2.1 Satellite data

We use NO₂ tropospheric column observations from the National Aeronautics and Space Administration's (NASA's) OMI and from the Royal Netherlands Meteorological Institute's (KNMI's) TROPOMI instruments in the inversion framework. TROPOMI was launched in October 2017 and provides 7.2×3.6 km² resolution NO₂ retrievals, upgraded to 5.6×3.6 km² resolution in August 2019 (Van Geffen et al., 2020; Veefkind et al., 2012). TROPOMI's sun-synchronous polar orbit crosses the Equator at approximately 13:30 local time (LT), allowing the instrument to achieve global coverage in one day. We assimilate the Level-2 tropospheric slant column retrieved from NASA's Earth Science Data Systems program (https://www.earthdata.nasa.gov/, last access: 9 December 2022). The data product is described in the Algorithm and Theoretical Basis Document (ATBD) for TROPOMI NO₂ (Van Geffen et al., 2019). We only consider TROPOMI observations with a quality flag greater than 0.5 and a cloud fraction lower than 30 % in the assimilation, following data product recommendations (Eskes et al., 2019). We use the latest publicly available versions of the TROPOMI retrieval for 2019 (versions 1.2.2 to 1.3.2) at the time of the analysis. Version 1.3 introduced updates to cloud processing that decreased noisy hotspots and broadened the range of acceptable air mass factors (Eskes et al., 2021). Information about the updates applied in each version and the dates on which updates were applied is given in Eskes et al. (2021). A research version with an updated retrieval applied to 2019 observations has been developed (Van Geffen et al., 2022) but was not yet standard and was not available at the time of this analysis. We discuss the impact of these latest updates in Sect. 3.3.

OMI, on board the Aura satellite launched in 2004, provides tropospheric NO₂ vertical and slant column retrievals with a resolution of 13×24 km² near nadir in a sun-synchronous polar orbit, with a local Equator crossing time of 13:45 LT. Global coverage is achieved in 2 d. We use the NASA Goddard Space Flight Center (GSFC) Level-2 NO₂ product (Krotkov et al., 2019b). OMI was impacted by a row anomaly beginning in 2008, reducing the number of usable pixels in the OMI retrieval (Boersma et al., 2018). We include only pixels with a cloud fraction lower than 30 % and a summary quality flag of 0. Detailed information about the NO₂ data product is included in the OMI ATBD (Chance, 2002) and in Krotkov et al. (2019a).

A low bias has been noted in the versions of TROPOMI NO₂ used for this study (Judd et al., 2020; Verhoelst et al., 2021). Although TROPOMI NO₂ retrievals from 2019 have been reprocessed with retrieval version 2.3.1, resulting in an improvement of the bias (Eskes et al., 2021), these reprocessed datasets were not yet available at the time this analysis was conducted. Figure 2 compares TROPOMI and OMI tropospheric vertical column densities (VCDs) for 2019, regridded to the CMAQ grid used. For the VCDs shown in the figure, we remove the effect of the assumed vertical profile of NO₂ from the original satellite product by recalculating the VCDs with the NO₂ vertical profile simulated by CMAQ. In the results, we discuss the low bias in TROPOMI data and explore its impact on emissions inversions.

Figure 22019 annual average TROPOMI and OMI vertical NO₂ vertical column densities, with CMAQ NO₂ profiles applied, and the ratio between them. Column density ratios are only shown for the grid cells where NO_x emissions updates are applied in the emissions inversion.

2.2 Hemispheric air quality modeling

Model simulations in the inversion framework were completed for January–December 2019 using CMAQ v5.3.2 (Appel et al., 2021; U.S. EPA Office of Research and Development, 2020). CMAQ has been used to simulate air quality over the Northern Hemisphere and has been shown to adequately capture chemical composition against observations (Mathur et al., 2017). Model inputs and satellite observations are summarized in Table 1. Simulations, designed to capture continental-scale pollutant transport, cover the Northern Hemisphere with 108 km horizontal grid spacing and a 44-layer vertical structure reaching 50 hPa (Mathur et al., 2017). The simulations use version CB6r3 of the Carbon Bond 6 chemical mechanism (Luecken et al., 2019), the AERO7 aerosol module (Xu et al., 2018) and updated halogen chemistry (Kang et al., 2021). Anthropogenic emissions are modeled using representative day-of-week emissions that change month to month. Representative-day emissions are created by averaging data from the prior emissions inventory on a day-of-week basis by month. For each day of the week and each month, there is a unique hourly emissions file that is used for every matching day of the week in that month. As a result, diurnal and weekly patterns are captured in the emissions, while daily variations that are specific to the prior emissions inventory year are averaged. The prior emissions inventory relies on the best available emissions data at the time of the study. Anthropogenic emissions for North America are from the U.S. Environmental Protection Agency's (EPA) 2017 National Emissions Inventory (NEI) modeling platform (Adams, 2020). Emissions in China are for the year 2015 (Zhao et al., 2018), and emissions for the rest of the hemisphere are based on the Hemispheric Transport of Air Pollution (HTAP) version 2, projected from their original 2010 date to 2014, with scaling factors from the Community Emissions Data System (CEDS). To initialize the 2019 prior and posterior simulations and to reduce the impact of chemical initial conditions on the results, we use a 1-year spin-up period not considered for the analyses. CMAQ model runs are driven by meteorology from a retrospective hemispheric simulation using the Weather Research and Forecasting (WRF) model (Skamarock et al., 2008) version 4.1.1, configured following Mathur et al. (2017) and Xing et al. (2015).

Table 1Prior emissions and model inputs.

^* GEIA – Global Emissions Initiative; FINN – Fire Inventory from NCAR; CAMS – Community Atmosphere Modeling System; MEGAN – Model of Emissions of Gases and Aerosols from Nature

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2.3 Chemical data assimilation in CMAQ

We adjust modeled NO₂ concentrations using satellite observations by coupling the CMAQ model to a data assimilation model, the National Centers for Environmental Prediction (NCEP) Gridpoint Statistical Interpolation (GSI) program version 3.3 (Shao et al., 2016). GSI performs 3D variational (3DVAR) data assimilation by minimizing the cost function, J:

where y is the observation innovation $\mathit{y}={\mathit{y}}_{\mathrm{o}}-H\left({\mathit{x}}_{\mathrm{b}}\right)$, x is the analysis increment $\mathit{x}={\mathit{x}}_{\mathrm{a}}-{\mathit{x}}_{\mathrm{b}}$, x_a is the analysis field (NO₂ concentration after application of chemical data assimilation), x_b is the model background (the simulated NO₂ concentration before application of chemical data assimilation), y_o is the satellite observations, B is the background error covariance matrix, R is the observation error matrix, and H is the observation operator. To compute the difference between the model column (x_b) and the satellite column (y_o), the observation operator H is applied, which transforms the model background to the form of the satellite observations. For TROPOMI data, the averaging kernel is first converted to scattering weights as

where A(z) is the vertically resolved TROPOMI averaging kernel for level z, M_total is the air mass factor provided with the satellite data, and w(z) is the vertically resolved scattering weights. Scattering weights accompany the OMI NO₂ data product, so this step is not needed to assimilate OMI data. Scattering weights are then applied to compute the model slant column as

where ${\mathrm{\Omega }}_{\mathrm{v}}^{\mathrm{m}}\left(z\right)$ is the model partial vertical column in the troposphere, interpolated to the satellite grid, and ${\mathrm{\Omega }}_{\mathrm{s}}^{\mathrm{m}}$ is the model tropospheric slant column density (SCD). The difference between the modeled and observed slant columns, or the observation innovation y in Eq. (1), is estimated as

where $\mathrm{\Omega }{{}^{\prime }}_{\mathrm{s}}$ is the analysis increment, ${\mathrm{\Omega }}_{\mathrm{v}}^{\mathrm{o}}$ is the satellite tropospheric VCD, and M_trop is the tropospheric air mass factor, distributed with the satellite data. We eliminate the influence of the a priori satellite vertical profile by computing the analysis increment with the modeled and observed SCD, which, unlike the VCD, does not rely on the a priori vertical NO₂ profile assumed by the satellite.

We compute B using the Generalized Background Error covariance matrix model (GENBE v2.0) (Descombes et al., 2015), which models background errors by comparing a free-running simulation and a simulation with either lightning or anthropogenic NO_x emissions perturbed. We use GENBE with the prior simulation and a simulation with a uniform −15 % perturbation to LNO_x to create three-dimensional background errors in the upper troposphere for the LNO_x assimilation. After updating LNO_x emissions (as described in Sect. 2.5), we create three-dimensional background errors in the boundary layer for the anthropogenic NO_x assimilation by using GENBE with the LNO_x posterior simulation and a simulation with a −15 % perturbation to surface anthropogenic NO_x emissions. Observation error R is provided with the satellite data.

Online coupling between GSI and CMAQ was developed in this study to perform the assimilation. At each model time step in which a satellite observation is available, the CMAQ model simulation is paused, and 3DVAR assimilation is performed. The CMAQ model state at that time step is used as x_b. After assimilation using 3DVAR within GSI, CMAQ returns to a free-running mode, and the new model state, x, is updated to more closely match the satellite observation. The difference in the monthly average NO₂ VCDs from the assimilation and no-assimilation runs is used in the inversion as ΔΩ.

2.4 Finite-difference mass-balance inversion

In the inversion framework developed, we iterate the approach of Lamsal et al. (2011). The FDMB process as applied here is summarized in Fig. 3. In the past, this approach has been used by directly comparing model and satellite columns (e.g., Itahashi et al., 2019; Cooper et al., 2017; Lamsal et al., 2011). We modify the approach by first updating model concentrations with assimilation of satellite observations and then updating the emissions using the difference between the modeled VCD with and without assimilated satellite information. All updates are performed on a monthly average basis.

Figure 3FDMB inversion. The red dashed line corresponds to the red dashed lines in Fig. 1, and the processes inside show additional details of the FDMB inversion. In this framework, the prior emissions (black box on the far left) are input to the CMAQ model. CMAQ simulations are performed with unperturbed prior emissions (100 % arrow and E₁₀₀) and prior emissions with a −15 % perturbation (85 % arrow and E₈₅). The resulting modeled VCDs are Ω₁₀₀ and Ω₈₅, respectively. These VCDs are used to compute the sensitivity, β (blue box). New emissions totals are calculated with FDMB (yellow box), using β, NO₂ VCD from a CMAQ simulation without assimilation (Ω), and NO₂ VCD from a CMAQ simulation with assimilation (Ω^′). When iteration is used, the posterior emissions from the previous iteration are used as input to the CMAQ model to simulate new VCDs, Ω and Ω^′.

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In FDMB, following Lamsal et al. (2011), emissions changes are inferred through the relationship

where ΔE is the inferred NO_x emissions change, E is the NO_x emissions prior, Ω is the model simulated NO₂ VCD without chemical data assimilation, and $\mathrm{\Delta }\mathrm{\Omega }={\mathrm{\Omega }}_{\mathrm{assim}}-\mathrm{\Omega }$ is the monthly average difference between the model simulated tropospheric NO₂ VCD with (Ω_assim) and without (Ω) chemical data assimilation. β is a unitless scaling parameter, the Jacobian, that linearly relates NO₂ VCD changes to NO_x emissions changes. β is calculated through finite differencing as

where E^′ is perturbed NO_x emissions, Ω_E is the tropospheric NO₂ VCD simulated with model emissions E, and ${\mathrm{\Omega }}_{E{}^{\prime }}$ is the tropospheric NO₂ VCD simulated with model emissions E^′. To estimate β, we use the same −15 % perturbation used to create background errors B in the boundary layer. Cooper et al. (2017) found that using perturbations ranging from 5 % to 20 % to calculate β changed posterior emissions estimates by less than 2 % globally.

2.5 Inverse modeling NO_x emissions

In our framework, LNO_x emissions are updated first, separately from anthropogenic emissions. Due to the satellite instruments' sensitivity to NO₂ in the upper atmosphere (e.g., Eskes and Boersma, 2003), small model biases there can influence the total column comparison and adversely impact the anthropogenic emissions adjustment. By updating LNO_x emissions, we aim to decrease this bias and its impact on the ANO_x inversion. We compute the scaling parameter for lightning emissions, ${\mathit{\beta }}_{{\mathrm{LNO}}_x}$, using the −15 % LNO_x perturbation simulations applied to create background errors for the upper troposphere. We then assimilate satellite NO₂ observations using the background errors for the upper troposphere and apply ${\mathit{\beta }}_{{\mathrm{LNO}}_x}$ in a single inversion iteration using the full tropospheric VCD to compute spatially varying LNO_x adjustment factors. Updates to LNO_x are calculated using monthly averages.

After LNO_x emissions are updated, ANO_x emissions are updated by iteratively applying an FDMB inversion independently for each month in 2019. Iterating the FDMB has been shown to improve emissions estimates compared to a single FDMB application (Cooper et al., 2017). In the FDMB iteration, each update to the emissions serves as the prior emissions for the subsequent iteration (represented as black dashed lines in Fig. 1). The number of iterations is determined based on the synthetic observation experiment described in Sect. 2.6. β is held constant during all ANO_x inversion iterations and is not recalculated each time to prevent instability in β as changes in the column become smaller with subsequent iterations. In the ANO_x emissions inversion, we only consider grid cells in which local anthropogenic NO_x emissions likely contribute significantly to the satellite-observed NO₂ column by only including grid cells in which anthropogenic NO_x emissions comprise at least 50 % of total NO_x emissions, following Lamsal et al. (2011); population density is greater than 15 000 people km⁻² (CIESIN, 2018); modeled cloud cover is less than 30 %; and the local time is 13:00 or 14:00 (OMI and TROPOMI overpass times). Only emissions in grid cells meeting these criteria are adjusted. Table S1 in the Supplement describes each simulation performed for the LNO_x and ANO_x inversions.

The FDMB method assumes that emissions impacts are local (i.e., emissions in one grid cell do not affect VCD amounts in neighboring grid cells). This assumption is most valid when NO_x lifetime is shorter than NO_x transport time to neighboring grid cells, which is typical near the surface in coarse-resolution models (Martin et al., 2003), such as the one used in this study. However, the assumption is less realistic at finer resolutions and in the upper troposphere, where the lifetime of NO₂ is longer than at the surface and where NO₂ concentrations are not directly impacted by coincident near-surface emissions. Even at coarse resolutions (e.g., 100 km grid spacing), emissions-smearing effects, which occur when the FDMB assumption of local emissions effects is incorrect and emissions are inappropriately adjusted, can appear due to NO_x transport, reservoir species, and chemical feedbacks (Turner et al., 2012; Cooper et al., 2017). Traditional FDMB, which directly compares modeled and remotely sensed columns, cannot address this effect. Assimilating the satellite VCD introduces an additional complication. The horizontal length scales (on the order of several hundreds of kilometers) used in the background error extend beyond the grid cell horizontal dimensions (nominally 108 km) in the middle and upper troposphere; as a result, NO₂ changes introduced by assimilation (ΔΩ) do not have a local relationship with surface emissions directly below. In our work, assimilating the observed column information instead of directly comparing modeled and satellite-retrieved VCDs allows the analysis to be restricted to the lower troposphere, mitigating both the misallocation errors of FDMB and the effect of horizontal length scales extending beyond the grid cell dimension. To that end, we limit the anthropogenic emissions analysis to the lowest 20 model layers, which is nominal from the ground to ∼720 hPa over non-mountainous terrain in the summer, and use that partial column to calculate ΔΩ in the FDMB inversion. ΔΩ for a single month above and below the threshold is illustrated in Fig. S1 in the Supplement. By applying this cutoff, we focus the inversion on surface anthropogenic NO_x.

2.6 Inversion system testing

We conduct a synthetic observation experiment to evaluate the ability of the inversion system to constrain emissions to a known perturbation. Artificial NO₂ observations were generated from CMAQ simulations with unperturbed emissions and NO_x emissions reduced by 15 %. As expected, assimilating the synthetic observations derived from a simulation with unperturbed emissions results in an analysis increment of zero. The results of an iterative emissions inversion based on the synthetic observations derived from the simulation with perturbed emissions are shown in Fig. S2. Across Northern Hemisphere regions, the normalized mean error (NME) relative to the known perturbed emissions and the rate at which it changes decrease with subsequent iterations. The NME is minimized after seven to nine iterations, depending on the region. In all subsequent results, emissions inferences made with eight iterations of the inversion system are shown and analyzed. Convergence of the inversion in different global regions adds confidence to the system's ability to constrain real-world emissions.

Figure 4Seasonal NO₂ VCD change (ΔΩ) from CMAQ simulation using prior emissions after assimilating OMI or TROPOMI tropospheric NO₂ observations and modeling atmospheric composition with prior NO_x emissions. ΔΩ shown for winter (DJF), spring (MAM), summer (JJA), and fall (SON).

3.1 Lightning NO_x emissions updates

Assimilation of retrievals from either satellite increases LNO_x emissions across all seasons, relative to the prior emissions (monthly climatology from GEIA), with the largest changes occurring during the summer (Figs. S3 and S4). Applying 2019 OMI data increases total LNO_x emissions in 2019 by 20 % over the GEIA climatology, while assimilation of TROPOMI data increases LNO_x emissions by 24 %. The emissions increases inferred by both satellite products are driven by NO₂ increases in the mid and upper troposphere due to assimilation, with changes near the surface being negligible in comparison. Increases in background areas with small NO₂ column totals and subsequent LNO_x increases in these areas suggest a low bias in modeled background NO₂ relative to observations from both satellites. A low bias agrees with the findings reported by other model and satellite NO₂ comparisons (Silvern et al., 2019; Qu et al., 2021; Goldberg et al., 2017). The LNO_x emissions adjustments inferred here decrease the differences between modeled and satellite-derived NO₂ in the upper troposphere and decrease the bias that differences in the upper troposphere can introduce to the subsequent ANO_x inversion.

3.2 Impact of assimilation on modeled NO₂ vertical column density

Figure 4 shows the change to CMAQ-modeled tropospheric VCD, (ΔΩ) caused by assimilating NO₂ observations from OMI or TROPOMI with background errors for the boundary layer, before applying any emissions adjustments. In Fig. 4 and throughout the results, ΔΩ reflects differences near the surface (as described in Sect. 2.5). Assimilating OMI NO₂ data generally increases modeled NO₂ columns near populated areas in China, India, and the US. In contrast, assimilating TROPOMI NO₂ data decreases modeled NO₂ columns more widely across the Northern Hemisphere. The changes brought about by assimilating satellite data are larger during the winter and fall and smaller in the spring and summer, when NO_x lifetime is shortest and when NO₂ columns are smaller. During the winter in northeast China, where the assimilation impacts are most apparent, the seasonal average change due to assimilation reaches 1.8×10¹⁵ molec. cm⁻² for OMI and $-\mathrm{2.8}\times {\mathrm{10}}^{\mathrm{15}}$ molec. cm⁻² for TROPOMI. The direction of ΔΩ after assimilation of OMI data is more heterogeneous and shows a stronger seasonality, while ΔΩ based on assimilating TROPOMI data is consistently negative. Over Europe, ΔΩ after assimilating OMI observations is close to zero in warm months and negative in colder seasons. Assimilating satellite-observed NO₂ increases the NO₂ levels modeled over the ocean and less-populous areas, such as the Sahara, with low NO_x emissions and small NO₂ column amounts.

Over polluted areas, the direction of ΔΩ for the TROPOMI or OMI data assimilations tends to differ. This discrepancy is likely due to the low bias in TROPOMI-derived tropospheric NO₂ columns, which has been reported to be approximately 10 % over the US, Europe, and India, and greater than 20 % over China when compared with the OMI Quality Assurance for Essential Climate Variables (QA4ECV) retrieval (Van Geffen et al., 2022; Verhoelst et al., 2021; C. J. Wang et al., 2020; Li et al., 2021). Over background areas, the analysis increments that result from assimilation of observations from both satellites generally agree. The consistency suggests a low bias in modeled background NO₂ concentrations and also agrees with the low bias in CMAQ-modeled free-tropospheric NO₂ reported by Goldberg et al. (2017). Such a bias can contribute to the positive analysis increment over background areas. However, NO₂ columns observed in these regions may be smaller than the retrieval accuracy of 0.7×10¹⁵ molec. cm⁻² (Van Geffen et al., 2019), reducing confidence in the analysis increment at these locations. In the anthropogenic emissions inversion, our filtering criteria exclude background areas which are more likely to have low VCD amounts.

3.3 Emissions inversion

Season-average β values, relating NO₂ vertical column differences to anthropogenic near-surface NO_x emissions updates, are shown in Fig. S5. Based on our criteria for grid cell inclusion in the inversion, described in Sect. 2.5, we consider 13 % of the grid cells in the domain, which represent 88 % of prior anthropogenic NO_x emissions. Seasonal domain-average values range from 1.33 to 1.66 and are lower in the winter and higher in the summer. A β value less than 1.0 results in an emissions update that is smaller than the VCD change, while a β greater than 1.0 has the opposite effect. β tends to be less than 1.0 in polluted regions during colder months and larger during warmer months and in less-polluted regions, although many grid cells which are less polluted are not considered in the analysis. The scaling factors are smallest over China and larger over the US, India, Mexico, and Europe. The differences among regions stem from local differences in NO_x lifetime and transport. In Indonesia and sub-Saharan Africa, lower emissions and a small response from tropospheric VCD to anthropogenic emissions perturbations can lead to large β values. To prevent overly large or small β values, we constrain the factor to between 0.1 and 10, following Cooper et al. (2017). Scaling factors estimated here are larger than the 1.16 global-average previously reported by Lamsal et al. (2011). However, in Lamsal et al. (2011), modeled NO₂ vertical columns were sampled at the morning SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) overpass time rather than at the afternoon OMI or TROPOMI overpass times; β tended to be closer to 1.0 during the morning in regions with high NO_x emissions (Li and Wang, 2019). Li and Wang (2019) show that, over rural regions with lower NO_x concentrations, β is larger at the OMI or TROPOMI overpass window than at the SCIAMACHY overpass window, suggesting that a larger overall β for analyses based on OMI or TROPOMI products should be expected. Additionally, NO_x emissions have decreased considerably in several regions of the Northern Hemisphere, including the US (Tong et al., 2015) and China (Miyazaki et al., 2017), after the Lamsal (2011) study was conducted, which has changed the sensitivity of NO₂ VCDs to NO_x emissions (Qu et al., 2021; Silvern et al., 2019).

Annual bottom-up prior ANO_x emissions estimates are shown in Fig. 5. Season-average ANO_x emissions inferences from the inversions based on OMI and TROPOMI observations are shown in Fig. 6. The use of OMI observations generally tends to increase emissions in most industrialized nations outside of Europe. NO_x emissions increases driven by OMI observations are largest in winter and spring and smaller, or slightly decreased, in summer and fall. In contrast, the use of TROPOMI retrievals tends to drive a decrease in NO_x emissions across all seasons and continents, with the largest impacts in the summer and the smallest in the spring. The largest emissions changes based on both OMI and TROPOMI retrievals are in northeast China during the winter. Over India, OMI-inferred changes are concentrated in central India, where prior emissions are lower, while the largest changes inferred from TROPOMI are in the northern, eastern, and southern zones, where prior emissions are highest. Relative NO_x emissions changes driven by TROPOMI observations tend to be small over dense urban areas, with more uniform decreases over cells with lower emissions.

Figure 52019 prior anthropogenic NO_x emissions totals. Data sources are described in Table 1.

Figure 6Season-average NO_x emissions changes from inverse modeling updates based on OMI and TROPOMI observations. Emissions changes are shown for winter (DJF), spring (MAM), summer (JJA), and fall (SON).

ANOx emissions totals and inferred changes are explored for China, India, Europe, Mexico, and the US (Fig. 7). We also show 2019 NO_x emissions totals from the Copernicus Atmosphere Monitoring Service's (CAMS's) bottom-up emissions inventory (Granier et al., 2019) and from the NASA Tropospheric Chemical Reanalysis products 2 (TCR-2) satellite-inferred inventory (Miyazaki et al., 2019, 2020). TCR-2 top-down NO_x emissions are constrained using satellite observations of NO₂, CO, O₃, and SO₂ at a resolution of $\mathrm{1.125}{}^{\circ }\times \mathrm{1.125}{}^{\circ }$ and are further described in Miyazaki et al. (2017). CAMS anthropogenic NO_x emissions are based on the Emissions Database for Global Atmospheric Research (EDGAR version 5.3) estimates for 2015 (Crippa et al., 2020), projected to 2019 using CEDS scaling factors, and are provided at $\mathrm{0.1}{}^{\circ }\times \mathrm{0.1}{}^{\circ }$. Both datasets provide monthly anthropogenic NO_x totals. Except for Europe, assimilation toward OMI retrievals increases annual emissions totals in the regions analyzed, while using TROPOMI retrievals decreases them. TCR-2 NO_x emissions estimates are larger than the prior emissions used by our inverse modeling framework, except for India, while CAMS totals are lower than the prior emissions estimates and are similar to TROPOMI inferred emissions. Across the regions considered, TROPOMI infers an average annual decrease of −33 % in NO_x emissions from the regions, while OMI infers a +9 % increase. In Europe, the only region where the sign of the inferred changes match, the use of OMI retrievals results in a −1 % change, while applying TROPOMI observations leads to a −36 % decrease in NO_x emissions. The largest total changes are inferred in the highest-emitting region, China, while the greatest relative changes, −41 % inferred with TROPOMI, are for India, where emissions are highly uncertain. Changes inferred with OMI observations over the US are greater than 1200×10³ short tons NO_x as NO₂ per year but smaller than the difference between our prior US emissions estimates and TCR-2 or CAMS estimates. A change of $-\mathrm{3000}\times {\mathrm{10}}^{\mathrm{3}}$ short tons NO_x as NO₂ emitted annually in the US, as inferred by TROPOMI, over 30 % of the prior emissions differs significantly from National Emissions Inventory estimates but leads to a total close to that of the 2019 CAMS inventory.

Figure 7Prior and satellite-inferred 2019 anthropogenic NO_x emissions in select global regions. Plot (a) shows total emissions (as NO₂) from prior emissions estimates, inference with OMI or TROPOMI observations (OMI and TROPOMI posterior), and CAMS or TCR-2 inventories in the US, China, India, Mexico, and Europe. Plot (b) shows the percent change (ΔENO_x) inferred with OMI or TROPOMI data, relative to prior emissions estimates, for each region.

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Across the months simulated, inferences using OMI retrievals consistently lead to higher NO_x emissions than using TROPOMI retrievals. Figure 8 shows monthly NO_x emissions totals and inferred changes for several global regions. The magnitude of changes is generally smallest in summer months and largest in winter months for both OMI- and TROPOMI-inferred emissions. Monthly prior emissions totals lay between the OMI and TROPOMI inferences, except for summertime emissions in India and Mexico, where both satellite inferences decrease NO_x emissions. Over Europe, both satellite products infer a decrease during the winter, although fewer valid satellite pixels due to snow cover at high latitudes and longer winter NO₂ atmospheric lifetimes may influence the inference.

Figure 8Monthly prior and satellite-inferred anthropogenic NO_x emissions in 2019 in select global regions. Total monthly emissions (as NO₂) from prior emissions estimates, inference with OMI or TROPOMI observations (OMI and TROPOMI posterior), and CAMS or TCR-2 inventories in the US, China, India, Mexico, and Europe are shown. Percent changes (ΔENO_x) inferred with OMI or TROPOMI data, relative to prior emissions estimates, for each region are shown by the purple and orange bars.

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Based on reported NO_x emissions trends (McDuffie et al., 2020; U.S. EPA, 2022a), changes from the prior emissions inventory (Table 1) to 2019 are expected. Relative to the prior emissions, significant decreases in NO_x emissions in China, estimated for 2015 in the prior inventory, and smaller reductions in Europe and North America, reported for 2014 and 2017 in the prior inventory, respectively, should be anticipated. TROPOMI-inferred emissions reflect the direction anticipated for these changes but with larger than expected magnitudes. For example, the 28 % decrease in anthropogenic NO_x emissions over China between 2015 and 2019 inferred from the TROPOMI observations is substantially larger than the 8 % decrease estimated between 2015 and 2017 by the Community Emissions Data System (McDuffie et al., 2020). Bottom-up estimates indicate that anthropogenic NO_x emissions in the US have decreased through 2019 (U.S. EPA, 2022a). Although the direction of the emissions change inferred from TROPOMI agrees with the trend in bottom-up estimates, its magnitude is larger than expected. An underestimation of US emissions in winter in the prior inventory when compared with OMI inferences contrasts with field study results reporting no bias in northeastern US winter emissions estimates (Jaegle et al., 2018; Salmon et al., 2018). In India, bottom-up emissions inventories report sustained growth of NO_x emissions (Kurokawa and Ohara, 2020; McDuffie et al., 2020), and NO₂ levels observed by OMI have been increasing since 2005 (Goldberg et al., 2021; Cooper et al., 2022). The decrease in anthropogenic NO_x emissions inferred by TROPOMI observations contrasts with these trends in bottom-up estimates and OMI observations.

The low bias known to affect TROPOMI NO₂ observations influences the results of the emissions inversion, which targets grid cells with high emissions, likely leading to decreases in inferred emissions that are larger than expected. We conduct an inversion using the reprocessed TROPOMI NO₂ version 2.3.1 (Van Geffen et al., 2022) to infer NO_x emissions for January 2019 and find that the updated data increase the TROPOMI posterior inference by 17 % over the US and 4 % in China relative to version 1.2.2. While using the updated retrievals shrinks the gap between OMI- and TROPOMI-inferred emissions, it does not change the overall trend of smaller posterior emissions using TROPOMI NO₂ (Figs. S10 and S11). The differences between emissions inferred by OMI and TROPOMI observations highlight the importance of ongoing efforts to harmonize OMI and TROPOMI NO₂ retrieval algorithms, such as the NASA Multi-Decadal Nitrogen Dioxide and Derived Products from Satellites (MINDS) (Lamsal et al., 2020) and the QA4ECV (Boersma et al., 2017) datasets.

In addition to smearing effects, coarse-resolution models can artificially alter nonlinear NO₂ chemistry, leading to biases in inferences of NO_x emissions from satellite NO₂ columns (Valin et al., 2011; Sekiya et al., 2021; Lamsal et al., 2011). Higher-resolution simulations can better resolve β and reduce biases caused by nonlinear chemistry. Additional errors in the emissions estimates may be associated with emissions from non-anthropogenic NO_x sources. Although the emissions inversion targets anthropogenic sources only, changes in NO₂ columns observed by the satellite instruments driven by natural NO_x emissions processes may not be captured in the air quality model simulations and subsequently lead to biased anthropogenic emissions inferences (Li et al., 2021).

The emissions resulting from the inverse modeling framework are comparable to CAMS and TCR-2 2019 emissions estimates in several ways. In the US, China, and Europe, the magnitudes of ANO_x emissions from OMI retrievals are comparable to TCR-2 NO_x emissions estimates and exhibit similar monthly patterns. Annual NO_x emissions inferred from OMI observations are also relatively similar to TCR-2 estimates for India and Mexico, although monthly emissions patterns differ. Unlike TCR-2 emissions estimates, which are also constrained by OMI NO₂ observations, 2019 CAMS emissions estimates are projected from 2015 bottom-up data. However, CAMS estimates provide a representation of anticipated emissions trends. In all regions considered, CAMS NO_x emissions estimates are close to the TROPOMI inference annual totals and lower than the prior emissions, OMI inferences, and TCR-2 estimates, potentially suggesting that global NO_x emissions have not decreased as much as anticipated by the CAMS inventory projections.

3.4 Impacts of emissions updates on modeled NO₂ and O₃

We evaluate and compare the CMAQ simulations' ability to reproduce observed pollutant concentrations when driven with NO_x emissions estimates from the prior inventory and with those derived by the inverse modeling framework. Figure 9 compares 2019 OMI and TROPOMI NO₂ VCD retrievals with modeled NO₂ VCDs using the prior emissions with no updates, LNO_x emissions updates, and LNO_x and ANO_x emissions updates. Satellite-based LNO_x emissions updates improve CMAQ model performance – correlation coefficient (R), normalized mean error (NME), and normalized mean bias (NMB) – when evaluated against tropospheric VCD retrievals, relative to model performance with the prior emissions. OMI-inferred ANO_x emissions updates further improve CMAQ model performance evaluated against VCD retrievals, decreasing NMB from −20 % to −5 % and NME from 38 % to 28 %. Model performance is improved by using OMI data in the inverse modeling framework across all seasons (Figs. S6–S9). Although LNO_x emissions updates derived from TROPOMI observations improve model bias and error relative to the CMAQ simulation using prior emissions estimates, TROPOMI-inferred anthropogenic emissions do not, except during summer months (Figs. 9 and S6–S9). The lack of significant improvements in CMAQ-simulated NO₂ VCDs after applying the emissions inversion with TROPOMI NO₂ retrievals prior to the version 2.3.1 update (Van Geffen et al., 2022) may be associated with changing chemical regimes that are not captured in the emissions inversion process.

Changes in modeled VCD due to assimilation and the emissions inferences calculated in the TROPOMI ANO_x inversion exceed the emissions perturbation and VCD changes used to calculate β. For example, over the eastern US, the −15 % emissions perturbation used to calculate β leads to VCD changes of −15 % on average in winter, but assimilating TROPOMI retrievals leads to VCD changes (ΔΩ) of −19 % on average in the winter, with individual changes exceeding −30 %. Modeled NO_x chemistry and NO₂ vertical profiles after assimilating TROPOMI retrievals may be different than those used in the calculation of β. As a result, assimilating TROPOMI retrievals in the ANO_x inversion may lead to modeled NO₂ vertical profiles which are inconsistent with the precalculated β used in the FDMB relationship and to less reliable subsequent emissions inferences. In contrast, the magnitude of VCD changes due to assimilating OMI retrievals over the eastern US in winter is 8 %, well within the magnitude of the VCD changes used to precalculate β. This highlights the importance of applying a β sensitivity valid for the magnitude of anticipated emissions changes in FDMB inversions and the potential consequences of relying on satellite-derived retrievals with pre-existing biases in emissions inversions.

Figure 9Impact of NO_x emissions updates on modeled NO₂ VCDs. Plots compare 2019 season-average CMAQ-modeled NO₂ VCD at each model grid cell in which NO_x emissions were updated by the inverse modeling framework against OMI and TROPOMI tropospheric NO₂ VCD retrievals averaged in each model grid cell. Modeled NO₂ VCD using prior emissions (Prior), inferred LNOx emissions (LNOx posterior), and inferred lightning and anthropogenic NO_x emissions (ANO_x posterior) are each compared with NO₂ VCD retrievals. Top-row plots compare retrievals and modeled VCD based on OMI observations, while bottom-row plots compare retrievals and modeled VCD based on TROPOMI observations. Linear regression line, correlation coefficient (R), normalized mean error (NME), and normalized mean bias (NMB), relative to tropospheric NO₂ VCD retrievals, are shown for each CMAQ simulation.

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Comparing CMAQ-modeled O₃ to ozonesonde measurements from the World Ozone and Ultraviolet Radiation Data Centre (WOUDC) network shows the impacts updating LNO_x emissions on simulated tropospheric O₃ (Fig. 10). Above 300 hPa, the model is biased low, but neither update has a major impact on this bias. However, within the free troposphere, the effects of LNO_x emissions updates are larger. LNO_x satellite-inferred emissions from both satellites increase O₃ and subsequently improve the model's low O₃ bias across all seasons, with the strongest effect in the summer. This suggests a low background NO₂ in our prior simulation, consistent with several studies demonstrating that models underestimate background NO₂ (Goldberg et al., 2017; Qu et al., 2021; Silvern et al., 2019).

Figure 10Ozonesonde observations from the WOUDC network and impact of lightning emissions inferences on modeled ozone. Left plot shows sonde observations averaged in each season and total number of launches per season. The NMB is shown for the prior emissions simulation. Plots on the right show the decrease in the NMB, relative to the prior simulation for simulations, with LNO_x emissions updated with OMI and TROPOMI data.

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Comparisons of CMAQ-modeled NO₂ and O₃ concentrations with ground-level measurements highlight the challenges of reproducing local air quality with a coarse scale model but suggest potential to improve model performance with satellite-derived NO_x emissions updates. Table 2 shows statistics evaluating modeled ground-level daily average NO₂ and maximum 8 h O₃ concentrations over the US against observations from 1218 monitoring sites in the Air Quality System (AQS) (U.S. EPA, 2022b), excluding near-road monitors for which the gridded NO₂ fields are not representative. Statistics for each season are included in Tables S2 and S3. There is a significant low bias in CMAQ-predicted ground-level NO₂ concentrations compared with monitoring site measurements, likely due to the model's coarse grid resolution and the aggregation of NO₂ monitors within urban areas with high NO_x emissions and large concentration gradients. CMAQ simulations at higher horizontal resolution do not show the same bias against NO₂ surface observations (Toro et al., 2021). Agreement between modeled and observed ground-level NO₂ concentrations is improved by using OMI-inferred NO_x emissions compared with the prior emissions simulation, particularly during winter and spring months. Model performance evaluated against ground-level O₃ measurements improves to a smaller extent with OMI-inferred NO_x emissions during winter and spring months. The use of TROPOMI-inferred emissions has mixed impacts on CMAQ performance against observed ground-level NO₂ and O₃ concentrations, leading to limited gains in seasonal R and some seasonal biases and errors but also less agreement with observations for other seasonal statistics. In the US, the network of ground-based air quality observations is relatively large. However, in some regions where emissions uncertainties are expected to be especially high, ground-based observations are significantly limited and less accessible. Assessing the impact of emissions updated against ground-based observations in these regions, although a challenge, would provide further evaluation of the inversion framework in locations where satellite retrievals have the largest potential to provide important constraints to emissions estimates.

Table 2CMAQ model performance evaluated against daily average NO₂ (DA NO₂) and maximum 8 h O₃ concentrations (MDA8 O₃) observed in 2019 by AQS monitoring sites in the US. Near-road monitors are not considered. Statistics are shown for simulations using prior emissions (Prior), lightning and anthropogenic NO_x emissions inferred with OMI data (OMI-inferred), and lightning and anthropogenic NO_x emissions inferred with TROPOMI data (TROPOMI-inferred). Coefficient of determination (R), normalized mean error (NME), and normalized mean bias (NMB), relative to AQS observations, are estimated for each CMAQ simulation.

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3.5 Impacts of emissions updates on long-range O₃ transport

Global NO_x emissions estimates affect model simulations of long-range air pollution transport. To explore these impacts, we examine the response of CMAQ-modeled trans-Pacific O₃ to the inverse modeling framework's NO_x emissions updates. Figure 11 shows season-average changes in simulated free-tropospheric O₃ over the North Pacific Ocean resulting from the use of OMI- and TROPOMI-inferred ANO_x emissions relative to the emissions simulation with LNO_x emissions updated. As expected, the emissions inversions lead to O₃ variations that follow NO_x emissions changes inferred for each satellite's observations, with OMI inferences resulting in higher O₃ concentrations and TROPOMI inferences resulting in lower O₃ concentrations over the North Pacific Ocean. Season-average differences with respect to the prior emissions simulation are as large as +1.8 ppb in winter, using OMI-based updates, and −1.9 ppb in spring, using TROPOMI-based updates. Combined with trans-Pacific wind patterns, the effects of the NO_x emissions inversions on modeled O₃ suggest potential implications of uncertain Asian emissions estimates for US air quality management and emphasize the impacts of biases in satellite retrievals on inverse modeling systems.

Figure 11Changes in 2019 season-average free-tropospheric O₃ concentrations (averaged between 750 and 250 hPa) simulated over the North Pacific Ocean using lightning and anthropogenic NO_x emissions inferred with OMI or TROPOMI observations, relative to simulations using prior ANO_x emissions and updated LNO_x emissions. Differences are shown for winter (DJF), spring (MAM), summer (JJA), and fall (SON). Arrows depict season-average free-tropospheric winds (750–250 hPa). Star marker indicates location of Trinidad Head, California.

At the Trinidad Head, California, a location where atmospheric composition is relatively unaffected by local emissions sources and is responsive to trans-Pacific pollution transport (Fig. 11), differences in modeled daily average free-tropospheric O₃ concentrations can reach +5 or −3 ppb. Figure 12 compares CMAQ-modeled vertical O₃ profiles to observations from 39 ozonesondes launched at Trinidad Head in 2019 (WOUDC, 2019). Relative to the CMAQ simulation using prior emissions, NO_x emissions updates inferred from OMI and TROPOMI data can improve the model's ability to reproduce ozonesonde O₃ distributions measured from the site, in particular during winter and spring, when the discrepancies between modeled and observed concentrations are largest. These impacts on modeled vertical O₃ profiles are largely driven by changes the modeling framework's updates to lightning NO_x emissions. The inferred LNO_x increases from each satellite improve O₃ biases, while subsequent anthropogenic updates have smaller impacts, suggesting that biases in O₃ could be driven by background NO₂ composition in the model and not solely by long-range transport resulting from anthropogenic emissions.

Figure 12Season-average vertical O₃ concentration profiles modeled by CMAQ and measured by ozonesondes launched at Trinidad Head, California, in 2019. Vertical distributions are shown for simulations using prior emissions (Prior), lightning and anthropogenic NO_x emissions inferred with OMI data (OMI-inferred), and lightning and anthropogenic NO_x emissions inferred with TROPOMI data (TROPOMI-inferred). Modeled season-average profiles are shown during winter (DJF), spring (MAM), summer (JJA), and fall (SON) for days and times matching ozonesonde launches. Shading around sonde and prior emissions profiles represent the maximum and minimum O₃ at each pressure level. Map shows location of the Trinidad Head launch site.