The SCS, located in the northwestern Pacific, is a semi-enclosed marginal sea with a maximum water depth of ca. 4700 m (e.g., Gan et al., 2006, 2010). The rhombus-shaped deep-water basin, with a southwesterly–northeasterly direction, accounts for about half of the total area of the SCS (Fig. 1). Largely modulated by the Asian monsoon and topography, the SCS exhibits seasonally varying surface circulation, river inputs, and upwelling. The circulation of the upper layer shows a large cyclonic circulation structure in winter (Fig. 1), while in summer it exhibits an anticyclonic circulation structure (Fig. 1; Hu et al., 2010). In the northern SCS, the Pearl River discharges into the SCS with an annual freshwater input of 3.26×1011 m3 (e.g., Dong et al., 2004; Dai et al., 2014). The area influenced by the Pearl River plume may extend southeastward to a few hundred kilometers from the estuary in summer because of the monsoonal wind stress (Dai et al., 2014). The northern and western coastal regions of the SCS feature summer coastal upwelling, such as the eastern Guangdong and Qiongdong upwelling systems in the northern SCS and the Vietnam upwelling systems in the western SCS (e.g., Cao et al., 2011; Chen et al., 2012; Gan et al., 2006, 2010; Li et al., 2020). These seasonal changes in sea surface circulation lead to strong seasonal characteristics of sea surface pCO2 in the SCS.

The SCS is subject to dynamic water exchanges with the East China Sea via the Taiwan Strait and the western Pacific via the Luzon Strait (Fig. 1). In winter, driven by the winter monsoon, the China coastal current (CCC; green line in Fig. 1; Han et al., 2013; Yang et al., 2021) flows south along the Chinese mainland through the Taiwan Strait, and occupies the northern SCS with cold, fresh, nutrient-rich waters. The strong northeasterly winds in winter also slow down the western boundary ocean current, forcing the intrusion of Kuroshio water, featuring high surface salinity and high total alkalinity, into the SCS via the Luzon Strait (orange line in Fig. 1; Du et al., 2013; Park, 2013; Yang et al., 2021). These water exchange processes increase the complexity of the spatial distribution of sea surface pCO2 in the SCS, which, as a result, has strong seasonal characteristics and spatial variability.

Data collected from field surveys during the study period 2003–2020 are summarized in Table 1. Most observations were made in July, with fewer observations made in March and December of each year. The rough sea state in the SCS in winter and early spring limited the field surveys during these seasons. Data collected from July 2000 to January 2018 were originally published in Li et al. (2020). The in situ pCO2 were collected from R/Vs Dongfanghong-2 and Tan Kah Kee (TKK) (shown in Table 1). During the cruises, sea surface pCO2 was measured during the cruise. The measurements and data processing followed the SOCAT (Surface Ocean CO2 Atlas) protocol (Li et al., 2020). More details of the data collection methods are provided in Li et al. (2020). The spatial coverage and frequency of the observations are shown in Fig. 2, revealing pronounced seasonal changes across a large spatial area. For example, the spatial coverage of the in situ data in spring and fall are relatively uniformly distributed, and the south end of the spatial coverage reaches 5∘ N in spring, whereas during other seasons the data are concentrated in the northern and central regions of the SCS. In addition, only one observation was made in the basin area in winter, while the northern coastal area was more frequently surveyed, especially in summer.

Figure 3 shows the spatial and temporal distributions of in situ sea surface pCO2. Seasonally, the lowest pCO2 occurs in January, and the highest concentrations occur in May and June. Spatially, the pCO2 distribution in the basin is relatively homogeneous, although is highly variable in the northern region. In the northern coastal area in summer, the pCO2 distribution is affected by the Pearl River plume (yielding low values) and coastal upwelling (yielding high values), which last into early fall. In winter and early spring, relatively low pCO2 values (∼350 µatm) were found in the near-shore area. In addition, the high pCO2 values recorded on the western side of the Luzon Strait in December demonstrate the influence of winter upwelling during some of the surveys.

In addition to the above in situ sea surface pCO2 data, we selected in situ sea surface pCO2 data collected during four independent surveys across the four seasons in September 2018 (fall), December 2018 (winter), August 2019 (summer), and April 2020 (spring) to verify the accuracy of our reconstruction model in extrapolating periods lacking training datasets. Furthermore, we used an additional dataset of sea surface pCO2 calculated from observed dissolved inorganic carbon and total alkalinity during 2003–2019 at the Southeast Asia Time-series Study (SEATs) station (data from Dai et al., 2022) to test the long-term consistency of the reconstruction.

The gridded (0.05∘ × 0.05∘) RS-derived pCO2 data cover almost the entire SCS (5–25∘ N, 109–122∘ E) and show major variations in sea surface pCO2 at the basin scale (Wang et al., 2021; Yu et al., 2022). Further details of the RS-derived pCO2 data can be found on the SatCO2 platform (http://www.SatCO2.com).

A grid-to-grid comparison was undertaken between the RS-derived pCO2 and the in situ pCO2 data (Table 2). The differences in between range from 35 to 120 µatm in the near-shore area. The largest biases occur in summer when the RMSE is up to 29.95 µatm (Table 2). Relatively large discrepancies may reflect the limitations of the current algorithm (MeSAA and nonlinear regression), which only considers biological processes and the turbidity induced by the Pearl River discharge (characterized by Chl a and the remote sensing reflectance at 555 nm (Rrs555) and does not take into account the riverine dissolved inorganic carbon and the input of other substances that may affect pCO2 (Bai et al., 2015; Yu et al., 2022; Wang et al., 2021).

To remove the influence of the bias in RS-derived pCO2 data on our reconstructed results, this study used the EOF method to compute the spatial patterns of the RS-derived pCO2 data as input data instead of directly using the RS-derived pCO2 data. Moreover, using EOF modes of the RS-derived pCO2 as input data in the reconstructed model can provide spatial constraints on the pCO2 reconstruction.

The RS-derived SST data produced by MODIS (Moderate Resolution Imaging Spectroradiometer; https://oceancolor.gsfc.nasa.gov/, last access: 8 October 2022) are adopted in our reconstruction. The uncertainty in this dataset in the SCS is ∼0.27∘ (Qin et al., 2014). For sea surface salinity (SSS) data, Wang et al. (2022) found relatively large differences between different open-source SSS databases (i.e., multi-satellite fusion data from https://podaac.jpl.nasa.gov/, last access: 8 October 2022; model data from https://climatedataguide.ucar.edu/, last access: 8 October 2022; multidimensional covariance model data from https://resources.marine.copernicus.eu/, last access: 8 October 2022) and the in situ SSS data. Thus, Wang et al. (2022) produced an RS-derived SSS database using machine learning methods based on the MODIS Aqua remote sensing data. The bias between the RS-derived SSS (Wang et al., 2022) and in situ data was near zero (mean absolute error, MAE, of ∼0.25). Next, we used Chl a (from https://oceancolor.gsfc.nasa.gov/, last access: 8 October 2022) as an indicator of biological influence, which has a bias of ∼0.35 on a log scale and ∼115 % in the SCS (Zhang et al., 2006). Atmospheric pCO2 also influences sea surface pCO2 through air–sea CO2 exchange. We chose the atmospheric CO2 mole fraction (xCO2) data from the monthly mean CO2 concentrations measured at the Mauna Loa Observatory, Hawaii (https://gml.noaa.gov/, last access: 8 October 2022), and then calculated the atmospheric pCO2 values from xCO2 using the method in Li et al. (2020).

As mentioned in the SatCO2 platform (http://www.SatCO2.com), RS-derived pCO2 datasets have some missing values. Thus, we used the pCO2 data-filling method, suggested by Fay et al. (2021), to obtain the missing data points. First, a scaling factor for a filled month was calculated according to Eq. (1): 1sfpCO2=meanx,ypCO2enspCO2clim, where sfpCO2 is the scaling factor, pCO2ens is the monthly RS-derived pCO2 data, and pCO2clim is the monthly climatology RS-derived pCO2 data. x and y indicate that we took the area-weighted average over longitude (x) and latitude (y) to produce the monthly sfpCO2 value. Then, the filled portion of the data can be calculated from the pCO2clim data multiplied by the sfpCO2 value (see Fay et al., 2021, for details of this method).

Briefly, this filling method scales the climatological monthly pCO2 field values to fill in the missing measurements. Therefore, although specific values may be biased, the interpolated measurements still retain the main spatial distribution pattern of the filled months.

As mentioned above, the pCO2 data-filling method may bias some of the actual values. To avoid the influence of such biases on the reconstructed results, instead of directly using the RS-derived pCO2 data as features in our reconstructed model, we used the EOF method to obtain the main spatiotemporal distribution patterns of the RS-derived pCO2 data as features in our reconstructed model. The EOF reflects the spatial commonality of variables shown in the time series, and thus it is widely used to calculate spatial patterns of climate variability (e.g., Levitus et al., 2005; Dye et al., 2020; McMonigal and Larson, 2022). Typically, the spatial commonality of variables (EOF modes) is found by computing the eigenvalues and eigenvectors of a spatially weighted anomaly covariance matrix of a field. Each EOF mode's corresponding variance represents its degree of interpretation of the spatial pattern of a variable. For each of the 12 months, the cumulative variance contribution of the first eight EOF values was consistently >90 %, indicating that it could explain the main pCO2 spatial characteristics during each month; we therefore selected them as features.

The features selected in our reconstructed model can be divided into two main categories. In the first category, the features are related to the underlying physicochemical mechanisms controlling the pCO2 distribution; for example, SST exerts a primary control on the seasonal variations in surface water pCO2 in the northern SCS (Zhai et al., 2005; Chen et al., 2007; Li et al., 2020). In the second category, they provide spatiotemporal information for the pCO2 reconstruction. Previous studies (Landschützer et al., 2014; Laruelle et al., 2017; Denvil-Sommer et al., 2019) have shown that Chl a plays a critical role in fitting the influence of biological activity to pCO2, especially in the northern SCS (Landschützer et al., 2014; Laruelle et al., 2017; Denvil-Sommer et al., 2019). Sutton et al. (2017) suggest that increasing atmospheric pCO2 controls the overall increase in seawater pCO2. For the features that provide spatiotemporal information for the pCO2 reconstruction, in the present study we selected the first eight EOF values of pCO2 as the main spatial distribution feature and the monthly information of the in situ datasets as the temporal feature.

Ensemble learning, which is the process of training multiple machine learning models and combining their output to improve the reliability and accuracy of predictions, is one of the most powerful machine learning techniques (e.g., Zhan et al., 2022; Cheng et al., 2020). In other words, several different models are used as the basis to develop an optimal predictive model. There are two main ways to employ ensemble learning, namely bagging (to decrease the model's variance) or boosting (to decrease the model's bias). The random forest algorithm (code from https://scikit-learn.org/stable/, last access: 6 May 2022) is an extension of the bagging method, as it utilizes both bagging and feature randomness to create an uncorrelated forest of decision trees. The light gradient-boosting machine (LightGBM; code from https://github.com/microsoft/LightGBM/, last access: 6 May 2022) is a gradient-boosting framework that uses tree-based learning algorithms. LightGBM can be used for regression, classification, and other machine learning tasks; it exhibits rapid, high-performance as a machine learning algorithm. CatBoost (code from https://github.com/catboost/, last access: 6 May 2022) is a gradient-boosting algorithm which improves prediction accuracy by adjusting weights according to the data distribution and by incorporating prior knowledge about the dataset. This can help to reduce overfitting and improve general performance.

From the above options, we chose three ensemble learning algorithms as the machine-learning-based regression portion and multilinear regression methods (Wang et al., 2021) as the linear regression portion. We then used the K-fold and cross-validation methods to verify the applicability of different regression algorithms in the pCO2 reconstruction for seasonal training data. The results show that, in summer, the CatBoost algorithm yields the best degree of accuracy, with an RMSE of 16 µatm (Table 3). In contrast, the RMSE of LightGBM was 27 µatm and that of random forest (RF) was 26 µatm. The RMSE was nearly 20 µatm, using the linear regression algorithm employed by Wang et al. (2021). Thus, CatBoost appears to provide a reliable algorithm for reconstructing pCO2. In the other three seasons, however, using different algorithms resulted in minor differences (∼2 µatm in RMSE).

It is necessary to evaluate the accuracy of any model based on certain error metrics before applying it to specific scenarios. Common model evaluation metrics include RMSE, mean absolute percentage error (MAPE), R2 (coefficient of determination), and MAE.

The mean squared error (MSE) is the standard deviation of the residuals (prediction error), and the residuals are the distances between the fitted line and the data points (i.e., the residuals show the degree of concentration of the reconstructed data around the regression line). In regression analysis, RMSE is commonly used to verify experimental results. To assess bias, the RMSE needs to combine the magnitude of the model data and is calculated as follows: 2RMSE=1n∑i=1n(yi-yri)2, where y stands for the in situ data, yr represents the reconstructed data, and n is the number of data points.

The MAPE is a statistical measure used to define the accuracy of a machine learning algorithm on a particular dataset. It is commonly used because, compared to other metrics, it uses a percentage to measure the magnitude of the bias and is easy to understand and interpret; the lower the value of the MAPE, the better a model is at forecasting. MAPE is calculated as follows: 3MAPE=1n∑i=1n|yi-yri||yi|. The regression error metric, the coefficient of determination (R2), can describe the performance of a model by evaluating the accuracy and efficiency of the modeled results; i.e., it indicates the magnitude of the dependent variable, as calculated by the regression model, that can be explained by the independent variable. It is calculated as follows: 4R2=1-∑i=1n(yi-yi‾)2∑i=1n(yi-yri)2. MAE is the average absolute difference between the in situ data (true values) and the model output (predicted values). The sign of these differences is ignored so that cancelations between positive and negative values do not occur. It is calculated as follows: 5MAE=1n∑in|yi-yri|.

In previous studies, RMSE and MAE have primarily been used to represent the uncertainties in reconstructed datasets. However, this expression of uncertainty ignores the sensitivity of the reconstructed model to the features; i.e., the biases that the features themselves pass to the reconstructed model are ignored. Moreover, it is clearly unreasonable to use a single RMSE or MAE value to represent the entire region because the spatial bias pattern in the coastal region clearly differs from that in the basin.

Thus, here we present a novel method for calculating uncertainty, as shown below: 6Uncertainty=MAX([∑i=1,j=1,k=1n|OR_Monthly_Data(i,j,k)-Obs_Monthly_Data(i,j,k)|Obs_Monthly_Data(i,j,k)num(i)+num(j),…,⋅∑i=1,j=1,k=nn|OR_Monthly_Data(i,j,k)-Obs_Monthly_Data(i,j,k)|Obs_Monthly_Data(i,j,k)num(i)+num(j)])⋅100%⋅pCO2_recon+∂pCO2∂FeaturedFeature. Equation (6) includes two terms. The first term is the conservative bias between the reconstructed pCO2 fields and the in situ data, and the second is the sum over sensitivity of the reconstructed model to the features. For the first term in Eq. (6), k stands for the kth month, OR_Monthly_Data(ijk) stands for the kth monthly reconstructed data at longitude (i) and latitude (j), and Obs_Monthly_Data(ijk) stands for the kth monthly in situ data at longitude (i) and latitude (j). Therefore, MAX in the first term stands for the maximum of the k monthly bias ratios. And pCO2_recon stands for the reconstructed pCO2 data. In the second term, dFeature stands for the bias of the features. We conducted a sensitivity analysis using a chain rule to evaluate the influence of these biases in the features on pCO2. Then we estimated pCO2 changes due to the variabilities in these features by constraining these features based on our model and computed ∂pCO2∂Feature. For example, for ∂pCO2∂SST, we only changed the value of SST and kept the values of the other features constant to calculate the effect of each additional unit of SST on the simulated pCO2.

The reconstructed pCO2 fields show relatively low values in the northern coastal region of the study area and generally high values in the middle and southern basins (Fig. 6). The continuous changes in the spatiotemporal distribution can be found in the reconstruction results (Fig. 6). The reconstructed pCO2 fields show a trend of slow but sustained increases from 2003 to 2020. Spatial patterns of pCO2 change between 2003 and 2020, such that the coastal portion of the northern SCS shows relatively complex variability from multiple controlling factors, such as coastal upwelling, river plumes, biological activity, etc. However, pCO2 values in the middle and southern basins are relatively homogeneous, as they are mainly controlled by atmospheric pCO2 forcing and SST. Temporal changes in pCO2 between 2003 and 2020 are relatively large (∼44 µatm) in summer and relatively small (∼33 µatm) in winter.

Figure 7 compares the monthly reconstructed and in situ data. For the training dataset, the reconstructed pCO2 fields of the four seasons fit the in situ data well (Fig. 7), with an average RMSE of 3.43 µatm and an average MAE of 2.14 µatm (Table 2). For the testing sets, although there are some outliers, most of the reconstructed pCO2 data are consistent with the in situ data, with RMSE averaging 10.79 µatm and MAE averaging 6.30 µatm. The R2 of the testing set is ca. 0.91. In terms of MAPE, the accuracies of the four seasonal models are all around 99 % (Table 2), with the highest value for spring data and the lowest value for summer data. The relatively large bias (14.67 µatm) in the summer may be the influence of relatively complex regional processes, such as river plumes and upwelling. The four evaluation metrics indicate that our reconstructed pCO2 field is highly accurate in simulating both the training and testing sets.

The distributions of the biases between the reconstructed fields and the in situ data for both the training and testing datasets can be found in Fig. 8. In terms of the temporal pattern, the larger biases were more concentrated in the summer. For the spatial pattern, the biases in the northern coastal area are much greater than those in the basin. However, 95 % of the biases are <±10 µatm; therefore, our reconstructed dataset exhibits relatively high accuracy.

Figure 9 shows the bias between our reconstructed fields and the four independent in situ datasets corresponding to the four seasons. This validation can verify the accuracy of the retrieval algorithm for months without observations, namely the applicability of the retrieval algorithm extrapolation. This comparison shows that the retrieval algorithm is relatively accurate in the basin, with a near-zero bias (MAE of ∼8 µatm; Fig. 9a). The largest bias occurs in the Pearl River plume area in summer (∼35 µatm). The retrieval algorithm also has a high accuracy for pCO2 spatial variability, except in the Pearl River plume area in summer (22–20∘ N; Fig. 9b–e). The effect of the Pearl River plume on the pCO2 spatial distribution in our retrieval algorithm is smaller than that shown by the in situ data. This is because, at around the survey time (24–28 August 2019), a large amount of precipitation (∼30 mm d-1; https://psl.noaa.gov/data/gridded/data.ncep.reanalysis2.surface.html, last access: 8 October 2022) occurred around the Pearl River estuary region (24–20∘ N), which led to the intensification of the Pearl River plume. The plume has relatively low pCO2 values that eventually decreased the observed values along the coast. However, the monthly average runoff of the Pearl River during that month (August 2019; http://www.pearlwater.gov.cn/, last access: 8 October 2022; see the Pearl River plume index in Wang et al., 2022) was low, indicating that our retrieval algorithm is still highly reliable from the perspective of monthly averages. Thus, the inconsistencies between the reconstructed (monthly average) and the in situ datasets are mainly due to the differences in the timescales of the remote sensing and the in situ data. The reconstructed data in this study were determined on a monthly scale, while the temporal resolution of the in situ data were on the order of hours. It is clear that relatively pronounced short-term changes in pCO2, such as the diurnal variability caused by short-term heavy precipitation, cannot be reflected in the reconstructed data.

Dai et al. (2022) produced a time series of in situ data from 2003 to 2019 at the SEATs station, which we used here to validate the accuracy of the long-term trends of our model data (results shown in Fig. 10). The long-term trend of reconstructed pCO2 data at the SEATs station is largely consistent with the in situ data, with differences mainly found before 2005. Thus, the long-term trend produced in our reconstructed model is also highly reliable.

As shown in Table 2, our reconstructed data have a high degree of accuracy, with an RMSE of ∼10 µatm and MAE of ∼6 µatm. According to Eq. (6), the bias of RS-derived pCO2 data used in the second term of Eq. (6) is ∼21 µatm (Table 2), the bias of SST is ∼0.27 ∘C (Qin et al., 2014), the bias of SSS is ∼0.33 (Wang et al., 2022), and the bias of Chl a is ∼115 % (Zhang et al., 2006). We then estimated the pCO2 changes due to the variations in these features by constraining these features based on our model and computed ∂pCO2∂Feature.

The overall uncertainty in the reconstructed dataset is greater in the coastal area (∼13 µatm) than in the basin (∼10 µatm; Fig. 11a), and this spatial pattern is mainly determined by the second term in Eq. (6). The spatial distribution of the first term in Eq. (6) (Fig. 11b), calculated from a max bias ratio, is consistent with that of pCO2 (Fig. 11b). The second term in Eq. (6) (Fig. 11c) is calculated from the propagation of the bias from each variable (Fig. 11c). The Chl a bias (Fig. 11f) shows that it has the greatest effect on the reconstruction, among all the features (Fig. 11f). Although the bias of the RS-derived pCO2 data is relatively large, the final influence that it has on the results from the retrieval algorithm is negligible due to the use of the EOF method (Fig. 11g).

The climatological monthly reconstructed pCO2 fields are shown in Fig. 12. The highest values occur in May and June, and the lowest values occur in January. In winter, pCO2 first decreases in December and then increases after January; the pCO2 value is ca. 325 µatm in the northern coastal area and ca. 350 µatm in the basin. In spring, pCO2 gradually increases from the basin to the northern coastal area, and the high pCO2 values in the central basin gradually expand outward starting in April. In summer, pCO2 gradually declines, starting in June. In fall, pCO2 increases from north to south, and the southern region shows consistently high values.

To better show specific regions in the northern coastal area, we magnified the reconstructed pCO2 fields at locations north of 18∘ N (Fig. 13). The reconstructed pCO2 fields successfully reflect the influence of the meso–microscale processes on pCO2 in this northern coastal area of the SCS. For example, in winter, the relatively low pCO2 values, which last into early spring, are mainly controlled by the low SST and the high pCO2 around Luzon Strait affected by winter upwelling. In summer, the reconstructed pCO2 field shows that the influence of the Pearl River plume on pCO2 is the strongest in July and lasts until September; it also effectively shows the influence of coastal upwelling in the northeastern shelf (∼23∘ N, 117∘ E). Thus, our reconstructed pCO2 fields clearly reflect the spatial pattern of the in situ pCO2 (Fig. 3), which are generally consistent with previously reported patterns (Li et al., 2020; Zhai et al., 2013; Gan et al., 2010).

We divided SCS into five subregions, according to Li et al. (2020). In Fig.14, Subregion_A stands for the northern coastal area of the SCS, Subregion_B stands for the slope area of the northern SCS, Subregion_C stands for the SCS basin, Subregion_D stands for the region west of the Luzon Strait, and Subregion_E stands for the slope and basin area of the western SCS. All_region indicates the whole region containing the five subregions described above. We then calculated the deseasonalized long-term trend of spatially averaged monthly data for each subregion, and the results are shown in Fig. 14 and Table 3. This deseasonalized trend is consistent with that of the in situ data, and its uncertainty is on the 95 % confidence interval (much lower than that shown by the in situ data). We can thus also infer that the long-term trend of our reconstructed data shows high reliability in all subregions and that our data can serve as an important basis for predicting future changes in pCO2 in the SCS.

In Fig. 14a–e, we found that the sea surface pCO2 of the entire SCS is slightly higher than the atmospheric pCO2, indicating that the SCS is a weak source of atmospheric CO2. This conclusion is consistent with previous studies (e.g., Li et al., 2020). Moreover, compared to the rate of atmospheric CO2 increase (∼2.2 µatmyr-1), for Subregion_A, the pCO2 trend is much slower than that of atmospheric pCO2, and the spatially averaged monthly mean pCO2 is lower than the atmospheric pCO2. Thus, carbon accumulation in this region is expected to increase in the future. For Subregion_C and Subregion_E, the spatially averaged monthly mean pCO2 is higher than the atmospheric pCO2; thus, these two regions will still provide a weak source of atmospheric CO2 in the future. Finally, whether Subregion_B and Subregion_D act as a source or sink of the atmospheric CO2 is influenced by seasonal changes and physical processes. Subregion_B can be a zone of significant sink of atmospheric CO2, as demonstrated by its low sea surface pCO2 when the Pearl River plume spreads more widely in summer. In contrast, in winter, when the Kuroshio intrusion is strong, both Subregion_B and Subregion_D have high sea surface pCO2, indicating both subregions are sources of atmospheric CO2.