The input data for emission quantification consists of the TROPOMI NO₂ data product (version 2.4.0) including the associated auxiliary product, which provides the a priori NO₂ profiles used in the AMF calculations. These datasets were obtained from the Copernicus Dataspace for the year 2021. Meteorological input is obtained from the ERA5 reanalysis product on single and pressure levels, including surface pressure, geopotential, temperature, specific humidity, mean surface net shortwave radiation flux, and the zonal and meridional wind at 10 m, 100 m and on pressure levels .

The CSF method requires an estimate of the effective wind speed, i.e., the mean transport wind speed in the plume. To compute this, ERA5 pressure levels were first converted to height above the surface. Any height levels below the surface, occasionally present in the dataset, were excluded. To enhance vertical resolution near the surface, wind vectors at 10 and 100 m were incorporated into the profile. The effective wind speed was then calculated as weighted mean using the GNFR-A standard emission profile for power plants . The profile provides a mean distribution for emissions from power plants. It assumes that the emissions are distribution between 170 and 990 m with about 50 % of emissions between 310 and 470 m. The profile provides a suitable estimate of the NO_x distribution near the source. A fixed profile is more robust and consistent than using, for example, the mean wind within the planetary boundary layer (PBL), which can be lower than the emission height, particularly in winter.

The CSF method is used to estimate the NO_x emission rate Q (in kg NO₂ s⁻¹) from satellite observations. The emission rate is calculated as 1Q=fD⋅u⋅q, where f is the NO₂-to-NO_x conversion factor, u is the effective wind speed, q is the line density (in kg m⁻¹), and D is the correction term for NO_x decay during transport. The decay term is computed as 2D=exp⁡-xuτ, where x is the distance from the source, and τ is the NO_x lifetime due to chemical decay . The combined correction factor c=f/D accounts for both the conversion of NO₂ to NO_x and the decay of NO_x during transport as described in Sect. .

The NO₂ line density q is derived by fitting a Gaussian curve with a linear background to the NO₂ column data in the plume area downwind of each source. The fitted function is 3g(y)=q2πσexp⁡-(y-μ)22σ2+my+b, where y is the across-wind direction, μ and σ are center position and standard width of the Gaussian curve, and m and b are slope and intercept of the linear background.

Figure provides an illustration of the different steps of our approach. The plume area used for fitting the Gaussian curve is defined by following the wind direction from 1 to 30 km downwind of the source. In the across-wind direction, the plume area extends ±40 km perpendicular to the wind direction (Fig. a). This spatial window ensures that the plume is sufficiently captured while minimizing interference from neighboring sources or background variability.

The air mass factors (AMFs) provided in the standard TROPOMI product are known to be biased in regions with strong local enhancements . This is because the global TM5 chemistry transport model, which provides the NO₂ profiles, has a coarse horizontal resolution of 1°, which is not sufficient to resolve narrow NO₂ plumes from individual point sources.

To address this limitation, we apply a correction to the AMFs using the averaging kernels (AKs) provided in the standard product and a modified vertical NO₂ profile . First, we fit the Gaussian curve with the linear background (Eq. ) to the uncorrected NO₂ image (Fig. b). Next, we enhance the standard TM5 NO₂ profile by adding the fitted NO₂ enhancements to the TM5 profile of each pixel. The enhancements are vertically distributed according to the GNFR-A emission profile (Fig. c). Finally, we recalculate the AMFs by applying the AKs to the modified NO₂ profile. Figure d shows that this approach increases the VCDs in the plume center (by 30 %–40 % in this example), while background VCDs are not modified. The corrected AMFs are then used to update the NO₂ column densities. Subsequently, Eq. () is re-fitted to the corrected NO₂ columns to obtain the AMF-corrected line density q, which is used in the CSF method to compute the final NO_x emission estimates (Fig. f).

To derive NO_x emissions from NO₂ satellite observations, it is necessary to estimate the NO₂-to-NO_x conversion factor f and the NO_x lifetime τ. In this study, we use a global approach, which is based on global chemistry transport simulations with GEOS-Chem, and a local approach, which is based on plume-resolving simulations with the MicroHH large-eddy simulation (LES) model for the Jänschwalde power plant. We detail the two methods below.

To ensure the reliability of individual emission estimates, estimates were visually inspected to identify potential causes of failure in the quantification process. Based on this assessment, we excluded all cases where either the shift or the standard width of the fitted Gaussian curve exceeded 10 km. A large shift typically indicates a misalignment between the observed plume and the wind direction used to define the plume axis, while an excessively broad standard width suggests that the fitting algorithm may have captured a diffuse source region or background enhancement upstream of the actual emission source. We also filter out estimates for wind speeds lower than 2.0 m s⁻¹, because of the large relative uncertainty of the wind speed itself and the NO_x chemistry correction factors. In particular, the correction factors are exceeding 3 for the local approach under low wind speeds, which introduces substantial uncertainty and reduces the reliability of the emission estimates.

Various approaches have been proposed to compute monthly and annual emission estimates from individual estimates . One method involves fitting a smooth function through individual estimates to reconstruct a seasonal cycle, which can then be integrated to obtain monthly and annual means . However, we found that the time series of bottom-up reports is not consistently smooth, making this approach less suitable for our dataset. Another commonly used method applies weighted averaging based on estimated uncertainties, but this introduces bias because the uncertainties in the CSF method are proportional to the magnitude of the estimated emissions (see next section). As a result, lower emission estimates, associated with smaller uncertainties, would receive disproportionately high weights, resulting in an underestimation of the true emissions.

In this study, we therefore compute monthly emissions by calculating the arithmetic mean of all valid individual estimates for each month. We deliberately avoid weighted averaging for the reasons outlined above. To derive annual emissions, we linearly interpolate monthly means to fill gaps in months where no valid estimates are available. The final annual emission value is calculated as the median of the twelve monthly values. This approach mitigates the risk of bias from isolated extreme values, which can occur if only a single estimate is available in a given month, particularly in winter.

The uncertainties in the top-down emission estimates are quantified using Monte Carlo simulations, which estimate the uncertainty by generating an ensemble of the input parameters for the CSF method. The Monte Carlo simulation assume that errors are uncorrelated, i.e., uncertainty reduces with the number of estimates. The uncertainty of line density q is derived from fitting the Gaussian curve using the precision of the TROPOMI NO₂ product. This precision is used to create an ensemble of line densities for each estimate. For wind speed, we assume an uncertainty of 1.0 m s⁻¹, consistent with the validation of the ERA5 reanalysis product e.g.,. To avoid negative wind speeds in the ensemble, we use a lognormal distribution centered on the effective wind speed, with a standard deviation is 1.0 m s⁻¹.

Wind speed uncertainty has a direct impact on the uncertainty of the chemistry correction, because it is required to calculate the time since emissions used in Eqs. () and (). For the local chemistry approach, we additionally include the uncertainties in the empirical parameters (m, r and f0) used for the NO₂-to-NO_x conversion factor. The NO_x lifetime is modelled using a lognormal distribution with a mean of 2.5 h and a standard deviation of 0.6 h, consistent with the distribution in the two-day simulation for Jänschwalde . For the global approach, we use an uncertainty of 0.10 for the ratio, which was obtained by comparing the machine-learning with the GEOS-Chem simulations. The uncertainty in the rate of change is negligible compared to the uncertainty in the time since emissions; therefore, it is not included.

To quantify the uncertainties in the estimated emissions, we compute 16th, 50th and 84th percentile of the Monte Carlo ensemble, corresponding to the median and the ±1σ confidence interval. For monthly and annual estimates, we account for a temporal sampling error of 30 % for each estimate, which was estimated from the bottom-up time series and is consistent with previous studies . The temporal sampling error is uncorrelated and decreased as the number of estimates increases. Finally, we account for a correlated error of 10 % in estimates that do not decrease with the number of estimates; this error is added to the uncertainty of the monthly and annual values.

The CSF method was applied to the six power plants in Europe and twelve power plants in the USA summarized in Table . Figure  shows three examples of NO_x emission estimates derived from TROPOMI NO₂ observations for the Jänschwalde (DE), Miami Fort (Ohio, USA) and Hunter (Utah, USA) power plants. The examples highlight some of the challenges associated with estimating NO_x emissions from satellite observations.

For the Jänschwalde power plant, the emission plume is clearly visible in the satellite image. Additional plumes from nearby plants (Schwarze Pumpe and Boxberg) can also be identified south of Jänschwalde. The plume area (yellow polygon), limited to 30 km downwind, effectively isolates the Jänschwalde power plant, minimizing the interference from neighboring sources. The across-plume NO₂ enhancement is well captured by the Gaussian curve, resulting in a top-down emission estimate of 16.2 ± 4.7 kt a⁻¹ using the local chemistry approach. This value is slightly larger but consistent with the bottom-up estimate of 13.5 ± 1.2 kt a⁻¹.

In contrast, the Miami Fort power plant example shows no discernible plume in the TROPOMI NO₂ image. On the day of observation, the reported emissions were very low with only 2.3 kt a⁻¹ and wind speeds were relatively high with 5 m s⁻¹, likely dispersing the weak plume below the detection limit. The top-down estimate was flagged as invalid, because both the center position and standard width of the Gaussian curve were larger than 10 km.

The third example is for the Hunter power plant and shows its emission plume with bottom-up reported emissions of 11.5 kt a⁻¹. There is also an additional enhancement from the Huntington power plant, which is located about 25 km north (point) of Hunter power plant (triangle) and has 6 kt a⁻¹ annual emissions. This case illustrates the complexity of accounting for NO_x chemistry in overlapping plumes. For an inert gas, like CO₂, the enhancements from multiple sources would simply add up, and the total emission estimate would reflect the sum of the individual contributions. However, for reactive species like NO_x, the chemistry correction introduces a non-linear effect. Since the correction factor is dominated by the decay term, a stronger correction is necessary for older plumes (cf. Sect. ). In this example, the NO_x from Huntington is significantly younger than the NO_x from Hunter. Consequently, the NO_x correction, assuming an older plume, strongly overcorrects the emission estimate. The resulting top-down estimate is 36.7 ± 8.2 kt a⁻¹, which is substantially higher than the combined bottom-up emissions of the two power plants.

Figure and Table  compare the annual NO_x emission estimates from the bottom-up and top-down approaches for the 18 power plants. The bottom-up estimates are shown for the CAMS-GLOB-ANT inventory and the CORSO point source database. CAMS-GLOB-ANT emissions are integrated for the energy sector and all other sectors within a radius of 30 km around the power plant. CORSO emissions are shown for the power plant and for other facilities within a radius of 30 km. A radius of 30 km was used because top-down emissions are estimated using TROPOMI measurements from up to 30 km downstream of the facility. The top-down estimates use the local NO_x correction from the MicroHH simulations and the global correction from the GEOS-Chem simulations. To provide spatial context, Fig.  shows maps of total NO_x emissions from the CAMS-GLOB-ANT emission inventory and location of CORSO point sources in a 2° × 2° region around each power station.

On average, total emissions from the CAMS-GLOB-ANT inventory are 70 ± 100 % larger than those reported in the CORSO database. The differences arise because CAMS-GLOB-ANT includes emissions not only from power plants, but also from other relevant NO_x combustion sources such as road transport, residential and commercial combustion and manufacturing industry, while CORSO is limited to major power plant, iron/steel production sites and cements plants. When considering only the CAMS-GLOB-ANT emissions reported for the power generation sector, differences with the CORSO database are much lower 30 ± 81 %, although significant discrepancies still exist at specific sites. For instance, emissions in CAMS-GLOB-ANT around Boxberg (Germany), which include the Schwarze Pumpe power plant, are only half of those reported in CORSO. Moreover, CAMS-GLOB-ANT includes emissions of some power plants that were decommissioned prior to 2021, such as the Gorgas power plant (reported at 4 kt a⁻¹ in CAMS-GLOB-ANT) east of James H Miller power plant in Alabama (Fig. ), which was permanently closed in 2019. This is probably because the CAMS-GLOB-ANT is based on a version of the EDGAR inventory, which uses the outdated CARMA version 3 power plant database from 2009 , whereas the CORSO database uses reported emissions from 2021. This issue has been resolved in more recent versions of EDGAR . In addition, spatial mismatches are evident in CAMS-GLOB-ANT with emission locations sometimes offset from actual stack coordinates, for example, in the case of the Hunter power plant. This is also related to the use of CARMA in the EDGAR inventory. The spatial analysis also shows that several facilities are located near urban areas or industrial complexes, as observed for Lippendorf (Germany), Weisweiler, (Germany) Miami Fort (Ohio), and Labadie (Missouri).

The top-down estimates using the local NO_x correction approach are 58 ± 8 % higher than those obtained with the global approach, due to the larger correction factor of the local approach (see Sect. ). When comparing CORSO bottom-up and top-down approaches for individual power plants, the local approach yields emissions 34 ± 34 % larger. However, satellite-based estimates are sensitive to the area surrounding the source. If we consider all point sources within 30 km of the power plant, the local approach is only 9 ± 20 % larger than bottom-up estimates. In contrast, the global approach still yields top-down estimates that are 31 ± 12 % lower than the bottom-up estimates within the same 30 km radius.

We find larger discrepancies for some power plants. One example is the Hunter power plant in Utah, which is located near the Huntington power plant (Fig. c), the NO_x correction appears to systematically overestimate emissions. Similarly, for the Miami Fort power plant in Ohio, top-down estimates exceed bottom-up values (cf. Table ). This facility is also surrounded by several nearby point sources, which may contribute to the overcorrection effect similar to what was seen at Hunter. Additionally, emissions during the summer months at Miami Fort were low and frequently below the satellite detection threshold (Fig. b). Since non-emitting days are not included when averaging, this may lead to an overestimation of annual emissions.

Figure c shows that the regression between CORSO bottom-up estimates (within 30 km) and local top-down estimates yields a slope of 1.06 ± 0.17 and an intercept of 0.3 ± 1.7 kt a⁻¹, with a correlation coefficient of approximately 0.70, showing good agreement.

To assess the influence of the NO_x chemistry on estimated emissions, Fig.  shows the temporal variability and the relationship between wind speed and the chemistry parameters (f, 1/D and c=f/D) for the Jänschwalde power plant in Germany. A second version of the figure with narrower y-axes is provided in the Supplement.

The conversion factor, f(t), derived from the local MicroHH simulations, shows strong temporal variability. This variability is driven by changes in wind speed, which affect the estimated time since emissions in Eq. () for a fixed plume area up to 30 km downstream. At low wind speeds, the plume remains longer in the area, allowing more time for converting NO to NO₂, resulting in lower conversion factors. Conversely, at higher wind speeds, less conversion occurs within the same area. Consequently, the conversion factor increases from 1.3 to 2.2 as wind speeds increase from 1 to 16 m s⁻¹. In contrast, the temporal variability of the conversion factor f for the global approach, based on GEOS-Chem, shows less temporal variability. The factor exhibits a weak seasonal cycle with smaller values during winter. However, it does not strongly depend on wind speed, as the approach lacks explicit information about time since emissions. The mean value of 1.4 is slightly larger than the background parameter f0=1.31 from the MicroHH simulations.

The decay correction term 1/D depends strongly on wind speed for both approaches, which is primarily driven by wind speed directly influences the time since emission in Eq. (). In fact, a constant lifetime of 2.5 h was used for the local approach. The global approach has lifetimes of about 5 h in summer and even longer lifetimes in winter. As expected, the correction term is largest for low wind speeds, because more NO_x has decayed within the 30 km plume length. For the local approach, the term ranges from 4.0 at 1 m s⁻¹ to 1.2 at 16 m s⁻¹. For the global approach, the correction term is smaller with a mean value of 1.1. The correction term can even become smaller than 1 in winter, indicating net NO_x production.

The combined term c=f/D is dominated by the decay term with larger values for low wind speeds. It ranges from 2.4 to 6.6 for the local approach and 1.1 to 3.8 for the global approach. The difference explains the systematic offset between the emission estimates using the two approaches. Importantly, the large correction factor associated with low wind speeds was the reason for filtering out top-down estimates with wind speeds below 2 m s⁻¹, because they introduce substantial uncertainty and potential overestimation.

The number of valid satellite overpasses per year ranges from 38 to 170, depending on the cloud frequency at the location and the isolation of the power plant. Fewer estimates are available for plants situated near other emission sources, as overlapping plumes and interference often lead to quality filtering and data rejection. For all European power plants, the number of valid top-down emission estimates during winter is notably low, with only 12 % of the total valid estimates occurring in that season. In January 2021, the Kozienice power plant in Poland is the only plant providing a valid estimate. For U.S. power plants, slightly more valid estimates (16 %) are available during winter (see Fig. S4 in the Supplement).

Figure compares top-down and bottom-up NO_x emission time series for six selected power plants. The time series for all analyzed plants are shown in the Supplement. The left column displays individual estimates, while the right column shows monthly values. For European power plants, bottom-up estimates are derived from the CORSO annual values scaled by power generation data, whereas for U.S. plants, daily NO_x emissions directly taken from CEMS measurements. We further computed relative mean bias (MB in %), reduced chi-squared values (χred2) and Pearson correlation coefficient (r2) for each time series.

For the Jänschwalde power plant, top-down estimates are slightly larger than bottom-up reports (MB ≈ 5 %). The correlation coefficients are low (r2≈ 0.3) preliminary due to the low variability of emissions of the plant. The reduced chi-squared value is moderately high for individual estimates (χred2=7.5), while the monthly value (χred2=1.5) is close to unity, suggesting that the differences between bottom-up and top-down estimates are broadly consistent with their estimated uncertainties. The time series for the Kozienice power plant shows generally similar performance, except for a pronounced outlier in January. This outlier was not flagged by the automatic quality filtering, resulting in a large mean bias for monthly values and, consequently, lower reduced chi-squared values and correlation coefficients (MB =68 %, χred2=4.0, r2=0.10). This highlights the importance of robust quality filtering in top-down approaches.

The four U.S. power plants exhibit strong variability in reported emission, which is reflected in the top-down estimates and results in high correlation coefficients (r2 ranging from 0.51 to 0.84 for monthly values). The mean bias is small for Intermountain and Thomas Hill (8 %) but larger for New Madrid (27 %). Reduced chi-squared values range from 10 to 20 for individual overpasses and fall below 4 for monthly values, generally indicating good agreement at the monthly scale. The Miami Fort power plant has a strong seasonal cycle with very low emissions reported from May to October. Top-down estimates capture this pattern, although the number of valid estimates is limited during summer, because emissions frequently fall below the detection limit (e.g., Fig. b). While the correlation coefficient is high (r2=0.84 for monthly values), the mean bias is quite large (MB =64 %) due to the presence of other sources in the vicinity (see Fig. ). This bias is reduced when considering all point sources within 30 km (Table ).

Figure shows MBs, χred2 and r2 for individual estimates and monthly mean values (see Table S1 in the Supplement for all values). Since we compare bottom-up emissions for the power plant, MBs can be large when plants are not isolated because top-down values are sensitive to surrounding sources, (cf. Fig.). The correlation coefficients span a large range, with low values for plants without a pronounced seasonal cycle and higher values for monthly averages. Reduced chi-squared values are generally below 5 for monthly values (χ¯red2=3.9, range: 1.5 to 11.5), with remaining deviation between top-down and bottom-up driven by the mean bias, due to missing neighboring sources, and uncertainties in the top-down method such as uncertainties in NO₂ columns (e.g., AMF correction), wind speed and NO_x chemistry correction.