The global ocean, excluding the perennial ice-covered waters in the core area of the Arctic Ocean and the permanently frozen areas around the Antarctic continent, has a total area of 336 million square kilometers, accounting for approximately 92.8 % of the global ocean surface area. This research focuses on the 0–10 m water layer in the ocean surface, which is a critical interface for air sea exchange. Due to the complex types of water bodies, sea surface pCO₂ is influenced by various factors. The global ocean was divided into research area scales based on water depth, identifying the areas beyond the continental shelf (water depth > 200 m) as far sea areas and the areas within the range (water depth ≤ 200 m) as near sea areas.

The potential influencing factors involved do not fully follow a normal distribution, and there is a non-linear relationship between pCO₂. Therefore, selecting appropriate correlation indicators is particularly crucial. The Spearman correlation coefficient can effectively reveal the correlation between data (Eq. 3). 3ρ=1-6∑i=1nDi2nn2-1

In the formula, ρ represents the correlation coefficient, D represents the level difference of the variable, and n represents the sample size of the variable. The range of values for ρ is between -1 and 1, where -1 indicates a complete negative correlation between the influencing factors and pCO₂, 1 indicates a complete positive correlation, and 0 indicates no correlation.

To evaluate the modeling ability of different algorithms for pCO₂, we constructed eight comparative models at different research regions, including multiple linear regression (MLR),convolutional neural network (CNN), gated recurrent unit (GRU), long short term memory (LSTM),generalized additive models (GAM), extreme gradient boosting (XGBoost), least squares boosting (LSBoost), and random forest (RF). MLR serves as a baseline that linearly links temperature, salinity and nutrients to sea-surface pCO₂. CNN extracts spatial features via convolution and pooling layers to produce fine-scale pCO₂ distributions, while GRU and LSTM, with their update-reset gates and memory cells, capture long-term temporal dependencies of oceanic periodic changes on pCO₂ for historical-to-future prediction. GAM relaxes the linearity assumption by modeling each predictor's additive nonlinear effect on pCO₂. XGBoost and LSBoost iteratively optimize tree ensembles through gradient boosting or weighted residuals to uncover complex nonlinear relationships between high-dimensional features and pCO₂. Finally, RF constructs and averages many decision trees on random feature subsets, delivering robust pCO₂ estimates for large-scale ocean datasets.

The datasets at different research regions were randomly divided into training, validation, and testing sets in an 8:1:1 ratio. Five statistical methods, Mean Absolute Error (MAE, µatm) – the average absolute difference between predicted and in-situ pCO₂, indicating overall bias; Mean Absolute Percentage Error (MAPE, %) – the relative error scaled by the observed pCO₂, enabling comparison across regions with contrasting background concentrations; Mean Squared Error (MSE, µatm²) – the squared deviations averaged over all samples, emphasizing larger pCO₂ discrepancies; Root Mean Squared Error (RMSE, µatm) – the square root of MSE, providing a metric in the original pCO₂ units that is sensitive to outliers; Coefficient of Determination (R2 ) – the proportion of pCO₂ variance explained by the model, with values approaching unity signifying high predictive skill. 4MAE=1n∑i=1ny^i-yi5MAPE=100%n∑i=1ny^i-yiyi6MSE=1n∑i=1ny^i-yi˙27RMSE=1n∑i=1ny^i-yi28R2=1-∑i=1nyi-y^i2∑i=1nyi-y‾i2

In the formula, n is the number of pCO₂ observations; yi denotes the in-situ measured pCO₂ (µatm) for the ith sample, y^i is the corresponding model-estimated pCO₂, y‾i represents the mean of all measured pCO₂ values.

The surface pCO₂ models were independently validated at different regional scales, inputting data independent of the model construction, comparing the accuracy of the fitted values with the true values, and evaluating the applicability and accuracy of the model in complex marine environments. The scatter plot with true values as the x-axis and fitted values as the y-axis was drawn, with colors representing kernel density to reflect the distribution trend of points. At the global ocean scale (Fig. 5), the scatter distribution of MLR, CNN, GRU, LSTM, and GAM shows a large elliptical shape, and the fitted values deviate significantly from the true values, especially around the extreme value of pCO₂ on the sea surface. The scatter distributions of XGBoost and LSBoost have shrunk. The RF model has the best fitting performance, with a clear convergence of the scatter distribution, concentrated on Y=X line, and can effectively avoid errors in the extreme value region, indicating that its fitted value is consistent with the true value and has good stability.

In far sea areas (Fig. 6), the scatter points of MLR, CNN, GRU, LSTM, GAM, and XGBoost models exhibit elliptical distribution and diverge at both ends, indicating their limitations in dealing with extreme fluctuations of surface pCO₂. The scatter distribution ellipse of the LSBoost model significantly shrinks, and the divergence situation converges at extreme values, improving the fitting accuracy. The scatter distribution of the RF model is a flat ellipse, with the minimum difference between the fitted value and the true value, effectively reducing extreme errors.

In the independent validation of models in near sea areas, each model showed different performances (Fig. 7). The scatter of MLR, CNN, GRU, and LSTM shows an irregular distribution, with significant differences between the fitted values and the true values, and severe divergence in high-value areas. This is due to the high variability in near sea areas, which makes it difficult for the model to cope with. The scatter distribution of GAM and XGBoost has begun to show an elliptical shape, which has certain adaptability to complex environments. The scatter distribution of LSBoost shows a clear elliptical shape, which improves the fitting stability. The RF model shows significant improvement in performance, with overall convergence of scatter distribution and no significant divergence in both low and high value oceans. It can effectively reduce extreme errors and reconstruct surface pCO₂ with high accuracy in complex near sea environments.

The multi-source data was input into the constructed RF model at different area scales, with extracting the variable values of influencing factors from the multi-source data grid by grid to fit the surface pCO₂ values of the corresponding grid. If there are missing values in a certain grid in the multi-source data, the corresponding surface pCO₂ value at that location will be output as a blank value, ensuring that the reconstructed results are completely based on the original data. The blank values are mainly due to the systematic exclusion of land pixels and the limitations of data acquisition in high latitude sea areas: the former is excluded because it does not participate in ocean processes, while the latter is due to the lack of satellite data for key parameters caused by sea ice coverage or insufficient light, resulting in the inability to reconstruct the values in the region. The final generation of the surface pCO₂ distribution map for the year 2000–2019 at 0.25° × 0.25° is based on the original data.

The reconstruction results of surface pCO₂ at the global ocean scale are consistent with the distribution characteristics of LDEO actual observation data, confirming that the RF model can effectively capture the spatial distribution pattern of global ocean surface pCO₂. Through the reconstruction results (Fig. 8), it was found that the spatial distribution of surface pCO₂ exhibits a clear latitude dependence, with a distribution pattern of “high at the equator and low at the poles”. The independent observation data based on the route was compared with the reconstruction results obtained at the closest collection time. The global ocean surface pCO₂ reconstruction result showed MAE of 11.067 µatm, MAPE of 0.037, MSE of 396.060 µatm², RMSE of 19.901 µatm, and R2 of 0.816. This indicates that the deviation between the reconstructed results and the actual observed data is small, and can accurately reflect the average distribution characteristics of surface pCO₂.

Compared with other existing studies on the reconstruction of surface pCO₂ (Fig. 9), these methods are highly consistent with our results in the reconstructed spatial model pattern (Chau et al., 2022, 2024; Zhong et al., 2022). Although different studies have used different data sources, models, or methods, similar conclusions can be drawn when describing the overall distribution characteristics of pCO₂ on the global ocean surface, which to some extent verifies the reliability and accuracy of the reconstructed results. This study uses high-resolution data and RF models to make the reconstruction results more detailed, especially in the high latitude marginal sea areas of the North and South Poles.

The reconstruction results of the far sea region showed that the surface pCO₂ in the equatorial low latitude region was higher, while the surface pCO₂ in the polar high latitude region was lower (Fig. 10). We evaluated the difference in fitting accuracy between the far sea regional model and the global ocean model in the far sea areas, by comparing independent observation data based on flight routes with the reconstructed results of the two models. The results showed that the MAE of the far-sea model was 9.060 µatm, the MAPE was 0.027, the MSE was 269.511 µatm², the RMSE was 16.417 µatm, and R2 was 0.826; the MAE of the global model was 9.125 µatm, the MAPE was 0.027, the MSE was 275.582 µatm², the RMSE was 16.601 µatm, and R2 was 0.822.The reconstruction accuracy of the far sea area model has slightly improved compared to the global ocean model in the far sea area (Fig. 11), indicating that the optimization of the far sea area model in local areas has improved the reconstruction accuracy. However, the global ocean model can still provide accurate surface pCO₂ fitting in the far sea area by adapting to the overall ocean environment.

To verify the accuracy of the time series reconstruction of the model, a comparative analysis was conducted on the temporal changes between the observation data of the Hawaii Ocean Time series (HOT) and the reconstruction results of the global ocean and far sea areas (Fig. 12). The results showed that the temporal trends of both scales were consistent with the actual measurement data of the Hawaii observation station. Research has shown that the model performs well in fitting the dynamic changes of time series and can accurately reflect the temporal evolution of surface pCO₂.

The reconstruction results of surface pCO₂ in the near sea area showed (Fig. 13) that the surface pCO₂ values in the low latitude near sea areas on both sides of the equator were higher, which was closely related to factors such as high seawater temperature and vigorous evaporation. The seawater temperature in high latitude oceans is lower, causing changes in ocean circulation and mixing processes, and the overall trend of surface pCO₂ is decreasing. A comparison was made between the fitting accuracy of the near sea area model and the global ocean model in the near sea region. The results showed that the MAE of the near-shore model was 20.145 µatm, the MAPE was 0.065, the MSE was 983.726 µatm², the RMSE was 31.364 µatm, and R2 was 0.797; the MAE of the global model was 20.324 µatm, the MAPE was 0.065, the MSE was 999.147 µatm², the RMSE was 31.609 µatm, and R2 was 0.794. The reconstruction effect of the near sea area model has been improved compared to the reconstruction results of the global ocean model in the near sea area (Fig. 14), indicating that the use of RF can model the complex marine environment in the near sea area and accurately reflect the distribution characteristics of surface pCO₂ in the region.

At the global oceanic scale (Fig. 15), the equatorial region experiences strong solar radiation and high temperatures, resulting in relatively low solubility of CO₂. Additionally, the presence of upwelling brings deep seawater rich in CO₂ to the surface, leading to an increase in surface pCO₂ concentration. Due to the low temperature environment in polar oceans, the solubility of CO₂ in seawater significantly increases. The sea ice coverage and strong wind fields in polar waters promote gas exchange between the atmosphere and the ocean, resulting in relatively low concentrations of pCO₂ on the sea surface. The surface pCO₂ in the Antarctic region is generally higher than that in the Arctic region, because the circulation system transports a large amount of seawater with high surface pCO₂ from low latitudes to high latitudes. At the same time, the melting and formation of sea ice also have an important impact on the distribution of surface pCO₂. Due to the wider coverage of sea ice, the Arctic region is less affected by the North Atlantic warm current, and its surface pCO₂ concentration is lower compared to the Antarctic region. In terms of time, the global ocean surface pCO₂ shows a trend of increasing year by year, which is related to global warming. The rising sea temperature in mid latitude waters leads to a decrease in CO₂ solubility and promotes an increase in surface pCO₂ concentration.

In the far sea areas (Fig. 16), the surface pCO₂ is higher in the low latitude areas near the equator, particularly in the eastern equatorial Pacific. Mainly due to the upwelling of seawater in the region, which brings cold water rich in CO₂ from deep layers to the surface of the ocean, resulting in an increase in pCO₂ concentration on the sea surface. In the mid to high latitudes of the far sea region, the surface pCO₂ shows a low characteristic, which is due to the ocean circulation pattern promoting the mixing of surface seawater and deep seawater, resulting in relatively low surface pCO₂ concentration. The low temperature and strong biological pumping effect enhance the absorption of atmospheric CO₂ by the ocean, leading to a low surface pCO₂ concentration. In terms of time, the surface pCO₂ shows a trend of increasing year by year, especially after 2015. This is closely related to global climate change, changes in ocean circulation patterns, and the impact of human activities.

The exchange of CO₂ between seawater and atmosphere is frequent, and the surface pCO₂ value is relatively high. In mid to high latitude oceans, low-temperature seawater, polar cold water sinking, and deep seawater upwelling result in relatively low concentrations of pCO₂. The reconstruction results of surface pCO₂ in the near sea area (Fig. 17) show that the equatorial region has strong solar radiation, high temperature seawater, and the influence of tropical cyclones and trade winds. The distribution characteristics of surface pCO₂ are significant along the eastern coast of Asia in the mid latitude region of the Northern Hemisphere. The surface pCO₂ in the Yellow Sea and Bohai Sea oceans is significantly lower than that in the coastal areas of eastern North America, which is related to the East Asian monsoon circulation and complex marine ecosystems. The surface pCO₂ in the border waters between Southeast Asia, the Indian Peninsula, North America, and South America is relatively high. Due to the influence of monsoon climate and tropical cyclones, high sea temperatures, as well as marine pollution caused by human activities, have collectively led to an increase in surface pCO₂. Temporally, the surface pCO₂ in near sea areas has been increasing year by year. Due to the increase in temperature in low latitude sea areas, the solubility of CO₂ in seawater decreases, and the upward trend of surface pCO₂ is more pronounced.