GEOS-Chem is a chemical transport model driven by meteorological data from the Goddard Earth Observing System (GEOS) of NASA's Global Modeling and Assimilation Office (GMAO) . In this study, we use GEOS-Chem Classic (GCC) v14.1.1 to simulate formaldehyde columns to constrain NMVOC emissions over China. The global simulation is run at 2° × 2.5° resolution and provides lateral chemical boundary conditions to the nested Asia domain updated every 3 h. The nested region (72–136° E, 17.5–54° N) has a horizontal resolution of 0.5° latitude × 0.625° longitude and 47 vertical layers. Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) meteorological fields are used to drive GEOS-Chem. Each simulation includes a 6-month spin-up period.

This model version incorporates detailed O₃-HO_x-NO_x photochemistry and fully coupled aerosol-O₃-NO_x-VOCs chemistry representation , coupled with a scheme for primary carbonaceous aerosols, dust, sea salt, and secondary inorganic species (sulfates, nitrates, and ammonium) and their distribution. To better simulate oxidant-aerosol reactions in the troposphere, GEOS-Chem v14.1.1 includes state-of-the-science tropospheric chemistry with recent updates to the oxidation mechanisms of isoprene , aromatics , ethylene, and acetylene . Since the satellite overpasses China mainly between 12:00 and 14:00 local time, the model outputs within this time window are sampled to calculate the formaldehyde columns for fair comparison with the satellite observations. After this temporal collocation and post-processing, samples of the formaldehyde tropospheric column simulation are presented in Fig. a.

The anthropogenic NMVOC emission input into the model mainly comes from the Multi-resolution Emission Inventory for China (MEIC; ). Since the MEIC inventory tailored for the existing chemical species in GEOS-Chem only extends to 2017, the MEIC inventory used in this study is the 2017 emission inventory. This inventory has a spatial resolution of 0.25° latitude × 0.25° longitude and includes industrial, transportation, power generation, and residential emissions. For chemical species used in GEOS-Chem but not included in MEIC and anthropogenic NMVOC emissions outside China, we use the 2019 CEDS global inventory as a supplement. The prior estimates of biogenic NMVOC emissions in this study are obtained from the MEGAN 2.1 model . Field straw burning is considered a major seasonal source of NMVOCs in China . In this study, the biomass burning emissions are taken from the GFED version 4 (GFED4) global inventory for 2020 . Before these prior emissions are used to drive GEOS-Chem simulations, the spatial resolution is coarsened to an average value on a 0.5° × 0.625° grid resolution consistent with the model configuration as used in Sect. .

Figure a presents the prior NMVOC emission inventories for 2020, which primarily relies on the anthropogenic emission inventory from MEIC, supplemented by the CEDS inventory for species not included in MEIC. Additionally, biogenic emissions are provided by MEGAN (offline calculation) for the year 2020 with an hourly temporal resolution, directly through the HEMCO emission component of GEOS-Chem; in this study, we did not run the MEGAN model separately. Biomass burning emissions are taken from GFED4. The combination of these three sources is treated as the prior emission inventory used in the following NMVOC emission optimization.

This study aims to constrain the NMVOC emissions in China by assimilating multiple formaldehyde satellite products. As aforementioned, formaldehyde is an important precursor to ozone, the optimization of the NMVOC emission inventories and concentrations are supposed to improve the ozone simulation simultaneously. To evaluate the magnitude and quality of this impact, the ground level ozone concentrations from the National Urban Air Quality Real-time Publishing Platform of the China National Environmental Monitoring Center (CNEMC, last access: 15 May 2024) are used in the validation. The ozone measurements utilized in this study are from 1602 sites across China. The MDA8 values of surface ozone observations are calculated based on the hourly data before they are compared against the model simulation. Results of the comparison will be described in Sect. 3.4.

This study employs the four-dimensional ensemble variational (4DEnVar) methodology to optimize NMVOC emissions with satellite formaldehyde observations. The goal of the assimilation is to find the most likely estimate of the state vector, which is the monthly NMVOC emission inventories f over the entire model domain. Note that f represents the vector of total NMVOC emissions, rather than separately gridded anthropogenic, biogenic, or biomass burning VOC emissions. To optimize emissions from these three sectors, additional observations or a well-defined spatial correlation structure are required, which are not available in this study. The prior estimate fb is from the inventories described in Sect. , and the formaldehyde observations y are described in Sect. . Mathematically, assimilation is performed via minimizing the cost function J as follows: 7J(f)=12(f-fb)TB-1(f-fb)+12y-HMfTO-1y-HMf The cost function J is the sum of two parts: background and observation penal term. The background term quantifies the difference between the optimal f and the prior emission inventories fb, while the observation term calculates the difference between the simulation driven by f and the satellite observations y. In addition to the fb that represents the prior NMVOC emission vector calculated from the anthropogenic, biogenic, and biomass burning sources as been illustrated in Sect. . The uncertainty in the NMVOCs simulation is assumed to be attributed to errors in the emission inventories, and can be compensated using a spatially varying tuning factor α: 8fi=fbi⋅αi in here fbi denotes the NMVOC emission rate in the given grid cell i. The α values are defined to be random variables with a mean of 1.0, a minimum of 0.1 and a standard deviation of 0.4, corresponding to a uniform 120 % uncertainty applied to the total NMVOC emissions rather than sector-specific settings as adopted in previous studies . The rationale for this choice is provided in the Supplement. This empirical value was found to provide sufficient spaces for resolving the observation-minus-simulation errors. A background covariance Bα is formulated as a product of the constant standard deviation and a spatial correlation matrix C: 9Bαi,j=σα⋅Ci,j where Ci,j represents a distance-based spatial correlation between two αs in the grid cell i and j, and is defined as: 10Ci,j=e-(di,j/l)2/2 where di,j represents the distance between two grid cells i and j. l here denotes the correlation length scale which controls the spatially variability freedom of the αs. A small value of l indicates that the tuning factors αs are less spatially correlated, thereby enabling emission optimization at a finer spatial scale. However, this also necessitates a larger number of ensemble runs to adequately represent the model realization from emission to simulation. An empirical parameter l=300 km which is used in to nudge the ammonia emission that has a rapid spatially variability is also taken in this study. With the covariance matrix Bα, the NMVOC emission background covariance B is obtained via a Schur Product: 11B=Bα∘C In the observation term, y is the observation vector, representing satellite observations, M is the GEOS-Chem model driven by emissions f, H is the observation operator that transfers the three-dimensional concentration into the observational space, and O is the observation covariance matrix. In this study, the assimilated observations include the OMPS total columns and TROPOMI tropospheric columns. A distinct observation operator H is configured to enable a fair comparison of the observation-minus-simulation mismatch. The satellite formaldehyde observations are assumed to be independent, therefore O is a diagonal matrix. The diagonal value here is calculated as: 12σtotal=σinstrument2+σrepresent2 In Eq. (), σtotal is defined as the total uncertainty, which is the square root of the sum of the squares of the instrument uncertainty σinstrument from the formaldehyde observations and the representative uncertainty σrepresent introduced when processing the data into monthly averages. The representative uncertainty σrepresent is represented by the standard deviation of the data. The spatial distribution of the total uncertainty is provided in Fig. S2 in the Supplement.

The assimilation methodology used in this paper is the four-dimensional ensemble variational (4DEnVar). Different from the classic 4DVar that requires adjoint in the cost function minimization, 4DEnVar emulates the GEOS-Chem formaldehyde simulating model using an ensemble-based linear approximation and hence is adjoint-free. The method is first proposed by and successfully implemented in our recent dust aerosol and ammonia emission inversion . The detailed procedures for minimizing the cost function Eq. () are illustrated in section “Minimization of the Cost Function in 4DEnVar” in the Supplement.

Figure  shows the vertical profiles of formaldehyde shape factors used to compute the reported satellite vertical columns before any model-based profile correction is applied. Both the OMI and OMPS retrievals use GEOS-Chem model outputs as their a priori profiles . Consequently, their shape factors are highly similar. formaldehyde shape factors generally decrease with altitude but exhibit characteristic peaks and troughs: a minimum at 750–850 hPa, a first peak ∼ 30 hPa above it, a second prominent peak at 600–700 hPa, and a third peak near 350 hPa that is strongest in April and August and weaker in January and November. Above 350 hPa, shape factor decay toward zero. These features agree well with previously reported formaldehyde profile shapes over China . Overall, the OMPS profile most closely matches GEOS-Chem, whereas OMI shows slight peak shifts or spurious upper-level enhancements in some regions, particularly during May and August.

In contrast, the operational TROPOMI retrieval uses the a priori profiles from the TM5-MP model , which places substantially more mass near the surface. This results in a markedly different vertical structure: an approximately logarithmic monotonic decrease with altitude, with only minor perturbations over SCB (∼ 300 hPa) and PRD (∼ 800 hPa) and very high near-surface shape factor. These differences in a priori profile shape are the primary reason why profile correction is essential for meaningful satellite–model comparisons .

Additionally, Fig.  clearly shows that stratospheric formaldehyde (>∼ 200 hPa) can be largely neglected in both the GEOS-Chem simulation and the OMPS and TROPOMI retrievals . Because the stratospheric contribution is negligible and no explicit stratospheric correction is applied in either retrieval, we hereafter use the term ”formaldehyde column” without distinguishing between total and tropospheric columns in subsequent discussion.

Uncertainty is a key component in the assimilation process and serves as a crucial indicator of satellite data quality. Fig.  illustrates the vertical distribution of retrieval uncertainties. In the mid- to upper troposphere (200–600 hPa), OMPS and OMI show comparable levels of uncertainty. However, below 600 hPa, OMPS uncertainties become substantially larger, likely due to cloud contamination and retrieval algorithm approximations . As shown in Supplement Fig. S2, the overall uncertainty of OMPS is significantly higher than that of the other two satellite datasets. At first glance, OMI data may appear superior, but this advantage largely results from strict filtering, which excludes a substantial fraction of problematic data. As illustrated in Supplement Fig. S3a, b, applying a threshold of 50 observations per grid cell drastically reduces spatial coverage, rendering OMI unsuitable for national-scale assimilation. Previous studies that assimilated OMI over China have typically interpolated the data to coarser resolutions to ensure applicability . Therefore, only OMPS and TROPOMI formaldehyde columns are assimilated in this study, while OMI is excluded for our high-resolution emission inversion due to the poor data coverage.

Figure  also presents satellite retrieval deviations from the prior model estimates. When all three satellite datasets exhibit the same sign of deviation (positive or negative) relative to the model, they are considered consistent. Such consistency is observed, for example, in February, May, and November over NCP and in February over PRD and SCB, where all three datasets show positive deviations; and in February and November over YRD and in August over SCB, where all show negative deviations. These cases indicate stronger reliability. In other situations, when OMPS and TROPOMI exhibit the same bias direction, they are also considered consistent, as in November over PRD and SCB. Overall, 10 out of 16 cases (62.5 %) exhibit consistency, with higher coherence primarily occurring in the cold season and during spring and autumn months over NCP and SCB. Subsequent analyses will explicitly consider this consistency to enhance the robustness of the conclusions.

The spatial characteristics of the NMVOC emissions in 2020 are clearly shown in Fig.  which presents the spatial distribution of four monthly average emissions from the prior simulation (a.1–a.4) and the posterior estimates constrained by OMPS (b.1–b.4) and TROPOMI (c.1–c.4) formaldehyde observations. Significant emission increments relative to the prior estimates are mainly concentrated in eastern and southern China. In most regions, the posterior results constrained by OMPS (d.1–d.4) and TROPOMI (e.1-e.4) exhibit broadly consistent adjustment patterns. However, notable differences between the two posterior estimates can still be observed, particularly over eastern China in August and southern China in May. The results reveal pronounced seasonal variability and regional heterogeneity in emission intensity, with the NCP, YRD, PRD, and SCB identified as major emission hotspots throughout the year.

Although the major high-emission regions can be clearly identified, the complexity of emission source types and the wide range of emission magnitudes render the maps visually dense, making it difficult to directly interpret regional characteristics and seasonal changes. Therefore, subsequent analyses are focused on these four representative regions to enable a more detailed investigation. Figure  further displays the monthly and annual totals of NMVOC emissions across China in 2020. In general, the two posterior estimates exhibit good agreement for most months. Specifically, both show consistent decreases during January, February, and October to December, while simultaneous increases are observed from March to May. But notable discrepancies are observed during the June–September period, which account for approximately 83 % of the total annual difference between the two posterior datasets – with July and August alone contributing around 56 %. This leads to different estimates of annual emissions: the annual total constrained by OMPS assimilation is estimated at 40.82 Tg, while that constrained by TROPOMI is 34.83 Tg, both differing from the prior estimate of 39.26 Tg. To more accurately assess the regional emission responses under different observational constraints, the consistent and inconsistent months are discussed separately in the following sections.

In months with high consistency, January–February, during the transition from winter to spring, both assimilation results show a reduction in emissions, with anthropogenic emissions exhibiting a particularly significant decline. This may be because the emission inventory includes winter heating emissions, while the actual heating demand has been reduced due to global warming, resulting in an overestimation . In spring, March-May, emissions gradually increase, likely driven by enhanced biogenic emissions due to rising temperatures and vigorous vegetation growth . After November, as the season shifts from autumn to winter, emissions decline again, with notable fluctuations in biogenic emissions in October, though anthropogenic emissions remain the primary contributor to the overall trend. In the inconsistent months (June–September, corresponding to summer and autumn), discrepancies arise between OMPS and TROPOMI results. These differences may arise from variations in emission characterization during summer, marked by strong convection, high humidity, and elevated cloud and aerosol content, which differentially impact the retrieval of optical depth and columns by OMPS and TROPOMI.

A clear regional divergence in NMVOC emission increments after assimilation is revealed in Fig. , with further analysis highlighting the sources of these discrepancies. In the NCP, OMPS assimilation results for July indicate a significant emission increase of 62.04 %, while TROPOMI shows a smaller increase. In August and September, the two datasets exhibit opposing trends. In contrast, increment differences are relatively minor in March–April, with OMPS assimilation results showing an increase of approximately 14 %, while TROPOMI remains largely unchanged. During January–February and November-December, both datasets display minimal changes. Overall, the prior inventory for the NCP appears underestimated in May–June. In the YRD, except for May and July, other months (e.g., June, August, and September) show opposing trends. In the PRD, nearly all months from March to September are classified as inconsistent. However, both regions demonstrate consistent emission reductions during the cold season, suggesting an overestimation in the a priori emission inventory for winter. In the SCB, negative emission increments during the warm season are particularly pronounced, generally exceeding 20 %, with reductions in June–July surpassing 35 %. During the cold season (January and October–December), both datasets show consistent declines with comparable values. Months with lower consistency are primarily concentrated in February-May, indicating a likely overestimation in the a priori emission inventory for this region.

In 2020, anthropogenic emissions in China were influenced by the COVID-19 pandemic, leading to observable changes. To better evaluate the general applicability of the proposed method, it is also necessary to conduct a comparative analysis for the pre-pandemic year of 2019. Fig. S5 in the Supplement presents the total NMVOC emission increments for the four major regions in 2019, based on data assimilation of OMPS and TROPOMI observations. In the NCP region, strong consistency is again observed in June, with posterior emissions increasing by 57.71 % and 30.09 % from OMPS and TROPOMI assimilation, respectively, further confirming the underestimation of prior emissions in this period. In the YRD, February, October, and November are identified as consistent months, aligning with the consistent periods in 2020, suggesting a likely overestimation in the prior inventory during these months. In the PRD region, consistency is found in January, February, June, July, November, and December, while in the SCB region, it occurs in January and from April to December. These consistent months largely overlap with those in 2020, though some differences are evident. For example, June and July emerge as new consistent months in PRD, while October and November remain consistent but exhibit notably smaller emission decreases compared to 2020. In SCB, April and May appear as additional consistent months, while the remaining consistent periods continue to exhibit decreases in emissions. Notably, from June to November, the two posterior datasets show an average decrease of 42.26 % compared to the prior emissions, indicating a high probability of overestimation in the prior inventory for this region during that period.

The spatial distributions of formaldehyde columns in February, May, August, and November 2020 are shown in Fig. . Panels (a.1)–(a.4) display the prior simulations of formaldehyde columns, (b.1)–(b.4) present the posterior simulations of formaldehyde columns assimilated by OMPS, (c.1)–(c.4) show the OMPS satellite observations of formaldehyde columns, and (d.1)–(d.4) illustrate the TROPOMI satellite observations of formaldehyde columns. In addition, the prior and posterior simulations of formaldehyde columns for 2020 are also provided in the Supplement Fig. S7. Regarding the spatial patterns, high formaldehyde columns in February are concentrated in the NCP, YRD, and PRD regions, with the posterior results showing an expanded high-value area in the NCP but a reduced coverage in the YRD. In May, overall formaldehyde columns increase nationwide, with particularly pronounced growth in the NCP and PRD. In August, formaldehyde columns increase in the NCP, YRD, and PRD, while they decrease in the SCB. In November, the changes are modest, but all four regions exhibit reduced formaldehyde columns.

The prior and OMPS-driven posterior simulations of formaldehyde columns were compared with the TROPOMI formaldehyde columns to evaluate the changes in formaldehyde. Scatter plots together with statistical metrics (R2, R, MAE, and RMSE) for the whole country and four subregions in 2020 are presented in Fig. . The prior simulation already shows reasonably good performance (a.1)–(e.1), with most points distributed close to the 1:1 line and exhibiting strong correlations with observations. Nevertheless, further improvements are still possible. After assimilating OMPS data, the posterior results compared with TROPOMI show higher R2 values across all regions, indicating strengthened correlations. For China and NCP, the improvements are comparable, with R2 increasing by about 0.027 (from 0.870 to 0.897 for China, and from 0.774 to 0.812 for NCP). In the YRD, the improvement is more pronounced, with R2 rising from 0.882 to 0.918, and the scatter around the regression line substantially reduced, with many outliers corrected. The most significant improvements occur in PRD and SCB, where R2 increases by approximately 0.05. In these regions, the overestimations present in the prior simulations are effectively mitigated, particularly for high-value cases. In terms of RMSE and MAE, decreases are observed in all regions except NCP. A comparison between Figures (b.1) and (b.2) indicates improvements in the low- and mid-value ranges, whereas substantial overestimations appear in the high-value range. This issue is likely related to the instrumental errors of OMPS observations, as discussed in Sects.  and , which introduce considerable uncertainties.

The monthly mean formaldehyde columns for 2020, derived from the prior simulation, posterior simulations constrained by the OMPS and TROPOMI observations, and satellite observations from OMPS and TROPOMI, are presented for China (a), NCP (b), YRD (c), PRD (d), and SCB (e) in Fig. . At the national scale, the overall changes resulting from assimilation are relatively modest, with the main adjustments occurring in summer and early autumn. The OMPS-driven posterior results show increases relative to the prior in June–July, whereas the TROPOMI-assimilated results exhibit decreases in July–August compared to the prior. These discrepancies may be attributed to differences between the satellite products in their responses to biogenic emissions and photochemical processes under high-temperature and high-radiation conditions .

Figure a presents the increments between the posterior and prior simulations over the four regions when assimilating OMPS or TROPOMI observations, respectively. In the NCP, the posterior results constrained by both OMPS and TROPOMI show consistent increases in May–June, suggesting that the prior inventory may have underestimated the contributions from active photochemical production and anthropogenic emissions during summer . In the YRD and PRD, stronger consistency is observed in the cold season (January–March and October–December), with both posterior results showing decreases, which is consistent with reduced anthropogenic activity and lower formaldehyde production rates under wintertime conditions. The SCB exhibits more distinct characteristics, with OMPS and TROPOMI assimilation results consistently showing decreases in the second half of the year, particularly pronounced in June, July, and October. This pattern suggests that the prior emissions in this region were overestimated. Previous studies have highlighted that the large uncertainties in biogenic emissions in the SCB are critical factors influencing the accuracy of NMVOC emissions and simulations .

The spatial distributions of observed MDA8 ozone at ground stations (a.1–a.4), together with the prior (b.1–b.4) and posterior simulations based on OMPS and TROPOMI assimilation (c.1–c.4, d.1–d.4), are shown in Fig. . As shown in panels (b.1–b.4), pronounced ozone hotspots are observed in NCP (February, May, and August), YRD (May and August), PRD (May, August, and November), and SCB (May and August). This is very similar to the observations shown in panels (a.1–a.4). It indicates that the prior simulation captures the general patterns of ozone hotspots reasonably well, but notable biases remain. For example, ozone is clearly overestimated in PRD during February, May, and August, while underestimated in SCB during May and August. After assimilation with OMPS or TROPOMI, the posterior MDA8 ozone simulations retain the overall hotspot distribution, but the direction and magnitude of changes vary by region. For instance, in August, ozone concentrations increase in NCP and PRD with OMPS assimilation but decrease with TROPOMI assimilation. In February, both assimilation results decrease in YRD, although the decrease is more pronounced in the TROPOMI-based results. Moreover, many regional changes are difficult to discern visually from the spatial maps alone, highlighting the necessity of using statistical metrics to quantitatively assess ozone variations.

The RMSE values between the simulated MDA8 ozone and the ground-based observations are calculated. To better visualize the assimilation benefits, the RMSE variation either assimilating the TROPOMI or assimilating the OMPS in the four key regions are also shown in Fig. b. Larger decreases in RMSE (darker blue) indicate more significant improvements, with the posterior ozone being closer to ground-based observations; conversely, larger increases in RMSE (darker red) indicate degraded performance, with the posterior ozone diverging further from the observations. In those inconsistent cases where the OMPS and TROPOMI posterior increments exhibit opposite signs (i.e., one increases while the other decreases), ozone simulation improvement is not guaranteed. For instance, in NCP during January-April and July, in YRD during June and September, and in PRD during April, May, August, and September, one assimilation leads to improvement while the other indicates deterioration. Moreover, in several additional months both posteriors even show degradation, making it difficult to effectively evaluate the improvement in posterior ozone simulations. By contrast, ozone simulation improvements are clearly observed in consistent cases where the OMPS- and TROPOMI-constrained posteriors exhibit the same sign (i.e., both reductions in ΔRMSE). In NCP, substantial improvements are observed in May and June, with the largest RMSE decrease in June, in agreement with the high-consistency pattern shown in Fig. a. In YRD and PRD, RMSE decreases by more than 30 % in December, representing the most significant improvement; in addition, PRD also shows clear improvements in January and October. These improvement months all correspond to periods of high consistency. In SCB, RMSE also decreases markedly during high-consistency months, including January, June, July, and September–December.

To further quantify ozone simulation improvements in consistent regions, statistics were performed for the months classified as consistent. Considering the similarity in monthly behavior between YRD and PRD, the two regions were combined in the analysis. The results indicate that the consistent regions include NCP in May–June, YRD/PRD in January–March and October–December, and SCB in January and June–December. Within these regions, except for March and November in YRD/PRD and August in SCB, all other months show ozone simulation improvements. Overall, 13 out of the 16 consistent months exhibit improvements, accounting for 81.25 %, with an average RMSE reduction of 24.7 %. This result suggests that constraining NMVOC emissions through formaldehyde assimilation not only substantially improves formaldehyde simulations, but also exerts a positive impact on ozone simulations, with particularly significant improvements in regions and months characterized by high consistency.

To more robustly substantiate this conclusion, it is necessary to examine whether similar features can also be identified in 2019. In that year, OMPS and TROPOMI satellite observations were assimilated independently to constrain NMVOC emissions. The posterior-prior increments from the OMPS- and TROPOMI-driven assimilations, together with the changes in MDA8 ozone ΔRMSE, are presented in Fig. S6 of the Supplement. In NCP, March, May, and June are identified as consistent months, during which the ozone RMSE values decrease, with the most pronounced improvement occurring in June. In YRD, the consistent months are February, October, and November, where the ozone improvements are relatively limited but nevertheless show better agreement with ground-based observations. In PRD, the consistent months include January, February, and June–December; with the exception of August, September, and November, the ozone RMSE decreases in the other months, with notable improvements in June and July. In SCB, the two posterior datasets exhibit the highest level of consistency in 2019, with synchronous increases and decreases throughout the year. Ozone simulations in this region show better performance in all months except March and April, with particularly large improvements in June, July, and September–November, when the RMSE decreases by an average of 25.74 %.

Across the four regions, 27 months are classified as consistent in 2019. Of these, 22 months exhibit improved ozone simulations, which corresponds to 81.48 % of all consistent months, with both assimilations producing MDA8 ozone values closer to ground-based observations. This proportion differs from that of 2020 by only 0.23 %, providing further evidence that ozone improvements are particularly significant in the months defined as consistent across the four regions.