The operational offline TROPOMI NO₂ TVCD product (S5P_L2__NO2___HiR2) (van Geffen et al., 2024) from NASA GES DISC (https://daac.gsfc.nasa.gov/datasets/, last access: 17 April 2026) for 2019–2024 is used in this study. TROPOMI is on board of ESA's Sentinel-5 Precursor (S5P) early-afternoon LEO satellite with a high signal-to-noise ratio (Veefkind et al., 2012). It provides global daily coverage with a spatial resolution of 7.0 km × 3.5 km before 6 August 2019 and updated to 5.5 km × 3.5 km thereafter. The data are filtered according to the following criteria: qa > 0.75 and cloud fraction (CF) < 0.3 to remove very cloudy scenes, ice-snow cover scenes and erroneous retrievals (van Geffen et al., 2022; Verhoelst et al., 2021); solar zenith angle (SZA) < 65° to exclude observations with low solar elevation, and viewing zenith angles (VZA) < 56° to minimize unfavorable viewing conditions at the edges of the swath, following Beirle et al. (2023).

Wind fields are provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis data (https://cds.climate.copernicus.eu/datasets/, last access: 17 April 2026). The 500 m wind fields are interpolated from hourly data on pressure levels, while the 10 m wind fields are directly obtained from hourly data on single levels. Both datasets have a spatial resolution of 0.25° × 0.25°. Details on the selection of wind heights and data processing are provided in Sect. 3.1.

The chemical data for NO and NO₂ are sourced from the Goddard Earth Observing System composition forecast (GEOS-CF) system (https://gmao.gsfc.nasa.gov/gmao-products/geos-cf/, last access: 16 April 2026) to derive the NOx/NO2 ratio. GEOS-CF integrates the offline GEOS-Chem chemistry module into the GEOS weather and aerosol modeling system, enabling global near real-time estimates (hindcasts) and 5 d forecasts of atmospheric constituents at a high spatial resolution of 25 km × 25 km (Keller et al., 2021; Knowland et al., 2022). The NOx/NO2 ratios are highest near emission sources because freshly emitted NO rapidly consumes local ozone and is subsequently oxidized to NO₂ as the plume mixes with background air (Meier et al., 2024). Following Beirle et al. (2021, 2023), NO₂ columns are converted to NO_x using the near-surface photostationary state, with the NOx/NO2 ratio from the near-surface model layer with a 1-hour temporal resolution (chm_tavg_1hr_g1440x721_v1) used in this study to better represent near-source conditions and the resulting NO_x gradients (Ayazpour et al., 2025; Sun, 2022).

Two inventories for natural and anthropogenic sources are used. Soil NO_x emissions are obtained from the CAMS global emission inventory (https://ads.atmosphere.copernicus.eu/datasets/cams-global-emission-inventories/, last access: 17 April 2026), which provides monthly estimates from fertilizer/manure application and atmospheric deposition at a 0.5° resolution (Hoesly et al., 2018; Simpson et al., 2014; Yienger and Levy II, 1995). Since the inventory is updated only until 2018 and soil NO_x variability is relatively small compared to total emissions, the 2018 data serve as a proxy for 2019–2024.

Biomass burning and vegetation fires NO_x emissions are derived from the CAMS global biomass burning emissions (GFAS) (https://ads.atmosphere.copernicus.eu/datasets/cams-global-fire-emissions-gfas/, last access: 17 April 2026). GFAS v1.2 provides near-real-time daily averaged fire NO_x fluxes using satellite observations of fire radiative power (FRP) on a global 0.1° × 0.1° grid (Kaiser et al., 2012). The data covers 2019–2024.

Anthropogenic NO_x emissions for validation are sourced from the Multi-resolution Emission Inventory model for Climate and air pollution research (MEIC, v1.4, 2019–2020, http://meicmodel.org.cn, last access: 17 April 2026) and the Emissions Database for Global Atmospheric Research (EDGAR, v8.1, 2019–2022, https://edgar.jrc.ec.europa.eu, last access: 17 April 2026). MEIC provides high-resolution, multi-scale databases of anthropogenic emissions for China at a 0.25° × 0.25° resolution (Geng et al., 2024; Li et al., 2017). EDGAR delivers global coverage at 0.1° × 0.1° resolution, with emissions derived through statistical downscaling of national inventories using high-resolution spatial proxies (Crippa et al., 2024; Solazzo et al., 2021).

The point source emissions derived from DDA are evaluated against the point source catalog provided by Beirle et al. (2023). For point source detection, their catalog uses coal, gas, and oil power plants with capacities ≥ 100 MW from the Global Power Plant Database (Byers et al., 2019), identifying over 1100 NO_x point sources worldwide. Their validation shows good agreement in Germany and the United States, demonstrating the catalog's reliability.

NASA's Black Marble nighttime lights (NTL) product suite, derived from the Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) onboard the Suomi National Polar-orbiting Partnership (SNPP), serves as a constraint on anthropogenic emissions (Román et al., 2018; Wang et al., 2021). The Lunar BRDF-Adjusted Nighttime Lights Yearly L3 Global 15 arcsec Linear Lat/Lon Grid product (VNP46A4) provides high spatial resolution at 500 m and is available from January 2012 onward (https://viirsland.gsfc.nasa.gov/Products/NASA/BlackMarble.html, last access: 17 April 2026). This study uses data from 2019 to 2023. Due to the current unavailability of VNP46A4 data for 2024, the 2023 dataset is applied as a substitute.

National accounts data of annual Gross Domestic Product (GDP) and provincial Gross Regional Product (GRP) are from National Bureau of Statistics of China (https://data.stats.gov.cn, last access: 17 April 2026).

The mathematical framework of the DDA is detailed in Sun (2022) and further developed by Ayazpour et al. (2025). Based on satellite-observed NO₂ TVCDs, NO_x emissions E can be estimated as: 1E=∂(fΩ)∂t+fu⋅∇Ω+Ωu⋅∇f+XfΩu0⋅∇z0+fΩτ, where ∇ denotes the two-dimensional horizontal vector differential operator in Cartesian coordinates, i.e., ∇= (∂/∂x, ∂/∂y). No terrain-following coordinate system is used in this formulation. Ω is NO₂ TVCD, f is the NOx/NO2 ratio, u is the profile-weighted horizontal wind from surface to a conceptual altitude (z1) which is not explicitly needed and defined, u0 is surface wind, and z0 is surface altitude. X and τ are fitting parameters representing the inverse of scale height and NO_x lifetime, respectively. The tendency term (∂(fΩ)/∂t) becomes negligible when averaging over a month or longer or under the steady-state approximation. It should be noted that this approximation may not hold for a single satellite overpass, potentially leading to significant errors (Koene et al., 2024). Assuming X and τ stay constant over the averaging period, the spatiotemporal averaged emissions E for a given time period and horizontal resolution can be expressed as: 2E=fu⋅∇Ω+Ωu⋅∇f+XfΩu0⋅∇z0+fΩτ, Here, the operator 〈〉 denotes spatiotemporal averaging. The first and second terms of Eq. (2) are referred as the DDf estimator (Ayazpour et al., 2025), reflecting the contributions of advection transport to local NO_x emissions. The third component is the topography correction as emphasized by Ayazpour et al. (2025), it is directly derived from the continuity equation rather than serving merely as an empirical adjustment (Koene et al., 2024). The sum of the first three terms is referred to as DDf_topo estimator. The last term describes the NO_x chemistry approximated by first-order loss.

Integration in DDA is performed from z0 to an intermediate altitude z1. While the ideal approach would involve winds at all vertical levels, the full wind profile is typically unavailable. Instead, a single-layer wind, known as the effective wind field, is used to approximate the average state of the full profile. Ayazpour et al. (2025) utilized the effective wind field height using WRF-CMAQ simulations and found that the 500 m wind is most suitable, which aligns with Beirle et al. (2023). Consequently, the horizontal wind u is interpolated to 500 m above the surface, while u0 directly obtained as the 10 m wind from ERA5.

To apply Eq. (2), the physics-based oversampling approach (Sun et al., 2018) is used to resample the level 2 pixels into 0.025° × 0.025° grid cells with appropriate weighting, then coarsened to 0.05° × 0.05°. Winds in ERA5, the NOx/NO2 ratio (f) in GEOS-CF data are resampled to match this spatial resolution and temporally aligned with satellite overpasses, allowing for the calculation of all bracketed terms in Eq. (2). Yearly NTL data from SNPP/VIIRS are also resampled at the same spatial resolution. The spatial differentiation in gradient calculation is conducted on 0.05° × 0.05° grid cells with second order central difference. All bracketed terms are averaged at a monthly scale before X and τ are fitted (see in Sect. 3.2) to derive emissions E in mol m⁻² s⁻¹, and the conversion to mass assumes NO_x as NO₂.

To avoid additional assumptions and external computations (Beirle et al., 2021, 2023), DDA performs a data-driven fitting approach based on monthly fluxes to determine X and τ across grids with negligible emissions (E≈ 0) (Ayazpour et al., 2025; Lonsdale and Sun, 2023; Sun, 2022), where Eq. (2) can be rewritten as: 3fu⋅∇Ω+Ωu⋅∇f=β0+β1fΩu0⋅∇z0+β2fΩ+ε, Here, -β1 is an estimate of X, -β2 is an estimate of the inverse of τ, β0 and ε represent the offset and random error in the predicted variable, which cannot be accounted for by any linear combinations of predictors.

Both the FDA and DDA methods in prior studies have exhibited substantial negative emissions and/or underestimation of total emissions (Ayazpour et al., 2025; Beirle et al., 2019, 2021, 2023; De Foy and Schauer, 2022; Lonsdale and Sun, 2023; Sun, 2022). A single τ fitted in relatively clean region tends to overestimate the chemistry lifetime, then the NO_x flux is underestimated. Therefore, a more realistic representation of NO_x lifetime is critical for accurate emission estimation (Beirle et al., 2023; Krol et al., 2024; Laughner and Cohen, 2019; Meier et al., 2024). The photochemical reactions of NO_x–O₃–VOCs depends on the concentrations of NO_x, O₃, and VOCs, as well as on photolysis and meteorological conditions (Pusede et al., 2015; Sillman et al., 1990; Souri et al., 2023). Even under identical NO_x concentrations and at the same latitude (Beirle et al., 2023; Lange et al., 2022), the lifetime still vary considerably due to the complex interplay of NO_x and VOC chemistry (Laughner and Cohen, 2019).

To derive more realistic lifetime, we fit β2 across stratified column amount intervals 〈Ω〉 within subregions instead of fitting a single lifetime across the domain to account for the NO_x reactivity nonlinearity. We partition the study domain into four subregions by employing NO_x concentration as the primary criterion due to its dominant control over chemical lifetime (Pusede et al., 2015) with additional consideration of latitude and terrain effects. Figure 1a shows the four subregions. The east (E) and west (W) sections are divided by the Hu line (HL) that extends from Heihe (127.54° E, 50.25° N) to Tengchong (98.50° E, 25.03° N). The E and W sections are further subdivided into north (N) and south (S) subregions by latitudes 35° N for the west and 30° N for the east. The resultant four subregions are denoted as WN, WS, EN, ES thereafter. The HL is a well-known natural geographical boundary that divides China into two contrasting regions in terms of terrain, climate, population density, and economic activity. The eastern part, encompassing most of China's plains and rivers (Fig. 1b), is dominated by the East Asian monsoon, supports 96 % of the population, contributes the majority of national productivity, and faces severe air pollution. In contrast, the western region is characterized by elevated terrain, a westerly climate, and sparse population (Hu, 1935; Zhang et al., 2022). So, the above factors implicitly account for variations in O₃ and its precursors influenced by human activities (Jin et al., 2020; Martin et al., 2004; Souri et al., 2023), differences in natural VOCs emissions from vegetation under varying climatic and geographical conditions (Guenther et al., 1995; Sprengnether et al., 2002; Palmer et al., 2006), and meteorological influences on transport and photochemistry (Duncan et al., 2010; Li et al., 2020; Pusede et al., 2015).

Given the small interannual variability and limited impact on reactive species emission estimation (Ayazpour et al., 2025), β1 is fitted using the same climatological months, whereas β2 is fitted for each individual month using NO₂ TVCD percentile bins constructed independently for that month and subsequently averaged over the same months for each subregion during 2019–2024. First, β1 is fitted in grid cells with rough terrain (0.001 m s-1<u0⋅∇z0< 0.1 m s⁻¹), where emissions are negligible (DDf < 5 × 10⁻⁹ mol m⁻² s⁻¹). Then, β2 is fitted in flat terrain (where u0⋅∇z0< 0.001 m s⁻¹) without strong NO_x emission sources (DDf_topo < 10⁻¹⁰ mol m⁻² s⁻¹). The fitting is performed across piecewise bins defined by NO₂ TVCD percentiles. TVCD percentiles are binned at 10 % intervals for each month in WN and EN, while in WS and ES, due to narrower lower percentile ranges, bin widths are expanded to 20 % below the 80th percentile and remain 10 % above it to ensure robust fitting performance. For month-bins where fitting fails (p>0.01 or β2>0), appropriate adjustments are made by merging neighboring bins or revising percentile thresholds. A total of 1393 month-bins are successfully fitted across the four subregions. The number of grid cells per bin ranges from 3 to 9388 (10th percentile: 17; median: 91; mean: 199), indicating that most bins contain sufficient data for robust lifetime fitting, while bins with very small sample sizes are rare and have negligible influence on the overall regression. For each subregion, average TVCD and β2 per month-bin are calculated from successfully fitted bins. TVCDs can be grouped into intervals as described above, the mean TVCD of each interval is matched to the nearest month-bin and the corresponding β2 is used to calculate flux.

The DDA quantifies total NO_x emissions, from which anthropogenic contributions to the total emission rates over a certain area need to be isolated by subtracting natural sources. Globally, anthropogenic emissions dominant, while natural sources, such as soil emissions, biomass burning, and lightning, account for approximately 30 %–40 % (Jaeglé et al., 2005; Müller and Stavrakou, 2005). Regional variation of natural sources contributions is substantial, with around 14 % in East Asia (Zhao and Wang, 2009), and 8 % in eastern China (Lin, 2012). Nevertheless, these estimates involve significant uncertainties (Ding et al., 2017; Rey-Pommier et al., 2022), including potential underestimation (Song et al., 2021). Previous studies typically designated regions dominated by anthropogenic emissions as mean NO₂ TVCDs higher than 1.0 × 10¹⁵ molec. cm⁻² (Li and Zheng, 2024; Liu et al., 2016a). However, due to the presence of unexpectedly high or poorly understood natural NO_x emissions over this threshold (Kong et al., 2023; Song et al., 2021), it is not applied to filter natural sources in this study. Since natural NO_x is primarily emitted during the summer and remains low in winter (Liu et al., 2016a; van der A et al., 2006), while anthropogenic NO_x emissions typically peak in winter (Lonsdale and Sun, 2023), we identify natural-source grid cells based on seasonal criterion and further constrain them using NTL data. Grid cells with either the highest averaged NO₂ TVCDs in summer or the lowest values in winter comparing to other seasons, and with NTL < 0.01 nW cm⁻² sr⁻¹, are classified as natural NO_x sources and excluded from the areal integration to get anthropogenic NO_x emission rates. For the remaining grid cells, we subtract soil and biomass burning emissions (from CAMS data) from the satellite-derived emissions to isolate anthropogenic contributions.

To quantify uncertainties, DDf is calculated as the mean directional derivative along the zonal/meridional (x/y) and diagonal directions (r/s) (Li et al., 2026) on a 0.05° × 0.05° grid: 4DDfx/y=fu⋅∇Ωx/y+Ωu⋅∇fx/y=fux⋅∂Ω∂x+fuy⋅∂Ω∂y+Ωux⋅∂f∂x+Ωuy⋅∂f∂y,5DDfr/s=fu⋅∇Ωr/s+Ωu⋅∇fr/s=fur⋅∂Ω∂r+fus⋅∂Ω∂s+Ωur⋅∂f∂r+Ωus⋅∂f∂s, Standard deviation of the difference between DDf_x∕y and DDf_r∕s is used to estimate random error σ of DDf: 6σ=0.5⋅SD(DDfx/y-DDfr/s), The random errors at daily, monthly, and annual scales for 2019–2024 consistently decrease as the mean satellite data coverage (N) increases (Fig. 2). This observed scaling follows the theoretical relationship σ=σ0/N (black line in Fig. 2), in agreement with the central limit theorem for independent random errors. Here, σ0 reflects the precision of a single satellite overpass, calculated at the monthly scale as: 7σ0=exp(〈logσi〉+0.5⋅〈logNi〉), where σi and Ni denote the random error and mean satellite coverage for month i, respectively. The results further demonstrate that temporal averaging effectively reduces random errors in emission quantification.

Since the topography correction and chemical loss terms in Eq. (2) are determined through fitting, only the overall Root Mean Square Error (RMSE) can be evaluated, rather than grid-level precision. Therefore, the random error of DDf is employed to characterize the uncertainties in DDA emission estimation, encompassing both satellite retrieval noise and the random error arising from the DDf estimator.

To illustrate the developments in this study, Fig. 3 compares three DDA-based results before and after applying the NOx/NO2 ratio correction and improved fitting scheme: (1) a constant NOx/NO2 ratio of 1.32 and monthly single-lifetime fitting (fixed_f and single_τ), corresponding to the original DDA framework by Sun (2022); (2) the variable NOx/NO2 ratio and monthly single-lifetime fitting (variable_f and single_τ), based on the modification by Ayazpour et al. (2025) and marking the first application of GEOS-CF chemical data in satellite-based emission estimation; (3) a combination of the variable NOx/NO2 ratio and piecewise fitting with nonlinear NO_x lifetime for each month (variable_f and nonlinear_τ), while the latter represents the major improvement in this study. Using a variable NOx/NO2 ratio better captures strong NO_x gradients near point sources, improving the accuracy of point source emission estimates. However, this approach still leads to notable underestimation of regional emissions. The nonlinear lifetime fitting more effectively accounts for the balance among local emissions, horizontal transport, and chemical loss, reducing negative emission grids and increasing regional emission estimates. Consequently, the improved fitting scheme minimizes artifacts in mountainous and remote regions compared to earlier results (Ayazpour et al., 2025; Beirle et al., 2023; Lonsdale and Sun, 2023; Sun, 2022).

The lifetime of NO_x is known as a complicated function of NO_x chemistry regimes (Laughner and Cohen, 2019). At very low NO_x concentration, NO_x lifetime increases with NO_x concentration. As NO_x concentration rises, the lifetime decreases because increased NO enhances the chain reactions involving organic compounds (RH) and HO_x (HOx= OH + HO2+ RO₂), accelerating RH oxidation to produce O₃ (“NO_x-limited” regime) and further oxidizing NO. At high NO_x concentration, as NO_x reaches saturation, the reaction between OH and NO₂ becomes much faster than the reaction between OH and RH, dominating the fate of HO_x and slowing O₃ production (“NO_x-suppressed” regime), resulting in the opposite trend in NO_x lifetime (Laughner and Cohen, 2019; Pusede et al., 2015).

Figure 4 shows the monthly climatology of NO_x lifetimes from the improved fitting scheme described in Sect. 3.2. For each subregion and each climatological month, the fitted lifetime is shown as bubbles corresponding to bins of NO₂ TVCD. The size of bubbles scales with the mean NO₂ TVCD for the bin. The results clearly demonstrate the nonlinear variability of NO_x lifetime as a function of TVCDs and show significant discrepancies between subregions. The results closely match the theoretical calculated NO_x lifetime versus NO_x concentrations under different VOC reactivities by Laughner and Cohen (2019), capturing the turning points marked by an increase in lifetime at low NO_x concentrations (region I), the subsequent decrease with rising NO_x (region II), and the eventual increase under NO_x-saturated conditions (region III). The range of lifetimes vary from 0.71–26.47 h, and the average values across the subregions range from 3.17–7.85 h. Due to fitting failures in July–August, the number of bins in WN is substantially reduced, requiring broad bin merging and resulting in lifetimes that are likely overestimated and unrepresentative. The results are consistent with the 2–8 h range reported by Lange et al. (2022) as well as the 2 h (low NO₂) to over 7 h (high NO₂) given by Laughner and Cohen (2019).

The consistent lifetime patterns highlight the dominant role of NO_x concentration in determining τ. However, even at comparable NO_x levels and over the same periods, τ exhibits subregional variations driven by distinct ambient conditions (e.g., O₃ and VOCs concentrations, meteorological parameters) and differences in NO_x emission sources. WN is located in the northern China, sees increased NO_x emissions during the colder half of the year due to heating demand. WS is situated on the sparsely populated Tibetan Plateau, has primarily natural NO_x sources, including unexpectedly high NO emissions from lakes (Kong et al., 2023). EN exhibits distinct anthropogenic emissions, with higher NO_x and longer τ in winter due to heating, and lower NO_x in summer, where intense photochemical reactions result in a shorter τ. ES is located in southern China with smaller annual temperature variations, shows less pronounced seasonal discrepancies in τ. Additionally, high natural VOCs emissions during the growing season of vegetables (Cao et al., 2022) in ES contribute to a longer τ (Laughner and Cohen, 2019).

We provide detailed comparisons of the lifetime fitting parameters for the three DDA-based approaches in Table S1 in the Supplement. The variable NOx/NO2 ratio correction improves the accuracy of source divergence and emission estimates, while the piecewise fitting approach captures nonlinear NO_x chemistry and yields a shorter overall lifetime with lower fitting RMSE. Across the four subregions, NO_x lifetimes without ratio correction and fitting scheme improvement are approximately 2 to 3 times those derived in this study, specifically 1.7 times in ES, 2.8–2.9 times in EN and WN, and 3.3 times in WS (figure omitted), although the values primarily represent the mean state associated with the nonlinear characterization of lifetime. These results highlight the great importance of accounting for the variable NOx/NO2 ratio and nonlinear NO_x lifetime, particularly in clean and heavily polluted regions, while the influence is comparatively less pronounced in moderately polluted areas.

In addition, the scale height (1/X) fitting results for each subregion are presented in Fig. S1. Scale height shows clear seasonal and regional variability, generally higher in the cleaner and more remote regions (WN and WS) than in the more polluted regions (EN and ES). Its variability is primarily controlled by boundary layer mixing, as X links surface concentration to column density, reflecting the effective vertical mixing depth (Lonsdale and Sun, 2023; Sun, 2022).

Point source emissions in DDA (from power plants in this study) are quantified by integrating over a 15 km radius, following the approach and locations of 124 power plants reported by Beirle et al. (2023). Figure 10a presents the estimated NO_x emissions from these plants in China for 2019. From 2019 to 2024, emissions from the 124 plants range from 0.02–2.13 kg s⁻¹, with uncertainties between 4 %–78 %, averaging 16 %. Overall, the plants show an average emission decline of 23 % over this period.

The resulting estimates are validated against Beirle et al. (2023) for 2019–2021, as shown in Fig. 10b. The two datasets show good agreement, with an R2 of 0.81, both indicating a decline in NO_x emissions from 2019 to 2021. Generally, NO_x emissions from the DDA are slightly lower than those from Beirle et al. (2023), with a slope of 0.83. For comparison, results from DDA test without ratio correction and fitting scheme improvement (fixed_f and single_τ) are also shown in Fig. S9, further illustrating the improvement in point source quantification achieved in this study. It should be noted that point source emissions include all fossil fuel emission sources within the defined radius, leading to a positive bias (Beirle et al., 2023).