The observational data for training the regression model were measurements of the seawater fugacity of CO₂ (fCO₂) extracted from the SOCAT database (2023 edition). fCO₂ represents the pCO₂ corrected for the nonideal behavior of the gas in seawater, and both are commonly used in oceanographic studies. SOCAT compiles quality-controlled fCO₂ measurements from various platforms, including research vessels, commercial ships, and moorings (Bakker et al., 2016). This study used the monthly gridded SOCAT coastal product with a spatial resolution of 0.25° × 0.25° (but with data gaps). The gridded product incorporated measurements with quality flags A and B (uncertainty of 2 µatm) and C and D (uncertainty of 5 µatm) (Bakker et al., 2016). Over the period of 1993–2021, the SOCAT product encompassed 55 347 grid cells within our study area (Fig. 2), accounting for approximately 2.9 % of the total number of grid cells in the NAACOM. The observational data show a lower sampling density in the areas north of Cape Cod and the western and southern GoMx (blue box in Fig. 2). The temporal distribution of the samples exhibits a notable bias, with reduced collection during winter (Fig. 2d). Despite these spatial and temporal heterogeneities, the SOCAT observations provide coverage across all subregions and seasons of the NAACOM (Fig. 2). This comprehensive, albeit sparse, coverage facilitates the reconstruction of the fCO₂ and pCO₂ field through interpolation and regression techniques.

The procedures for developing and reconstructing the pCO₂ product are illustrated in Fig. 3. Initially, the input variables and sea surface fCO₂ data were matched to create a comprehensive dataset. To maintain consistency with the SOCAT database, which reports seawater CO₂ concentrations as fCO₂, we adopted fCO₂ as the model training label and first-step output variable in our model. During the model development phase, fCO₂ measurements served as training labels for the machine-learning algorithm. The matched dataset was then divided into two sets: X1, encompassing the periods 1993–2003 and 2006–2021, and X2, covering 2004–2005. Set X1 was randomly subdivided further, with 80 % allocated for model training and the remaining 20 % for the validation test. Set X2 served as an independent test set. The model training set (80 % of X1) was used to develop a two-step RFR–LR (random forest regression–linear regression) model. The RFR model is designed to capture complex, nonlinear relationships between the input variables and the target variable (i.e., fCO₂), while the LR model is subsequently applied to mitigate potential systematic biases in RFR-derived fCO₂ values arising from spatiotemporal heterogeneities in the SOCAT observational dataset (Fig. 2). RFR, an ensemble learning technique, combines multiple decision trees to produce more accurate and stable predictions (Breiman, 2001; Lu et al., 2019). Each decision tree in the RFR model is trained on a randomly selected subset of the input data, with the final prediction derived from the average output of all the trees. This approach mitigates overfitting and enhances the generalization performance of the model, making it particularly suitable for large datasets with complex, nonlinear variable relationships. The RFR model was trained using 10-fold cross-validation with optimized hyperparameters, including a minimum leaf size of 1, a bagging method for ensemble aggregation, and 300 learning cycles after tuning. After RFR model training, the LR model was applied to the RFR-estimated fCO₂ (fCO_2est) output to make sure that the RFR model was not systematically biased: 1fCO2obs=a×fCO2est+b+ε, where fCO_2obs is the observed fCO₂ from SOCAT, a is the linear regression coefficient, b is the intercept, and ε is the residual that the linear model cannot resolve. This additional step was implemented to mitigate potential systematic bias in the RFR model that could arise from areas with a higher sampling density, thereby ensuring a more balanced representation across the entire study region. The comparison between the estimated pCO₂ before and after LR calibration is presented in Appendix A. The calibration was applied to each grid cell individually. To increase the data pool for linear regression, samples within a 5 × 5 grid window in space (i.e., 1.25° × 1.25°) were aggregated for LR model development. As the available measurements could not cover every grid cell and were insufficient to produce continuous spatial maps of the calibration coefficients (i.e., a and b in Eq. 1), we employed a locally interpolated regression strategy similar to that of Carter et al. (2018). Mathematically, given the spatial and temporal continuity of fCO_2est and fCO_2obs, the coefficients a and b must also be continuous in space and time. Therefore, we linearly interpolated the coefficients a and b across the NAACOM. The interpolated coefficients were subsequently used to adjust the RFR-derived fCO_2est.

The validation set, comprising 20 % of X1 randomly sampled from 1993–2003 and 2006–2021, serves as a critical monitoring step for model evaluation. This subset plays two key roles: first, it tests hyperparameter tuning by providing independent performance metrics on unseen data, and second, it helps detect potential overfitting by monitoring the divergence between training and validation performance. While the validation set itself cannot prevent overfitting, it enables the detection of overfitting patterns when the performance of the model improves on training data but deteriorates on validation data. Through this continuous evaluation process, the validation set ensures more robust model development and helps achieve better generalization capabilities.

The independent test set (X2), covering the years 2004–2005, serves as a critical evaluation period specifically designed to assess the reliability of the model in predicting values for years that were completely excluded from both the training and validation phases. Because we intentionally withhold these 2 years from model development, this approach directly tests the capability of the model to generate reliable predictions and fill temporal data gaps for periods without observational data.

Finally, the trained model is applied to all the satellite and reanalysis data to generate the final gap-free reconstructed fCO₂ data. As most products reported seawater CO₂ concentrations as pCO₂, we subsequently converted the reconstructed fCO₂ values into pCO₂ using the following equation (Takahashi et al., 2020), and our final product reports both fCO₂ and pCO₂: 2pCO2=fCO2×(1.00436-4.669×10-5×SST).

The input variables for training the regression model are longitude (long), latitude (lat), month, sea surface temperature (SST), sea surface salinity (SSS), sea surface height (SSH), and atmospheric pCO₂ (pCO_2air). Longitude, latitude, and month serve as spatiotemporal predictors, enabling the algorithm to identify and capture regional and seasonal variability in fCO₂ within the study area (Su et al., 2020; Yang et al., 2024). SST, SSS, and SSH are critical variables that characterize the physical and biogeochemical ocean settings, which play a crucial role in determining the spatial and temporal variability of fCO₂. pCO_2air represents the atmospheric forcing in the air–sea CO₂ exchange. Including pCO_2air is essential for accurately assessing the decadal pCO₂ trend.

SST data were obtained from the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation Sea Surface Temperature (OISST) v2.1 product (Huang et al., 2021). The OISST dataset is a global gridded SST analysis that blends observations from various sources, including satellites, ships, and buoys. The dataset employs an optimum interpolation technique to combine these observations and generate a daily SST field at a spatial resolution of 0.25° × 0.25°. For this study, the daily SST data were averaged to create a monthly product.

SSS data were obtained from the Simple Ocean Data Assimilation (SODA) v3.15.2 product (Carton et al., 2018). SODA is a comprehensive reanalysis dataset that integrates a global ocean model with observational data to estimate ocean state variables consistently. The SODA system assimilates observations from multiple sources, including floats, moorings, and ship-based measurements, thereby constraining the model output and enhancing the accuracy of the represented ocean physical properties, including SSS. The SODA v3.15.2 product offers monthly SSS data with a temporal resolution of 1 month and a spatial resolution of 0.5° × 0.5°, which were linearly interpolated to a 0.25° × 0.25° grid resolution to maintain consistency with other input variables and the gridded SOCAT fCO₂ data. Note that such interpolation could potentially introduce additional errors. We doubled the SSS uncertainty in the region, assuming that this would encompass its true uncertainty (see Appendix B).

SSH data were extracted from the Global Ocean Gridded L4 Sea Surface Heights (CMEMS, 2021) created by the Copernicus Marine Environment Monitoring Service (CMEMS). Since 1993 (ongoing) this product has provided daily SSH data derived from altimeters with a spatial resolution of 0.25° × 0.25°. Daily SSH data were averaged to monthly means.

pCO_2air data converted from the mole fraction of CO₂ in dry air (xCO_2air) were downloaded from the NOAA Marine Boundary Layer (MBL) reference product (Lan et al., 2023). The MBL reference product provides weekly zonal average xCO_2air measurements from a global observation network. The xCO_2air data were linearly interpolated to the same spatial and temporal resolution as the other input variables (0.25° × 0.25°, monthly). xCO_2air was converted into pCO_2air with the equation 3pCO2air=xCO2air×(P-pw), where P is the total atmospheric pressure on the sea surface, which was downloaded from the fifth-generation reanalysis (ERA5) of the European Centre for Medium-Range Weather Forecasts (ECMWF) (Hersbach et al., 2019), and pw is the water vapor pressure, which was calculated using the formula of Weiss and Price (1980), SST from OISST, and SSS from SODA.

The accuracy of the model outputs was assessed using several statistical metrics, including the coefficient of determination (R2), root-mean-square error (RMSE), mean absolute error (MAE), and mean bias error (MBE). These metrics were calculated for the training and validation set phases as well as for the independent validation set: 4R2=1-∑iNyobs,i-yest,i2/∑iNyobs,i-yobs‾2,5RMSE=1N∑iNyobs,i-yest,i2,6MAE=1N∑iNyobs,i-yest,i,7MBE=1N∑iNyobs,i-yest,i, where i denotes the ith sample, yobs and yobs‾ are the observed pCO₂ values from SOCAT and their average, yest represents the predicted pCO₂ values from the final model, and N is the total number of matched samples.

The uncertainty of the estimated pCO₂ in our product for each grid cell was accumulated from four sources of uncertainties: the direct pCO₂ measurement uncertainty from SOCAT (uobs), gridding uncertainty (ugrid), mapping uncertainty (umap), and the uncertainty accumulated from the input variables (uinputs). The first three sources of uncertainty were calculated according to the approach used by earlier reconstructed pCO₂ products (Landschützer et al., 2014; Roobaert et al., 2024a; Sharp et al., 2022). uobs is inherited from the SOCAT observations. The SOCAT database uses discrete samples with quality flags A and B (accuracy <2 µatm) and C and D (accuracy <5 µatm) to create the gridded file. Adopting a conservative approach, we used the maximum uobs of 5 µatm. ugrid was calculated as the standard deviation of the samples used to calculate the gridded fCO₂ in each grid cell. umap is introduced by reconstructing the pCO₂ using the RFR–LR model. It was evaluated as the RMSE between the reconstructed pCO₂ and the observed pCO₂ values following Roobaert et al. (2024a) and Sharp et al. (2022). Given that the derivation of uobs, ugrid, and umap is contingent upon SOCAT observations, these three uncertainties and the total uncertainty upCO2 are reported on a subregional basis.

In addition to these three sources of uncertainty, this study incorporated cumulative uncertainties from input variables (uinputs), including SST, SSS, SSH, and pCO_2air. These satellite-derived or reanalysis-based variables inherently possess uncertainties that propagate nonlinearly through the regression model, ultimately affecting the estimated pCO₂ values (Wang et al., 2021, 2023). We employed a Monte Carlo simulation to calculate uinputs. For each input variable (SST, SSS, SSH, and pCO_2air), we added white noise following a normal distribution N(0,uxi), where uxi is the uncertainty of the respective input variable xi. We then recalculated pCO₂ using these noise-added inputs and determined the resulting changes in pCO₂. This process was repeated 100 times for each input variable, and the resulting uncertainty in pCO₂ from each variable was calculated as the standard deviation of the differences between the original reconstructed pCO₂ and the pCO₂ values after adding noise to each grid cell. The final uinputs was computed as the square root of the quadratic sum of these individual uncertainties from the four input variables. Detailed procedures for determining uinputs are described in Appendix B.

Assuming that these sources are independent, the uncertainty of the estimated gridded pCO₂ in our product, upCO2, was calculated using the error propagation (Hughes and Hase, 2010; Taylor, 1997): 8upCO2=uobs2+ugrid2+umap2+uinputs2.

The ReCAD-NAACOM-pCO₂ product was evaluated through comparisons with seven reconstructed pCO₂ products developed for the global ocean and used in the Global Carbon Budget 2023 edition (Friedlingstein et al., 2023) and one reconstructed pCO₂ product specifically developed for the global coastal ocean (ULB_SOMFNN_coastal_v2; Roobaert et al., 2024a). These data products reconstructed pCO_2sea data using different machine-learning algorithms. Detailed information on the products is summarized in Table 1.

Our product employs a two-step RFR–LR algorithm to retrieve pCO₂. The initial RFR step accurately captures most seasonal and decadal pCO₂ variations across all six subregions (Appendix A). When comparing only at matching grid cells where SOCAT measurements are available, the differences (N=12) in the monthly mean climatology between the SOCAT- and RFR-derived pCO₂ are less than 2 µatm on average, with standard deviations below 5 µatm across all the subregions (Fig. A1). However, the RFR-derived pCO₂ shows lower accuracy in capturing long-term pCO₂ changes in the GoMe and SAB. The subsequent LR calibration improves the performance significantly: R2 values increase from 0.69 to 0.81 in the GoMe and from 0.83 to 0.93 in the SAB, while the RMSE decreases from 12.43 to 10.51 µatm in the GoMe and from 10.83 to 8.12 µatm in the SAB (Fig. A2).

The ReCAD-NAACOM-pCO₂ product demonstrated robust performance and high accuracy in capturing pCO₂ variability across the NAACOM (Fig. 4). During the model training phase, the product achieved an R2 of 0.96, an RMSE of 9.1 µatm, an MAE of 5.92 µatm, and an MBE of 0.05 µatm (Fig. 4a). The model demonstrated comparable performance metrics during the validation phase (Fig. 4b). To further evaluate the generalizability and robustness of the model, we also conducted an independent test using data from 2004 to 2005 in which not all the data samples were included in the model training and validation sets. During this independent test phase, the pCO₂ product maintained high accuracy, with R2=0.64, RMSE = 27.2 µatm, MAE = 18.86 µatm, and MBE = 0.07 µatm (Fig. 4c). Additionally, most independent validation samples were distributed around the 1:1 correspondence line, proving the ability of the models to predict pCO₂ across unsampled spatial and temporal domains without overfitting. The model consistently demonstrated strong performance during the training, validation, and independent test phases across all the subregions (Table 2). Overall, compared with all the available samples in SOCAT, it achieved an R2 of 0.92, an RMSE of 12.70 µatm, an MAE of 7.55 µatm, and an MBE of 0.13 µatm for the entire NAACOM (Table 2), highlighting the generalizability of the ReCAD-NAACOM-pCO₂ product and robustness in effectively capturing the variability in pCO₂ and providing reliable predictions of pCO₂ across the studied regions.

The ReCAD-NAACOM-pCO₂ product exhibited a negligible area-mean bias of +0.13 µatm with a standard deviation of 12.70 µatm when compared to all SOCAT observation grid cells across the entire NAACOM (Fig. 5 and Table 2). This small average difference suggests no consistent overestimation or underestimation by the regression model, indicating the reliability of the product in estimating the monthly and annual mean climatology of pCO₂ across the entire NAACOM region.

While the area-averaged difference is small, the differences are distributed heterogeneously in space. Larger differences (absolute difference >10 µatm) tend to occur in nearshore regions, particularly along the coastlines of the GoMx and SAB, as well as in northern areas such as the GoMe, SS, and GStL&GB (Fig. 5). These regional variations can be attributed to complex coastal processes such as terrestrial inputs, sparse observations in the northern areas (Lavoie et al., 2021; Rutherford et al., 2021; Salisbury and Jönsson, 2018), and less accurate satellite observations in the nearshore regions (Song et al., 2023). Conversely, smaller differences (absolute difference <2.5 µatm) are observed in the central parts of the GoMx, offshore regions of the SAB and MAB, and some nearshore regions of the SS and GB, which is likely due to more stable oceanic conditions in those regions. The regional MBEs for different machine-learning development phases (training, validation, and test sets) are detailed in Table 2. Despite these regional differences, the MBEs of both the validation set (-1.0 to 1.0 µatm) and the independent test set (-4.5 to 7.5 µatm) demonstrate minimal values across the subregions (Table 2), underscoring the effectiveness of the product in capturing the broader pCO₂ patterns across the NAACOM.

One of the primary objectives of this product is to capture the seasonal cycle of pCO₂ across the NAACOM region. Figure 6 showcases the applicability of the product in capturing the pCO₂ seasonal cycles across the southern and northern areas of the NAACOM (red and blue boxes in Fig. 2). The comparison of monthly climatologies between the gap-filled product and SOCAT observations reveals strong agreement in the southern region despite the coverage difference, with the product-estimated monthly means being only 3.05 ± 5.60 µatm higher than those of SOCAT (Fig. 6a) and suggesting that our product effectively captures the seasonal cycle where data are abundant.

In the northern region where SOCAT data are sparse, the gap-filling ability of the product is also demonstrated well. In the northern region, the area-averaged monthly pCO₂ climatology calculated from the continuous reconstructed product is 22 ± 11.12 µatm lower than the SOCAT observations, which can be attributed to the limited observational coverage in this area. This area is characterized by sparse sampling, with the observational density approximately 50 % lower than in the southern region (Fig. 2) due to the smaller area and limited cruise coverage. For instance, the GStL region only has one summer cruise in the SOCAT database (Fig. 2b), and the SS and GoMe have particularly sparse winter observations (Fig. 2d). The higher latitudes typically exhibit larger seasonal amplitudes in pCO₂, making the limited sampling from SOCAT particularly problematic for accurate characterization. Our gap-free product provides comprehensive spatial and temporal coverage, enabling more robust analysis of pCO₂ patterns and variability in these historically undersampled regions.

Over the 29-year period, the product predicts smaller monthly standard deviations in the southern region (less than 40 µatm; error bars in Fig. 6a), suggesting higher model accuracy and less interannual variability in these areas. Conversely, larger monthly standard deviations are observed in the northern areas, suggesting potentially lower accuracy and remarkable interannual variability. However, the larger interannual variability in these areas may be an artifact of the limited observational data available for regression model training, resulting in greater uncertainty in the predictions. Despite differences in the mean monthly climatology, the similar seasonal pCO₂ cycles calculated from SOCAT and the reconstructed product demonstrate the ability of the ReCAD-NAACOM-pCO₂ product to represent seasonal pCO₂ variability across diverse coastal environments. Nevertheless, there exist larger differences between the observations and reconstructed pCO₂ in some months and regions (Fig. 6b), highlighting the importance of the gap-free product in an unbiased understanding of regional carbon cycles (Ren et al., 2024). Detailed sea surface pCO₂ seasonal cycles and their controlling mechanisms across different subregions of the NAACOM will be presented in our subsequent work.

The ReCAD-NAACOM-pCO₂ product demonstrates the capability to resolve fine-scale regional spatial distributions of pCO₂. Figure 7 illustrates the spatial distribution of the annual mean climatology of pCO₂ across the NAACOM as observed by SOCAT and predicted by different global open- and coastal-ocean pCO₂ products. Despite being affected by missing data, SOCAT observations (Fig. 7a) reveal significant regional variations in pCO₂. In the Louisiana Shelf (LAS) estuary plume region (box 1 in Fig. 7), pCO₂ values consistently remain below 340 µatm, while the West Florida Shelf (WFS; box 2 in Fig. 7) exhibits elevated values exceeding 400 µatm. These contrasting patterns have been reported in previous regional studies (Kealoha et al., 2020; Robbins et al., 2018; Wu et al., 2024b).

The ReCAD-NAACOM-pCO₂ product demonstrates superior alignment with SOCAT observations in capturing those regional features that have been reported in previous observation-based studies (Fig. 7b), accurately representing the low pCO₂ values in the LAS Mississippi River plume (box 1) and the elevated pCO₂ levels in the WFS (box 2). In contrast, the global reconstructions of pCO₂, represented by the ensemble of seven open-ocean pCO₂ products (Fig. 7c), face challenges in resolving these regional pCO₂ variations, as previously discussed in Wu et al. (2024b). The coastal pCO₂ product from Roobaert et al. (2024a; ULB_SOMFFN_coastal_v2) also captures some small-scale structures like the low pCO₂ in the LAS (Fig. 7d), but the ReCAD-NAACOM-pCO₂ product exhibits values that are closer to the observations. In the northern region (box 3), the ReCAD-NAACOM-pCO₂ product predicts higher pCO₂ levels that are closer to observations in the nearshore region (Fig. 7b). This is not surprising, as ULB_SOMFNN_coastal_v2 is a global product known for its high accuracy on the global average.

In addition to these previously documented regional variations, our product reveals several notable features not previously captured by observations or other existing products. For instance, the GoMe displays intermediate pCO₂ levels of around 380 µatm, which is distinctly higher than surrounding waters at comparable latitudes, a feature previously documented by a pCO₂ product reconstructed using multiple linear regression (Signorini et al., 2013) and 5-year (2004–2009) mooring and cruise data (Vandemark et al., 2011). However, this contradicts two other studies based on numerical models (Cahill et al., 2016; Rutherford et al., 2021). In the southern GStL (S.GStL; box 4 in Fig. 7), pCO₂ values are slightly higher compared to adjacent waters at similar latitudes, aligning with high nutrient concentrations typically observed in these river-influenced waters (Lavoie et al., 2021). These regional patterns could not be captured completely by the global products (Fig. 7c and d). The ability of the ReCAD-NAACOM-pCO₂ product to resolve such regional features demonstrates its potential value for investigating coastal carbon dynamics and their responses to local and regional forcing factors in the NAACOM.

Using pCO₂ products to accurately reconstruct pCO₂ linear trends in coastal regions presents significant challenges due to the high spatial heterogeneity of coastal pCO₂ dynamics. This heterogeneity often leads to sea surface pCO₂ changes that deviate from atmospheric trends (Laruelle et al., 2018). Even when utilizing similar observational datasets, derived products may not consistently reflect the underlying trends. For instance, Wu et al. (2024b) examined the ability of various products to reflect pCO₂ changes in the GoMx, a region where pCO₂ trends exhibit significant spatial variability. Despite this heterogeneity, seven global open-ocean products (listed in Table 1) indicate trends similar to atmospheric pCO₂ across the entire GoMx without regional differences. In contrast, the GoMx-specific regional product developed by Chen and Hu (2019) demonstrates no significant overall trend. The discrepancy in trend detection stems primarily from the design of the regression model and the selection of the input variables. These factors are critical in capturing the complex spatiotemporal variability of coastal pCO₂ and its long-term evolution.

To assess the capability of the product in resolving decadal pCO₂ trends, we conducted an analysis of the pCO₂ evolution using three distinct regions within the NAACOM (three boxes in Fig. 7) as representative examples (Fig. 8). Decadal trends of deseasonalized time series were calculated following the protocol established by Sutton et al. (2022). The LAS (box 1 in Fig. 7) has been identified as an increasing CO₂ sink characterized by a negative pCO₂ rate increase from 2002 to 2021 (Wu et al., 2024b). Our product results for the extended period of 1993–2021 indicate that pCO₂ increased at a rate of +0.44 ± 0.11 µatm yr⁻¹ (Fig. 8a). This rate is significantly lower than the observed atmospheric pCO₂ increase in this region during 2002–2021, which is approximately +1.8 µatm yr⁻¹. These findings corroborate our previous conclusion that the LAS is an increasing CO₂ sink, demonstrating the capability of our product in revealing long-term pCO₂ trends in this dynamic river plume region, extending the analysis period by nearly a decade compared to previous studies. In contrast, the WFS (box 2 in Fig. 7) exhibits an accelerated pCO₂ increase that is faster than the atmospheric pCO₂ of around +2.0 µatm yr⁻¹ (Fig. 8b), aligning with observations reported by Robbins et al. (2018), who found a transition from a CO₂ sink to a source in this region during the 1990s.

Both ReCAD-NAACOM-pCO₂ and SOCAT consistently report a pCO₂ trend of around +2.3 to +2.5 µatm yr⁻¹ in the northern region (box 3 in Fig. 7) over 1993–2021 (Fig. 8c), which is faster than the atmospheric pCO₂ increase (around +2.0 µatm yr⁻¹), suggesting that these areas are becoming a decreasing CO₂ sink. However, limited observational data in this area necessitate cautious interpretation and warrant further validation in future research. Overall, the spatiotemporal heterogeneity in surface-ocean pCO₂ trends across the NAACOM underscores the importance of long-term monitoring to elucidate the drivers of these trends, particularly in regions influenced by major current systems and in areas with limited observational data.

The uncertainty of the reconstructed pCO₂ values in each grid cell was estimated by accumulating uncertainties from mapping (umap), gridding (ugrid), measurement (uobs), and input variables (uinputs; see Sect. 2.5 for further details on the calculation). To maintain a conservative estimate, we adopted the larger value of 5 µatm as uobs for all the data points. The gridded fCO₂ values from SOCAT are reported as the averages of all samples collected within each grid cell. Accordingly, ugrid was quantified as the standard deviation of samples within each grid cell, calculated across six subregions. Following the previous literature (Roobaert et al., 2024a; Sharp et al., 2022), umap was calculated using the RMSE values of the model validation phase reported in Table 2. The uncertainty from the validation set (20 % of X1) was chosen for its sample size that was larger than the independent test set (X2) and for consistency with the 10-fold cross-validation results while avoiding potential underestimation from the training set. uinputs was calculated using a Monte Carlo simulation (Appendix B). These four sources of uncertainty were evaluated across different subregions of the NAACOM, as shown in Table 3. umap contributes the largest portion to the total number of uncertainties across all the sub-subregions, with a maximum value of up to 20.12 µatm in the GoMe. Overall, the ReCAD-NAACOM-pCO₂ product demonstrates uncertainties ranging from 16 to 28 µatm across the six subregions and an average uncertainty of 23.25 µatm for the entire NAACOM.

Our uncertainty estimation employs a conservative estimation using maximum values at the calculation step. This approach likely overestimates the true uncertainty. Despite this conservative method, our calculated uncertainty for the Atlantic margins is comparable to the 43.4 µatm reported by Sharp et al. (2022) for areas within 100 km of the North American Pacific margins, suggesting good performance of our product. It is important to note that our uncertainty calculation assumed independence among all the sources, which is a simplification. Recent research has highlighted that these uncertainties are often correlated (Ford et al., 2024). Future studies should consider these inter-variable correlations to refine uncertainty estimates. In addition, the uncertainties reported in this section and provided in the NetCDF file represent the propagated errors for individual pCO₂ values in each grid cell. Methods to calculate uncertainties in regional averages of pCO₂ or air–sea CO₂ fluxes over specific spatial and temporal domains are detailed in Roobaert et al. (2024a) and Landschützer et al. (2014).

Even though ReCAD-NAACOM-pCO₂ resolves regional pCO₂ variability with high accuracy in the NAACOM, this product still has room for improvement in the future. Potential areas of improvement include the 0.25° spatial resolution, which is inadequate for resolving submesoscale variability at the scale of 0.1–10 km (McWilliams, 1985). Furthermore, during the independent validation phase, the accuracy of the model-predicted values decreased in the GoMe (R2=0.49) and GoMx (R2=0.46) (Table 2), which may be due to the complex biological and physical conditions in the estuary plume regions in these two gulfs. In this study, we opted not to include chlorophyll-a (Chl-a) concentrations and wind speeds as input variables for model training and prediction. This decision was primarily due to the limited temporal coverage of satellite-derived Chl-a data, which only extends back to 1997 with the launch of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) satellite (O'Reilly et al., 1998). The inclusion of Chl-a would have restricted the temporal range of our model, potentially limiting its ability to capture long-term trends and variability in pCO₂. Future versions of our model will aim to address this limitation. One potential approach is to develop a two-phase model: one phase for the period before 1997 without Chl-a data and another for the post-1997 period incorporating Chl-a information. Alternatively, we may explore methods to reconstruct historical Chl-a data or use proxy variables that correlate with biological productivity and are available for the entire study period.

In our previous work, we demonstrated that incorporating wind speeds and sea surface roughness data derived from synthetic aperture radar (SAR) could enhance model performance in predicting pCO₂ at submesoscale resolutions (Wang et al., 2024). In this work, we evaluated the inclusion of wind speed as an input variable in our model. However, at the 0.25° resolution employed here, the addition of wind speed data did not significantly improve the model performance (it only increased the R2 by 0.1). Moreover, when using the same Monte Carlo simulation approach applied to other variables, incorporating wind speeds would introduce an additional 6 µatm uncertainty to pCO₂ estimates, doubling the input-related uncertainties. Consequently, we excluded wind speeds from our regression model to reduce input-related uncertainties. Despite this omission, our product demonstrates robust capability in resolving regional variations, seasonal cycles, and decadal trends in pCO₂, making it valuable for future studies.