The study area spans from 35–50° N latitude and 70–100° E longitude, including Xinjiang and parts of Kazakhstan, Kyrgyzstan, Uzbekistan, Tajikistan, Afghanistan, Pakistan, and adjacent regions. The climate in this region is predominantly temperate continental, including cold and dry winters and hot and arid summers, with large diurnal and annual temperature variations. The Xinjiang area has extensive coal mining and many coal-dependent industries. The region also contains rural areas where residential solid fuel combustion and occasional biomass burning may contribute to seasonal CO variability. In addition, coal is widely used to generate power which is then exported to areas in eastern China. This leads to significant emissions of CO and other combustion byproducts. Similarly, Kazakhstan, Kyrgyzstan, and Uzbekistan also have many industries related to energy and minerals, and also play a crucial role in the regional CO emissions landscape. Figure 1 illustrates the study area together with the coal bases, steel plants, and power plants included in the source-category analysis. These facilities are located in Xinjiang and adjacent parts of Gansu and Qinghai, whereas the satellite-based inversion was conducted over the entire study domain. For the category-level temporal analysis, only steel plants and coal-fired power plants that operated continuously throughout 2019–2024 were retained, resulting in a fixed sample of 4 steel plants and 53 coal-fired power plants.

The MFIEF is utilized to estimate CO emissions (Li et al., 2023; Qin et al., 2023). Equation (1) takes into account factors such as CO column changes, chemical decay and production, and transport, and relies on retrieved data from TROPOMI CO and HCHO to approximate the weighting coefficients (αi) of the underlying partial differential equations that govern the transformation between CO and its driving factors, using the same equations used by world-leading chemical transport models (Cohen and Prinn, 2011). Specifically, emissions cause CO to increase, acting as a source term, while chemical reactions and mixing between in-plume and out of plume regions may lead to the loss or gain of CO, and are represented by a first order linearization of differential equations acting upon and by the CO concentration. The transport of CO is also an important factor, affected by both pressure-induced and advective processes, with the advective term representing the horizontal movement of CO due to wind, and the pressure-induced transport term accounting for the convergence or divergence of the atmosphere itself, accounting for the gain or loss due to non-uniform winds across the concentration and emissions gradients. As such, the transport terms can either increase or decrease the CO column in a given location depending on the direction and magnitude of the flow (Li et al., 2025; Lu et al., 2025a), which account for topography, land–sea breezes, variable weather systems, and more simplified atmospheric conditions in which there is a substantial concentration gradient due to strong variation in emissions sources in space, with a non-uniform wind field. Combining these terms yields the CO emissions Eq. (1), where: 1ECO=dVCOdt+α2⋅VCO+α3⋅∇u⋅VCO-α4⋅VHCHO VCO represents the TROPOMI CO column loading after conversion to units of (µgm-2). α2⋅VCO represents the sink of CO with α2 (s-1) as the inverse CO lifetime. α4⋅VHCHO represents CO production, with α4 (s-1) as the inverse HCHO lifetime. ∇(u⋅VCO) represents the daily zonal and meridional dispersion of CO with a unit of (µgm-2s-1), and α3 (m-1) represents the transport distance. This mass conservation equation for CO provides a framework for understanding and quantifying the changes in CO columns in the atmosphere, considering the various processes that influence its distribution, following Li et al. (2025).

The emission, production, and transport terms of Eq. (1) are initialized, TROPOMI observations and their retrieved uncertainties, meteorological data, and either an initial a priori emissions dataset, or our own previously inverted emissions dataset in the case of multiple iterations. The fitting is based on multiple least squares regression for each grid cell on a month-by-month basis, reflecting the differences in albedo, elevation, land-surface use, emissions type, and differences in confounding variables on each pixel specifically grouping all daily data from TROPOMI and the ECMWF reanalysis where they all occur. This process provides sufficient data to compute the weighting terms αi, while also accounting for the changes in land-surface, atmosphere, and other factors. In the case where a pixel in any given month either does not have enough data or produces a fit with a p value larger than 0.05, the values of the model are set to NaN on that grid cell during that month. To ensure physically realistic and mathematically consistent values for the coefficients α2, α3, and α4, physical cutoffs are applied. Any value that is not positive (α>0) is set to NaN.

Equation (1) is then used to calculate estimates of CO emissions across all grid cells. To estimate the maximum probability density of the coefficients during the corresponding grid cell-by-grid cell and month-by-month basis, the solution distribution of α within the valid range (from the 10th percentile to the 90th percentile of the Probability Density Function (PDF)) is sampled 1000 times per grid cell. The mean value of this distribution is assigned as the day's average emission in that grid cell, and its standard deviation was used to characterize parameter-induced variability in the estimated CO emissions. This process allows us to estimate the coefficients and their uncertainties, taking into account the available data and the physical constraints on the parameters, providing a more robust and accurate representation of the CO mass conservation equation in the study region.

For the calculation of CO emissions, grid-cell filtering based on the distribution of retrieved values is required following the method established by (Zheng et al., 2026). Random errors are expected to cluster around zero and to produce approximately symmetric positive and negative values. For each grid cell, we identify the most negative retrieved emission value, -θ µgm-2s-1, and define a symmetric interval from -θ to θ µgm-2s-1. Values within this interval are treated as being dominated by retrieval noise rather than a resolvable positive emission signal and are excluded. This screening reduces the influence of grid cells for which the inversion cannot distinguish a true positive emission signal from the effects of observational noise.

The accuracy and precision targets for TROPOMI total CO column prior to launch were 15 % and 10 % respectively (Landgraf et al., 2016; Martínez-Alonso et al., 2020; Veefkind et al., 2012). There hasn't been enough research on specific issues which impact the column retrievals of CO and HCHO including aerosol loadings and microphysical properties, cloud cover under low cloud conditions, changes in surface reflectivity from pixel to pixel, and the initial CO and CH4 data, which could result in greater uncertainty than what has been mentioned (Hu et al., 2024; Lu et al., 2024). The uncertainty in TROPOMI CO total column has implications for CO emission calculations. First, emission calculation relies on accurate and precise CO column concentration data. Second, since emissions estimation requires the use of a non-linear gradient operator (Lu et al., 2025b; Zheng et al., 2026), uncertainty in the spatial domain plays an additional role. Consequently, if small perturbations within the observational uncertainty range lead to relatively large changes in inverted emissions, this indicates that the computed emission estimates may be strongly affected by noise (Beekmann and Derognat, 2003; Rao, 2005; Reilly et al., 1987). In such instances, the emissions cannot be regarded as stable; thus, their reliability is questionable. This makes it difficult to assess the robustness of the inverted emissions and may reduce confidence in the retrieved emission estimates. Accordingly, this study propagates the assumed observational uncertainties through MFIEF and quantifies the corresponding range of variation in the inverted emissions and allows for a more robust product.

Random perturbations were applied to both the retrieved CO and HCHO column data within conservative retrieval uncertainty bounds. The perturbations were randomly added to (or subtracted from) the observed data and a bootstrap resampling was performed to sufficiently sample the perturbation space. Specifically, each data point of CO column and HCHO column retrieved from TROPOMI, on a daily and gridded basis, was randomly perturbed within ±10% of its original value. In addition to point-wise perturbations, the non-linear influence on spatial gradients was also evaluated. For example, given two neighboring grid cells, if there is an overlapping portion of the data range after the random ±10% perturbations are applied, the direction of the computed gradient, and therefore the emissions may shift. In these cases, the resulting gradient becomes unstable, and therefore the emissions estimate is also not likely trustworthy. The calculated changes define the emission uncertainty range associated with propagation of the perturbed observational inputs. Specifically, the relative emission response was calculated by Eq. (2): 2Eresp=ECO(±)-ECOECO ECO(±) denotes the newly calculated CO emission, ECO denotes the initial CO emission, Eresp denotes the change of CO emission result, i.e., the observational contribution to emission uncertainty. The distribution of these responses quantifies the observational contribution to emission uncertainty, and forms a minimum of the total top-down emissions uncertainty. Grid cells exhibiting responses larger than the adopted threshold are classified as exceeding this uncertainty range and are excluded from the final emission product, following Zheng et al. (2026). The CO emission calculation and uncertainty-screening workflow is summarized in Fig. 2.

Regional means were calculated from daily spatial means. To quantify the temporal trend in regional CO emissions, we fitted an ordinary least-squares regression to the monthly mean emission series from January 2019–December 2024. The model included continuous time, expressed in years since January 2019, and calendar-month fixed effects to account for seasonality: 3Et=β0+β1Tt+∑m=212γmMm,t+ϵt where Et is the regional monthly mean CO emission flux, Tt is the time elapsed since January 2019, and Mm,t represents calendar-month indicator variables. Heteroskedasticity- and autocorrelation-consistent standard errors with a maximum lag of 12 months were used to account for serial correlation in the monthly series. As a non-parametric robustness test, we also applied the seasonal Mann–Kendall test with a period of 12 months and calculated the corresponding seasonal Sen's slope. Statistical significance was evaluated at the 0.05 level. The regression used all 72 monthly observations. The percentage change between the 2019 and 2024 annual means was reported as a descriptive endpoint comparison and was not interpreted as the regression slope. Trend coefficients are reported with 95 % confidence intervals.

Figure 3a presents the spatial distribution of the average TROPOMI CO total column from 2019–2024 across the study area, revealing a domain-wide mean of 1.54×1018molec.cm-2. The concentration is predominantly influenced by anthropogenic activities, with elevated values (>2.0×1018molec.cm-2) located in, around, and downwind of major urban and industrial centers such as Urumqi, Fergana, Almaty, Jiayuguan, and the Zhundong Coalfield. In contrast, natural areas like the Tianshan and Altai Mountains exhibit lower concentrations, averaging around 1.0×1018molec.cm-2. Moderately high CO levels are also observed in the desert regions of central Xinjiang, likely due to enhanced photochemical production from VOCs under intense ultraviolet radiation. Elevated CO is also found in parts of northwestern Kazakhstan, where biomass burning and residential solid fuel combustion may contribute to seasonal variations in the regional background CO, particularly during the heating season. The statistical distribution of the CO total column, shown in Fig. 3b, deviates from a normal distribution and is distinctly bimodal, with the 25th and 75th percentiles for the entire period calculated at 1.23 and 1.83×1018molec.cm-2, respectively. Analysis of interannual variability shows that the highest CO levels occurred in 2021, with an annual mean of 1.59×1018molec.cm-2, particularly in high-value zones. Conversely, 2022 marked the lowest concentrations across both high- and low-value zones, with the mean dropping to 1.44×1018molec.cm-2. The values subsequently rebounded to an intermediate level in 2023 (1.52×1018molec.cm-2), followed by a further increase in 2024 (1.56×1018molec.cm-2). This is consistent with findings indicating that the general air pollution policies implemented by China are driving CO (Li et al., 2025; Liu et al., 2024) more than lockdowns related to COVID-19 (Fan et al., 2021; Zheng et al., 2021).

Figure 4 presents the available daily CO total columns from 2019–2024 in the 0.05°×0.05° resampled grid cells containing the Wugonggou underground coal-fire site (44.075° N, 88.156° E), the center of Urumqi (43.825° N, 87.575° E), Xinjiang Daan Special Steel (42.700° N, 93.542° E), and Shenhua Guoneng Hami Power Station (42.411° N, 93.009° E). Each time series represents one selected grid cell. The mean CO total columns at these four locations were 1.96, 2.17, 2.25, and 2.05×1018molec.cm-2, respectively. All locations generally exhibited higher values in winter and lower values in summer, reflecting the combined effects of seasonal emissions, atmospheric transport, boundary-layer mixing, and faster CO oxidation associated with higher OH abundance in summer (Liu et al., 2022; Sun et al., 2023; Yang et al., 2021). The Wugonggou grid cell exhibited weaker seasonality, with a monthly amplitude of 0.32×1018molec.cm-2, compared with 0.71-0.77×1018molec.cm-2 at the other three locations. This weaker variation is consistent with the relatively persistent nature of underground coal combustion and the weaker influence of seasonally varying urban and industrial activities in the surrounding area.

To distinguish dust-dominated regions from other aerosol types, we utilized the AAOD ratio between 443 and 880 nm. Mineral dust typically exhibits stronger absorption at shorter wavelengths due to its iron oxide content, leading to higher AAOD443/AAOD880 ratios, whereas other aerosols like black carbon show less spectral dependence. A higher ratio thus suggests a greater contribution of dust to total absorption. Based on this spectral behavior, we selected a threshold of AAOD443/AAOD880>4.5 to identify and mask dust-dominated areas, thereby minimizing potential biases in CO emission estimates associated with dust contamination. Grid cells exceeding this threshold were excluded, effectively removing spurious emission signals caused by enhanced atmospheric absorption and scattering from absorbing aerosols which impact the retrieval of CO and HCHO. As shown in Fig. 5a, the spatial distribution of AAOD ratios highlights extensive dust-affected areas, primarily in the desert and arid parts of western China and southern Kazakhstan. This screening process resulted in the exclusion of approximately 14 % of the study area, underscoring the importance of aerosol correction in satellite-based emission inversion.

To quantify emission uncertainty associated with observational inputs, we varied the total column concentrations of CO and HCHO within ranges of ±10% and ±20%, representing the adopted TROPOMI retrieval uncertainty ranges. Grid-cell estimates were retained when the relative change in emissions remained within the corresponding uncertainty bound. As illustrated in Fig. 5b, under the ±10% and ±20% perturbation thresholds, 31.3 % and 33.7 % of grid cells, respectively, remained within the corresponding uncertainty bound over the 6-year period. Figure 5b shows how the emission estimates change as observational uncertainty propagates through the inversion, with estimates falling within the corresponding bounds retained. Furthermore, Fig. 5c shows the number of days with reliable emissions after applying the ±10% filter, with a spatial average of approximately 135 valid days per grid cell. The results indicate that stricter observational-uncertainty filtering leads to a gradual reduction in retained emission estimates, quantifying how input-column uncertainty affects the inversion outcomes. This is an important point, since many papers calculating emissions using satellites have assumed that reducing uncertainty leads to a more precise end result (Estrada et al., 2025; Shen et al., 2023), whereas this result demonstrates that both very high and very low emissions results are both impacted by observational noise.

Following application of the ±10% observational-uncertainty filter, the spatial distribution of the MFIEF-derived emissions broadly corresponds to the major features of the CO total column distribution. Figure 6 summarizes the annual spatial distributions, probability density distributions, and spatial variability of the derived emissions from 2019–2024. Regional mean emissions and the mean intensity of the identified hotspot regions decreased over the study period, while the emission distributions shifted toward lower values.

Regional mean CO emissions decreased from 4.93 µgm-2s-1 in 2019 to 3.06 µgm-2s-1 in 2024, corresponding to a 37.9 % endpoint reduction. The seasonally adjusted trend was -0.33µgm-2s-1yr-1 (95 % confidence interval: -0.52 to -0.15µgm-2s-1yr-1; HAC-adjusted p<0.001). A seasonal Mann–Kendall test independently supported the decreasing trend: -0.20µgm-2s-1yr-1 (p<0.001). This overall trend toward lower emissions is further reflected in the evolution of emission hotspots, which we defined as regions where the emission flux exceeded twice the study area's mean (6.72 µgm-2s-1). A total of 11 such hotspots were identified, primarily situated between 39.83–46.58° N and 81.08–98.23° E. Their average intensity decreased markedly from 9.51 µgm-2s-1 in 2019 to 5.63 µgm-2s-1 in 2024, representing a total reduction of 40.8 % or an average annual decrease of 0.68 µgm-2s-1yr-1. The PDFs of the emissions (Fig. 6b) provide further evidence of this systematic reduction, showing a distinct leftward shift toward lower values. The distribution peak decreased from 3.34 µgm-2s-1 in 2019 to 2.85 µgm-2s-1 in 2024. Concurrently, the PDFs of the standard deviations (Fig. 6c) indicate a significant weakening of spatial heterogeneity, with the peak value dropping from 1.66 µgm-2s-1 to below 1.30 µgm-2s-1. In summary, the results depicted in Fig. 6 clearly highlight a marked downward trend in CO emissions between 2019 and 2024, characterized by reduced hotspot intensity, a systematic shift of the emission distribution to lower values, and reduced spatial variability. These observed changes may reflect the combined effects of emission-control policies, industrial restructuring, energy use, meteorology, sampling, and non-industrial sources; their individual contributions cannot be separated here. Together, these results indicate a statistically significant regional decline, reduced hotspot intensity, and weaker spatial variability over the study period.

Figure 7 presents the monthly regional mean CO emissions and the mean number of valid emission-estimate days per grid cell from January 2019–December 2024. A valid day is defined as a day for which a grid cell retains an emission estimate after the quality and perturbation-response screening described above; the plotted valid-day metric is the spatial mean of this monthly count across the study domain. Overall, CO emissions exhibited a clear downward trend, decreasing from an exceptionally high level of 9.25 µgm-2s-1 in January 2019 to around 2.5–3.0 µgm-2s-1 after 2022, with occasional wintertime rebounds (e.g., 5.07 µgm-2s-1 in December 2023). Seasonal fluctuations are evident, with higher emissions generally observed in winter and early spring, and lower values during late spring and summer, consistent with stronger heating-related combustion sources during colder times, annual production cycle which ends on Chinese New Year varying from mid-January through mid-February. The number of valid observational days shows substantial variability, ranging from fewer than 2 d per month (e.g., July 2020 and August 2022–2024) to more than 5 d per month (December 2021). The valid-day series is presented only as a sampling diagnostic and is not interpreted as a physical driver of emission variability.

Figure 8 illustrates the temporal evolution of gridded CO emissions at four representative locations: the Wugonggou underground coal-fire site, Urumqi city center, Xinjiang Daan special steel plant, and Shenhua Guoneng Hami coal-fired power plant. Because the inversion is performed at a spatial resolution of 0.05°×0.05°, these estimates represent the net emissions from all sources within the corresponding grid cell rather than emissions from an individual facility. Over 2019–2024, the mean emission fluxes were 4.50 µgm-2s-1 at Wugonggou, 4.75 µgm-2s-1 in central Urumqi, 5.77 µgm-2s-1 at the selected steel-plant grid cell, and 4.43 µgm-2s-1 at the selected coal-fired power-plant grid cell. The largest observed emission values generally occurred near the beginning of the study period, followed by a pronounced weakening of high-emission episodes. At Wugonggou, for example, the maximum daily emission flux of 14.0 µgm-2s-1 occurred in December 2019, while the maximum observed values in subsequent years declined to 9.98, 7.65, 5.09, 5.42, and 4.97 µgm-2s-1 from 2020–2024, respectively. Its annual mean similarly decreased from 6.38 µgm-2s-1 in 2019 to 3.03 µgm-2s-1 in 2024. The temporal evolution further indicates that the long-term reduction was particularly evident in the weakening of wintertime high-emission episodes, whereas changes during the remaining months were weaker and less monotonic. Similar attenuation of high-emission episodes was observed in the Urumqi and power-plant grid cells, while the steel-plant grid showed a smaller overall reduction. However, wintertime sampling was sparse in some years, and these seasonal differences should therefore be interpreted as descriptive temporal patterns rather than independent trends. Moreover, the causes of the observed changes cannot be uniquely separated among changes in source activity, emission-control measures, atmospheric transport and chemical loss, and temporal sampling. In particular, Wugonggou is an uncontrolled underground coal-fire source rather than an engineered industrial stack, and its temporal evolution should not be interpreted in terms of the same emission-control mechanisms as the urban and industrial grid cells.

Table 1 includes industrial facilities that operated continuously throughout 2019–2024. The screened sample contains 53 coal-fired power plants and 4 steel plants; the city-center and underground coal-fire categories each contain 8 locations. Based on grid-scale estimates from this fixed sample, mean emissions decreased from 6.47–3.74 µgm-2s-1 at city-center locations (42.2 %), from 7.09–4.18 µgm-2s-1 at underground coal fire locations (41.0 %), from 6.22–4.08 µgm-2s-1 at steel-plant locations (34.4 %), and from 4.94–3.02 µgm-2s-1 at coal-fired power-plant locations (38.9 %) between 2019 and 2024. The 90th-percentile values also decreased, including from 11.00–6.58 µgm-2s-1 at steel-plant locations and from 8.20–4.69 µgm-2s-1 at coal-fired power-plant locations.

Figure 9 compares estimated coal consumption with satellite-derived grid-scale CO emissions for 11 selected coal-fired power plants in 2023. Coal consumption ranged from approximately 57–206 ktcoalyr-1, while the mean grid-scale CO emissions ranged from approximately 2.8×103-4.0×103tCOyr-1. A moderate positive association was observed between coal consumption and the inferred CO emissions (r=0.59, p=0.058, N=11; Fig. 9a), indicating that plants with higher coal consumption generally tended to be located in grid cells with higher inferred emissions. However, the relationship did not reach the conventional significance level of p<0.05. The relatively broad 25th–75th percentile ranges also indicate substantial temporal variability in the grid-scale emission estimates.

The grid-scale CO emission-to-coal-consumption ratio, calculated as the satellite-derived CO emission from the 0.05°×0.05° grid cell containing each power plant divided by the reported coal consumption of that plant, ranged from approximately 14–53 gCOkg-1 coal. This ratio is used only as a comparative metric rather than a facility-specific emission factor, because the satellite-derived emissions represent the combined emissions from all sources within the corresponding grid cell rather than actual stack emissions. The ratio showed a strong inverse relationship with coal consumption (r=-0.93, p<0.001, N=11; Fig. 9b). However, because coal consumption is included in the denominator, the relationship is partly affected by mathematical coupling. Contributions from other sources within the grid cell may further influence the ratio, particularly for plants with lower coal consumption.