Anthropogenic NO x emissions of China, the U.S. and Europe from 2019 to 2022 inferred from TROPOMI observations

Anthropogenic nitrogen oxide (NO x ) emissions are closely associated with human activities. In recent years, global human activity patterns have changed significantly owing to the COVID‐19 epidemic and international energy crisis. However, their effects on NO x emissions are not yet fully understood. In this study, we developed a two-step inversion framework using NO2 observations from the TROPOMI satellite and the GEOS-Chem global atmospheric chemical transport model, and inferred global anthropogenic NO x emissions from 2019 to 2022, focusing on China, the United States (U.S.), and Europe. Our results indicated an 1.68% reduction in NO x emissions in 2020 and a 5.72% rebound in 2021 across all regions. China rebounded faster than the others, surpassing its 2019 levels by July 2020. In 2022, emissions declined in all regions, driven mainly by the Omicron variant, energy shortages, and clean energy policies. Our findings provide valuable insights for the development of effective future emission management strategies.


Introduction
Nitrogen oxides (NO x = NO + NO 2 ) are significant atmospheric pollutants that have a profound impact on human health and serve as crucial precursors of ozone and nitrate aerosols (Shukla et al 2022).Anthropogenic emissions from sectors such as transportation, industry, and fossil fuel combustion dominate NO x sources (Miyazaki et al 2012, Zhang et al 2023b).However, existing globally harmonized NO x emission inventories only cover data up to 2019, failing to encompass the influence of the COVID-19 epidemic and other significant factors affecting global atmospheric pollutant emission changes in recent years (Forster et al 2020, Qu et al 2021, Zhang et al 2021, Tzortziou et al 2022).In addition, bottom-up emission inventories for the available years have larger uncertainties and significant discrepancies between different studies (Elguindi et al 2020, Qu et al 2022).Consequently, studies on longterm changes in emissions before and after the pandemic have been severely hampered.
Satellite NO 2 observations offer an effective topdown approach to evaluate recent NO x emissions.The tropospheric monitor of the TROPOMI satellite provides enhanced spatial resolution and lower noise measurements of atmospheric NO 2 column concentrations (Veefkind et al 2012, Sekiya et al 2022).In contrast, the OMI satellite meets the requirement for a long-term series of NO 2 concentration observations.Currently, these two satellite data sources dominate the studies on NO 2 concentrations (Van Geffen et al 2020, Ding et al 2022, Zhang et al 2023b).Various inversion methods such as plume and box models, mass balance, 4D-Var, and integrated Kalman filters employ satellite observations and atmospheric chemical transport models (CTM) to estimate atmospheric pollutant emissions (Martin et al 2003, Lamsal et al 2011, Duncan et al 2013, Ding et al 2015, Qu et al 2017, Gaubert et al 2020, Xue et al 2022).Several studies analyzed recent anthropogenic NO x emission trends using satellite observations (Forster et al 2020, Zheng et al 2020, 2021, Doumbia et al 2021, Chen et al 2022, Tzortziou et al 2022), but most focus on localized areas around the time of the first COVID-19 outbreak, leaving unexplored changes in global anthropogenic NO x emission trends in the years following the outbreak of COVID-19 and other factors influencing emissions.Since 2019, the global economy and human activities have been affected by the multi-year impact of COVID-19 and volatile international situations such as sudden conflicts and energy crises in 2022.However, there is still a lack of harmonized research on the impact of these changes on anthropogenic NO x emissions.
In this study, a two-step inversion framework was developed to infer global anthropogenic NO x emissions.Our framework employs the mass balance principle and utilizes the GEOS-Chem CTM to invert the monthly changes in global anthropogenic NO x emissions from 2019 to 2022.We employed the TROPOMI satellite NO 2 observations to constrain the CTM-simulated concentrations.After confirming the accuracy of our inversion by comparing it with satellite and in situ observations, we focused our analysis on three major NO x -emitting countries and regions: China, the United States (U.S.), and Europe and examined the spatial and temporal dynamics of their monthly anthropogenic NO x emissions from 2019 to 2022.

TROPOMI data
The satellite NO 2 vertical column densities (VCDs) used in this study were sourced from TROPOMI, part of the Copernicus Sentinel-5 Precursor (Sentinel-5P) mission.The European Space Agency and the Netherlands co-funded this mission.TROPOMI builds on the SCIAMACHY satellite instrument from the Royal Netherlands Meteorological Institute and OMI from the National Aeronautics and Space Administration.Launched in October 2017, TROPOMI provides NO 2 retrievals with a high spatial resolution of up to 7.2 × 3.6 km 2 (alongtrack × across-track) at nadir, and improved to 5.6 × 3.6 km 2 in August 2019 (Van Geffen et al 2020).Sentinel-5's sun-synchronous polar orbit crosses the equator at approximately 13:30 local time every 16 d, allowing global coverage in a single day (https://sentinels.copernicus.eu/web/sentinel/missions/sentinel-5p/orbit).
For this study, we employed v2.3.1, a reprocessing version of the TROPOMI retrievals sourced from the Sentinel-5P Product Algorithm Laboratory.We used the HARP toolkit of the data harmonization toolset for scientific Earth observation data to register the TROPOMI data, as in previous studies (Omrani et al 2020, Anderson et al 2023).The TROPOMI data were regrided to a resolution of 2.0 • × 2.5 • for alignment with the horizontal resolution of the GEOS-Chem model used in this study.To ensure high-quality inversion results, we only considered TROPOMI observations with a quality flag greater than 0.5, and a cloud fraction below 30% for inversion.

GEOS-Chem simulation
We used the GEOS-Chem model v14.0.0 (GEOS-Chem 2022), and global simulations were conducted using the standard full-chemistry model, with a horizontal resolution of 2.0 • × 2.5 • and 47 vertical levels.Our study used MERRA-2 meteorological data (Gelaro et al 2017) with a fine horizontal resolution of 0.5 • × 0.625 • and 72 vertical levels up to 0.01 hPa, including 14 levels located below 2 km altitude (Yang et al 2023) to drive the model.We merged 72 vertical levels of MERRA-2 into 47 levels from approximately 2 hPa to 70 hPa in every two or four grids and resampled the horizontal grids to 2.0 • × 2.5 • .The anthropogenic NO x emissions inventory for 2019 was derived from the Community Emissions Data System version 2 (CEDSv2) (McDuffie et al 2020).For natural source NO x emissions, the wildfire emissions inventory was obtained from the GFED4 emissions inventory (Randerson 2017), soil NO x emissions was generated using the algorithm developed by Hudman et al (2012), and lightning NO x emissions largely followed Murray et al (2012).We applied the TROPOMI tropospheric averaging kernel to smooth the vertical layers of the simulated concentrations and integrated the vertical layers using the tropopause pressure of TROPOMI to obtain the simulated NO 2 VCDs.The TROPOMI tropospheric averaging kernel was computed as A trop = A • AMF total /AMF trop , where A denotes the TROPOMI averaging kernel, the AMF total and AMF trop denote total and tropospheric air mass factors, respectively (Eskes andBoersma 2003, Van Geffen et al 2022a).To reduce simulation errors, we performed an initial simulation for six months prior to the study period.Our study specifically focused on NO 2 concentrations in historical diagnostics output.Details of the GEOS-Chem model are provided in text S1 of supporting information.

Inversion model framework
In this study, we developed a two-step inversion framework that combined TROPOMI satellite observations of NO 2 VCDs with GEOS-Chem simulations to estimate global anthropogenic NO x emissions.In the first step, the anthoropogenic emission for one year without available inventory is updated using the annual ratios of TROPOMI NO 2 VCDs in each grid between that year and the base year.In the second step, the relationship between NO 2 VCDs changes and NO x emissions is calculated using the GEOS-Chem model, and the emissions of each grid are optimized again using a finite-difference massbalance (FDMB) approach (Lamsal et al 2011).The GEOS-Chem model quantifies the sensitivity of NO 2 VCDs to NO x emissions by calculating the simulated NO 2 VCDs changes for a fixed percentage change in NO x emissions.Subsequently, anthropogenic NO x emissions of each grid are allocated based on the proportion of anthropogenic to natural NO x emissions within that grid.To ensure precision, we conducted simulations at hourly intervals, and sampled the simulations corresponding to the time and grid of each satellite observation.Subsequently, we averaged the sampled simulations for each day to generate monthly data.
We excluded data that deviated significantly from the mean plus or minus two standard deviations of the sectoral emissions involved in the calculation.This exclusion was based on the original model framework and aimed to prevent regions with excessively high emissions from disproportionately influencing the calculation process.In the method, the sum of the corrected emissions of individual sectors was scaled to be consistent with the total emissions of the inversion.This approach ensures that highemission regions do not introduce significant bias, because they are not directly involved in the calculation of individual sector emissions.In this study, we applied the two-step inversion framework to invert the anthropogenic NO x emissions from 2020 to 2022 and optimized the emissions in 2019 using only the second step.
To validate the applicability of the inversion framework in our study region, we conducted an observing system simulation experiment (OSSE) (Atlas 1997).We reduced the 2019 CEDS inventory by 30% to represent the true emissions for 2020.The inversion results demonstrate an 91.2% reduction in prior errors (figures S1 and S2).Additionally, expanding the independent 2018 HTAPv3 inventory (Crippa et al 2023) as prior emissions and CEDSv2 inventory as true emissions for 2019 led to an 81.5% reduction in prior errors (figure S3).These OSSE results indicate that our inversion framework could effectively reduce the prior uncertainties.The inversion model framework detailed described in text S2 in the supporting information.

Uncertainty estimation
Our inversion framework encountered uncertainties originating from two primary sources: satellite observations and the inversion methodology.Although TROPOMI boasts a high signal-to-noise ratio and meets the design bias requirements (<10%) (Zhao et al 2020), it still underestimates tropospheric NO 2 levels by approximately 23% in polluted regions, which is attributed to biases in cloud pressure inversion, surface albedo climatology, and low-resolution prior profiles derived from global simulations (Van Geffen et al 2022b).Therefore, we conducted an additional inversion experiment with enlarged TROPOMI NO 2 VCDs, and treated the inversion result as the upper bound of the uncertainty.The inversion process is also subject to uncertainty, primarily stems from missing satellite observations and uncertainties in the CTM.For example, the reduced effective grids of TROPOMI in winter at high latitudes may have affected the spatial distribution of the results.Based on the OSSE experiment, despite our inversion framework can reduce the prior bias by 91.2%, an uncertainty of 8.78% remained in the inversion method, and it was considered as the bottom bound of the uncertainty in this study.

Inversion evaluation
To assess the effectiveness of the inversion, we compared the simulated NO 2 VCDs using the CEDS anthropogenic emissions as prior emissions and inverted anthropogenic NO x emissions as posterior emissions against the TROPOMI satellite observations of NO 2 VCDs (figures 1(a)-(c)).The NO 2 VCDs in the Northern Hemisphere experienced a notable decline in 2020, followed by a rebound after 2021, ultimately reaching levels comparable to those observed in 2019 (figure S4).The simulation in 2019 using the CEDSv2 inventory was significantly different from the satellite-observed NO 2 VCDs, indicating a large uncertainty in the bottom-up emission inventory (figure S5).The posterior simulations from 2019 to 2022 in the study area exhibited smaller deviations from the TROPOMI satellite observations.Among the three regions, China and Europe had larger average deviations (4.13% and 3.42%, respectively), and the U.S. had a smaller average deviation (0.27%).This suggests that our two-step inversion framework is effective in capturing anthropogenic NO x emissions in regions that are strongly influenced by human activities.
Compared with prior simulations, posterior simulations of NO 2 VCDs exhibited significant improvements.In China, the mean bias (MB) decreased by 94.0%.The coefficient of determination (R 2 ) increased from 0.40 to 0.95, and the root mean square error (RMSE) decreased by 0.22 (Pmolec cm −2 ).In Europe and the U.S., the posterior simulations of NO 2 VCDs also demonstrate improvement, with MB decreasing by 64.3% and 94.6%, R 2 improving from 0.49 to 0.86 and from 0.16 to 0.91, and RMSE decreasing by 0.32 and 0.11 (Pmolec cm −2 ), respectively.
To validate the performance of the inversions independently, we collected ground in-situ observations to evaluate the accuracy of both prior and posterior simulations over China, the U.S., and the European Union (E.U.).The In-situ observations in there three regions were obtained from the National Urban Air Quality Real-Time Release Platform of China, the U.S. Environmental Protection Agency, and the European Environmental Agency, respectively.The evaluation involved linearly fitting the monthly average time series of in-situ observations from 2019 to 2022 with the simulated surface NO 2 concentrations of the corresponding grid cells for both prior and posterior emissions.Figure S6 illustrates the difference between posterior and prior results of R 2 and relative RMSE for the three regions to reflect temporal consistency.Most stations exhibited a higher fitting accuracy with posterior simulated concentrations, indicating improved accuracy after inversion.The decline in validation accuracy in the Nordic region may be due to the absence of a satellite grid at high latitudes.
We also compared the concentrations at each site with those of the corresponding modeled grid averaged over the study period (figures 1(d)-(f)) to assess the spatial consistency of the inversion results.When multiple sites were present in one model grid, the average concentrations were used for fitting.The results showed that both the prior and posterior simulations underestimated the surface concentrations, but the posterior simulations effectively reduced the underestimation and showed better agreement with the in-situ observations.This underestimation may be due to the coarse spatial resolution of the simulations, resulting in large differences in the spatial representation between the in-situ observations and the simulations.Ground sites typically use the chemiluminescence monitoring method to estimate ground-level NO 2 concentrations, which can lead to an overestimation of ground-level concentrations during afternoon hours (Lamsal et al 2008).The TROPOMI observations also transitioned in the afternoon; therefore, this underestimation could be partly caused by the overestimate in in-situ observations.Additionally, satellite observations used to constrain the inversion were underestimated by an average of 23% (Van Geffen et al 2022b).We increased the satellite-observed NO 2 VCDs by 23% and inverted the anthropogenic NO x emissions (figure S7).After enhancing the satellite constraints, the posterior concentrations were slightly closer to the groundbased observations, with the MB and RMSE decreasing by only 5.6% and 5.8%, respectively.Therefore, the uncertainty in satellite observations is not the primary cause of the underestimation.
Furthermore, we compared the inverted emissions in mainland China with the recently released MEIC inventory for 2019-2020 (Zheng et al 2018) as shown in figures S8 and S9.The results indicate that the inverted emissions in 2019 effectively addressed the underestimation of emissions in China compared to the prior emissions inventory.However, the inverted NO x emissions remained lower than the MEIC inventory.After considering the uncertainties in the inverted results, the MEIC inventory is close to the upper bound of the uncertainties.Figure S9 shows a comparison for the spatial distribution of the prior and posterior emissions against the MEIC inventory in 2019.Compared to the prior emissions, the posterior emissions have lower differences in most grids.However, it also could be found that in the developed regions and most provincial capital cities, the posterior emissions are much lower than the MEIC inventory, one possible reason is that MEIC also overestimated the emissions in these regions (Feng et al 2024).Overall, independent validation through in-situ observations and comparison with the MEIC inventory provides additional evidence of the improved accuracy achieved through the inversion framework, highlighting its effectiveness in estimating anthropogenic NO x emissions and simulating atmospheric NO 2 concentrations.

Seasonal variations of emissions
Figure 2 provides an overview of the total monthly anthropogenic NO x emissions from the terrestrial areas of China, the U.S. and Europe.This reveals distinct seasonal emission patterns for each region.The margin of uncertainties in the emissions primarily arises from the underestimation in satellite observations and uncertainties in the inversion process, which were calculated to be 13.6% and 3.5% in China, 25.7% and 4.6% in the U.S., and 20.6% and 16.3% in Europe, respectively.In these three regions, the emissions were generally higher during the cold season than during the warm season, which can be attributed to the increased demand for heating and fuel combustion during the colder months.
Excluding China, the seasonal trends in anthropogenic NO x emissions for the other regions remained consistent over the four years.China exhibited a more complex monthly variation in emissions.This complexity can be attributed to the stringent control policies implemented in response to the COVID-19 pandemic in early 2020 (Feng et al 2020), with the epidemic's impact becoming the dominant factor influencing anthropogenic NO x emissions.Although epidemics also influence emission changes in other regions, seasonal variations remain Y Mao et al the primary driver.The results indicated that in 2020, all three regions had the lowest anthropogenic NO x emissions, with a total decrease of 1.68% compared with 2019, followed by a total increase of 5.72% in 2021.This trend aligns with the global anthropogenic CO 2 emission trends reported by the United Nations (IEA 2023), highlighting the significant impact of the initial COVID-19 outbreak on human activities across all regions.
This emission trend corresponds to the initial COVID-19 outbreak in China and the subsequent implementation of control policies.China was the first country to be affected by and respond to the outbreak, resulting in a significant reduction in emissions from transportation, fuel combustion, and other sectors during the implementation of control policies (Feng et al 2020), which shifted as work and production gradually resumed in July and August 2020.From June to December 2020, China's monthly emissions saw a significant increase, surpassing 4.53% of the same period in 2019, whereas other regions still showed lower emissions than in 2019.According to China's official export data, the country experienced seven consecutive months of export growth since June 2020.Total exports in 2020 reached a recentyear record, showing a 4% increase from 2019.The rebound in China can be partly attributed to the increased exports resulting from the time difference in the impact of the pandemic.China's emissions trend in 2022 is similar to that in 2020, which is due to the wide-spread Omicron variant of COVID-19 in China.Economic recovery after August led to a new rebound in China.The intricate interplay between the COVID-19 pandemic, control policies, and economic resumption contributed to the unique emission patterns observed in China during the study period.Understanding these dynamics is essential to assess the effectiveness of emission control measures and their impact on regional air quality.
The NO x emissions in Europe and the U.S. from 2019 to 2022 also revealed significant trends in response to the COVID-19 pandemic and changes in the international situation.Although seasonal variations in NO x emissions in the U.S. and Europe remained relatively stable, there were notable fluctuations in emissions between different years.In 2020, a global decline in industrial activity and energy demand due to the COVID-19 pandemic resulted in lower emissions in both the U.S. and Europe than in 2019, with reductions of 3.7% and 5.2%, respectively.In 2021, emissions rebound significantly in response to economic stimulus measures and widespread vaccination efforts, surpassing pre-pandemic levels by more than 4.6% and 4.0%, respectively.The NO x emissions rebound in 2021 proves that after a long period of stagnation, the global economy stimulated overall growth in energy, transportation and industrial demand, which was the primary driver of global NO x emissions.The United Nations' Greenhouse Gas' Report reached the same conclusion (IEA 2023).
By 2022, NO x emissions in the U.S. and Europe unexpectedly decrease by 1.1% and 1.6%, respectively.This decline can be attributed to several factors.Economic activity stabilized in 2022 after a year of recovery, leading to reduced energy and industrial demand.Moreover, global energy constraints and disruptions in the traditional fuel trade, particularly owing to localized conflicts in 2022, played a significant role in reducing emissions, particularly in Europe.Although the NO x emissions in Europe during the first half of 2022 were comparable to those in 2021, they decreased in the latter half of the year following the ban on oil transportation from Russia.According to the U.S. EPA's National Emissions Inventory (NEI), U.S. NO x emissions have decreased by 3.3% since 2021.Detailed sectorial analysis revealed a 1.1% decrease in fuel combustion emissions and a 5.8% decrease in transportation emissions.Furthermore, the Inflation Reduction Act, enacted on 16 August 2022, increased investments in clean energy and introduced incentives for electric vehicles to promote cleaner transportation, thereby accelerating the transition to cleaner energy sources in the U.S.

Spatial distributions of emissions
The regional distribution of emissions aligns closely with the local population distribution (figures S10-S13) (CIESIN, 2018).China's emissions are predominantly concentrated in the southeastern coastal regions.Emissions are primarily concentrated in Western Europe.In the U.S., emissions are concentrated in the eastern region and the west coast.Notably, emission centers tend to form in large cities.
We compared the relative spatial distribution differences in total terrestrial anthropogenic NO x emissions from 2020 to 2022 with the 2019 emissions (figure 3).This also shows that recent changes in NO x emissions have been primarily driven by the impact of the COVID-19 pandemic and global energy shifts.Consistent with the findings in figure 3, there was a significant and widespread decline in NO x emissions in the regions in 2020, which was mainly attributed to the global outbreak of the COVID-19 pandemic.In 2021, anthropogenic NO x emissions exhibited signs of a rebound across all three regions, with notable increases in southern China, the southeastern and western coastal regions of the U.S., and parts of Russia and Eastern Europe.Emissions in Western Europe also increased, but did not exceed emissions in 2019.Emissions change in 2021 shows the opposite trend from 2020 (figure S14), where regions with rapid emissions growth coincided with areas severely impacted by the 2020 pandemic, indicating that emissions rebound along with economic recovery (IEA 2022).
In 2022, China experienced a significant decline in anthropogenic NO x emissions, which was largely attributed to the widespread spread of the Omicron variant of COVID-19 (figures S14).Stringent control measures were implemented in response, particularly in areas heavily affected by the variant, such as Shanghai and its surrounding regions (Tan andWang 2022, Lonsdale andSun 2023).Consequently, emissions in southeastern China, notably in the Yangtze River Delta region, decreased substantially by 6.85% during the first half of 2022.In contrast, Europe and the U.S. also observed lower NO x emissions in 2022, which are primarily influenced by factors such as climate change and the international energy crisis (Meng et al 2023, Zhang et al 2023a).The Russo-Ukrainian conflict directly contributed to a significant reduction of 11.0% in Ukraine's NO x emissions.In Europe, gas shortages resulting from the conflict, coupled with drought conditions and warm winters, led to reduced energy emissions, with Western Europe experiencing a 3.8% decrease and Russia a 3.6% decrease.In the U.S., emissions reductions have been driven by the transition from coal to natural gas combustion and the growth of clean energy sources.Notably, the deployment of clean energy technologies such as renewable energy, electric vehicles, and heat pumps in China and Europe has played a role in avoiding additional emissions (IEA 2023).

Conclusion
In this study, we propose a two-step inversion framework that utilizes the FDMB approach to estimate the global anthropogenic NO x emissions from 2019 to 2022.Our results demonstrate a high accuracy between NO 2 simulated by inverted anthropogenic NO x emissions with global tropospheric NO 2 VCDs and in-situ observations.We examined anthropogenic NO x emission changes in four major NO x -emitting regions.Our findings suggest that the COVID-19 outbreak, changes in the international energy situation, and national energy policies will collectively influence the trends in anthropogenic NO x emissions from 2019 to 2022.
There are several ways to improve and advance the future.First, enhancing the temporal and spatial resolutions of the inversion process and allocating emission changes among sectors can reduce the uncertainty and provide a more detailed analysis of anthropogenic NO x emissions.Additionally, integrating diverse data sources and complementary information can enhance the reliability and accuracy of inversion results.This may include ground-level observations, atmospheric measurements, or other relevant datasets that reduce the systematic errors in the NO x inversion framework.
Overall, this study presents a dependable inversion framework for analyzing anthropogenic NO x emission trends from 2019 to 2022, providing Y Mao et al valuable insights for air quality assessment and policy development.

Figure 1 .
Figure 1.Comparison of prior and posterior simulations with TROPOMI NO2 VCDs and in-situ NO2 observations from 2019 to 2022 in China, the U.S. and Europe.(a)-(c) Seasonal variations of prior (blue) and posterior (red) NO2 VCDs simulations and TROPOMI observations (black) from 2019 to 2022 in (a) China, (b) the U.S., and (c) Europe.(d)-(f) Scatter plots of the prior (blue) and posterior (red) NO2 simulations versus in-situ observaitons averaged from 2019 to 2022 in (d) China, (e) the U.S., and (f) Europe, with slope, coefficients of determination, MB and RMSE for the linear fits given in the legend.

Figure 2 .
Figure 2. Monthly anthropogenic NOx emissions for (a) China, (b) the U.S., and (c) Europe from 2019 to 2022.The histograms in each figure show the annual emissions in each region.The shaded is the range of uncertainty for the inverted emissions.

Figure 3 .
Figure 3. Relative differences of total annual NOx emissions relative to emissions in 2019.(a)-(c) relative differences between 2020 and 2019 in China, the U.S. and Europe, respectively.(d)-(f) relative differences between 2021 and 2019.(g)-(i) relative differences between 2022 and 2019.