission for the EDGAR inventory is 4.38 t h⁻¹ for 2021–2023. This value is substantially lower than the satellite-derived estimate and corresponds to approximately 11 % of the emission magnitude inferred from the improved source pixel method. Sectoral attribution indicates that emissions are dominated by waste-related sources (e.g. solid waste and waste water), contributing about 53 % of the total, followed closely by fossil fuel-related activities at approximately 45 %. Other sectors represent only a minor fraction of the inventory-based emissions (Fig. c).

Figure  presents a comparison between our satellite-derived emission estimates based on improved source pixel method, three widely used gridded bottom-up inventories, and six recently published top-down studies. Overall, our estimates consistently exceed the gridded inventory values across all three cities, ranging from 1.3 to 10.2 times the publicly available EDGAR inventory. For London, comparison between emission estimates derived from our study and the NAEI inventory indicates that bottom-up estimates generally underestimate urban methane emissions, with the exception of 2021, and the discrepancy reaches up to 45 % in 2022. For the U.S. cities, the EPA inventory similarly reports lower emissions than our satellite-based results, with underestimations of approximately 56 % for Los Angeles and 84 % for New York.

The magnitude of city-scale methane emission estimates can vary substantially depending on how the urban domain is delineated, particularly when large point sources, such as landfills, are located along the urban fringe. These studies adopt different definitions of urban area and generally include contributions from nearly all source sectors. For example, and quantify urban emissions based on the U.S. Census Bureau's Topologically Integrated Geographic Encoding and Referencing system (TIGER)/Line urban area definitions to standardize the spatial extent across the contiguous United States (CONUS) . Most studies use aircraft measurements, tower observations or satellite retrievals combined with atmospheric chemical transport models to infer methane emissions , while others use characteristic urban ΔCH4/ΔCO enhancement ratios integrated with existing inventories to estimate methane emission rates . applied a two-dimensional Gaussian model to estimate the local emissions required to reproduce the observed satellite retrievals. Our emission estimates can be directly compared on a like-for-like basis only with those of , who developed a new high-resolution (0.02°×0.02°) methane emission inventory for New York for 2019 based on an analytical inversion of aircraft measurements. Even when using the same gridded urban domain, a large discrepancy remains, which may be largely attributable to differences in the reporting period. Direct comparisons between our results and urban emission estimates from other studies remain challenging because of differences in urban domain definitions and reporting periods, as discussed in previous studies . Overall, the estimates reported in these studies are broadly consistent with ours, with most falling within our uncertainty bounds, except for those of , which represent relatively high urban-scale emission estimates.

To ensure spatial consistency in the comparison, we converted the reported emissions from previous studies into emission intensities (emission rate per unit area) and subsequently rescaled them to our defined urban domain. reported a posterior estimate of 28.65±0.55 t h⁻¹ based on sustained station observations for Los Angeles, which is very close to our estimate of 26.21±23.03 t h⁻¹. A study using TROPOMI observations to estimate methane emissions over U.S. urban areas reported substantially higher values of 60.62 t h⁻¹ for Los Angeles and 86.76 t h⁻¹ for New York . However, after scaling their estimates to the same urban domain used in this work, these values decrease to 33.27 and 45.09 t h⁻¹, respectively, which align well with our results. and adopted the same U.S. Census urban area definition but applied different emission quantification methods. They found different emission estimates for New York city, although the reported ranges largely overlap with the uncertainty bounds of our derived emissions. After scaling to the same urban domain, our estimated emission range remains consistent with the uncertainty reported by , while remaining higher than the estimate from . For Los Angeles, although our study employs a different definition of urban boundary and a different emission quantification method, our estimates remain consistent with those of under both scaled and non-scaled conditions. We need to acknowledge the relatively large uncertainty involved in this rescaling, especially considering the heterogeneous attribution of urban emission sources such as landfills and gas infrastructure. Given the relatively strict urban domain defined in our study based on administrative boundaries, as well as the use of different emission quantification methods, our emission estimates are likely to approach those reported by if more suburban emission sources are included.