We use GEMS v3.0 Level-2 tropospheric NO₂ columns to infer monthly NO_x emissions over the pan-Asian region (50–160° E, 10° S–55° N) from December 2020 to November 2021. Although the model domain extends beyond the GEMS field of view (75–145° E, 5° S–45° N), atmospheric transport allows these observations to infer emission estimates both within and proximal to the satellite's footprint (Fig. S1 in the Supplement). As the first geostationary spectrometer of its kind, GEMS provides high-resolution hyperspectral measurements (300–500 nm; 0.6 nm full width half maximum) that enable the retrieval of multiple trace gases via Differential Optical Absorption Spectroscopy (DOAS) . This study focuses on NO₂ due to its direct link to NO_x emissions and its impacts on public health, both directly and indirectly through O₃ and aerosols , while establishing a framework for future multi-species chemical data assimilation. As its v3.0 quality flags are still maturing, we found that restricting the inversion to “best-quality” flags (flag = 0) was overly conservative. Following consultation with the GEMS team, we adopted a broader selection filter – Solar Zenith Angle <70°, Viewing Zenith Angle <70°, and Cloud Fraction <0.3 – to retain a robust dataset of approximately two billion retrievals. Data density peaks between 09:45 and 14:45 local time (KST) and during the warm season (April–September), reflecting optimal solar geometry and longer daylight hours (Fig. S2). Spatially, retrieval frequency is highest in the southeastern portion of the domain (Figs. S3, S4).

In addition to tropospheric NO₂ column densities, the assimilation process requires two critical parameters: retrieval uncertainties and averaging kernels. The former characterises the observational error budget, while the latter describes the vertical sensitivity of the GEMS instrument to the true NO₂ profile.

The GEMS product includes a unitless “RootMeanSquareError” variable; however, this only captures the DOAS fitting error and does not represent the total observational uncertainty. We thus follow the methodology of and to estimate the total uncertainty based on the standard deviation of retrievals within a pristine, pollution-free reference region. Although recommended by , the tropical Pacific (80–130° E, 5° S–5° N) can be influenced by seasonal biomass burning from Southeast Asia ; therefore, we identify a stable reference region (100–120° E, 20–30° N; Fig. S1) that is less influenced by major emission sources. The resulting estimated uncertainty of 0.0107 DU is comparable to the 0.011 DU reported for OMPS Level-2 data by . While we acknowledge that pixel-level errors vary with cloud fraction, geometry, and aerosol loading, we adopt a uniform observation error of 0.0107 DU in the absence of analytical pixel-level estimates. To account for the uneven spatial distribution of GEMS observations (Figs. S3, S4), we scale this uncertainty by the square root of the number of valid observations per model grid cell on a monthly basis . This adjustment ensures a spatially balanced cost function within the GEOS-Chem 4D-Var framework, as detailed in Sect. .

Regarding vertical sensitivity, the GEMS NO₂ product provides a 47-layer averaging kernel (a), spanning the surface to 0.01 hPa. For our study, the troposphere is defined by layers below 230 hPa. The averaging kernel normalizes the scattering weights (w) by the reported air mass factor (AMF) such that a(z)=w(z)/AMF, where z represents the vertical layer index. Following , we interpolate the modelled NO₂ profiles to the GEMS vertical grid (xcomp) and apply the kernels to derive a model-equivalent tropospheric column (ccomp′) that is directly comparable to the GEMS retrieval: 1ccomp′=∑za(z)×xcomp(z), where z goes from the surface to the tropopause. We note that this process differs from the application of the MOPITT and similar averaging kernels . This is because the DOAS method retrieves a vertical column, whereas MOPITT and similar instruments retrieve vertical profiles using a Bayesian optimal estimation framework. Consequently, there is no need, nor is it possible, to introduce an additional term representing the difference between the retrieved and a priori profiles.

The GEOS-Chem model is a global 3-D chemical transport model driven by assimilated meteorological fields from the Goddard Earth Observing System (GEOS) of the NASA Global Modeling and Assimilation Office (GMAO). The GEOS-Chem adjoint model extends this forward simulation, providing a computationally efficient platform for calculating the sensitivity of a scalar cost function to a vast suite of model parameters (e.g., emissions) within a single backward integration . While these sensitivities can be used for direct sensitivity analysis, they are most often used within a 4D-Var data assimilation framework to optimize emission estimates, provided that the cost function is properly defined. To rigorously assess the added value of GEMS geostationary tropospheric NO₂ observations for monthly NO_x emission constraints and subsequent air quality modelling, we define the cost function (J) to be minimized as follows: 2J=12∑c∈ΩHc-cobsTSobs-1Hc-cobs+12γrσ-σaTSa-1σ-σa, where c is the vector of ccomp′ mapped to the observation space by the observation operator H; cobs is the vector of GEMS tropospheric NO₂ retrievals; Sobs is the observation error covariance matrix; Ω is the spatiotemporal domain over which modelled and observed tropospheric NO₂ are compared; σ=ln⁡(E⊘Ea) is the vector of logarithmic scaling factors for the monthly NO_x emissions, on which sensitivities are calculated and which are optimized by the quasi-Newton L-BFGS-B algorithm , with E and Ea denoting the a priori and a posteriori monthly NO_x emissions, respectively; σa is the prior estimate of the parameter scaling factors (set to zero in this study, meaning that our initial guess for E equals Ea); Sa is the error covariance estimate of the parameter scaling factors; and γr is a regularization parameter that balances the relative weights of the observation and penalty terms in the cost function.

For each GEMS tropospheric NO₂ retrieval within the spatiotemporal domain Ω, spanning the pan-Asian region for each month from December 2020 to November 2021, the observation operator H identifies the corresponding model grid cell. The modelled value is then adjusted using the averaging kernels at the assimilation time step most proximal to the retrieval time. We assume the observation error covariance matrix, Sobs, is diagonal; the diagonal elements represent the total estimated uncertainty, scaled by observation density as detailed in Sect. , while the off-diagonal elements are set to zero, assuming spatially uncorrelated observation errors. The specification of the a priori error covariance matrix, Sa, is contingent upon the emission inventories employed. Although recent versions of the GEOS-Chem forward model support a diverse array of state-of-the-science inventories, the adjoint model supports a more restricted subset. While 4D-Var inversions are primarily constrained by atmospheric observations and are thus less sensitive to the initial a priori selection, utilizing contemporary emission inventories remains preferable to facilitate superior convergence during the optimization process . Following the implementation of aromatic chemistry and a suite of contemporary emission inventories into the GEOS-Chem adjoint by , we extend those inventories to align with our study period. Anthropogenic emissions for China are derived from the Multi-resolution Emission Inventory for China (MEIC), updated to 2020 , while the MIX-Asia inventory is applied to the remainder of the Asian domain. Global anthropogenic emissions outside of Asia are taken from the Community Emissions Data System (CEDS) . Biomass burning emissions are sourced from the Global Fire Emissions Database version 4.1 (GFED4s) , extended through 2021. Natural NO_x precursors, including lightning , soil , and biogenic sources , are calculated online within the GEOS-Chem framework. We assign an a priori uncertainty of 40 % to anthropogenic emissions, representing a 2020 emission-weighted average of the uncertainties reported for MEIC and MIX-Asia . For non-anthropogenic emissions, we assign a broader uncertainty of 100 %, consistent with previous inverse modeling studies across the pan-Asian region . The a priori error covariance matrix, Sa, is also assumed to be diagonal. This neglects spatial error correlations, a simplification justified by the fact that the correlation length scales of individual emission sources are typically smaller than the model's grid resolution . To further mitigate potential adverse effects of neglecting error correlations, we apply a regularization parameter (γr) to enforce a smoother solution. We set γr to 10, a value identified as optimal through L-curve analysis in similar 4D-Var applications .

While we acknowledge that the specifications for Sobs, Sa, and γr entail inherent uncertainties, a comprehensive parameter sensitivity analysis is beyond the scope of this work. Instead, this study focuses on a relative assessment of the added value provided by geostationary sampling. By maintaining consistent parameter settings across our experimental suite, the contrast between inversions serves as a controlled metric for evaluating the impact of high-frequency observations. We distinguish between two primary experiments: a “GEMS-based” inversion using the full hourly dataset and a “LEO-proxy” inversion that serves as a surrogate for LEO instruments (e.g., OMI, OMPS, TROPOMI) by sub-setting observations to 13:45 local time (KST). Specifically, the “GEMS-based” inversion ingests all GK2_GEMS_L2_YYYYMMDD_hhmm_NO2_[Scan area]_DPRO_ORI.nc files, whereas the “LEO-proxy” inversion ingests only those with hhmm = 00:45 UTC (13:45 KST). For both cases, the cost function is minimized over ten iterations; we found that further iterations yielded marginal improvements, thus ten iterations represent an optimal balance between computational efficiency and convergence accuracy. The simulations are conducted at a global horizontal resolution of 2° × 2.5° with 47 vertical layers, driven by GEOS-FP meteorological fields (1 h temporal resolution for 2-D fields; 3 h for 3-D fields) . While nested-grid simulations at 0.25° × 0.3125° are possible for sub-regions like China, the 2° × 2.5° resolution was selected to ensure computational feasibility across the entire pan-Asian domain. Initial conditions were established via a long-term spin-up starting in January 2019 to eliminate the influence of initial state concentrations on the inversion results.

Following the updates to the GEOS-Chem adjoint framework, we perform a dual-phase evaluation of the model's performance. First, we execute a localized gradient consistency test by disabling horizontal transport processes. Under this configuration, the sensitivity of the observational cost function (excluding the regularization term) within an individual grid cell with respect to the local emission scaling factor (σ) becomes mathematically equivalent to the total sensitivity across the entire domain. This simplification allows for a direct, grid-by-grid comparison between sensitivities derived from the adjoint method and those calculated via the finite difference method. We verify the numerical accuracy of the adjoint-based gradients by using the finite difference results as a benchmark: 3∧=Jobs(σ+δσ)-Jobs(σ-δσ)2δσ, where Jobs is the observation part of the cost function. We adopt a perturbation of δσ=0.01 to calculate the finite-difference gradients, a value found to optimally balance truncation and round-off errors .

Second, we evaluate the internal consistency of the inversion by comparing modelled tropospheric NO₂ columns against the GEMS retrievals both before (a priori) and after (a posteriori) the optimization. While this assessment is not independent of the assimilation process, it serves as a critical diagnostic to verify that the 4D-Var framework effectively minimizes the model-observation mismatch and that the adjoint system is functioning as intended.

To reiterate, we conduct two distinct 4D-Var inversion experiments for each month from December 2020 to November 2021 across the pan-Asian region to rigorously quantify the added value of geostationary sampling for monthly NO_x emission constraints and subsequent air quality modelling:

GEMS-based inversion. This experiment assimilates the full temporal suite of GEMS tropospheric NO₂ retrievals, leveraging the high-frequency diurnal sampling inherent to geostationary observations.

To evaluate the chemical propagation of the monthly NO_x emissions inferred from the “GEMS-based” and “LEO-proxy” inversions, we employ a diverse suite of independent in situ measurements. Hourly measurements of surface concentrations of NO₂, O₃, CO, SO₂, NH₃, and fine and coarse particulate matter are obtained from four national monitoring networks: the China National Environmental Monitoring Center (CNEMC), AirKorea, the Japanese Environmental Observatory of the National Institute for Environmental Studies, and the Indian Central Pollution Control Board (CPCB). Due to varying reporting standards across these networks, modelled outputs are converted to the respective reported units and evaluated separately for each network. The spatial distribution of these surface monitoring stations is illustrated in Fig. S1. For vertical column validation, we use high-frequency measurements from the Aerosol Robotic Network (AERONET) and the Pandonia Global Network (PGN). While AERONET is primarily recognized for aerosol characterization, it provides valuable columnar NO₂ and O₃ at intervals up to 15 min; 94 AERONET sites are available within our domain (Fig. S1). We complement these data with columnar NO₂ from seven PGN sites, which offer sampling frequencies as high as every 2 min. To ensure data robustness and computational efficiency, we retain only PGN retrievals with the highest quality flag (flag = 0) and aggregate them into hourly averages for comparison with the model.

To rigorously evaluate the modelled atmospheric constituents against in situ measurements, we sample the model at the exact time and location of each observation. Although the “GEMS-based” and “LEO-proxy” inversions only update monthly NO_x emissions, these updates are spatially heterogeneous and therefore exert non-uniform impacts on the modelled atmospheric constituents across both space and time. We thus compile the paired data into GEOS-Chem grid composites at multiple temporal scales to assess the model performance driven by the two sets of inferred NO_x emissions. The temporal scales include the afternoon at 13:45 local time (KST), daytime averages (07:45 to 16:45 KST), and full daily averages. The first two correspond to the overpass periods represented by the “LEO-proxy” and “GEMS-based” inversions. This multi-temporal approach enables us to assess how the assimilated observations influence model performance both during the outside the observation periods. To quantify the agreement between modelled and measured values, we employ a suite of geometrically related statistical metrics, including the Pearson correlation coefficient (R), normalised standard deviation (NSD), and normalised centralised root-mean-square error (NRMSE), defined as follows: 4R=∑i=1N(Mi-M‾)(Oi-O‾)∑i=1N(Mi-M‾)2∑i=1N(Oi-O‾)2,5NSD=1N∑i=1N(Mi-M‾)21N∑i=1N(Oi-O‾)2,6NRMSE=1N∑i=1N((Mi-M‾)-(Oi-O‾))21N∑i=1N(Oi-O‾)2, where M and O denote the modelled and measured values, respectively; M‾ and O‾ represent their respective means; and N is the total number of paired data. Collectively, these metrics provide a comprehensive evaluation of model performance: R captures the ability to reproduce temporal and/or spatial variability; NSD indicates the relative magnitude of modelled variability compared to the observations; and NRMSE quantifies the overall deviation, normalised by the measured variability. Following the geometric relationship NRMSE2=1+NSD2-2⋅NSD⋅R, these three metrics can be jointly visualised in a Taylor diagram . In this coordinate system, R is represented by the azimuthal angle, NSD by the radial distance from the origin, and NRMSE by the distance from the reference point (denoting perfect performance where R=1 and NSD=1). Such a diagram offers an intuitive and concise framework to summarise and compare our evaluation results across both inversions and multiple temporal scales.

The three metrics described above, however, do not capture the overall bias between modelled and measured values. We therefore additionally define and visualize the normalized mean bias (NMB) on the same Taylor diagram to complement the model evaluation: 7NMB=∑i=1N(Mi-Oi)∑i=1NOi. From R and NSD, we further define an overall model skill metric (S) that combines both metrics as follows: 8S=4(1+R)(NSD+1/NSD)2(1+R0), where R0 represents the maximum achievable correlation coefficient given measurement uncertainties; for the purposes of this study, R0 is set to 1. The resulting model skill score, S, ranges from 0 to 1, where a value of 1 signifies perfect agreement between modelled and observed values. We present this metric in a bar chart positioned beneath each Taylor diagram; together, these visualisations facilitate a robust comparison of the model performance yielded by the “GEMS-based” and “LEO-proxy” inversions.

We investigate the capacity of GEMS geostationary tropospheric NO₂ observations to enhance monthly NO_x emission estimates and subsequent air quality modelling across a full annual cycle (December 2020–November 2021). Our analysis reveals that the contrasts between the “GEMS-based” and “LEO-proxy” inversions primarily follow two distinct seasonal patterns: non-summer (September to May) and summer (June to August). To capture these patterns efficiently, we validate our adjoint model updates using two representative months: January and July 2021. For each representative month, we perform both a 6 h and a 1 d simulation. The 1 d simulation incorporates the full suite of GEMS retrievals, while the 6 h simulation subsets only those observations at 13:45 local time (KST) to serve as a LEO surrogate. This configuration ensures the validation conditions closely mirror the operational “GEMS-based” and “LEO-proxy” inversions. Figure  shows that the linear correlation coefficients and regression slopes between the adjoint-based and finite-difference-based sensitivities are nearly unity for both months and durations. These results verify the successful integration of contemporary emission inventories, aromatic chemistry, and new observation operators into the GEOS-Chem adjoint framework.

While accurate sensitivity computation is a prerequisite, the ultimate objective is the optimization of the logarithmic scaling factors of monthly NO_x emissions within the 4D-Var framework. Figure  presents an evaluation of the modelled tropospheric NO₂ columns against GEMS retrievals both before and after the optimisation. Although these evaluations are not independent, as the GEMS data are used for both constraint and evalution, they provide a necessary internal consistency check. We find that both inversions consistently reduce the model-observation mismatch across all months, with the most significant improvements observed during the non-summer (September to May) period. For instance, the overall model skill, S, has been improved by 0.47 %–208.65 % and 0.32 %–200.36 % during this period in the “GEMS-based” and “LEO-proxy” inversions, respectively. Despite the differing data densities between the “GEMS-based” and “LEO-proxy” experiments, the consistent performance enhancements demonstrate that the updated adjoint model effectively optimises emissions. This successful evaluation provides the foundation for our subsequent assessment of the added value of GEMS geostationary observations of tropospheric NO₂ for monthly NO_x emission constraints and related air quality modelling.

Here we present the comprehensive model evaluation results against independent measurements of both columnar and surface NO₂ obtained from the in situ datasets detailed in Sect. . To complement this overarching evaluation, independent model evaluation results for other chemical species within selected subregions are provided in Sect. . In that section, we further explore the contrasts in modelled atmospheric constituents between the “GEMS-based” and “LEO-proxy” inversions to quantify the added value of geostationary sampling.

Figure  shows the independent model evaluation results against columnar NO₂ measurements from AERONET. We observe that during the non-summer months (September to May), both inversions yield substantial improvements over the a priori simulation across all investigated temporal scales, including afternoon, daytime, and daily averages. Crucially, the model performance driven by NO_x emissions from the “GEMS-based” inversion is generally superior or comparable to that of the “LEO-proxy” inversion. For instance, the largest improvements in the overall model skill, S, from the “LEO-proxy” inversion to the “GEMS-based” inversion occur in March or April, corresponding to 9.53 %, 6.09 %, and 5.02 % increases in the afternoon, daytime, and daily-average evaluations, respectively. Conversely, during the summer months (June to August), the performance of both inversions degrades relative to the a priori simulation. In this period, the “GEMS-based” inversion performs slightly worse than the “LEO-proxy” counterpart. This seasonal discrepancy is also reflected in the independent validation against PGN columnar NO₂ measurements (Fig. S5), although the limited number of PGN sites constrains the statistical robustness of these findings. To address this, we selected a specific site in Beijing characterised by high data coverage and more recent a priori emission data. The scatterplots of modelled versus measured columnar NO₂ at this site (Fig. S6) further corroborate the contrasting patterns between the non-summer and summer periods identified in the broader PGN dataset.

Figures S7 and S8 show the independent model evaluation results against surface NO₂ measurements from CNEMC and CPCB, respectively. Consistent with the columnar evaluation, we observe a seasonal divide in China: both inversions yield performance improvements during the non-summer months (September to May) but result in degradations during the summer months (June to August). Notably, the “GEMS-based” inversion exerts a more pronounced influence on the magnitude of these performance shifts compared to the “LEO-proxy” version. In contrast, model performance in India remains largely unchanged from the a priori simulation across all seasons and experiments. This lack of sensitivity is likely attributable to the lower density of GEMS tropospheric NO₂ retrievals over the Indian subcontinent relative to China (Figs. S3, S4). For both the CNEMC and CPCB datasets, the model demonstrates higher skill when evaluated against daytime and daily averages rather than specific afternoon values. This suggests that high-frequency hourly measurements, which are not quality-screened, may contain stochastic noise that is effectively smoothed through temporal averaging. Furthermore, the relatively coarse spatial resolution of the model (2° latitude × 2.5° longitude) likely contributes to this trend, as temporal averaging helps mitigate the spatial representativeness mismatch between point-based in situ measurements and grid-averaged model values.

Ideally, a direct comparison between GEMS tropospheric NO₂ retrievals and in situ measurements would help reveal the factors driving the observed model degradation during summer. However, such an analysis is precluded by the absence of the requisite averaging kernels for both datasets, preventing a mathematically consistent comparison. We therefore speculate that the reduced model performance during the summer months is partly attributable to the markedly lower values of GEMS tropospheric NO₂ columns in summer than in non-summer months (Figs. S9–S11), which are primarily due to enhanced photochemical losses under stronger solar radiation . The low signal-to-noise ratios under low-NO₂ conditions likely make it more challenging for the 4D-Var inversion to effectively constrain monthly NO_x emissions. Additionally, during summer months lightning and other background sources likely contribute a larger fraction of these low tropospheric NO₂ columns, and their greater uncertainties than those of anthropogenic sources further complicate the inversion. The “GEMS-based” inversion assimilates a larger volume of observations with these characteristics, potentially explaining why it performs even more poorly than the “LEO-proxy” inversion, even though summertime exhibits much stronger diurnal variability (Fig. S12 versus S13). In this sense, at least for our 4D-Var framework, the magnitude of the tropospheric NO₂ columns appears to play a more important role in inversion performance than the additional diurnal information provided by geostationary sampling.

Table  provides a summary of the adjustments made to the a priori anthropogenic NO_x emissions by the “GEMS-based” and “LEO-proxy” inversions, alongside a comparison of their respective a posteriori estimates. The spatial distributions of these emission adjustments and the differences between the two inversions are presented in Figs. S14–S16. Focusing on the non-summer period (September to May), both inversions generally result in widespread increases in anthropogenic NO_x emissions. However, the magnitude of these adjustments varies spatially and temporally; the “GEMS-based” estimates are either higher or lower than the “LEO-proxy” values depending on the specific region and month. For instance, Figs. c1 and S17c show that in April 2021, the “GEMS-based” inversion produces higher anthropogenic NO_x emission estimates across much of North China Plain, whereas the inverse is true over Northern India. This spatial divergence largely mirrors the differences in the distribution of the full GEMS dataset compared to the 13:45 KST subset (Figs. c2 and S17i). This relationship is further confirmed by a statistically significant Pearson correlation coefficient (R=0.49) between the differences in a posteriori emissions and the differences in GEMS retrievals (Fig. c4). While the updates to a priori emissions primarily propagate linearly to modelled tropospheric NO₂ concentrations (Fig. a12 and b12), some non-linearities persist. Consequently, the differences in modelled NO₂ between the two experiments (Figs. c3 and S17f) also align with the retrieval differences, showing a strong correlation of R=0.71 (Fig. c4). Although we omit a detailed discussion for every non-summer month for the sake of brevity, the significant month-to-month variability underscores the necessity of performing independent monthly inversions, as the results of one cannot serve as a direct proxy for another.

By aggregating anthropogenic NO_x emissions over the pan-Asian region and categorising the contributions from areas where the “LEO-proxy” inversion either increases or decreases emissions, Fig.  illustrates the monthly variations in adjustment patterns between the two experiments. In line with the summary in Table , both inversions yield widespread increases in anthropogenic NO_x emissions during the non-summer months across the domain. Consequently, the regionally aggregated anthropogenic NO_x emissions (Fig. c) are primarily driven by contributions from areas where the “LEO-proxy” inversion identified emission increases (Fig. b). The “GEMS-based” inversion produces higher anthropogenic NO_x emission estimates than the “LEO-proxy” inversion in March, May, and September, reflecting more uniformly robust upward adjustments across the region. Conversely, during other non-summer months, emissions from the “GEMS-based” inversion are comparable to the “LEO-proxy” results, as the former applies a mixture of stronger and weaker upward adjustments depending on the sub-region. Overall, the anthropogenic NO_x emissions aggregated over the pan-Asian region from the two inversions differ by 0.2–52.6 Gg N per month during the non-summer months, representing 0.02 %–5.06 % of the respective a priori values. Although these regional differences appear modest, they represent bulk averages over a vast and heterogeneous domain; significantly larger contrasts emerge at finer spatial scales, as previously illustrated in Figs.  and S17 and further explored in Sect. .

Following the analysis in Sect. , we maintain April 2021 as a representative month to illustrate the contrasts in modelled atmospheric composition resulting from the “GEMS-based” and “LEO-proxy” inversions. Because the “GEMS-based” inversion yields larger emission increases over North China Plain and smaller increases over Northern India than the “LEO-proxy” inversion, it provides an opportunity to examine how several key atmospheric constituents that are closely coupled to NO_x emissions respond to these regional differences. Specifically, we focus on NO₂, O₃, OH, CO, HCHO, SO₂, NH₃, and secondary inorganic aerosols (sulfate, nitrate, and ammonium). For several of these species, independent in situ measurements are available to facilitate a rigorous performance evaluation.

Figure  demonstrates that the spatial hotspots of divergence in modelled constituents generally align with the spatial patterns of inferred NO_x emission differences shown in Figs. c1 and S17c. For instance, the “GEMS-based” inversion produces higher columnar and surface NO₂ concentrations across the North China Plain compared to the “LEO-proxy” inversion, while the inverse is observed over Northern India. Increased NO₂ can enhance HNO₃ formation and thus shift NH₃ partitioning to the particulate phase, resulting in similar patterns for secondary inorganic aerosols but an opposite pattern for NH₃. The uniform response of O₃ to different NO_x adjustments in the North China Plain and Northern India highlights the contrasting VOC-limited and NO_x-limited regimes governing O₃ production in these respective regions. Similar spatial distributions are evident for OH, which, together with O₃, determines the atmospheric oxidation capacity and consequently the removal of HCHO, CO, and SO₂. As a result, these species exhibit spatial patterns opposite to those of OH and O₃.

We acknowledge that the contrasts in modelled atmospheric constituents between the two inversions are relatively modest for most species, typically within 10 %, with surface-level changes being more pronounced than columnar adjustments. NO₂ is a notable exception, exhibiting changes of up to 20 % in both columnar and surface concentrations. This is likely because NO₂ is more directly coupled to primary NO_x emissions, whereas other species are influenced by a broader array of precursors and environmental factors. Consequently, the two inversions yield nearly identical model–observation biases for all non-NO₂ species and surface NO₂ (Fig. S18). Nonetheless, the “GEMS-based” inversion does reduce model–observation biases for AERONET columnar NO₂ measurements relative to the “LEO-proxy” for most days in April 2021 over both the North China Plain and Northern India (Fig. ). Together with the overall model evaluation presented in Sect. , these results indicate that the “GEMS-based” inversion generally matches or exceeds the “LEO-proxy” inversion in improving model agreement with independent in situ measurements during non-summer months, when retrievals provide strong constraints owing to elevated NO₂ concentrations. We therefore anticipate that other atmospheric constituents also benefit from the high-frequency constraints of the “GEMS-based” inversion; even where these differences appear small, such changes can have significant implications for health and environmental impact assessments.

To understand the added value of GEMS geostationary observations of tropospheric NO₂ for NO_x emission constraints and subsequent air quality modelling during the non-summer months, we examine the diurnal variability of the observational part of the cost function (Jobs). Figure S19 illustrates an example for April 2021. Although Jobs at 13:45 local time (KST) accounts for only a small fraction (12.1 %) of the total Jobs, it correlates well with the total Jobs, with a Pearson correlation coefficient of 0.89. This indicates that the 13:45 KST retrievals, used in the “LEO-proxy” inversion, capture a substantial portion of the information content in the full GEMS dataset. Nevertheless, the remaining 87.9 % of Jobs from other hourly retrievals also contributes to the optimization process. The degree to which these additional observations differ from the 13:45 KST retrievals, and thus provide unique information, ultimately determines the added value of the GEMS geostationary sampling.