The concept of DQ-1 was first proposed in 2012 with the aim of developing a satellite-borne lidar system analogous to the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) onboard CALIPSO, and it was officially approved as a national project in 2017 (Zhang et al., 2024). Unlike conventional environmental monitoring satellites, DQ-1 is distinguished by its breakthrough active remote sensing payload – the Atmospheric Carbon Dioxide Differential Absorption Lidar (ACDL) – which enables active “top-down” observations of atmospheric CO2 (Zhang et al., 2023). The ACDL underwent successive stages of laboratory prototype development and airborne validation before its successful launch onboard the DQ-1 satellite into a near-polar sun-synchronous orbit at an altitude of ∼705km on 18 April 2022. Operational observations commenced in late May of the same year. This study primarily analyzes data collected August 2022.

The ACDL operates on the principle of Integrated Path Differential Absorption (IPDA) lidar, retrieving atmospheric column-averaged CO2 concentrations (XCO2) via differential absorption techniques. The inversion methodology and data product specifications have been described in detail elsewhere; here, we provide only a brief overview (Han et al., 2025). The instrument transmits two nearly simultaneous laser pulses: one at a strong absorption line of CO2 (R16, referred to as the “online” wavelength) and the other at a nearby weak absorption line (the “offline” wavelength). These are stabilized at 6361.225 and 6360.981 cm-1, corresponding to 1572.024 and 1572.085 nm, respectively. By comparing the differential attenuation between the online and offline signals, the system effectively mitigates the influence of aerosols and other interfering species, except water vapor, thereby enabling accurate retrievals of XCO2. The inversion process relies on dedicated algorithms, with the central concept being that the small wavelength offset produces differential absorption, which enhances the sensitivity of CO2 detection (details of the ACDL XCO2 retrieval algorithm are provided in the Appendix A1).

Figure 2 illustrates the schematic of the DQ-1 measurement principle. The XCO2 products generated by ACDL are provided in a point-sampling mode analogous to that of GOSAT. The lidar records one footprint of approximately 70 m every ∼350m along the satellite ground track. Additional details of the ACDL operating parameters are provided in the Appendix A1.

TROPOMI is a nadir-viewing spectrometer onboard ESA's Sentinel-5 Precursor (S5P) satellite, which was launched in October 2017. Operating in an ascending Sun-synchronous polar orbit with an equator crossing time of approximately 13:30 local time, TROPOMI measures a range of trace gases as well as cloud and aerosol properties across four spectral channels (ultraviolet, visible, near-infrared, and shortwave infrared). The instrument's minimum pixel size was about 3.5×7km2 at nadir before being reduced to ∼3.5×5.5km2 on 6 August 2019 (Veefkind et al., 2012). In this study, we used the S5P-PAL dataset (consistent with version 2.3.1) covering the period from 1 August–1 September 2022, obtained from https://data-portal.s5p-pal.com (last access: 29 January 2026).

To ensure data quality, we filtered out pixels with a qa_value<0.75 (Qin et al., 2023), and, following van Geffen et al., removed cloudy pixels (cloud radiance fraction>50%) as well as anomalies (e.g., eclipses) from the TROPOMI NO2 dataset (Van Geffen et al., 2022). To test our algorithm framework on a robust dataset, we selected summer NO2 observations for three cities located in the mid-latitudes of the Northern Hemisphere, avoiding winter measurements that may be complicated by potential snow cover. Furthermore, given the need for city-scale accuracy, air mass factor (AMF) corrections were applied locally following the method described in Beirle et al. (2023).

Sun et al. proposed an oversampling algorithm to project multi-satellite, multi-species observations onto a common grid, with code publicly available on GitHub (https://github.com/Kang-Sun-CfA/Oversampling_matlab/, last access: 29 January 2026) (Sun et al., 2018a). In this work, we applied this algorithm to the pre-processed TROPOMI overpass data, generating oversampled grids at 1 km resolution following the procedure described in Sun (2022).

For the estimation of CO2 emissions through model simulations, we utilized meteorological parameters from the National Centers for Environmental Prediction Final (NCEP FNL) operational global analysis dataset. The ds083.3 dataset is provided on a 0.25°×0.25° latitude–longitude grid and updated every six hours via the Global Data Assimilation System (GDAS) (https://rda.ucar.edu/datasets/ds083-3/, last access: 29 January 2026). It covers 32 vertical levels, ranging from the surface to the top of the atmosphere, including the ground level and 31 isobaric layers from 1000–1 hPa. Essential variables such as surface pressure, geopotential height, temperature, relative humidity, and zonal and meridional wind components were used as the main meteorological inputs for driving the WRF-STILT simulations.

The wind vector data were obtained from the ERA5 reanalysis dataset (10.24381/cds.adbb2d47) (Hersbach et al., 2023). We extracted hourly 10 and 100 m wind vectors at 0.25° spatial resolution for the three selected cities during the period from 1 August–1 September 2022. The 10 m wind vectors are used to approximate near-surface winds, whereas the 100 m wind vectors represent horizontal transport within the planetary boundary layer. These data were averaged to daily values and subsequently interpolated to match the grid resolution of the column concentration fields described in Sect. 2.3.1.

Digital elevation data were obtained from the GMTED2010 dataset (https://www.usgs.gov/coastal-changes-and-impacts/gmted2010, last access: 29 January 2026) (Danielson and Gesch, 2011). The DEM was resampled and mapped to the same spatial grid as the concentration and wind fields to ensure consistency across all datasets.

In this study, multiple emission inventories were used to estimate fossil fuel CO2 (ffCO2) emissions and to calculate the CO2-to-NOx ratio. In the urban observation system simulation experiment (Sect. 3), the GEMS inventory (0.1° resolution) for NOx and CO2 emissions (Huang et al., 2017) was used to derive the prior CO2-to-NOx ratio (available at: https://gems.sustech.edu.cn/data, last access: 29 January 2026). For comparison, we also employed the gridded fossil fuel CO2 emissions inventory from the Open-source Data Inventory for Atmospheric Carbon dioxide (ODIAC, Version 2024, 1 km resolution; https://db.cger.nies.go.jp/dataset/ODIAC/, last access: 29 January 2026). In Sect. 4, we further utilized the sectoral and 0.1° gridded NOx and CO2 inventories from the Emissions Database for Global Atmospheric Research (EDGAR; https://edgar.jrc.ec.europa.eu/emissions_data_and_maps, last access: 29 January 2026) (Crippa et al., 2018), as well as the sectoral NOx and CO2 inventories from the Multi-resolution Emission Inventory model for Climate and air pollution research (MEIC; http://meicmodel.org.cn/, last access: 29 January 2026) (Team, 2012). Using different approaches to calculate the CO2-to-NOx ratio, we quantified the variations arising from different inventory inputs and assessed their impact on emission inversions.

In previous studies, numerous works have detailed the theoretical derivation for inferring gridded fluxes from column observations (Huang et al., 2024; Koene et al., 2024; Qin et al., 2023; Rey-Pommier et al., 2025; Sun, 2022). Such frameworks are generally based on solutions to the atmospheric continuity equation. Divergence-based approaches typically rely on several key assumptions: (1) exchanges above the planetary boundary layer (column top) and at the surface (column bottom) are neglected, effectively assuming two-dimensional diffusion; (2) horizontal turbulent transport is ignored at coarse grid resolutions; and (3) the deposition term S is treated using a first-order chemical approximation. Starting from the unsteady, source-driven atmospheric continuity equation, the gridded flux of a given species, such as NO2, can be derived from satellite column observations, with the resulting flux 〈ENO2〉 expressed as in Eq. (1). 1〈ENO2〉=〈u×(∇VNO2)〉〈VNO2u10×(∇z0)〉H+〈VNO2〉τ The detailed derivation is provided in Appendix A2. To fully exploit the available data while accounting for observational errors, spatial gradients were computed along the zonal, meridional, and both diagonal directions. Gradients were numerically approximated using second-order central differences, multiplied by the corresponding decomposed wind vectors, and then averaged. For boundary grid points, one-sided differences were applied. Although using gradients in multiple directions helps reduce directional dependence, the finite-difference gradient operator can amplify high-frequency retrieval noise in the original NO2 column field. Therefore, the divergence-derived NOx fluxes should not be interpreted as purely deterministic grid-cell emissions. Instead, they represent monthly aggregated estimates subject to retrieval noise, wind-field uncertainty, chemical-parameter uncertainty, and possible structured errors introduced by gradient operations and gridding. We further evaluate this sensitivity in Appendix A5.

Nitrogen oxides (NOx=NO+NO2) do not exist independently in the troposphere, as NO and NO2 continuously interconvert, while the total NOx remains relatively stable. To convert between NO2 column densities and total NOx columns, Sun et al. (2018a) applied a fixed coefficient of 1.32. In this study, we adopt a more rigorous approach to derive the conversion factor, as expressed in Eq. (2) (Beirle et al., 2023), based on the photostationary steady-state assumption: 2VNOx=αVNO2=1+JKXO3VNO2J=k1×exp⁡-k2cos⁡(SZA)K=k3×exp⁡-k4T here, J represents the photolysis frequency of NO2, calculated following the methodology in Dickerson et al. (1982). The rate constants k1 and k2 are set to 0.0167 and 0.575, respectively. The solar zenith angle (SZA) can be directly determined from the local latitude, longitude, and time; in this study, SZA values are obtained from the TROPOMI satellite metadata. K denotes the chemical reaction rate constants for NO with O3, expressed in cm3(mols)-1 and recommended by IUPAC, with k3=2.07×10-12 and k4=1400. The ozone mixing ratio, XO3, is derived from the ESCiMo project (Jöckel et al., 2016), and T represents the boundary-layer mean temperature obtained from ERA5 reanalysis data. Under these definitions, Eq. (2) can be rewritten as: 3X=α×〈ENO2〉 Using Eq. (3) we can obtain grid-resolved estimates of NOx fluxes, which serve as the prior distribution for fossil fuel CO2 (ffCO2) emissions. These estimates provide a data-driven prior inventory for subsequent steps in the inversion framework.

Regarding the selection of scale height and first-order chemical lifetime, previous studies, such as Beirle et al., employed fixed empirical scale height values and adjusted terrain correction terms to obtain optimal estimates (Beirle et al., 2023). Their chemical lifetime was calculated using a compensation method that accounted for losses integrated over residence times within a 15 km buffer. While effective at point-source scales, this approach is not directly applicable to our study. In the present work, we follow Sun et al.'s (2018b) purely data-driven approach, which leverages observational data without introducing additional assumptions, constructing a linear regression model to determine these parameters (Sun, 2022). This observation-driven fitting method not only reduces errors arising from new assumptions but also mitigates biases caused by grid resampling and near-surface wind selection.

To suppress excessive noise in single-day fits, we perform monthly regressions and adopt the temporal and spatial mean over the month as the final estimate, representing an aggregate over the full spatial domain, the entire month, and the troposphere. The retrieved scale height and first-order chemical lifetime are then applied back into Eqs. (4) and (6) to obtain the final gridded NOx vertical fluxes.

After terrain correction, the gridded flux fields remove a substantial portion of strong emission signals obscured by wind divergence and negative divergence artifacts, while the chemical correction term adjusts residual minor negative biases (Sun, 2022; Beirle et al., 2023). Any remaining small negative values after these corrections are set to zero.

We used the prior CO2-to-NOx ratio in combination with TROPOMI-derived NOx emission distributions to obtain an initial characterization of urban prior ffCO2 emissions. Following the approach of Feng et al. (2024), who calculated the CO2-to-NOx ratio by dividing gridded CO2 and NOx emission inventories, we derived city-specific prior CO2-to-NOx ratio using the 0.1° CO2 and NOx inventories from GEMS (https://gems.sustech.edu.cn/data/database, last access: 29 January 2026). Unlike Feng et al. (2024), who focused on grid-level CO2-to-NOx ratio, we fitted the gridded ratios across each study region to obtain an integrated city-level CO2-to-NOx ratio, which is more suitable for subsequent inversion analyses (Fig. 3). Details on the associated uncertainties are provided in Sect. 4.1.

Figure 3 illustrates our method for calculating the prior CO2-to-NOx ratio. By fitting the 0.1° gridded ratios for each city, we obtained overall city-scale values. The coefficients of determination (R2) for Paris, Cairo, and Beijing were 0.96, 0.917, and 0.76, respectively.

Recently, an increasing number of studies have employed NOx emissions to estimate ffCO2 emissions (Feng et al., 2024; Zheng et al., 2020; Xu et al., 2025b; Yang et al., 2023; Zhang et al., 2022). In inversion methods based on NOx emissions, the choice of the prior CO2-to-NOx ratio directly affects the emission estimates. Uncertainty in the prior ratio propagates to the estimated ffCO2 emissions, influencing both their magnitude and spatial distribution. To evaluate this effect, we selected several widely used CO2-to-NOx ratio calculation methods and systematically assessed their associated uncertainties (results see Sect. 4.1 and Appendix A6).

M.1 Grid-level CO2-to-NOx ratio derived directly from gridded CO2 and NOx inventories (Feng et al., 2024). Since this study scales emissions to the city level, we further fitted the grid-level ratios to obtain city-integrated CO2-to-NOx ratios. M.1 calculations were based on the GEMS gridded inventory.

Distinguishing anthropogenic emission signals from the surrounding “clean” background in XCO2 observations is a central challenge for constraining urban carbon emissions via satellite. Definitions of “background” vary across studies. In this work, we define the background as atmospheric XCO2 that is unaffected by local emissions within the study region. Following the approach proposed by Ye et al. (2020) in constraining urban emissions using OCO-2 observations, we adopt a baseline calculation strategy that incorporates latitudinal gradients.

In this framework, XCO2 is decomposed into two components: XCO2trend, representing the regional-scale, non-local trend, and XCO2local, whose standard deviation σlocal characterizes local-scale variability. Samples satisfying XCO2<XCO2trend+0.5σlocal are selected as “background samples,” as they exhibit lower local spatial variability compared with data influenced by fossil fuel emissions. These background samples are then subjected to linear regression to derive the background baseline and characterize its spatial variation.

We employ the X-STILT V1 model to trace CO2 concentration variations driven by prior emission information. X-STILT integrates satellite profile data and enables a comprehensive uncertainty assessment of urban XCO2 enhancements on a per-observation basis (Wu et al., 2018). Originally developed to extract urban signals from passive OCO-2 XCO2 observations, we have adapted the framework for use with the active CO2 satellite DQ-1, with appropriate modifications. The relationship between XCO2Lidar (DQ-1 XCO2 observations) measurements and the CO2 vertical profile, CO2(p), can be formulated as follows: 4XCO2Lidar=∫p_surfacep_toaCO2(p)WF(p)∫p_surfacep_toaWF(p)dp=∑n=1toaWF(pn)IWF×CO2(pn) here, p_toa represents the pressure at the bottom height of the ACDL, and p_surface represents the pressure corresponding to the surface elevation at the laser footprint. WF and IWF denote the weighting function and the normalized weighting function of the ACDL, respectively. A detailed description is provided in Appendix A1.

We approximate the CO2 concentration by summing the background concentration with the simulated ffCO2 enhancement. Here, the simulated ffCO2 enhancement, ΔCO2ffCO2(p)=〈ffCO2,foot(p)〉, is obtained by interpolating the modeled ffCO2 fluxes along tracer-tagged footprints. Consequently, the relationship between the ffCO2 fluxes and the simulated XCO2modLidar, is established, yielding the modeled fossil fuel CO2 enhancement XCO2ffCO2,modLidar along the lidar track: 5XCO2ffCO2,modLidar=XCO2modLidar-XCO2backgroundLidar=∑n=1toaWF(pn)IWF×〈emissions,foot(pn)〉 XCO2backgroundLidar represents the background concentration along the selected DQ-1 orbit (see Sect. 2.2.2 (1)). The operator 〈,〉 denotes an inner product, emissions is the prior emission flux, and foot(pn) represents the modeled footprint at different vertical layers. Using the above formulation, the mathematical foundation for the inversion is established. By integrating footprints across multiple release heights, the equation can be further simplified. In this study, we define the ffXCO2 enhancement simulated via the atmospheric transport model as: 6XSTILTLidar=∑n=1toaWF(pn)IWF×foot(hn)7XCO2ffCO2,modLidar=〈XSTILTLidar,emissions〉 here, XSTILTLidar is defined as the column-averaged footprint, corresponding to the column-averaged CO2 concentration. The inner product of the column-averaged footprint and the prior emission flux yields the simulated XCO2 enhancement.

We used the NOx emissions obtained previously as prior fluxes and, through the CO2-to-NOx ratio, established the relationship between the prior emissions and the XCO2 observed by DQ-1 (Eq. 9). The XCO2 enhancements estimated from DQ-1 observations were then employed to impose “top-down” constraints on the simulated results. Following the approaches of Che et al. (2024); Ye et al. (2020); Sheng et al. (2025), we applied a Bayesian inversion framework to optimize the prior emission estimates. 8yobs=ysim×λ+εp here, yobs and ysim represent the observed ffXCO2 enhancements and the simulated NOx enhancements, respectively. The symbol λ denotes the CO2-to-NOx ratio, and εp represents the observational error, which encompasses contributions from DQ-1 measurement uncertainties, model errors, and errors in model parameters. It is defined as follows: 9yobs=∫latitude1latitude2ffXCO2obsdtysim=∫latitude1latitude2〈X,footprint〉dt10εobs=σmeasurement2+σsim2 In this context, ffXCO2obs represents the DQ-1 XCO2 enhancement after background concentration removal. The notation 〈Xfootprint〉 denotes the simulated NOx enhancement, obtained by convolving the NOx emission inventory X with the STILT-derived footprint (It should be noted that the footprints used here represent hourly footprints during the simulation period, whereas the NOx emissions are monthly emissions derived using the method described in Sect. 2.2.1. Therefore, we use the New High Resolution Temporal Profiles in EDGAR dataset (https://edgar.jrc.ec.europa.eu/dataset_temp_profile, last access: 29 January 2026) to distribute the monthly NOx emissions to each hourly footprint). Pseudo-observations, ffXCO2obs, are generated by averaging DQ-1 measurements over one-second intervals along the satellite track (∼7km), together with the corresponding simulated values.

Following the Bayesian inversion approach, the state vector λ is expressed in terms of the CO2-to-NOx ratio, representing the relationship between urban fossil fuel CO2 and NOx emissions. The Jacobian matrix is derived from the simulated NOx enhancement ysim. Here, σmeasurement2 represents the observational error variance, and σsim2 denotes the model transport error variance. DQ-1 observations are assumed unbiased with respect to the true state. To account for measurement uncertainty, random Gaussian noise with a standard deviation of 0.3 ppm – representing the lower limit of observational error – is added to the observations.

By minimizing the loss function, we obtain the posterior CO2-to-NOx ratio λ^ and posterior uncertainty σ^: 11λ^=λ+σsim2ysimTysimSobsysimT+Sobs-1×(yobs-ysimλ)12σ^2=ysimTSobs-1ysim+σsim-2-1 here, Sobs is a diagonal matrix, with the diagonal entries representing the observational error variances εobs2 for each orbit. The prior uncertainty σsim is primarily derived from the uncertainties in the prior NOx emission distribution σNOx and the prior CO2-to-NOx ratio σC/N as Eq. (13): 13σsim=σNOx2+σC/N2

Complex horizontal wind fields can lead to elongated and non-Gaussian plume structures in simulated ffXCO2 distributions (Ye et al., 2020). This feature is illustrated in Fig. 5c–f. Figure 5a and b show the simulated and observed XCO2 along two overpasses (simulated XCO2 is obtained by adding the simulated ffXCO2 to the background derived in Sect. 2.2.2 (1)). Along these overpasses, ffXCO2 enhancements exceeding 5 and 10 ppm were observed, with the measured enhancements consistently larger than the simulated values. Although the simulated peak on 7 August is narrower than the observed peak, and the observed peak near 48.4° on 21 August shows a ∼0.3° displacement relative to the simulation, the overall magnitude of simulated ffXCO2 agrees well with observations.

To further evaluate the feasibility of constraining fossil fuel CO2 emissions using the NOx inventory, we performed a comparative analysis using the ODIAC inventory. We compared simulated ffXCO2 during the satellite overpasses based on the NOx and ODIAC inventories (colored shaded areas in the figure), as well as their contributions to the pseudo-observed XCO2 at the satellite locations (colored dots), where the red line represents enhancements derived from the NOx inventory and the green line represents those from ODIAC. Over Paris, the NOx-based simulation yields higher ffXCO2 enhancements than ODIAC, likely due to uncertainty in the prior CO2-to-NOx ratio. Nonetheless, both inventories capture enhancements exceeding 4 ppm. Moreover, the line plots indicate that the temporal variation and magnitude of the simulated concentration contributions (red and green lines) are nearly identical.

We examined local ffXCO2 enhancements during two overpasses of Cairo on 2 August 2022 at 11:00 and 19 August 2022 at 23:00 LT. As shown in Fig. 6, the simulated ffXCO2 peaks exceed 6 ppm. In contrast to Paris, where enhancements are widespread, diffuse, and lack clear structure, and Beijing, where plumes exhibit complex patterns, the simulated ffXCO2 over Cairo is strongly influenced by northwesterly winds, resulting in well-defined plumes. Figure 5a illustrates that the simulations based on both inventories on 2 August produce similar magnitudes and trends, consistent with the Paris results, where the NOx-based simulation exceeds that from ODIAC. Notably, the simulated peaks on 2 August also show a spatial offset relative to the observations. Following Ye et al., 2020, such offsets are attributed to the satellite trajectory crossing the plume edges nearly parallel to the plume axis, making the simulated ffXCO2 highly sensitive to errors in the horizontal wind field.

Notably, the overpasses above Paris and Cairo (Figs. 5a and 6b) exhibit higher latitudinal gradients in the background XCO2, as indicated by the background lines. The approach used to derive these background lines provides a reliable estimate of background XCO2 because, within the relevant regions, the observed and modeled cumulative ffXCO2 enhancements along the satellite track are largely consistent. Consequently, these findings highlight the effectiveness of the background line method for inferring satellite-observed background XCO2. They also emphasize that the spatial scale of satellite data analysis is closely linked to the constraints imposed by local emission sources. Neglecting the latitudinal gradient of background XCO2 may introduce biases in the estimation of ffXCO2 and, consequently, in derived emission fluxes (Ye et al., 2020).

Figure 7 illustrates the investigation of local ffXCO2 enhancements over Beijing using two DQ-1 overpasses and corresponding simulated ffXCO2. In the figure, the colored shading represents XCO2 concentrations accumulated over the previous 24 h simulated by STILT, while the colored dots indicate satellite-observed XCO2 enhancements, calculated by subtracting the background values (see Sect. 2.2.2). The red contours outline the urban area of Beijing. As shown, ffXCO2 over this region can reach approximately 6.0 ppm.

Notably, simulations based on the NOx inventory (Fig. 7c and d) show that the spatial distribution of ffXCO2 enhancements varies significantly with meteorological conditions and emission patterns. In contrast, for Paris and Cairo, the simulated ffXCO2 is more concentrated. Over Beijing, however, the ffXCO2 distribution is more dispersed and comprises multiple plumes. When comparing simulations using NOx and ODIAC inventories for Paris and Cairo, the overall plume structures remain largely unaffected. Over Beijing, the simulations using the ODIAC inventory (Fig. 7e and f) display an almost identical ffXCO2 enhancement distribution across different wind conditions, showing pronounced anomalies in the urban area. Such similarity is unrealistic.

We attribute this behavior to the ODIAC inventory allocating disproportionately high fossil fuel emissions to central Beijing. When STILT footprints intersect the urban area, the high emission gradients in ODIAC (central urban emissions far exceeding suburban values) amplify ffXCO2 enhancements in the inner city. ODIAC's low-emission thresholds are influenced by nighttime light saturation, with median differences ranging from 47 %–84 %. Consequently, ODIAC artificially concentrates emissions in the city center while underrepresenting surrounding suburban areas. This makes it challenging to accurately constrain CO2 fluxes in the peripheral regions using ODIAC. Observations from the TCCON Xianghe site further highlight the limitations of ODIAC's emission allocation in the Beijing area.

Figure 8 presents the comparison of August ffXCO2 at the TCCON site with simulations using the ODIAC and NOx inventories. Unlike the ffXCO2 calculation described in Sect. 2.2.2, the TCCON observations provide daily-averaged fossil fuel CO2 enhancements, where TCCON ffXCO2 is calculated as TCCON XCO2 minus background XCO2 and NEE contributions (details in the Appendix A3). In Fig. 8a, the dark blue line represents ffXCO2 simulated at the TCCON site using the NOx inventory, the green line shows the ffXCO2 simulated after optimization with the inversion using DQ-1 observations, the light blue line corresponds to ODIAC-based simulations, and the red line depicts TCCON-observed ffXCO2.

Figure 8b quantifies the accuracy of the simulations by plotting the difference between the simulated ffXCO2 and TCCON observations on the same day and summarizing the monthly mean and standard deviation. The monthly mean absolute difference for the NOx inventory is 0.82 ppm, while ODIAC exhibits a much larger discrepancy of 5.19 ppm. The inversion-constrained NOx inventory reduces the mean absolute difference to 0.52 ppm, closely matching TCCON observations. Figure 8c shows the cumulative probability distribution of the differences between simulated and observed ffXCO2. The differences for the NOx and inversion-constrained NOx simulations are largely centered around zero (blue and red lines), whereas for ODIAC, approximately 30 % of differences exceed 5 ppm.

These results indicate that for Beijing in August, simulations based on the NOx inventory outperform those using ODIAC. Given that the prior ffCO2 emissions in both inventories are of similar magnitude, the observed discrepancies are primarily attributable to the spatial allocation of emissions in ODIAC. The combined inversion using TROPOMI and ACDL data provides a more accurate reconstruction of urban ffXCO2 plume structures.

This section presents the inversion results of urban carbon emissions for Cairo, Paris, and Beijing, based on TROPOMI and DQ-1 satellite overpass observations (see Table 2). In the inversion, we systematically accounted for observational errors and uncertainties in atmospheric transport to improve the reliability of the emission estimates. From the posterior results, we derived city-specific CO2-to-NOx ratios and, by combining them with TROPOMI-derived NOx emissions, further quantified fossil fuel CO2 (ffCO2) emissions. This approach not only enables quantitative assessment of emissions but also provides a scientific basis for cross-city comparisons of emission characteristics, while demonstrating the potential of multi-satellite data for urban emission monitoring.

For the selected orbits, the posterior CO2-to-NOx ratios were 428–512 for Cairo, 731–742 for Paris, and 553–640 for Beijing (Table 2). These ratios exhibited clear temporal variability under different background conditions. The magnitude of emissions captured by each orbit depended strongly on its distance from major emission regions and the contemporaneous domain-averaged wind conditions (Che et al., 2022). The domain-averaged wind speeds for the study month (Fig. 9), as well as the high-resolution wind fields at overpass time (black arrows in Figs. 5–7), were consistently greater than 3 ms-1. Under such meteorological conditions, the posterior estimates represent emissions from several hours prior to satellite overpass. The posterior uncertainties of the CO2-to-NOx ratio were 15.09 %–18.86 % for Cairo, 14.72 %–18.67 % for Paris, and 14.08 %–16.24 % for Beijing. Overall, uncertainties were larger for Cairo and Paris compared with Beijing.

As described in Sect. 4.1, the prior uncertainty of the CO2-to-NOx ratio was prescribed based on available statistics and emission characteristics. Owing to more comprehensive statistics and advanced manufacturing processes, large metropolitan areas typically exhibit better-characterized emission features. Accordingly, the prior uncertainties for Beijing and Paris were smaller than those for Cairo. Table 2 further shows that the relative contributions of observational and transport errors differed across cities. In Cairo, transport errors dominated over observational errors, whereas in Paris the opposite held true. For Beijing, the relative magnitudes of transport and observational errors varied across orbits. The overall smaller posterior uncertainty for Beijing compared to Cairo and Paris reflects its more stable prior emission characteristics.