Given the complexity temporal dependence and nonlinear relationship between XCO₂ and the environmental variables, we selected the At-BiLSTM model to relate the XCO₂ data with the 16 response variables affecting atmospheric CO₂, and further reconstruct the XCO₂ data at a fine spatial resolution. The LSTM model is a variant of RNN that excels in modeling temporal sequences and capture long-range dependencies (Hochreiter and Schmidhuber, 1997; Graves and Schmidhuber, 2005), which is essential for understanding the seasonal variations of XCO₂ and dynamic feedbacks between XCO₂ and environmental drivers we selected. Each LSTM cell includes an input gate, a forget gate and an output gate. The forget gate ft determines which information from the previous time step to forget (Eq. 1): 1ft=σ(Wf⋅ht-1,xt+bf) where σ, Wf, [ht-1,xt], and bf denotes the sigmoid activation function, vectors of weights, concatenation of the hidden state at timestep t-1 and the current input, and the bias vector, respectively.

The input gate it governs the selective storage of the data in current time step, and the output from forget gate ft and input gate it are combined in the cell state Ct (Eqs. 2–3): 2it=σWi⋅ht-1,xt+bi3Ct=ft⋅Ct-1+it⋅tanhWc⋅ht-1,xt+bc where Wi and Wc denote the weight matrix for the input gate and the current cell state, respectively; bi and bc are the bias vector of the input gate and the current cell state, respectively; Ct-1 and tanh represent the cell state at timestep t-1 and the activation function.

Lastly, the output gate ot controls the flow of information from the cell state to the next time step (Eq. 4). 4ot=σ(Wo⋅ht-1,xt+bo) where Wo and bo denotes the weight matrix and the bias vector of the output gate, respectively.

These gate structures effectively manage the flow of information within the LSTM, enabling it to capture the temporal dependencies present in the data (Yuan et al., 2020; Wang et al., 2022). Bidirectional LSTM consists of two directional LSTM, in which the data flows forward and backward (Graves et al., 2013). The bidirectional structure was chosen to enhance the capability of LSTM by allowing the model to consider both past and future context in the time series, thereby providing a more comprehensive understanding of the underlying temporal dynamics.

We also defined a multi-dimensional attention layer behind the BiLSTM to focus on more critical timesteps and give them higher weights (Bahdanau et al., 2016). This is particularly important when dealing with high-dimensional input data comprising multi-timestep variables, as it allows the model to assign different weights to different timesteps, thereby improving interpretability and predictive performance (Liu and Guo, 2019; Wang et al., 2024b). Based on this framework, the At-BiLSTM model offers a robust and flexible framework for linking XCO₂ with multiple environmental variables and reconstructing XCO₂ at a fine spatial resolution with improved accuracy and spatiotemporal consistency.

The At-BiLSTM consists of one input layer, three Bidirectional LSTM (Bi-LSTM) layers, one attention layer, one dropout layer to prevent overfitting, and one fully connected layer (i.e., dense layer) for the final output. Each Bi-LSTM includes 512 hidden units and tanh activation in both forward and backward directions. The attention mechanism learns a weight distribution over the time dimension using a Dense layer with softmax activation, then multiplies these weights with the BiLSTM output to emphasize important time steps. The detailed deployment and output are provided in Table 3. The model was implemented using the TensorFlow and Keras deep learning APIs in Python. A time step of 3 was used, and the model was trained for 200 epochs with the mean squared error (MSE) as the loss function. A step-wise decay strategy was applied to the learning rate, where the rate was reduced by a factor of 10 every 50 epochs to enhance training stability and convergence. Prior to training, all input data were normalized using the mean and standard deviation of the dataset.

In this study, we adopted the sample-based cross-validation (CV) method to evaluate the model performance and the in-situ validation to assess the accuracy of reconstructed XCO₂ products. We also compared the reconstructed XCO₂ products with the original OCO XCO₂ products and the CAMS-EGG4 GHGs data. Four metrics, including coefficient of determination (R2), root mean squared error (RMSE), mean absolute error (MAE) and mean bias, were calculated as follow, to assess the model performance. 5R2=1-∑i=1n(yi-fi)2∑i=1n(yi-y‾)26RMSE=∑i=1n(yi-fi)2n7MAE=∑i=1n|fi-yi|n where n is the total number of data samples, and fi, yi are the observed results and model-estimated results, respectively.

The global distribution of annual mean XCO₂ concentration from 2015 to 2021 is illustrated in Fig. 9. The results reveal pronounced spatial heterogeneity in XCO₂ concentrations, characterized by a marked hemispheric asymmetry. Specifically, the Northern Hemisphere exhibited systematically elevated XCO₂ levels compared to the Southern Hemisphere, consistent with latitudinal gradients driven by anthropogenic emission patterns and atmospheric transport dynamics. Regionally, North America, East Asia, Central Africa, and northwest of Southern America were identified as persistent hotspots of enhanced XCO₂. The high concentrations of XCO₂ in North America and East Asia stem primarily from the fossil fuel emission from energy production and transportation sectors. Whereas the tropical regions (i.e., Central Africa and South America) are influenced by coupled biomass burning and land-use changes.

We also provided the annual OCO-2 XCO₂ data from 2015 to 2019 and OCO-3 XCO₂ data from 2020 to 2021 in Fig. 10. Spatially, our reconstructed XCO2 dataset (Fig. 9) demonstrates robust consistency with satellite observations, particularly in mid-latitude industrialized regions where both datasets capture emission hotspots. Notably, OCO-3 exhibits denser observational sampling due to its improved spatial coverage and swath width compared to OCO-2's narrow tracks. However, persistent data gaps remain prevalent in both two satellite products after annual aggregating. These spatial coverage limitations hinder fine-scale global analysis, particularly in assessing localized emission sources and regional scale carbon flux.

Figure 11 presents the spatial distribution of the 7-year (2015–2021) averaged XCO₂ concentration and trend over the globe. The average XCO₂ concentration from 2015 to 2021 was 406.90 ± 0.80 ppm worldwide. The highest concentration of XCO₂ mainly occurs in the northern low-to-mid-latitudes (10–45° N). More frequent human activities and carbon emissions contributed to higher atmospheric CO₂ concentrations in the Northern Hemisphere. In contrast, the lowest XCO₂ concentration was 404.02 ppm, occurring in the Southern Hemisphere where 81 % of the area is ocean. The oceans act as a vital carbon sink and absorb most atmospheric CO₂. For the continent scale, the XCO₂ concentrations showed a slight variation (±1 ppm) between different continents. The largest XCO₂ were mainly occurred in Asia and North America over years, while the lowest XCO₂ concentration all presented in Oceania (Table 5). In terms of temporal trend, the atmospheric CO₂ exhibited a distinct increasing trend over time, with the mean growth rate of 2.32 ppm yr⁻¹. The large growth rate meanly occurs in the northern low latitudes (0–30° N), especially the Middle East and North Africa (growth rate over 2.5 ppm yr⁻¹). Globally, the XCO₂ increased by 14.16 ppm over seven years (Table 4), especially in 2021, with increased values of up to 3 ppm. This result is consistent with the Global Carbon Budget 2022 (Friedlingstein et al., 2022), which reported that the global average atmospheric CO₂ increased sharply in 2021 and reached 414.71 ppm.

To better explore the dynamics of global carbon change, we further calculated the XCO₂ anomalies based on the full-coverage XCO₂ products and presented their global distributions from 2015 to 2021 (Fig. 12). The XCO₂ anomalies were calculated by the statistical filtering method, that is, subtracting the global median XCO₂ value from the global XCO₂ distribution (Hakkarainen et al., 2016). The spatial pattern of XCO₂ anomalies were relatively consistent over seven years with no significant variations. From the global perspective, high XCO₂ anomalies mainly occurred in the Northern Hemisphere. East Asia has the largest XCO₂ anomalies with values ranging from 2 to 3 ppm, such as the east part of China. The Middle East, North Africa and the southern part of Northern America also experienced high XCO₂ anomalies. Nevertheless, negative XCO₂ anomalies were also identified in the Northern Hemisphere, specifically in regions such as Tibet in China, eastern Canada, and southern Russia. Most negative XCO₂ anomalies were observed in the Southern Hemisphere, which behaves as a carbon sink. However, some positive XCO₂ anomalies are also observed in the tropical regions (e.g., Amazonia), which indicates the Amazonia has changed into a carbon source due to the deforestation and fire occurrence in recent years (Hubau et al., 2020; Gatti et al., 2021).

Figure 13 illustrates the detailed spatial distribution of XCO₂ concentrations and anomalies over six regions with high XCO₂ retrievals in 2020. High concentrations of XCO₂ were typically associated with energy-intensive heavy industrial activities, such as Toa Oil Keihin Refinery Factory located in Kawasaki City, Japan (Fig. 13f), and the Shippingport Industrial Park in Pennsylvania, United States (Fig. 13a). Moreover, certain metropolitan transport hubs also exhibited elevated CO₂ anomalies attributable to dense populations and intensive activities. Examples included Shanghai Station in China (Fig. 13e) and John F. Kennedy International Airport in New York, USA (Fig. 13b). Attention has also been drawn to natural sources of emissions. Driven by the significant impact of agricultural mechanization and agro-industrial activities on cropland (Lin and Xu, 2018), the XCO₂ anomalies also occurred in the agricultural areas northwestern Jiangsu, China (Fig. 13d). Additionally, we also observed the high XCO₂ anomalies in Amazonia forest in Colombia, which have been suffered from deforestation (Gatti et al., 2023). In conclusion, our products could successfully capture the XCO₂ anomalies from different sources over the globe.

To validate the effectiveness of our model and resulting XCO₂ products, we compared our results with current studies which focuses on global XCO₂ reconstruction (Table 6). As for the in-situ validation, most existing studies report high accuracy with almost all R2 over 0.9, RMSE less than 2 ppm. Regarding spatial resolution, the various products differ substantially, ranging from 1° down to 0.01°. It should be noted that increasing spatial resolution tends to compromise the accuracy of XCO₂ retrievals. However, our XCO₂ product achieves an optimal balance between spatial detail and measurement precision, exhibiting both high spatial resolution (0.05°) and robust accuracy (R2= 0.91, RMSE = 1.54 ppm) in comprehensive evaluations.

To evaluate the advancement of our XCO₂ product, we compared it with original OCO-2 observations and publicly available global XCO₂ datasets (Wang et al., 2023; Sheng et al., 2022; Zhang et al., 2023) across four regions: North America, Europe with northern Africa, Asia, and Oceania (Fig. 14) in January 2015. Despite monthly aggregation, OCO-2 data exhibit persistent spatial discontinuities, limiting the capacity to analyze monthly XCO₂ variability at regional and national scales. Existing XCO₂ products (spatial resolution of 0.25, 1, and 0.1°, respectively) broadly reproduce large-scale XCO₂ patterns but fail to resolve fine-scale heterogeneity. In comparison, our reconstructed XCO₂, with the highest spatial resolution, provides a more detailed and accurate representation of the regional XCO₂ patterns. For example, lower XCO₂ concentrations are clearly identified in eastern Canada (The first row of Fig. 14) and Papua New Guinea (The fourth row of Fig. 14), regions characterized by dense forest cover. This correspondence highlights the substantial carbon sink potential of these forested areas. Our high-resolution product better identifies the CO₂ heterogeneity associated with different land cover types, whereas the coarse-resolution products smooth these signals. This limitation primarily stems from the neglect of high-resolution land cover dynamics and dependence on coarse-resolution assimilated/reanalysis datasets (e.g., CAMS XCO₂, CarbonTracker), resulting in oversmoothed spatial patterns that obscure satellite-derived high-resolution signals. Unlike assimilation-dependent approaches, our method avoids XCO₂ reanalysis inputs, preserving satellite-scale fidelity through high-resolution environmental variables modeling while maintaining precision.

Though our XCO₂ products achieved full spatial coverage and high accuracy, however, there are still several limitations need further improvement. In terms of the satellite data, OCO-2 and OCO-3 provide different spatiotemporal coverages. Analyzing OCO-2 and OCO-3 data simultaneously may introduce several uncertainties due to these differences. However, OCO-3 has a similar sensor and inherits the retrieval algorithms of OCO-2. According to Taylor et al. (2023), the mean differences between OCO-3 and OCO-2 are around 0.2 ppm over land. Therefore, we suppose that the discrepancies between their datasets are minimal, and the combined analysis of data from these two satellites will have a negligible impact on our results.

Additionally, though our model integrates multiple environmental variables associated with surface carbon flux variations, it does not account for vertical atmospheric transport. As XCO₂ represents the column-averaged CO₂ concentration, vertical redistribution of CO₂ through atmospheric transport (e.g., mixing, convection) can alter the relationship between surface carbon fluxes and column concentrations (Shirai et al., 2012). The absence of such vertical transport indicators may reduce the model's accuracy in regions or periods with strong vertical mixing. Future efforts will incorporate vertical transport-related variables, such as planetary boundary layer height, vertical wind components, and other reanalysis-derived indicators, to better represent the atmospheric processes that influence the column-averaged CO₂ signal.

Moreover, while OCO missions currently provide some of the most accurate carbon satellite-based XCO₂ retrievals, they still encounter some retrieval errors and data gaps driven by algorithmic limitations and variable meteorological conditions. A critical research frontier is the refinement of XCO₂ retrieval algorithms to mitigate systematic biases in high-aerosol-load regions (e.g., industrial regions and biomass-burning plumes). Additionally, next-generation hyperspectral satellites, such as the upcoming CO2M (Copernicus Anthropogenic CO₂ Monitoring Mission) with 2 × 2 km² resolution and GeoCarb (Geostationary Carbon Observatory) offering hourly monitoring, will enhance spatial-temporal coverage and reduce cloud-induced data gaps (Reuter et al., 2025).