This study employs TROPOMI Level-2 data products of column-averaged CO (XCO) and CH₄ (XCH₄). The TROPOMI instrument onboard the Sentinel-5 Precursor (S5P) satellite operates in a polar sun-synchronous orbit, and provides daily global XCO and XCH₄ observations at approximately 13:30 local solar time, thereby enabling near-global daily coverage. The pixel resolution of the TROPOMI XCO and XCH₄ products was improved from 7.0×7.0 km² to 7.0×5.5 km² in June 2019.

TROPOMI retrieves XCO and XCH₄ by measuring Earth-reflected radiation in the shortwave infrared (SWIR) spectral range (2305–2385 nm). For XCO, the retrieval shows high sensitivity to the tropospheric boundary layer under clear-sky conditions; however, this sensitivity is reduced under cloudy conditions due to changes in photon path length and scattering effects (Landgraf et al., 2016). For XCH₄, the operational retrieval algorithm simultaneously estimates column-averaged dry-air mole fractions of CH₄ together with atmospheric scattering parameters. High retrieval accuracy and precision are generally achieved under clear-sky conditions over land after strict filtering of scenes affected by clouds, aerosols, or high surface albedo variability (Hu et al., 2016).

The TROPOMI Level-2 CO and CH₄ products used in this study were obtained from the NASA GES DISC Sentinel-5P/TROPOMI archive for the period 2019–2023. We used the OFFL (Offline) datasets. Specifically, the CO product used is S5P_L2__CO_____HiR, Version 02 (Copernicus Sentinel-5P (processed by ESA), 2021a), while the CH₄ product used is S5P_L2__CH4____HiR, Version 02 (Copernicus Sentinel-5P (processed by ESA), 2021b). These Version 02 products include updated spectroscopic parameters and improved treatments for non-scattering clouds compared with earlier releases. The CO product was converted to XCO, and the CH₄ product is reported as XCH₄. Both XCO and XCH₄ are reported as column-averaged dry-air mole fractions in parts per billion (ppb). To ensure the quality and reproducibility of the satellite observations, we applied product-specific quality screening and retained only TROPOMI retrievals with a quality value (qa_value) greater than 0.5 for subsequent analysis, following the recommended quality-screening threshold for the Sentinel-5P CO and CH₄ Level-2 products.

This study employs the GEOS-Chem model, a global three-dimensional atmospheric chemistry model driven by meteorological input from the Goddard Earth Observing System (GEOS) of the NASA Global Modeling and Assimilation Office (GMAO). We employed version 14.1.1 (https://geoschem.github.io/, last access: 9 September 2026), which is driven by GEOS-FP meteorological data. The most recent GEOS-5 meteorological data product to be provided by NASA/GMAO is GEOS-FP (“forward processing”) (https://geoschem.github.io/overview.html, last access: 9 September 2026). This product has a native horizontal resolution of 0.25° latitude × 0.3125° longitude and a temporal resolution of hourly data and 3-hourly data.

To balance computational cost and regional spatial detail, GEOS-Chem simulations were performed at a 2° × 2.5° horizontal resolution for global simulations, and at a 0.25° × 0.3125° nested resolution for regional simulations over China. The model time steps were set to 300 s for convective and advective transport, and 600 s for chemical processes.

The simulations incorporated detailed region-specific emission inventories. Anthropogenic emissions were sourced from the Air Pollutant Emission Inventory (APEI) v2016 for Canada, the National Emission Inventory (NEI) v2015-03 for North America, DICE-Africa for Africa (Marais and Wiedinmyer, 2016), and the MIX v1.1 inventory combined with HTAP for Asia (Li et al., 2017). Global aircraft and ship emissions were provided by the Community Emissions Data System (CEDS) (Hoesly et al., 2018), while biomass-burning CO emissions were obtained from the Quick Fire Emissions Dataset (QFED) versions 2.1, 2.2, and 2.4.

Based on these inputs and physical processes, GEOS-Chem simulates three-dimensional CO and CH₄ fields. However, XCO and XCH₄ are not direct native outputs; they were diagnosed during post-processing from the simulated vertical profiles. Specifically, the dry-air mole fraction profiles were vertically averaged using pressure-layer thickness as weighting, producing column-averaged dry-air mole fractions consistent with the definitions used by TROPOMI and TCCON. The resulting fields were converted to parts per billion (ppb) for use in the fusion framework.

In the proposed fusion framework, these GEOS-Chem simulations serve as large-scale physical priors. To match the spatial resolution of satellite observations, the global 2° × 2.5° GEOS-Chem fields were regridded to a 0.25° × 0.25° target grid, while the China 0.25° × 0.3125° fields were regridded to a 0.05° × 0.05° target grid. Regridding was performed using inverse distance weighting (IDW) to interpolate GEOS-Chem fields onto the target grids.

TCCON employs a Fourier Transform Infrared Spectrometer (FTS) to measure direct solar light in order to determine the total column concentrations of greenhouse gases in the atmosphere, including carbon dioxide (CO₂), CH₄, CO, and others (Buschmann et al., 2016; Kiel et al., 2016; Sha et al., 2020; Yang et al., 2020). These data are extensively utilized to validate satellite remote sensing data (e.g., Chander et al., 2013; Imasu et al., 2023; Lin et al., 2024; Loew et al., 2017; Wu et al., 2019; etc.) and to evaluate the performance of climate models. Due to its high precision, standardized retrieval algorithm, and consistent calibration across sites, TCCON is widely regarded as a primary ground-based reference network for validating satellite greenhouse-gas products (Wunch et al., 2011; Herkommer et al., 2024). They are rigorously calibrated and validated with high accuracy and reliability. TCCON's observing stations are situated in numerous regions worldwide, providing a comprehensive understanding of the global greenhouse gas distribution. These stations are capable of observing a diverse array of climates and ecosystems. Harmonized processing is implemented for each site's data. In order to guarantee data consistency and comparability, the data from each station is processed in a consistent manner. TCCON's XCO and XCH₄ Dry Air Mole Fraction (Xgas) in ppb are employed in this study. Site-specific and time-scale data are accessible through the official website of TCCON (https://tccondata.org/, last access: 9 September 2026), and users may select the data that is most relevant to their research requirements. The validation of XCO and XCH₄ products from TROPOMI and GEOS-Chem is frequently conducted using TCCON (Borsdorff et al., 2019; Cogan et al., 2012; Inness et al., 2022; Schneising et al., 2019).

In this study, we employed the TCCON GGG2020 data release (Laughner et al., 2023), with site-specific datasets accessible through the official TCCON website (https://tccondata.org/2020, last access: 9 September 2026). The TCCON sites used in this study, shown in Fig. S1 and listed in Table S1 in the Supplement, were selected based on data availability during 2019–2023, temporal overlap with the TROPOMI and GEOS-Chem datasets, and geographical representativeness. The selected sites cover broad latitudinal ranges and different environmental conditions, including remote background regions, mid-latitude continental sites, high-latitude regions, island sites, and urban-influenced or emission-affected regions. All stations listed in Table S1 were included in the comprehensive TCCON validation whenever valid collocated samples were available after applying the temporal and spatial matching criteria described in Sect. 3.1. A subset of these stations was additionally selected for representative time-series and scatterplot examples based on data completeness and relatively continuous records; these illustrative examples were not used as the sole basis for the overall validation statistics.

Regarding data filtering, TCCON FTS instruments measure direct solar radiation, and the retrievals are therefore already subject to the network's standard clear-sky retrieval and quality-control procedures. In this study, we applied the standard quality control provided with the TCCON GGG2020 data release and did not impose additional cloud-cover filters on the TCCON measurements. Additional filtering related to satellite data availability, including the TROPOMI missing-rate criterion within the 2° collocation window, is described separately in Sect. 3.1.

Data preprocessing is essential for ensuring the reliability of the fusion results. To reconcile the spatial resolution differences between satellite retrievals and model simulations, TROPOMI XCO and XCH₄ retrievals with qa_value below 0.5 were excluded, and the remaining observations were aggregated onto a global 0.25° × 0.25° grid (720×1440) using area-weighted averaging (Wang et al., 2018). GEOS-Chem outputs were subsequently interpolated to the same grid using inverse distance weighting (Setianto and Triandini, 2013). The 0.25° spatial resolution was selected to balance the representation of mesoscale spatial variability with computational efficiency for multi-year global fusion analyses (Hu et al., 2024; Wang et al., 2023).

To evaluate the influence of the resolution mismatch between GEOS-Chem simulation results and the final fused product, we used the 2019 CO data to conduct a one-year resolution sensitivity experiment. In this experiment, we used GEOS-Chem simulation data at the native 2° × 2.5° resolution and aggregated TROPOMI XCO to the 2° × 2.5° resolution using the area-weighted averaging method. The related fusion calculation framework was directly implemented on the 2° × 2.5° grid; subsequently, the obtained fused XCO data at the 2° × 2.5° resolution were compared with the fused product obtained by aggregating the fused XCO data at the 0.25° resolution to the same 2° × 2.5° grid using the area-weighted averaging method.

We conducted an additional sensitivity test to examine the influence of TROPOMI averaging kernels (AKs) on the comparison between satellite retrievals and model simulations. For 2019, quality-screened TROPOMI CO Level-2 retrievals (qa_value >0.5) were collocated with GEOS-Chem CO vertical profiles. Two GEOS-Chem XCO datasets were then generated for comparison. For the first dataset, GEOS-Chem XCO was diagnosed from the simulated CO profiles by vertically averaging the dry-air mole fractions using pressure-layer thickness as weighting, consistent with the standard post-processing procedure described above. For the second dataset, the GEOS-Chem CO profiles were first interpolated to the TROPOMI pressure layers and then smoothed using the TROPOMI CO column averaging kernels. Finally, both the original GEOS-Chem XCO and the AK-smoothed GEOS-Chem XCO were compared with TROPOMI XCO in ppb.

Previous studies have shown that emission inventories typically underestimate GEOS-Chem simulation results (Hu et al., 2018; Liang et al., 2023). Despite these magnitude biases, GEOS-Chem simulations generally remain consistent with TROPOMI observations in terms of spatio-temporal variability, exhibiting similar temporal evolution patterns, including concurrent increases and decreases. This consistency suggests that the spatio-temporal correlation between GEOS-Chem simulations and TROPOMI observations can be effectively exploited. By leveraging this relationship, a data fusion framework based on signal-domain reconstruction can be used to generate datasets with improved spatial continuity and more complete coverage (Chen et al., 2022; He et al., 2022; Wang et al., 2021).

We assume that a spatio-temporal relationship exists between the GEOS-Chem simulations and TROPOMI observations for XCO and XCH₄, as expressed below: 1XT=fXG,Lat,Lon,Date where Lat, Lon, and Date denote latitude, longitude, and time, respectively; XG represents the GEOS-Chem XCO and XCH₄ concentration field; and XT represents the corresponding TROPOMI observation field. In other words, the TROPOMI value at a given spatio-temporal coordinate can be approximated using the modeled concentration and its spatial and temporal information.

To simplify the representation of this relationship, Eq. (1) is reformulated as an element-wise scaling of the GEOS-Chem field by a spatio-temporal transformation matrix ρ: 2XT=XG⋅ρ where ⋅ denotes element-wise multiplication, also known as the Hadamard product. The matrix ρ represents the local spatio-temporal relationship between GEOS-Chem and TROPOMI at each grid cell and time step. It has the same dimensions as XT and XG. Known values of ρ can be obtained at valid TROPOMI pixels by comparing XT and XG, while missing values of ρ need to be reconstructed.

The parameter matrix ρ is assumed to be smooth in space and time, inspired by previous studies on filling missing values in spatio-temporal data and enhancing data smoothness using multidimensional discrete cosine transforms (Elharar et al., 2007; Garcia, 2010; Robinson and Kecman, 2003; Okolie and Smit, 2022; Peng et al., 2005; Rao and Yip, 2014; Wang et al., 2023). We therefore propose a spatio-temporal 3D matrix smoothing algorithm based on the discrete DCT and SVD to enhance data smoothness and fill missing values in spatio-temporal data. The method effectively handles spatio-temporal data with missing values while maintaining spatio-temporal correlation by combining spatio-temporal nearest-neighbor interpolation and regularized optimization techniques.

We find the spatio-temporal 3D matrix ρ^ that minimizes Eq. (3) by means of the 3D DCT. The objective function includes the residual term on the left-hand side and the smoothing term on the right-hand side: 3Eρ^=||ω12⋅(ρ^-ρ)||2+ϵ||∇2ρ^||2 where ||⋅|| denotes the Euclidean paradigm, ω is a binary mask indicating the availability of a parameter corresponding to the spatio-temporal location of ρ, ϵ denotes the smoothing parameter, and ∇2 denotes the Laplace operator. The satisfied condition ρ^ can be solved by iteration of Eq. (4): 4ρ^=αIDCT3Γ3⋅DCT3ω⋅ρ-ρ^+ρ^+1-αρ^ where α is a parametric factor for accelerating convergence, Γ3 denotes the 3D spatio-temporal filtering matrix associated with the smoothing term, which can be obtained through Eq. (5), and DCT3 and IDCT3 denote the 3D discrete cosine signal transform and its inverse transform, respectively. 5Γi1,i2,i33=11+ϵ∑k=1321-cos⁡(ik-1)πnk

Here, ik denotes the i-th value along the k-th dimension and nk denotes the size of ρ along the k-th dimension. This means that the value at each position of this three-dimensional spatio-temporal filtering matrix is completely determined by its position. The closer its position is to the element at position (1, 1, 1), the larger (the closer it is to 1) the value is, and vice versa. The value at position (1, 1, 1) is 1. Since the low-frequency components of the discrete cosine transformed signal matrix are mainly located close to position (1, 1, 1), this filtering matrix allows us to search for a smoothed ρ in the frequency domain. In this study, the total number of iterations is empirically set to 100, α is set to 0.75, and ϵ is selected through an automated search within 10⁻³ to 10⁻¹, using the value that minimizes the reconstruction error on valid observations. This optimization is performed independently for XCO and XCH₄ and for the global and China domains.

Equations (6) and (7) define the forward and inverse three-dimensional discrete cosine transforms used in the iterative update in Eq. (4). Specifically, DCT3 transforms the spatio-temporal parameter matrix ρ from the latitude–longitude–time domain into the frequency domain, where the dominant large-scale and slowly varying structures are represented by low-frequency coefficients. After the smoothing filter Γ3 in Eq. (5) is applied to these coefficients, IDCT3 transforms the filtered signal back to the original spatio-temporal domain. Therefore, Eqs. (6) and (7) provide the mathematical basis for the frequency-domain smoothing and reconstruction of ρ.

The 3D DCT, denoted as DCT₃, is defined as: 6F(u,v,w)=2NMP∑x=0N-1∑y=0M-1∑z=0P-1f(x,y,z)cos⁡π(2x+1)u2Ncos⁡π(2y+1)v2Mcos⁡π(2z+1)w2P where u=0,1,2,…,N-1, v=0,1,2,…,M-1, and w=0,1,2,…,P-1. N, M, and P represent the size of the signal in each of the three dimensions.

The inverse 3D DCT, denoted as IDCT₃, is defined as: 7f(x,y,z)=2NMP∑u=0N-1∑v=0M-1∑w=0P-1F(u,v,w)cos⁡π(2x+1)u2Ncos⁡π(2y+1)v2Mcos⁡π(2z+1)w2P where x=0,1,2,…,N-1, y=0,1,2,…,M-1, and z=0,1,2,…,P-1. N, M, and P represent the size of the signal in each of the three dimensions. Through the repeated application of DCT3 frequency-domain filtering, and IDCT3, missing values in ρ can be reconstructed while preserving the dominant low-frequency spatio-temporal structure.

Furthermore, the 3D discrete cosine transform requires a complete 3D matrix for signal conversion. Consequently, we first interpolate ρ with missing values using the spatio-temporal autocorrelation property of ρ. Subsequently, SVD is applied to retain the dominant components of the reconstructed parameter matrix and reduce weak noisy components. In this study, 80 % of the cumulative singular-value energy is retained as a practical and computationally efficient truncation threshold for the preliminary reconstruction. The rule of SVD is illustrated in Eq. (8), which is used to preserve the primary components of ρ for the iteration in Eq. (4): 8A=UΣVT where A∈Rm×n, U∈Rm×m are orthogonal matrices whose column vectors are called left singular vectors; Σ∈Rm×n is a diagonal matrix whose diagonal elements are the singular values σ1≥σ2≥⋯≥σr≥0, and r is the rank of the matrix A. V∈Rn×n is an orthogonal matrix whose column vectors are called right singular vectors.

To evaluate whether this empirical threshold materially affects the reconstruction, we conducted an additional threshold-sensitivity experiment for the 2019 daily global XCO reconstruction. Daily GEOS-Chem XCO simulations and collocated TROPOMI CO retrievals on the 0.25° × 0.25° grid were used to construct the TROPOMI/GEOS-Chem ratio fields. The same DCT-SVD reconstruction procedure was repeated using cumulative singular-value energy thresholds of 70 %, 75 %, 80 %, 85 %, 90 %, and 95 %, with the 80 % case used as the reference. The results are summarized in Table S8 and Fig. S2.

Calculate the total energy of the singular values as Etotal=∑i=1rσi2, and find the smallest k such that the first k singular values account for at least 80 % of the total energy, i.e., (∑i=1kσi2)/Etotal≥0.8. Then, setting the last r–k smaller singular values in Σ to zero yields the truncated diagonal matrix Σk=diag(σ1,σ2…,σk,0,…,0). Finally, reconstruct the approximation matrix using the truncated singular value matrix Ak=UΣkVT.

To further enhance the reconstruction quality, we introduced a residual learning module based on a deep neural network to refine the preliminary DCT/SVD reconstruction. Although the signal-domain reconstruction captures the dominant spatiotemporal structures shared by GEOS-Chem and TROPOMI, local nonlinear discrepancies may still remain because of retrieval noise, regional emission variability, transport errors, and meteorological influences. Therefore, a residual U-Net was employed to learn pixel-level corrections between the preliminary fused field and valid TROPOMI observations.

Because the target grids are finer than the native GEOS-Chem grids, the residual-learning step should be interpreted as observation-constrained reconstruction rather than pure model downscaling. GEOS-Chem provides the large-scale physical background, while the residual network learns corrections between the preliminary DCT/SVD reconstruction and valid TROPOMI observations on the target grid. Therefore, fine-scale variations in the fused datasets are constrained primarily by satellite-observed spatial patterns and auxiliary meteorological information, rather than being generated solely from the coarse GEOS-Chem fields.

Let XDCT denote the preliminary fused XCO/XCH₄ field obtained from the DCT/SVD-based reconstruction, and XTROPOMI be the valid observational values from the satellite. The residual between the fusion estimate and the true value (only available at observed locations) is defined as: 9ΔXtrue=XTROPOMI-XDCT,whereM=1

Here, M∈{0,1}H×W is a binary mask indicating the presence (1) or absence (0) of valid satellite data. The goal is to train a model Fθ(⋅) parameterized by θ to predict the residual ΔXpred across the entire domain: 10ΔXpred=Fθ(XG,XDCT,A) where XG denotes the GEOS-Chem full-coverage simulation data; XDCT denotes the DCT/SVD-reconstructed preliminary fusion; A denotes the auxiliary information such as meteorological fields and emission inventories. Precursor meteorological data simulated by GEOS-Chem and emission inventory were used in this study. The final fused data is obtained by correcting the DCT/SVD estimate with the predicted residual: 11Xfused=XDCT+ΔXpred

The model is trained using only the valid observations, i.e., locations where M=1. The masked loss was used because reliable TROPOMI targets are available only at valid retrieval pixels; pixels affected by clouds, aerosols, or retrieval failures do not provide trustworthy reference values. The mask therefore avoids penalizing the network at invalid or missing satellite pixels. Although the loss is computed only at valid pixels, the trained residual model is applied to the full spatial domain because its inputs, including GEOS-Chem simulations and the preliminary DCT/SVD reconstruction, are spatially complete or reconstructed before residual learning. Thus, the model transfers residual relationships learned from valid observations to missing regions with similar spatiotemporal patterns represented by the two input fields, following the logic of recent masked-learning atmospheric gap-filling studies (Wei et al., 2023; Sun et al., 2026). The loss function is designed to minimize the residual error at these observed locations: 12L(θ)=1∑Mi,j∑i,jMi,j⋅ΔXpred(i,j)-ΔXtrue(i,j)2

This masked mean squared error ensures that the learning focuses on valid TROPOMI retrievals. However, because valid retrievals may be spatially or temporally clustered in cloud-free regions, the masked loss may introduce sampling bias and affect extrapolation in persistently cloudy or aerosol-affected areas where valid observations are sparse. This risk is partly mitigated by the use of spatially complete predictors, including GEOS-Chem simulations and the preliminary DCT/SVD reconstruction, which provide physical and spatiotemporal constraints across the full domain. Nevertheless, fused data in regions with persistent data gaps should be interpreted with caution.

In this study, we employed a lightweight residual U-Net architecture to predict the full-domain residual field ΔXpred, which represents the correction from the DCT/SVD reconstruction to the expected TROPOMI observation. The network inputs include two channels: the GEOS-Chem simulation and the DCT/SVD reconstruction output (Wang et al., 2025). The TROPOMI mask is not used as an input but is instead applied during the loss computation to focus learning only on valid pixels.

The residual U-Net consists of an encoder–decoder structure with skip connections and lightweight residual blocks. The network contains 10 convolutional layers in total, including the convolutional layers inside the residual blocks. All hidden convolutional layers use 32 filters, with two input channels and one output channel for the predicted residual field. The input and output spatial dimensions remain unchanged (i.e., 720×1440 at 0.25° resolution), enabling pixel-wise learning of spatial residuals. The model was trained using daily global maps from 2019 to 2023. Training was performed for 5 epochs with a batch size of 4. We used the Adam optimizer with a fixed learning rate of 1×10-4, and no learning-rate scheduler was applied. No dropout layer or data augmentation was used in the final configuration. To improve numerical stability, all input variables were normalized before training. The final output is truncated to avoid physically implausible corrections, by enforcing: 13ΔXpred<γ⋅σTROPOMI,γ=3 where σTROPOMI denotes the standard deviation of observed valid values, and γ is a hyperparameter controlling confidence bounds. This truncation is applied only to the neural-network-predicted residual correction, not directly to the final XCO or XCH₄ concentration fields. Its purpose is to prevent unphysical residual corrections arising from unstable extrapolation in regions with sparse valid TROPOMI observations. We acknowledge that such truncation may partly dampen extremely large residual corrections and could therefore reduce the magnitude of rare local extremes. However, because the truncation is imposed on the residual term rather than on the full concentration fields, the large-scale and physically consistent extreme signals already present in the GEOS-Chem simulations, TROPOMI observations, or DCT/SVD reconstruction are retained. Thus, the constraint mainly suppresses anomalous correction spikes while preserving the dominant extreme-event signals.

To explicitly isolate the contribution of each component in the proposed two-stage framework, we conducted an ablation study using site-based validation across all TCCON stations for the year 2021. Five configurations were compared: (1) only DCT fusion (Garcia, 2010), (2) DCT and SVD mixed-signal reconstruction (Bengherabi et al., 2008; Majhi and Pal, 2021), (3) residual CNN (Jiang et al., 2024), (4) residual U-Net (Ronneberger et al., 2015; Yan et al., 2022), and (5) residual XGBoost (Naseem et al., 2024). The performance was assessed using the coefficient of determination (R2), root mean square error (RMSE), and mean bias (μ). This design allows the contribution of the DCT/SVD signal-domain reconstruction stage and the residual-correction stage to be evaluated separately. The site-based validation results are summarized in Tables S2 and S3.

Our evaluation methodology includes TCCON site validation, spatial-distribution assessment, and application-oriented analyses. For TCCON site validation, GEOS-Chem simulations, TROPOMI observations, and fused XCO and XCH₄ data are compared with TCCON measurements at both individual-site and all-site scales. The evaluation metrics include the coefficient of determination (R2), root mean square error (RMSE), mean bias (μ), and standard deviation of the bias (σ) (Karunasingha, 2022; Kobayashi and Salam, 2000; Wang et al., 2023). These metrics are used as descriptive validation statistics, and no formal hypothesis tests or p-value thresholds are applied. The spatial-distribution assessment includes comparisons among GEOS-Chem simulations, TROPOMI observations, and fused XCO and XCH₄ data over multiple temporal scales, including multi-year averages, seasonal variations, and annual metrics. Application-oriented analyses include the evaluation of TROPOMI data availability, the responses of XCO and XCH₄ to extreme events, and the comparison of multi-year column concentration trends across different regions.

Based on the same TCCON collocation strategy, we first performed an ablation analysis to clarify the contribution of each component in the proposed two-stage framework before evaluating the final fused datasets. As summarized in Tables S2 and S3, the comparison between “Only DCT” and “DCT/SVD mixed-signal reconstruction” isolates the contribution of the SVD-based low-rank constraint, while the comparison between “DCT/SVD mixed-signal reconstruction” and the residual-learning configurations isolates the contribution of the residual-correction stage. For XCO, adding SVD to DCT increased R2 from 0.8227 to 0.8335 and reduced RMSE from 10.439 to 10.1166 ppb. The residual U-Net further improved R2 to 0.8450 and reduced RMSE to 9.7616 ppb. For XCH₄, adding SVD increased R2 from 0.7056 to 0.7320 and reduced RMSE from 17.5156 to 16.7111 ppb, while the residual U-Net further improved R2 to 0.7598 and reduced RMSE to 15.8212 ppb. These results indicate that both the DCT/SVD signal-domain reconstruction stage and the residual U-Net correction stage make measurable contributions to the final fused datasets.

After confirming the contribution of each component, we further evaluated the final fused datasets against TCCON observations at representative stations and across all qualified station-day collocations.

The sensitivity experiment showed that the reconstructed XCO fields were highly stable across the tested SVD energy thresholds. Relative to the 80 % reference case, all threshold experiments yielded spatial correlation coefficients higher than 0.9998, RMSE differences below 0.62 ppb, spatial standard deviation ratios close to unity, and hotspot overlap ratios greater than 0.97 (Table S8). The cumulative singular-value energy analysis further showed that the first, first two, and first three singular values explained approximately 92.0 %, 96.6 %, and 97.5 % of the total energy, respectively (Fig. S2). These results indicate that the XCO reconstruction is not sensitive to the exact SVD truncation threshold within the tested range of 70 %–95 %, supporting the use of 80 % as a stable and computationally efficient threshold.

Figures 2 and 3 illustrate representative time series of daily GEOS-Chem simulations, TROPOMI observations, fused data, and TCCON XCO and XCH₄ measurements at selected ground stations. The ground stations were selected according to the following criteria. For each gas, we first screened TCCON stations that retained a relatively large number of valid spatially collocated data pairs after applying the 13:30 ± 1 h temporal window, the 2° spatial matching radius, and the TROPOMI quality filter (qa_value >0.5). Among these qualified stations, we further selected those with relatively continuous multi-year records and limited long data gaps to illustrate the temporal consistency among GEOS-Chem, TROPOMI, the fused data, and TCCON observations. Therefore, easttroutlake01, lamont01, and parkfalls01 were selected as representative XCO time-series examples, while edwards01, nicosia01, and pasadena01 were selected as representative XCH₄ examples. These selected stations were used only for illustrative time-series comparison, whereas the quantitative site-level and overall validation statistics were calculated separately using all qualified TCCON station-day collocations under the corresponding validation criteria. Compared with TCCON observations, both GEOS-Chem XCO and XCH₄ simulations show systematic underestimation; nevertheless, they capture similar temporal variations, i.e., comparable increase–decrease patterns over time. This indicates that GEOS-Chem can provide useful spatiotemporal reference information for the fusion process. The temporal variations of both TROPOMI and fused XCO and XCH₄ are generally consistent with those observed by TCCON. Compared with TROPOMI, the fused data show reduced biases μ (-0.79, -3.58, and -1.08 ppb for XCO; -5.43, -2.49, and -4.34 ppb for XCH₄) and lower standard deviations σ (9.93, 4.26, and 5.73 ppb for XCO; 5.99, 6.87, and 6.77 ppb for XCH₄) at the selected representative sites.

GEOS-Chem simulations show a systematic low bias relative to TCCON observations. The raw, uncorrected GEOS-Chem simulations are used as the physical prior in the fusion and reconstruction framework. The mean-bias adjustment is applied only for the diagnostic GEOS-Chem–TCCON comparison and is not used in generating the fused datasets. For each TCCON station and each gas, we calculate the mean difference between GEOS-Chem simulations and TCCON observations over all valid collocated days, and then subtract this mean bias from the GEOS-Chem time series at that station. This procedure removes the station-mean offset while preserving the model's day-to-day variability, allowing a clearer assessment of whether GEOS-Chem captures the temporal variations observed by TCCON. All figures and tables involving this bias-adjusted GEOS-Chem diagnostic comparison are explicitly labeled to indicate that the GEOS-Chem results were bias-corrected before validation.

Following the representative time-series comparison, we further evaluated site-level statistical agreement using scatterplots at selected representative stations under sparse TROPOMI coverage conditions in Figs. 4 and 5. This selection was based on the number of valid collocated samples after applying the missing-rate criterion, rather than on validation performance. Specifically, for each TCCON station, we first applied the qa_value >0.5 quality filter, the 13:30 ± 1 h temporal window, the 2° spatial collocation radius, and the site-day missing-rate criterion (MR >0.5). Subsequently, stations with a relatively large number of valid collocated samples after applying the missing-rate screening criterion were selected for visualization, whereas the overall validation statistics were calculated using all qualified high-missing-rate site-day collocations rather than only these representative stations. For XCO validation, burgos01, izana01, and nicosia01 were selected as representative sites (Fig. 4). At burgos01 and izana01, the fused data show improved agreement with TCCON compared with GEOS-Chem simulations and the original TROPOMI retrievals, as indicated by higher coefficients of determination (R2), lower root-mean-square errors (RMSE), smaller biases (μ), and lower standard deviations (σ). At nicosia01, the fused data do not show a clear improvement over TROPOMI but remain comparable, indicating that the fusion method does not degrade the validation performance at this site. For XCH₄ validation, burgos01, rikubetsu01, and xianghe01 were selected as representative sites (Fig. 5). At burgos01 and xianghe01, the fused data show improved statistical consistency with TCCON relative to GEOS-Chem and modest improvements relative to TROPOMI across several evaluation metrics, including R2, RMSE, μ, and σ. At rikubetsu01, the fused data remain comparable to TROPOMI, further indicating the robustness of the fusion method across different sites. Tables S4 and S5 present the validation results for all qualified individual sites for XCO and XCH₄, respectively. Overall, as shown in Tables S4 and S5, the fused data improve at least one of the three reported site-level metrics relative to the original TROPOMI retrievals at 14 of 18 XCO sites (77.8 %) and 10 of 17 XCH₄ sites (58.8 %). Here, improvement refers to higher R2, lower RMSE, or smaller |μ|.

Figure 6 presents the overall validation results for XCO and XCH₄ across all qualified TCCON site-day collocations under sparse TROPOMI coverage conditions (MR >0.5). For XCO, the fused dataset substantially reduces the systematic low bias of GEOS-Chem and shows improved agreement with TCCON compared with the original TROPOMI retrievals across several validation metrics. The fused XCO dataset achieves an R2 of 0.91, which is higher than that of TROPOMI, indicating an improved ability to capture the variability observed by TCCON. Its RMSE and standard deviation of the bias are 5.65 and 5.48 ppb, respectively, both lower than those of TROPOMI. The mean bias (μ) is also comparable to that of TROPOMI, suggesting that the fusion process preserves the overall magnitude while reducing random deviations. For XCH₄, the fused dataset also shows improved statistical consistency with TCCON. The fused XCH₄ dataset achieves an R2 of 0.83 and a lower standard deviation of the bias than TROPOMI under the same validation protocol. Although its RMSE and mean bias are comparable to those of TROPOMI, the reduced dispersion indicates that the fused dataset provides more stable estimates under sparse-observation conditions. Overall, these results demonstrate that the proposed fusion approach improves the consistency and robustness of XCO and XCH₄ estimates relative to GEOS-Chem and maintains comparable or improved performance relative to TROPOMI, particularly under high-missing-rate conditions.

To demonstrate the performance of our fused datasets under different TROPOMI coverage, we conducted experiments using different MR thresholds. Tables S6 and S7 further quantify how the performance of the fused datasets varies with TROPOMI coverage. For XCO, when the missing rate is low or moderate (MR <0.3 and 0.3≤ MR ≤0.5), TROPOMI shows slightly higher R2 values and lower RMSE values than the fused dataset, indicating the high reliability of TROPOMI retrievals under relatively good coverage conditions. However, under sparse TROPOMI coverage conditions (MR >0.5), the performance of TROPOMI decreases, with its R2 decreasing to 0.89 and RMSE increasing to 6.16 ppb. In contrast, the fused XCO data maintain a higher R2 value of 0.91 and a lower RMSE value of 5.65 ppb, indicating greater robustness under high-missing-rate conditions. For XCH₄, a similar pattern is observed. TROPOMI performs better than the fused product under low and moderate missing-rate conditions, with higher R2 and lower RMSE. However, when MR >0.5, TROPOMI performance decreases markedly, with R2 declining to 0.81 and RMSE increasing to 15.84 ppb. The fused XCH₄ data show a slightly higher R2 of 0.83 and a lower RMSE of 15.40 ppb under the same high-missing-rate condition. Although the fused XCH₄ bias is larger than that of TROPOMI, the higher R2 and lower RMSE suggest that the fused dataset reduces overall errors under sparse-observation conditions. Overall, under conditions of good TROPOMI coverage, the fused XCO and XCH₄ datasets perform comparably to the TROPOMI datasets. When TROPOMI retrievals are sparse, the fused datasets show relatively high reliability. These results indicate that our fusion framework is effective for gap-filling applications.

To further position the proposed fused datasets within the current landscape of atmospheric composition products, we compared our TCCON-based validation results with reported accuracies of representative existing products in the literature, rather than conducting a direct pixel-level comparison. Direct product-to-product comparison is not straightforward because existing products differ in target species, input observations, assimilation or fusion methods, spatial and temporal resolutions, and validation protocols. For example, CAMS-EGG4 provides global greenhouse-gas reanalysis fields for CO₂ and CH₄ by combining model and satellite information within the ECMWF Integrated Forecasting System, but it does not provide a TROPOMI-based XCO product directly comparable to the fused XCO dataset developed here (Agustí-Panareda et al., 2023). Agustí-Panareda et al. (2023) reported that CAMS-EGG4 generally shows monthly systematic and random errors for CO₂ and CH₄ within about 1 % during 2003–2020, while also noting caveats related to changes in assimilated observations and fixed underlying emissions. Wang et al. (2023) developed a daily seamless 0.25° global XCO₂ and XCH₄ fusion product from GOSAT, OCO-2, and CAMS-EGG4, and reported TCCON validation statistics of σ≈1.18 ppm for XCO₂ and σ≈11.3 ppb for XCH₄, with R2 values of 0.91–0.95 for XCO₂ and 0.90 for XCH₄. In comparison, our fused datasets achieve R2 values of 0.91 for XCO and 0.83 for XCH₄ against TCCON. Although these values are not strictly comparable because of differences in target gases, input data, and validation settings, they indicate that the proposed TROPOMI–GEOS-Chem fusion framework provides competitive TCCON-based validation performance while extending daily gap-free mapping to both XCO and XCH₄ at global 0.25° resolution and China-specific 0.05° resolution.

Note that averaging kernels (AKs) were not explicitly applied in the TCCON comparison. This choice was made because the validation focuses on column-averaged dry-air mole fractions after strict quality filtering and spatial–temporal aggregation, for which AK-related smoothing differences are expected to be smaller than retrieval noise, sampling gaps, and spatial representativeness errors. Previous TROPOMI XCH₄/XCO validation studies have shown that AK-related adjustments can be small when column averaging kernels are close to unity in the lower atmosphere (Schneising et al., 2026), although rigorous validation studies still account for smoothing uncertainty and a priori profile effects (Sha et al., 2021). Nevertheless, we acknowledge that ignoring AKs may introduce residual smoothing uncertainty, especially under cloudy conditions or in regions with strong vertical gradients.