Observationally constrained global NOx and CO emissions variability reveals sources which contribute significantly to CO2 emissions

There has been a significant amount of research into trace gas assessment due to the various impacts that these have on the atmospheric environment^1,2, ecosystems³, climate change⁴ and even human health^5,6. Previous studies have made substantial advancements in constraining emissions with various spatial and temporal resolutions^7,8,9,10. However, there remains a need for approaches that incorporate high-resolution satellite data to achieve more accurate geospatial assessments of emission intensities across diverse regions. While there is a sufficient amount of work to evaluate well-known urban, industrial, and transport sources and large and clearly identified fires in areas that have access to many measurements, there are still many gaps in the Global South where measurements are sparse, and in regions throughout the world which are undergoing rapid economic, political, industrial, pandemic, and environmental changes^11,12. Precisely quantifying rapid changes in the temporal and spatial distribution of emissions is critical for evaluating extreme events. Neglecting these variations and relying only on long-term average values can introduce significant biases in calculations related to the atmospheric energy budget¹³, radiative forcing¹⁴, cloud cover¹⁵, rainfall formation¹⁶, and pollution event exceedances¹⁷.

Present emission inventories used by atmospheric and environmental communities for global, mesoscale, and local models, as well as for evaluating climate impacts and radiative forcing, are mostly built using bottom-up approaches. These inventories include both anthropogenic sources, such as EDGAR (Emissions Database for Global Atmospheric Research) and MEIC (Multi-resolution Emission Inventory for China), and fire emission source, such as FINN (The Fire Inventory from NCAR) and GFED (Global Fire Emissions Database)^18,19,20. They are constructed based on differing methodologies, which all rely heavily on statistical data and information of emissions factors, fuel consumed, etc. The fire-based emissions products also include some indirect satellite-derived data of fire activity or land cover change. However, all of these emissions datasets are not based on directly observed concentrations or columns of NO_x or CO. These methods often struggle to identify sudden pollution events in areas without any a priori source information, particularly in regions experiencing rapid changes or unexpected events⁸. Given the rapid changes in the climate, it has been repeatedly demonstrated that the bottom-up approach is not the best way to model and understand many significant atmospheric events.

Top-down studies have been used and found to be effective for very-long-lived species, such as N₂O (Nitrous Oxide) and CH₄ (Methane), and CFCs (Chlorofluorocarbons)^21,22. Top-down approaches for NO_x (Nitrogen Oxides) and CO (Carbon Monoxide) require knowledge of the atmospheric column at high spatial and temporal resolution^1,2, due to the fact that they are not well mixed throughout the troposphere. With appropriate observational data and knowledge of the first-order sources and sinks, the top-down approaches for shorter-lived species with lifetimes similar to NO_x (Nitrogen Oxides) and CO (Carbon Monoxide) can be effectively performed, as demonstrated in this work. However, the observations require sufficient robustness to quantify and bound their uncertainty so that the signal can be differentiated from noise. While ground-based measurements, such as those from AERONET (for BC)²³, TCCON (for CO) and Max-DOAS (for NO₂)^24,25,26, can enhance local emission estimates by providing higher quality data, their effects are limited by their low spatial density. There are recent direct scaling and 3D/4DVar approaches^27,28 for NO₂ (Nitrogen Dioxide) and AOD (Aerosol Optical Depth) that have shown improvements in capturing time series of known pollution events, such as urban air pollution episodes and wildfire emissions, although these methods have also been shown to frequently lead to spatial-temporal mismatches¹. However, these methods often struggle to identify sudden pollution events in areas without any a priori source information, particularly in regions experiencing rapid changes or unexpected events^29,30. Other studies have focused on Kalman Filters or other more advanced assimilation methods, which face challenges due to the need to quantify uncertainties in observational data and model parameters, factors that are often difficult to determine precisely³¹. While there are existing global-scale studies that have used top-down methods to constrain NO₂ and CO emissions^{32,33,34,35,36,37}, these studies are based on models that are not always available for public use and when accessible are hard to change or modify, produce results at lower spatial and/or temporal resolution, are not readily adapted to suit local emissions and environmental conditions or policies, and frequently make scientific assumptions about emissions ratios of NO to NO₂, as well as NO_x to CO. This work emphasizes a more flexible and accessible framework that can be broadly utilized by both scientific and applied communities, and across greater environmental and emissions conditions and standards.

NO_x and CO are two key factors in emission inventories related to ozone prediction, acid rain, carbon balance, hydroxyl (OH) radical and its impacts on the field of atmospheric chemistry, secondary aerosol formation, and both ecosystem and human health effects³². Compared with the pre-industrial period, CO emissions have increased 2 or 3 times³⁸, especially for biomass burning (from 47 to 99 Tg CO per year)². For the Southern Hemisphere, CO emission has increased 2 times than before but still has a significant uncertainty³⁴, and the total emission for mainland China, including unknown sources based on TROPOMI (Tropospheric Monitoring Instrument) products, is 24.75 ± 5.98 Tg NO₂ per year³⁹. However, some studies using satellite data have found that CO emissions have been on a downward trend in recent years, while NO_x emissions have not been stable, with some showing a large increase in Asia^10,40, and others localized decreases also in Asia.

This work aims to construct a newly constrained emission inventory based on direct measurements of remotely sensed columns of trace gases (NO₂ and CO) using a model-free, mass-conserving framework. The overall equation is based on a simple representation of physics, chemistry, dynamics, and in situ processing, all constrained together by the measured profiles. This method explicitly considers the ratios between NO, NO₂, and CO, therefore better accounting for the overall oxidative properties of the atmosphere where the emissions occur. Although challenges with vertical profile differences are unavoidable, the NO₂ to CO ratio serves as an effective indicator in biomass-burning regions, providing improved representation when both gases are analyzed together¹. Furthermore, this process calibrates the underlying model components across a wide range of emission magnitudes, source types, wind speeds, and UV radiation conditions by finding the smallest possible error in terms of the underlying partial differential equations, which still allows for effectively sampling the breadth of in situ atmospheric conditions. This process makes the simpler modeling approach used herein more representative and flexible than traditional models, which may not be calibrated for local conditions or under extreme events.

Spatial and temporal distribution of source areas

The regions include emissions from biomass-burning sources (Amazon, Southeast Asia, central Africa, and southern Africa), urban sources (eastern US, China (CO/NO₂), Europe), and industrial and energy-related sources (China (NO₂) and South Africa), as given in Fig. 1. The resulting time series exhibit both highly recurring patterns in time (biomass burning dominant) as well as random time patterns (urban, industrial, and high wind variability dominant). A good match is found between the climatological observed column concentrations over the respective SVD regions and the PCs over all four types (positive and negative of NO₂ and CO), as given in Fig. S2. The climatological mean and standard deviation of the spatial distributions of observed NO₂ and CO after filtering are displayed in Fig. S3. The mean and standard deviation of remotely sensed NO₂ and CO measurements compare reasonably well with both the merged emissions a priori from existing inventories (Fig. S1) and SVD₁ results in terms of geographic distribution.

Geographic distribution of all 15 subregions derived from SVD₁ including positive and negative of NO₂ and CO geographical decomposition signal.

Full size image

SVD₁ defines 15 unique geographic regions (Table 1) which include 76.5% of a prior NO₂ emission and 89.4% of a prior CO emission. Some high-emission pixels, particularly those associated with stable sources (e.g., continuous industrial emissions) or pixels affected by data gaps or data quality issues, are not fully captured in our statistical approach. This approach is designed to be unbiased toward the location, timing, and type of emissions. Furthermore, certain highly episodic long-range transport events that do not contribute sufficiently to the overall emissions variability across the 11-year dataset may also be excluded from SVD₁.

The relationship between emissions and satellite observed column concentration is computed via Eqs. (1) and (2). While, in general, regions with larger emissions have a larger mean observed column loading, this pattern does not exist everywhere, with contributions from meteorological conditions, source thermodynamics, and in situ processing also contributing. Across all regions, significant variations in the NO₂ to CO ratio are observed, likely due to the combined effects of regional differences in emission source types, the influence of different atmospheric aging on the species, varying upwind conditions, and varying different spatial loadings. In the first case, it is known that NO_x emissions are strongly related to the temperature of combustion, while CO is related partially to combustion temperature, as well as the total amount of fuel or biomass combusted. In the second case, it is known that the atmospheric chemical lifetime of CO is longer than that of NO_x. The third case acknowledges that upwind conditions may themselves also have significant amounts of emissions. The overall mixture of each of these three driving factors all play a role in the observed ratio of NO₂ to CO, as shown in Fig. S4.

Factors driving emissions estimation

In different regions, there are significant differences observed in the underlying thermodynamics, first-order atmospheric loss, and transport terms, including regions that have a similar level of economic development. This is consistent with environmental factors and anthropogenic drivers both contributing (i.e., climate, weather, type and location of local emissions source, duration of emissions, geography, UV radiation and temperature), creating a different set of underlying driving factors compared with bottom-up emissions approaches.

PDFs of the best-fit value of ({a}_{1}), ({a}_{2}), ({a}_{3p}) and ({a}_{3n}) of NO₂ are shown in Fig. 2, and demonstrate consistency with conditions expected in different source regions, allowing for results that are based on the local conditions and can therefore be used to improve existing bottom-up approaches or approach top-down approaches in a consistent manner. The range of coefficients is given across the 10th, 30th, 50th, 70th and 90th percentiles as a means to understand the range of variability of the underlying forcing terms. On a global basis, the respective values of ({a}_{1}) are 1.4, 2.4, 4.1, 8.5, 24.0, while the values in the Amazon and central Africa are 2.0, 4.6, 10.0, 18.3, 36.8 and 1.4, 2.2, 3.4, 5.9, 13.7, respectively, demonstrating a closer agreement with the small number of observations available than existing modeling studies^12,39.

PDF analysis of ({a}_{1}), ({a}_{2}[{hours}]), ({a}_{3{rm{n}}}[{km}]), and ({a}_{3{rm{p}}}[{km}]) of MCMFE NO_x over representative regions from SVD₁, red line represents the coefficients for each region, and the blue line represents all global coefficients, a Amazon; b central Africa; c China (NO₂); d South Africa; e southern Africa; f Southeast Asia.

Full size image

There are significant differences observed between ({a}_{1}) in the Amazon and in Southeast Asia, although both are considered clean during their respective non-biomass-burning seasons and driven by biomass burning of native and secondary forests⁴¹. One possible explanation for this is given by the temperature at which combustion occurs, with a critical transition occurring around 1200 °C⁴². This finding is consistent with work demonstrating that the Amazon may have large amounts of co-emitted methane from the stems of floodplain trees⁴³, which would allow the net combustion temperature of methane plus wood to exceed this threshold⁴⁴, while the combustion of pure wood in Southeast Asia does not. The findings are both further supported by the fact that ({a}_{1}) in the Amazon is higher than some industrial areas, and second by the more frequent pyro-convection in the Amazon compared with Southeast Asia.

Central Africa is different from other biomass-burning areas due to a broad mixture of sources (anthropogenic, small industrial, grass burning, biomass burning, and forest burning), making it difficult to identify a single value of ({a}_{1}) on a single day across the region. The resulting distribution is due to the high amount of variability on a grid-by-grid and day-by-day basis, and the statistics of ({a}_{1}) being similar overall to the global value herein. Southern Africa, on the other hand, is slightly lower due to a mixture of less grass and other low-temperature fires and a greater amount of industry and urbanization.

Another interesting point is that the region China (NO₂) is found to be lower than global values, which reflects two significant changes. First, the majority of sources are from industry, vehicles and residential sources, and second, this is a signal of increasing energy efficiency with lower efficiency combustion sources being phased out for higher energy efficiency⁴⁵. The region of China with the largest amount of variability in the ratio of NO_x to NO₂ is observed in the far western, energy-intensive areas, which have been undergoing considerable transition in terms of observed absorbing aerosols over the same timeframe⁴⁶, indicating efforts to reduce emissions overall and improve environmental standards.

The coefficient ({a}_{2}) represents the lifetime of NO₂, typically ranging from a few hours to several dozen hours, primarily influenced by geographical location and emission source characteristics. Globally, the 10th, 30th, 50th, 70th and 90th percentiles of ({a}_{2}) are 3.0, 7.6, 13.1, 21.4, and 36.3 h, respectively. In the Amazon and China (NO₂), these percentiles are 1.6, 4.8, 9.3, 15.7, 32.4, and 36.8 h, and 4.8, 10.7, 17.7, 28.6, and 37.3 h, respectively. The lifetime of NO₂ is notably shorter in biomass-burning regions compared to others, with a majority of ({a}_{2}) values falling below 20 h. This is consistent with the general lifetime being shorter due to due to more rapid oxidation and uptake of NO₂ onto co-emitted particles in biomass-burning regions. It is also consistent with the higher plume-rise heights observed in these regions, which leads to increased overall dispersion into the third dimension, especially so when it rises above into the generally cleaner free troposphere. This term is consistent with both chemical loss due to OH, photolysis, mixing into less polluted air, and transfer/oxidation from the gas phase into nitrogen-based particulate matter. Therefore, regions with a lower ({a}_{2}) generally are those that have a greater impact of nitrogen on the behavior and distribution of NO₂ in the atmosphere and climate.

The coefficient of both ({a}_{3n}) and ({a}_{3p}) represent the net transport out of and into the region of interest, respectively. Due to the shorter lifetime of NO₂, the overall transport is expected to be shorter than CO when co-emitted at the same place and time. The 10th, 30th, 50th, 70th and 90th percentiles of ({a}_{3n}) and ({a}_{3p}) are −77.9, −23.9, −11.5, −5.6, −1.9 km and 1.9, 6.1, 11.9, 24.5, 73.9 km, respectively.

The five percentile values of ({b}_{1}) show a notable difference between global and Amazon regions, with values of −136.7, −56.5, −30.6, −17.2, −6.7 h for the global dataset, and −82.0, −35.4, −22.0, −11.5, −3.6 h for the Amazon, respectively. However, in specific areas with diverse emission sources like southern Africa, the five percentile values are −144.1, −62.4, −34.3, −19.5, and −9.2 h, showing a distribution of ({b}_{2}) that is highly consistent with global patterns.

There are two important findings related to transport distance, as observed for both NO_x and CO. First, the transport distance of biomass-burning regions (Amazon, Southeast Asia, etc.) has a lower value than other classifications (urban, industrial, and mixed), consistent with the more rapid removal of NO_x on the surfaces of co-emitted aerosols and faster chemical loss due to more concentrated emissions. Also observed is the decay around the edges of plumes in the middle troposphere being faster than near the surface, due to the lower background concentrations⁴⁷. Second, in China (CO/NO₂), China (NO₂), and the eastern US, even though these have large local sources, there is still a net import of NO_x from other regions of the world, a factor only previously considered in idealized studies¹³, or in terms of rare long-range transport events¹. This implies that long-range transport of moderate pollution events may be more important than the global modeling community is currently about to capture. Europe, on the other hand, is still found to be a region of net emissions export.

The range of variation for ({b}_{1}) indicates significant uncertainty in global CO emissions, with values spanning from 0.5 to 1.3 (Fig. 3). In specific, higher values are observed in China (NO₂) and South Africa. One possible reason is that both regions have high amounts of atmospheric oxidation potential due to their large industrial bases, coupled with large amounts of natural and anthropogenic VOCs, leading to considerable rapid secondary production of CO¹³. A second reason for this is related to sensor accuracy under high CO conditions⁴⁸, due to a combination of reduced radiance in and around the 2300 nm waveband due to high cloud coverage, high AOD, and rising global methane (also retrieved in the same waveband)⁴⁹. This is consistent with the fact that both regions have large amounts of diverse aerosol sources due to industry and have large coast lines allowing for intermittent thick cloud cover. Additionally, in South Africa, there is also a period of the year when upwind biomass burning from other areas transports CO into the region, during which it may be of a similar order of magnitude to the local urban and industrial sources.

PDF analysis of ({b}_{1}), ({b}_{2}[{hours}]), ({b}_{3{rm{n}}}[{km}]), and ({b}_{3{rm{p}}}[{km}]) of MCMFE CO over representative regions from SVD₁, red line represents the coefficients for each region, and the blue line represents all global coefficients, a Amazon; b central Africa; c China (NO₂); d South Africa; e southern Africa; f Southeast Asia.

Full size image

Additionally, due to its longer lifetime, CO is observed to be transported further, as observed in the magnitude and distribution of coefficient ({b}_{3}). The net input and net output are generally consistent across all six regions in Fig. 3, but in the Amazon region, the dynamic transport shows less significance in the MCMFE model, whereas in South Africa, it plays a more significant role. This difference can be attributed to the fact that the Amazon dataset covers late August to early November, a period of weak monsoon activity, while the location of South Africa at the southernmost tip of Africa is exposed to stronger sea breezes during the same time period. This physical difference leads to a difference in the MCMFE-based coefficient derivation during these specific times in these specific regions.

Differences between MCMFE and existing inventories

The retrieved NO_x and CO emissions shown in Figs. 4 and 5 represent intensities tied to specific coefficients derived from the SVD analysis, capturing temporal variations across different local times of the year in each region. These results reflect the dynamic nature of emissions influenced by local geographic, meteorological, and source-related factors. Standard deviations, indicating emission variability, are provided in Figs. S5 and S6 for additional clarity. The different coefficients (10th through 90th percentile) correspond to different local times of the year in each region. Based on this perspective, biomass-burning regions exhibit significant differences during different times of the year. In the Amazon and Southeast Asia, the NO_x emissions on the 10th are both high, while one is also high on the 30th and the other on the 50th consistent with^50,51. South Africa exhibits a peak on the 90th, due to a mixture of local and transported biomass burning. The mostly urban regions are more stable throughout the year compared with biomass burning, although there are still differences across the percentiles. First, the timings of the extreme peak values in the biomass-burning areas are consistent with individual findings on the ground of when these fires occur, and their overall duration⁵². Second, the emissions during non-peak times will be lower than or similar to current emission inventories, while the values during peak times will always be much higher. This is due to the fact that most inventories currently in use today are produced using low temporal resolution data, and they are not able to capture the magnitude of extreme events as well⁴¹. Another factor is that existing inventories tend to overestimate known individual large sources while ignoring or not addressing a larger number of small sources. Although the grid-by-grid approach in this study identifies emissions in regions such as the Middle East, Northwest China, and Australian mining areas, these regions were excluded from the primary analysis due to their relatively smaller scale and insufficient data to yield robust MCMFE results. It is hoped that additional remote sensing products in the future will allow successful emissions inversions over these regions as consistent with⁵³.

Mean of MCMFE NO_x emissions with different percentiles coefficients based on the merged a priori emissions and MCMFE in 2010 [µg · (m⁻² · s⁻¹)]. a The 10th percentile; b the 30th percentile; c the 50th percentile; d the 70th percentile; e the 90th percentile.

Full size image

Mean of MCMFE NO_x emissions with different percentiles coefficients based on the merged a priori emissions and MCMFE in 2010 [µg · (m⁻² · s⁻¹)]. a The 10th percentile; b the 30th percentile; c the 50th percentile; d the 70th percentile; e the 90th percentile.

Full size image

The findings with respect to CO emissions are somewhat similar to those with NO_x emissions in terms of timing of the peaks when analyzing the results over different biomass-burning areas. In these areas, the major differences are related to the ratio, which is different in each biomass-burning area, which reflects the different combustion sources and conditions. In contrast to NO_x, the CO emissions observed in industrial areas are found to have a higher value than most a priori studies, indicating that assumptions of highly efficient use of coal into a final CO₂ end product may not actually occur on the ground⁴². The relatively temporally constant CO emissions in these regions, as compared with biomass burning and urban regions, may require further work trained more locally to fully capture these persistent emissions, indicating that the results herein, although already larger than existing inventories, still yield an underestimate in these regions.

The MCMFE results and a priori inventories for NO_x and CO at each percentile are shown in Table 2 and Table 3. In terms of NO_x, the temporal minimum of emissions is observed in Europe (1% of current inventory) while the temporal maximum is observed in the Amazon (15.1 times current inventory), with an average across all regions of about 2.56 times of the priori dataset. The emissions results based on the MCMFE model in China (CO/NO₂) are much lower than current inventories, consistent with the fact that the region is normally heavily polluted, and the extremes observed by the MCMFE method are, in fact, the smaller number of very clean days. In terms of CO emissions, the total emissions in China (CO/NO₂) inversion are the lowest (8% of current inventory), while the temporal maximum is observed in Central Africa (12.6 times of the emission priori), with an average of 2.36 times the global inventory, and the time series of MCMFE and the priori emissions comparison in different regions over time are shown in Fig. S7 (NO_x) and Fig. S8 (CO).

Estimation of additional CO₂ production via CO oxidation

In the atmospheric environment, all emitted CO is fully oxidized to CO₂ by OH. In addition, as the largest sink of OH, changes in CO also have indirect effects on the lifetime of methane and ozone, which further impact radiative forcing, although these indirect effects are not further considered herein^54,55,56. In comparison with EDGAR CO₂ emissions (Table 3), the increase in CO emissions in Amazon and Central Africa, when chemically converted into CO₂ in situ, has a statistically significant impact on the actual CO₂ emissions. This value has a maximum temporal increase as high as 22.% and 10.% respectively, and an annual increase of 6.1% and 3.5%, respectively. CO in other regions also has an impact on CO₂ emissions, although the value is found to be under 1%, except for, as noted, the fact that industrial sources are underestimated in this work. This finding, we hope, will help the community address the assessment as to why there are still large uncertainties in both the loadings of CO₂ and longwave radiative forcing.

Nitrogen dioxide (NO₂) and Carbon Monoxide (CO) are important due to their contributions to atmospheric oxidation and methane, as well as aerosol formation and growth. The current generation of emissions estimations from both bottom-up and large-scale averaged top-down and approaches do not provide a sufficiently accurate, robust, and precise assessment of rapidly changing or extreme emissions events in both space and time. This work employed a first-order model-free, mass-conserving equation, using day-by-day and grid-by-grid observations from OMI and MOPITT and underlying properties of the environment in an unbiased manner to derive and attribute global emissions of NO_x and CO due to extreme events or regions undergoing significant change, the cases in which current emissions inventories are currently most uncertain.

This work identifies 15 regions globally and classifies them into urban, industrial, biomass burning, mixed, and long-range transport types, consistent with their different properties in terms of emissions thermodynamics, first-order atmospheric loss, and long-range transport. Biomass-burning areas are found to have a higher amount of NO and shorter lifetime and a wider range of transport distances compared with the other regions, consistent with co-emitted heat inducing a rise of emissions into the middle atmosphere. Atmospheric transport is also observed to relate to physical geography, meteorology, precipitation, time of year, and source type, allowing identification of mixed source types. Furthermore, the results show that classifying emitting regions into developed and developing economies is insufficient, with differences observed between the USA and EU, as well as industrial regions in Northern and Central China.

The results yield an inventory that captures both geographical and temporal variability uniformly for NO_x and CO with medium confidence. Emissions are captured with medium to low confidence in regions with a previously identified source type but incorrect timing (i.e., where the timing of emissions is lagged from the database) or duration of the peak event (i.e., the center of the inventory’s timing is correct, but its duration is wrong), where both changes in driving factors over space and time, and downwind plume transport are identified as underlying reasons. There is also a significant amount of emissions analyzed to occur outside of urban areas, which is subsequently advected into urban regions, a phenomenon which has been discussed in idealized studies, but is not consistently found in observational studies and presently is not included in most modeling studies, which assume clean upwind conditions.

Due to its chemical transformation in situ into CO₂, the resulting significant changes in CO emissions from biomass-burning areas yield significant changes in the net country-by-country CO₂ emissions over some countries studied. The impacts on the national reported CO₂ range from −5% to 21.5% of CO₂ emitted in the respective regions based on the time of the year. This net change may lead to additional erroneous estimates of direct global radiative forcing, as well as further indirect effects due to the impact of CO on atmospheric oxidation and methane, which are not discussed herein.

The work then uses CO observations from MOPITT (Measurement of Pollution in the Troposphere) and NO₂ observations from OMI (Ozone Monitoring Instrument), in combination with mass conserving equations, reanalysis meteorology, and both urban and biomass burning a priori emissions data to produce a grid-by-grid and day-by-day (NO_x) and week-by-week (CO) global emissions products. These products illustrate the spatial distribution of the sources that contribute to the changes in emissions around the globe and include: industrialization, energy, transportation, residential, biomass burning, forest fires, and mixed types^8,47. For China, a priori emissions are from the combination of FINN (biomass burning) and MEIC (anthropogenic) while for other regions, FINN is coupled with EDGAR (anthropogenic). This process quantifies the contributions of physical, chemical, and long-range transport effects, using remotely sensed observations to generate a new optimized, long-term, high-resolution emissions inventory and uncertainty range.

Remotely sensed observations

The OMI on the NASA Aura satellite observes in the near-ultraviolet/visible spectrum with a 13 × 24 km² coverage^57,58 and has a ~1:30 p.m. local overpass time. OMI has been used to monitor various atmospheric trace gases in the troposphere, including total column NO₂. In this study, we use OMI Level 3 NO₂ data from 2006 to 2016. To ensure data quality, screening is performed to ensure cloud coverage is less than 30% and QA (Quality Assurance) larger than 75%. The NO₂ observations are linearly interpolated onto a 0.1° × 0.1° grid.

Since there is no way to directly observe NO, assumptions are made based on the pseudo-steady-state assumption to link NO to NO₂³⁹. In the boundary layer, NO_x is short-lived, with a lifetime under 1 day, which rises to up to 3 days when injected directly into the free troposphere due to biomass burning^1,59. Recent studies have utilized column measurements of NO₂ from OMI and TROPOMI to constrain NO_x emissions, making strong assumptions regarding the NO to NO₂ ratio. These studies focus on specific geospatial domains, using well-validated a priori measurements and detailed knowledge of local conditions, particularly in urban⁶⁰, energy-intensive⁹, and strongly biomass-burning regions⁶¹. While there have been top-down studies using OMI and TROPOMI data to constrain NO_x emissions in various global regions, including North America and Europe, much of the detailed high-resolution analysis remains focused on Asia^62,63. Furthermore, there are very few global studies that provide daily or weekly top-down emissions at high resolution. It is expected that due to variations in emission magnitudes, technological and industrial levels, and local environmental conditions, the assumptions applied will need to be adjusted to accurately reflect the characteristics of emissions sources in different parts of the world and during times of the year.

MOPITT on the NASA Terra satellite detects concentrations of CO in the NIR (Near-infrared Radiation) and FIR (Far-infrared Radiation) regions and has a ~10:30 a.m. local overpass time⁶⁴. The data used herein is observed twice daily (day and night) at 1° × 1°, with measurements from 2006 to 2016, and interpolated into 0.1° × 0.1° resolution (Version 8, level 3, TIR (Thermal-infrared radiation) + NIR, daytime).

A priori emissions inventories

MEIC is a high-resolution inventory of anthropogenic air pollutants and carbon dioxide emissions in China, covering more than 700 anthropogenic emission sources including SO₂ (Sulfur dioxide), NO_x, CO, NMVOCs (Non-methane volatile organic compounds), NH₃ (Ammonia), PM_2.5, PM₁₀, BC (Black carbon), OC (Organic carbon) and CO₂^65,66. This work uses NO_x and CO emission data from V1.3. This data is then linearly interpolated from 0.25° × 0.25° to 0.1° × 0.1° resolution.

EDGAR is a European Commission database providing global past and present anthropogenic air pollutant and greenhouse gas emissions database. EDGAR data is based on the IPCC’s national greenhouse gas emissions inventories and international statistics of economic activity and emissions factors. It then relies on a bottom-up approach to estimate global emissions data. This study utilizes NO_x and CO emissions data from version 4.3.2 for 2010²⁰, the only year for which monthly data at a 0.1° × 0.1° resolution is available.

FINN provides a daily 1 × 1 km emissions globally of open biomass burning based on FRP (Fire Radiative Power) observed and land cover types measured by MODIS (Moderate Resolution Imaging Spectroradiometer)¹⁹, as well as emissions factors and assumptions about combustible material. This work uses FINN V1.5 data. The final results are aggregated up to 0.1° × 0.1° resolution.

Geospatial properties of the merged a priori emissions inventories of NO_x and CO are shown in Fig. S1. In general, the areas of high emissions are located in regions with high population density, rapid development, or extensive forested areas, aligning with the distribution patterns of NO_x and CO in 2010.

ERA5 reanalysis meteorology

ERA5 (fifth generation ECMWF atmospheric reanalysis) provides reanalysis products that include multiple variables for the global climate and weather for the past decades⁶⁷. It uses the data assimilation to merge the model data and the observations all over the world, which can produce the newest datasets of the atmosphere state. this work uses U-component and V-component of wind from ERA5 hourly data on pressure levels in 2010 at a resolution with 0.25° × 0.25°, and then interpolated into 0.1° × 0.1° resolution.

SVD (singular value decomposition) approach

SVD is a s a fundamental mathematical technique that employs orthogonal basis functions to decompose data matrix to obtain the factors that have the greatest influence on its variability. This method has been widely used in the field of atmospheric remote sensing to extract key information (i.e., monthly average climatological AOD, weekly average climatological CO and daily average climatological NO₂)^1,2. In this work, we used the method to simultaneously extract the temporal and spatial variations of the total column loads of NO₂ and CO after filtration to more accurately identify the typical source emission regions on a global scale during 2006–2016.

The Singular Value Decomposition (SVD) process is a powerful mathematical tool used to decompose a data matrix, in this case representing spatial-temporal column loading data for NO₂ and CO, into three component matrices: (A=Usum {V}^{T}). The matrix (A) is organized by spatial (grid) locations over time, with each entry containing column loading values. The matrix (U) comprises the left singular vectors, capturing spatial patterns across the data. Each column of (U) corresponds to a specific spatial mode, illustrating how column loadings vary across different regions. The matrix (Sigma) is a diagonal matrix containing singular values that quantify the strength of each mode, allowing us to identify and prioritize the most significant spatial patterns. Finally, ({V}^{T}) comprises the right singular vectors, representing temporal patterns; each row in ({V}^{T}) reflects how column loadings vary over time for a given spatial mode.

In this study, we applied SVD to identify the dominant spatial patterns of emissions in our dataset. The first mode of SVD (SVD₁) represents the largest variance in the data, explaining 87.3% of the total variability. However, to ensure that the mathematical model makes physical sense, two additional criteria are employed. First, each area must have a minimum continuous area larger than 100 pixels, ensuring spatial significance. Second, only regions with SVD values greater than the 95th percentile or smaller than the 5th percentile are retained, emphasizing the importance of highly contributing modes to the decomposition process. This approach guarantees that our spatial-temporal domain contains the most significant signals of the change in remotely sensed NO₂ and CO fields.

MCMFE (mass conservation model free approximation of multispecies emissions) approach

This work introduces a new approach using daily total column NO₂ and CO from remote sensing measurements and a 4-term approximation of the mass conservation equation. This system is driven by reanalysis of 3-hourly meteorological fields, initialized by monthly CO and NO_x emissions a priori inventories. Coefficients (({a}_{1}), ({a}_{2}), ({a}_{3}) for NO_x and ({b}_{1}), ({b}_{2}), ({b}_{3}) for CO) in the equations are estimated through pixel-level least-squares regression, minimizing the residuals between modeled and observed total columns. These two equations include mathematical terms approximating the underlying physics, chemistry, and thermodynamics driving the production of NO_x and CO, including in situ dynamic transport, first-order atmospheric loss (chemical decomposition, dilution at the edges of the plume and signal uncertainty, etc.), and fast in situ processing (Eqs. 1, 2).

First, this work assumes a linear transformation between NO_x and NO₂, NO_x = ({a}_{1})*NO₂, to constrain the fact that the total in situ NO_x is a function of the observed total column NO₂ measurements, as well as underlying atmospheric and combustion processes (such as biomass burning and industrial processes)³³. The actual value of ({a}_{1}) also accounts for the observed uncertainty of the NO₂ columns. The total term of ({a}_{1}) is constrained within a range from 1.0 to 50, which consists of a ± 25% uncertainty bound applied to an a priori range of observed NO_x/NO₂ in the range from 1.3 to 40¹². The contribution of first-order chemical decay of NO_x is represented by factor ({a}_{2}), after being scaled by ({a}_{1}). The advective transport and pressure-induced transport of NO_x are represented by the factor ({a}_{3}), after being scaled by ({a}_{1}). Specifically, ({a}_{3p}) denotes only positive transport values (net import), while ({a}_{3n}) denotes only negative transport values (net export). In terms of CO, the value of ({b}_{1}) accounts solely for the observed uncertainty of the CO, which, due to a lack of consensus, we assign a relatively conservative value of ±50%. ({b}_{2}), after being scaled by ({b}_{1}), and ({b}_{3}), after being scaled by ({b}_{1}), similarly account for the first-order atmospheric loss of CO and the combination of advective and pressure-induced transport of CO following the approach of total NO_x.

Where ({E}_{{{NO}}_{x}}) and ({E}_{{CO}}) represent the total atmospheric emissions of NO_x and CO to the troposphere, calculated on a grid-by-grid basis with a day-to-day resolution for NO_x and a week-to-week resolution for CO. ({V}_{{{NO}}_{2}}) and ({V}_{{CO}}) denote the tropospheric column concentrations of NO₂ and CO, respectively. The terms (nabla cdot left(begin{array}{c}mathop{{boldsymbol{u}}}limits^{ rightharpoonup }* {V}_{N{O}_{2}}+mathop{{boldsymbol{v}}}limits^{ rightharpoonup }* {V}_{N{O}_{2}}end{array}right)) and (nabla bullet left(mathop{{boldsymbol{u}}}limits^{ rightharpoonup }* {V}_{{CO}}+mathop{{boldsymbol{v}}}limits^{ rightharpoonup }* {V}_{{CO}}right)) represent the gradients of daily zonal and meridional fluxes, as well as variations in air column mass and density. These gradients were calculated by multiplying the gridded ({V}_{{{NO}}_{2}}) and ({V}_{{CO}}) values with the central wind vector at each grid point.

Sensor errors and retrieval uncertainties lead to an uncertainty associated with both the geospatial and temporal observations from both satellite platforms. Since the MCMFE method requires computing both gradients (spatial and temporal derivatives), such uncertainties will possibly produce larger uncertainties in the emissions inversions computed herein. To ensure that only data of the highest quality is used in this work, all data below minimum quality thresholds are subsequently discarded and not used. Quality thresholds of >1.0 × 10¹⁵ molecules/cm² for NO₂ and >9 × 10¹⁷ molecules/cm² for CO were applied to enhance data reliability. The NO₂ threshold reflects its measurement uncertainty (approximately 1.0 × 10¹⁵ ± 30% molecules/cm²)^68,69, where values below this level are likely influenced by noise, compromising emission estimates. For CO, due to the lack of literature about what the established cutoffs should be, we used the 10th percentile of the observed distribution to minimize noise in low-concentration regions, thereby improving the robustness and reliability of the results.

Probabilistic emissions analysis

To further assess the uncertainty stemming from various percentile coefficients in computing emissions using MCMFE methods, this work utilized five different sets of percentile coefficients (({a}_{n}) and ({b}_{n})) to estimate emissions across different regions, then these estimates were then compared with current emission inventories. These diverse percentiles were chosen based on subregions identified through SVD, filtering out data with strong signals during different time periods of each region includes multiple liner or non-liner combinations of these different percentile emissions. The specific emissions calculated using each percentile set are mathematical results derived from the relationship between emission priors and satellite measurements during corresponding periods across various regions.