Estimating surface pCO₂ and its long-term variability in the East China Sea using machine learning with satellite data

Abstract

Accurate estimation of sea surface partial pressure of CO₂ (pCO₂) in optically complex coastal waters remains challenging due to significant biogeochemical heterogeneity. This study develops a machine learning approach to reconstruct pCO₂ in the East China Sea (ECS) from 2003 to 2023, utilizing MODIS-derived optical classification. Using normalized water-leaving radiance at 555 nm (nL_w555) as a threshold (1.5 mW cm^-2µm^-1 sr^-1), the ECS was classified into two distinct regimes: Clear Water (CW) and Turbid Water (TW). Then, the pCO₂ was reconstructed using a Categorical Boosting (CatBoost) model that integrates multi-spectral satellite variables as numerical predictors with an optically-derived Water Case as a categorical input feature to account for heterogeneity. Evaluated on the test dataset, this approach achieved high overall accuracy (R² = 0.86, RMSE = 16.55 µatm), notably reducing prediction errors (RMSE) in TW by up to ~81% compared to conventional models. The model maintained robust regime-level generalization (CW: R² = 0.82, RMSE = 15.64 µatm; TW: R² = 0.82, RMSE = 22.01 µatm). The 21-year climatology reveals distinct mean pCO₂ levels for CW (361.2 µatm) and TW (415.1 µatm). While CW exhibits strong summer biological drawdown, TW functions as a highly variable net CO₂ source driven by positive non-thermal anomalies (+28.09 µatm). Over the 21-year period, the atmospheric CO₂ growth rate (+2.41 µatm yr^-1) significantly outpaced the surface pCO₂ increases in both regimes (CW: +0.66 µatm yr^-1; TW: +1.11 µatm yr^-1). This growing thermodynamic gradient overwhelmingly drives an increasingly negative flux anomaly (−0.182 mmol m^-2 d^-1 yr^-1), statistically intensifying the CW carbon sink. Crucially, recognizing the TW as a weak net source (+0.50 Tg C yr^-1) rather than a sink reveals that conventional models overestimate ECS carbon uptake by ~46% (~4.04 Tg C yr^-1). Ultimately, this study provides a highly refined long-term carbon budget for the ECS, demonstrating that accounting for spatial heterogeneity is key to accurately assessing coastal carbon dynamics.

1 Introduction

Since the Industrial Revolution, the escalating concentration of atmospheric carbon dioxide (CO₂) has been identified as a primary driver of global warming and climate change (Canadell et al., 2023). In response, the ocean has played a pivotal role as a buffer, mitigating the pace of climate change by absorbing approximately 25% of anthropogenic CO₂ emissions (Gruber et al., 2019; Friedlingstein et al., 2022). The exchange of CO₂ at the air-sea interface is governed by the difference in the partial pressure of carbon dioxide (pCO₂) between the two reservoirs (ΔpCO₂^sea-air = pCO_2,water - pCO_2,air) (Takahashi et al., 2002). While atmospheric pCO₂ is relatively uniform globally due to rapid mixing (Zhang et al., 2021), sea surface pCO₂ exhibits significant spatiotemporal variability driven by diverse factors such as sea surface temperature (SST), sea surface salinity (SSS), biological activity, and physical mixing (Ciais et al., 2014). Therefore, precise estimation of the highly variable sea surface pCO₂ is essential for accurately quantifying the ocean’s role in the global climate system.

Coastal margins, in particular, account for only about 8% of the global ocean surface area but are characterized by high carbon flux rates and variability due to substantial terrestrial inputs and active biological productivity (Aufdenkampe et al., 2011; Dai et al., 2022). Among these regions, the East China Sea (ECS) is one of the largest continental shelves in the world, receiving massive amounts of freshwater and sediment from the Changjiang (Yangtze) River, and is characterized by significant physical and biogeochemical heterogeneity (Chen, 2009).

The primary challenge in resolving the carbon cycle of the ECS lies in its profound biogeochemical heterogeneity, which mainly stems from the spatiotemporal distribution and role of suspended particulate matter (SPM). Generally, in summer, the Changjiang Diluted Water (CDW) acts as a strong CO₂ sink due to phytoplankton blooms triggered by nutrient-rich freshwater discharge (Tseng et al., 2011; Guo et al., 2015). Interestingly, most suspended sediments discharged from the Changjiang during this period are rapidly trapped near the river mouth west of 123°E (DeMaster et al., 1985; Yuan et al., 2008). Consequently, the CDW extending offshore maintains low salinity but exhibits optically clear characteristics with low sediment concentrations.

In contrast, during autumn and winter, the Subei coasts experience large-scale sediment resuspension driven by strong tidal currents and northwesterly monsoons. Specifically, the radial sand ridges—covering approximately 20,000 km² (Song et al., 2018) (Figure 1)—act as a massive source of resuspended sediments. These sediments are transported southeastward by the Yellow Sea Coastal Current (YSCC), forming a turbid plume that extends toward Jeju Island. Beyond its optical impact, this suspended matter serves as a biogeochemical reactor, where the remineralization of organic carbon releases CO₂ (Li et al., 2015; Bartl and Thrush, 2025). As a result, a clear spatial contrast emerges: while the outer shelf absorbs CO₂ via the biological pump, the turbid coastal waters act as a CO₂ source due to the decomposition of organic matter (Cai, 2011). Based on these contrasting dynamics, the ECS comprises biogeochemically distinct systems.

Figure 1

Approaches using satellite-derived data have been widely employed to estimate surface pCO₂ within such a biogeochemically complex environment. Early approaches utilized empirical relationships with proxies such as SST, SSS, and chlorophyll-a (Chl-a) (Zhu et al., 2009; Tao et al., 2012). Recent advancements have introduced more sophisticated methods, including Mechanistic Semi-Analytical Algorithms (MeSAA) that explicitly account for thermodynamic and mixing processes (Bai et al., 2015; Yu et al., 2023) and machine learning (ML) techniques capable of resolving complex non-linear relationships (Jo et al., 2012; Li et al., 2023).

However, a critical limitation persists in these approaches. Although they attempted to resolve the heterogeneity by incorporating various input variables, they predominantly relied on an algorithm framework without explicitly classifying the domain into distinct regimes. This structural limitation becomes a primary cause of prediction bias, as applying a uniform model to such a heterogeneous environment inevitably leads to the mechanical averaging of opposing dominant drivers. Specifically, standard algorithms often misinterpret high optical backscattering signals in turbid waters as high biomass, erroneously predicting biological uptake where turbidity-induced light limitation (Lin et al., 2024) and sediment respiration (Li et al., 2015) actually dominate. This mechanistic mismatch often leads to systematic prediction errors, notably the underestimation (~30 µatm) in high pCO₂ regions (Chen et al., 2016). Similarly, Wang et al. (2023) highlighted that previous MeSAA approaches failed to fully account for localized processes, resulting in substantial uncertainties (~45 µatm). Most notably, these conventional models (including MeSAA and ML) treat optical proxies as continuous numerical inputs, which can lead to signal blurring where contrasting bio-geochemical drivers are averaged within a single regression domain.

To overcome these methodological limitations and explicitly reflect the distinct bio-geochemical characteristics, this study adopts a classification of ECS into Clear Waters (CW) and Turbid Waters (TW). We utilize nL_w555 (Normalized Water-leaving Radiance at 555 nm) as a key indicator. Specifically, nL_w555 serves as a robust optical proxy for turbidity, effectively distinguishing sediment-dominated waters from clearer, biologically productive waters while minimizing chlorophyll interference (Shi and Wang, 2009; Saldías et al., 2012). Previous studies have demonstrated that the 555 nm wavelength is the optimal optical proxy for identifying turbid water environments in complex coastal waters, as it minimizes the influence of chlorophyll absorption while sensitively capturing scattering signals from suspended matter (Yuan et al., 2008; Saldías et al., 2012). Crucially, unlike previous studies that utilize nL_w555 as a continuous predictor, we implement it as a categorical Water Case variable. This structural partitioning enables the algorithm to perform partitioned learning, explicitly recognizing the boundaries between distinct water masses.

Beyond resolving spatial heterogeneity, establishing a multi-decadal perspective is equally critical. Recent syntheses emphasize that the future trajectory of the coastal carbon sink remains highly uncertain due to concurrent shifts in land-ocean-atmosphere interactions under anthropogenic forcing (Gruber, 2015; Dai et al., 2022). As highlighted by Gruber (2015), the coastal interface is a mosaic of opposing sinks and sources, making it difficult to capture secular trends hidden within high spatiotemporal variability. While recent studies have clarified seasonal drivers in the ECS (Shim et al., 2007; Guo et al., 2015; Chen et al., 2024), relying on short-term observations limits the understanding of how these distinct regimes respond to long-term climate signals such as rapid warming (McKinley et al., 2017). In this context, approaches using satellite-derived data provide a unique capability to resolve trends in dynamic river-dominated shelves, filling the gap left by sparse in-situ measurements.

Therefore, this study aims to enhance the accuracy of sea surface pCO₂ estimation in the ECS by developing a machine learning model optimized. Furthermore, based on the constructed 21-year (2003–2023) time series, we perform a thermodynamic decomposition analysis to quantitatively elucidate the distinct controlling mechanisms (thermal vs. non-thermal effects) driving pCO₂ variability in the ECS. Ultimately, this study aims to estimate air-sea CO₂ fluxes in the ECS and to contribute to reducing uncertainties in coastal carbon budgets.

2 Data and methods

2.1 Collection of in-situ pCO₂ data

The study utilized field observations of pCO₂, SST, and SSS from the ECS region for its analysis. The primary composite data sources included the Lamont-Doherty Earth Observatory (LDEO) Version 2019 (available online: https://www.ncei.noaa.gov/access/ocean-carbon-data-system/oceans/LDEO_Underway_Database/; accessed on 25 Jul 2026) (Takahashi et al., 2020) and Surface Ocean CO2 Atlas (SOCAT) version 2024 (available online: http://www.socat.info/; accessed on 25 Jul 2026) (Bakker et al., 2024).

To supplement the spatial and temporal coverage, three additional regional datasets were incorporated. Data from Zhai (2019) and Liu et al. (2022) were included to secure coastal observations primarily around the Changjiang estuary. The Zhai (2019) dataset was obtained from a public repository (available online: https://figshare.com/articles/dataset/9768215; accessed on 26 Aug 2026). The dataset from Liu et al. (2022) was extracted directly from the supplementary materials of their original publication. Lastly, the observational data from Shim et al. (2007), which provide measurements covering the northern ECS, were obtained through direct request to the original authors. Table 1 summarizes the observation periods, spatial coverage, and statistical characteristics of each dataset. The spatial distribution of these data is shown in Figure 1.

To ensure the highest data quality and prevent the model from overfitting to observational noise, we utilized SOCAT data with quality flags A and B (uncertainty < ± 2µatm) (Bakker et al., 2024). Through this rigorous quality control process, a total of 3,671 matchups were retained for model training and evaluation, ensuring that the algorithm learns physically and biogeochemically sound relationships.

Since the data from SOCAT and Zhai (2019) were provided as fugacity of CO₂ (fCO₂), they were converted to pCO₂ using the following equation (Equation 1) (Takahashi et al., 2020):

Since LDEO and SOCAT are composite datasets, they contain overlapping data from individual cruises. Duplicate records from these two synthesis datasets were integrated for this study. Furthermore, to maintain data consistency, all pCO₂ values were corrected for the in-situ SST.

2.2 Satellite and reanalysis data

2.2.1 Environmental predictors for the machine learning model

In this study, pCO₂ in the ECS was estimated using satellite-derived products. For this purpose, Aqua-MODIS Level 3 Monthly 4 km data from January 2003 to December 2023 were used. The Aqua-MODIS data were obtained from the NASA Ocean Biology Processing Group L3 & L4 Browser (available online: https://oceandata.sci.gsfc.nasa.gov/l3/; accessed on 25 Jul 2026). The variables utilized from Aqua-MODIS included SST, Chl-a, remote sensing reflectance (R_rs) bands (centered at 443,488, and 555 nm), diffuse attenuation coefficient for downwelling irradiance at 490 nm (K_d490), and photosynthetically available radiation (PAR). SSS data were sourced from the Copernicus Marine Service (CMEMS) Global Ocean Reanalysis and Simulation (GLORYS) global-reanalysis-phy monthly product, which has a spatial resolution of 0.083° x 0.083° (available online: https://data.marine.copernicus.eu; accessed on 25 Jul 2026). GLORYS data demonstrated suitability for ECS SSS with r = 0.76 and RMSE = 1.41 psu. To eliminate short-term temporal autocorrelation along continuous ship tracks, all in-situ measurements falling within the same 4 km pixel during the same calendar month were averaged into a single monthly representative value prior to the machine learning matchups. Furthermore, to align datasets with different spatial footprints, the GLORYS SSS data were interpolated to match the unified 4 km grid spacing. Importantly, the absolute coarsest native resolution among all machine learning predictors is 0.083°, which is strictly small enough to prevent any spatial leakage during our spatial block partitioning validation (detailed in Section 2.3.4).

2.2.2 Variables for air-sea CO₂ flux calculation

Data for 10 m wind speed, 2 m temperature, and mean sea level pressure (SLP) were sourced from the ERA5 reanalysis product provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) (available online: https://cds.climate.copernicus.eu/datasets/reanalysis-era5-pressure-levels-monthly-means; accessed on 25 Jul 2026). These data were used as monthly averages on a 0.25° x 0.25° grid.

2.3 Design of pCO₂ algorithm: input variables preprocessing

In this study, a machine learning algorithm was developed to estimate pCO₂ in the ECS based on satellite data. The algorithm development process consisted of two main stages: (1) construction and preprocessing of the model dataset (input variables), (2) development of the pCO₂ estimation model.

2.3.1 Basic input variables (SST, SSS, Chl-a, R_rs bands, K_d490, and PAR)

SST is a key variable related to the solubility of CO₂ in seawater and is known to have a positive correlation with pCO₂ (Takahashi et al., 1993; Jang et al., 2017). Chl-a is used in the algorithm as a biological indicator that regulates pCO₂ concentration through photosynthesis and respiration. However, due to the high skewness of its distribution, the Chl-a values were transformed using a common logarithm for use in this study (Nakaoka et al., 2013).

Along with SST, SSS influences CO₂ solubility and carbonate formation and it has positive correlation with pCO₂ (Takahashi et al., 1993, Takahashi et al., 2002). The R_rs (centered at 443, 488, and 555 nm) represent the optical properties of phytoplankton, suspended solids, and colored dissolved organic matter (Stramski et al., 2008). K_d490 signifies water clarity and is related to light penetration and biological activity (Morel and Maritorena, 2001). PAR indicates the amount of light available for photosynthesis. Together with K_d490, it was used as a variable representing biological dynamics (Frouin and Pinker, 1995).

2.3.2 Baseline pCO₂ variable (pCO_{2, baseline})

The variable pCO_{2, baseline} is a thermodynamic term proposed by Yu et al. (2023) to describe thermodynamic variations driven by atmospheric pCO₂ forcing. This is based on the assumption that sea surface and atmospheric pCO₂ reach equilibrium via air-sea exchange within approximately one year. Building on the Thermodynamic Control term from Bai et al. (2015), the thermodynamic effect of temperature on pCO₂ is expressed as an exponential relationship of approximately 4.23%°C^-1 (Takahashi et al., 1993). In essence, this variable accounts for changes driven by both atmospheric forcing and the effect of temperature. It was calculated based on the annual mean atmospheric pCO₂ and SST through the following process (Yu et al., 2023) (Equations 2, 3).

where pCO_{2, air(yr)} is the annual mean atmospheric pCO₂, and T(yr) is the annual mean SST. The pCO_{2, air} was calculated from the atmospheric mole fraction of CO₂ in dry air (xCO₂), SLP, and the vapor pressure of water (pH₂O) at 100% relative humidity, based on the method of (Weiss and Price, 1980). The xCO₂ and SLP data were obtained from NOAA’s CarbonTracker CT2022 dataset, which has a spatial resolution of 3° x 2° (available online: https://gml.noaa.gov/aftp/products/carbontracker/co2/CT2022/molefractions/; accessed on 25 Jul 2026). While this atmospheric product is inherently provided on a coarse 3° x 2° grid, atmospheric CO₂ is highly well-mixed at regional scales. Consequently, within our framework, these CarbonTracker data serve purely as a spatially uniform, temporal background forcing. The actual high-resolution spatial variability of the final calculated pCO_2,baseline feature is entirely driven by the native 4 km Aqua-MODIS SST used in Equation (3). Therefore, the effective native spatial resolution of this specific predictor remains 4 km, strictly ensuring that no localized spatial leakage occurs across our 0.1° validation blocks. The CT2022 dataset provides data from 1 January 2000 to 31 December 2020. For the period from 2021 onward, data from the CT-NRT.v2024–5 product were used (available online: https://gml.noaa.gov/aftp/products/carbontracker/co2/CT-NRT.v2024-1/; accessed on 25 Jul 2026).

2.3.3 Water case classification

The classification of water types into CW and TW was primarily based on the bimodal distribution of nL_w555 observed in the study area. Following the methodology of Saldías et al. (2012), which adapted the histogram analysis of Cayula and Cornillon (1992), we determined the optimal threshold (τ) by maximizing the inter-cluster variance. The explained variance ratio, θ(τ) was calculated as follows (Equations 4–6):

V(τ) represents the inter-cluster variance according to the threshold τ, where µ₁ and µ₂ denote the mean values of the two clusters separated by τ. N₁ and N₂ are the number of samples in each cluster, and N (N = N₁ + N₂) is the total number of samples in the domain. S denotes the total variance, and the explained variance ratio, θ(τ) is the ratio of the inter-cluster variance to the total variance with a value ranging from 0 to 1.

To ensure the spatiotemporal continuity of the pCO₂ estimations and to avoid potential step-like artifacts near the threshold, a sensitivity analysis was performed by varying the threshold from 1.0 to 2.0 mWcm^-2μm^-1sr^-1 (detail in Supplementary Table S1). To verify its robustness under varying seasonal conditions, this analysis was evaluated for both the entire dataset and independently for each season. The explained variance showed a significant increase and plateaued at approximately 0.85 as the threshold approached 1.5 mWcm^-2μm^-1sr^-1 (where the marginal increase, dropped below 0.01, representing less than 1% of the total variance across all seasons), serving as a practical criterion for identifying the statistical boundary between the two water masses. To validate this statistical threshold physically, we examined the SSS characteristics. Consistent with the findings of Saldías et al. (2012), the waters classified as TW by this threshold (> 1.5 mW cm^-2μm^-1sr^-1) distinctively captured the low-salinity signal of turbid river plumes. Consequently, τ = 1.5 mW cm^-2μm^-1 sr^-1 was selected as the boundary to classify the ECS into CW and TW.

2.3.4 Splitting of training and validation data

The performance of the developed machine learning algorithms was evaluated through a rigorous validation process designed to prevent data leakage. In oceanographic satellite data, adjacent pixels are often highly correlated, meaning that conventional random splitting can lead to spatial autocorrelation and inflated model performance (Schaeffer et al., 2016). To strictly address this, we implemented a spatial block cross-validation strategy. Guided by Schaeffer et al. (2016), the study area was partitioned into 0.1° x 0.1° spatial grids to define these spatial blocks. Crucially, because this 0.1° block size mathematically exceeds the absolute coarsest native resolution among all our machine learning predictors (0.083°for GLORYS SSS), this partitioning structurally ensures strict spatial independence and prevents localized feature leakage. This structural independence is further empirically supported by the semi-variogram analysis discussed below.

Geometrically, each 0.1° block encapsulates multiple 4 km pixels. By assigning an entire 0.1° block exclusively to one dataset (training, validation, or test), all temporal records associated with that specific location remain together. This structurally guarantees that the model never trains on a location in one month and tests on the exact same location in another month, effectively preventing long-term temporal leakage. To quantitatively evaluate whether this block size is practically sufficient to mitigate local feature leakage, an empirical semi-variogram analysis of the model residuals was conducted. The analysis indicated that the spatial decorrelation range of the predictive errors drops off steeply within 14.3 km. Although our 0.1° (approximately 11.1 km) block size is slightly smaller than this decorrelation scale, the steep initial rise of the variogram demonstrates that the vast majority of exploitable spatial variance is already absorbed within this block size. Therefore, the 0.1° grid effectively mitigates the most critical spatiotemporal dependence without severely reducing the training data volume.

The ECS is characterized by highly dynamic biogeochemical gradients across the coastal-offshore transition. The 0.1°configuration provides a sufficiently large number of independent spatial blocks to preserve these fine-scale gradients. In contrast, expanding the block size to 0.15° or 0.2° geometrically reduces the total available blocks, which severely limits the spatial degrees of freedom and induces severe data imbalance during the stratified splitting within the narrow coastal regime. Therefore, the 0.1° grid was strategically selected. A detailed quantitative evaluation of model performance and stability across these different spatial block sizes is discussed in Section 4.2.

Based on these spatial blocks, the entire high-quality dataset (N = 3,671) was partitioned using a stratified group k-fold approach. This method grouped geographically adjacent samples within the same 0.1° block into the same fold, guaranteeing complete spatial independence between the training and evaluation phases. The dataset was split into a training set (N = 2,477, CW = 2,179, TW = 298), a validation set (N = 630, CW = 541, TW = 89), and an independent test set (N = 564, CW = 495, TW = 69).

To ensure that each independent set was highly representative of the complex biogeochemical environment, the splitting process was stratified based on the Water Case and pCO₂ concentration levels. This guaranteed that the validation and test sets contained a balanced proportion of TW data (approximately 12–14%), enabling a robust and unbiased evaluation of the algorithm’s performance across contrasting water regimes.

2.4 Design of pCO₂ algorithm

In this study, we developed a regime-aware unified framework to capture the nonlinear relationship between pCO₂ and the input variables while accounting for coastal heterogeneity in the ECS. The framework employs a single modeling architecture in which the Water Case (a categorical index distinguishing CW and TW) is explicitly incorporated as an input variable. This design enables the models to learn regime-dependent relationships within a prediction framework.

2.4.1 Conventional machine learning algorithms

To construct the unified framework, five machine learning algorithms with different learning mechanisms were considered and implemented using the Python programming environment. Categorical Boosting (CatBoost) is a gradient boosting algorithm that effectively processes categorical features and prevents overfitting in noisy datasets using an ordered boosting technique (Prokhorenkova et al., 2019). eXtreme Gradient Boosting (XGBoost) is an optimized framework that iteratively learns residuals to maximize predictive accuracy (Chen and Guestrin, 2016). Random Forest (RF) is an ensemble method that builds multiple independent decision trees to reduce variance and sensitivity to observational noise (Breiman, 2001). Support Vector Machine (SVM) employs margin maximization and kernel tricks to learn complex non-linear relationships (Cortes and Vapnik, 1995). Lastly, Multi-layer Perceptron (MLP) is an artificial neural network that utilizes multiple hidden layers and activation functions to capture intricate patterns among input variables (Rumelhart et al., 1986). The hyperparameters for each model were optimized using a Bayesian search method (Optuna framework in python) with 6-fold cross-validation.

2.4.2 Model training and hyperparameter optimization

A comprehensive ablation study was conducted to identify the optimal algorithm and input-variable combination for pCO₂ estimation in the ECS. To ensure a rigorous and fair comparison, all models were evaluated using the exact same spatially independent datasets constructed via the spatial block partitioning (Section 2.3.4).

The models were trained on the training set (N = 2,477) and optimized based on their performance on the independent validation set (N = 630). Because distance-based algorithms such as SVM and MLP are highly sensitive to the scale of input features, all input variables were standardized to have a mean of 0 and a standard deviation of 1 prior to training.

Hyperparameter optimization was systematically performed using the Tree-structured Parzen Estimator (TPE) Bayesian search algorithm within the Optuna framework. For each model, the tuning process involved up to 1,000 iterations of the search. To mitigate overfitting, which is a frequent concern in spatial modeling, validation-based early stopping was implemented. Training was automatically terminated when the validation metrics failed to improve over a predefined number of iterations, thereby preventing models from memorizing noise and encouraging them to learn physically generalizable patterns. The validation metrics used for model evaluation were the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE), defined as follows (Equations 7–9):

where y_i represents the observed value, represents the predicted value, and represents the mean of the observed values, and n denotes the number of observations.

This training protocol was applied uniformly across all five algorithms. Furthermore, to evaluate the sensitivity of the models to different predictors and to quantitatively demonstrate the necessity of the regime-aware approach (Water Case), the performance of each tuned model was analyzed across 10 distinct input variable combinations (Exp. 1–10), as detailed in Table 2.

2.5 Decomposition of thermal and non-thermal effects

To quantitatively decouple the mechanisms driving seasonal pCO₂ variability into thermodynamic (thermal) and biogeochemical/physical (non-thermal) processes, we applied a linear decomposition method based on the relationship proposed by Takahashi et al. (2002). To eliminate the influence of long-term trends and focus on seasonal dynamics, anomalies were calculated relative to the year-specific annual mean rather than the long-term climatological mean. The decomposition was performed in the following steps: First, the thermal component anomaly (ΔpCO_2,therm), which represents the pCO₂ variation driven solely by SST changes assuming constant chemical composition, was calculated as Equation 10:

where pCO_2,mean(yr) and SST_mean(yr) are the annual mean pCO₂ and SST for a specific year, respectively, and SST_t is the observed SST at each time step. The coefficient 0.0423 °C^-1 represents the temperature dependence of pCO₂ (Takahashi et al., 1993). Second, the non-thermal component anomaly (ΔpCO_2,non-therm), which accounts for changes driven by biological activities (photosynthesis and respiration), mixing was derived as the residual by subtracting the thermal anomaly from the total observed anomaly (ΔpCO_2,t):

Here, a positive ΔpCO_{2, non-therm} indicates a pCO₂ increase driven by non-thermal factors, acting as a source relative to the annual mean. Conversely, a negative value indicates a pCO₂ decrease driven by factors such as biological uptake, acting as a sink.

2.6 Effect size (Cohen’s d)

Cohen’s d was calculated as the difference between the means of the two groups divided by the pooled standard deviation (S_pooled), as defined by (Cohen, 1988) (Equations 13, 14):

We adopted the standard benchmarks proposed by Cohen (1988) for interpreting the effect size: values of 0.2, 0.5, and 0.8 were considered indicative of small, medium, and large effects, respectively. This approach allows for a robust assessment of whether the optical classification captures substantial biogeochemical heterogeneity beyond mere statistical significance.

2.7 Air-Sea CO₂ flux estimation and trend analysis

The air-sea CO₂ flux refers to the exchange of CO₂ occurring at the interface between the ocean and the atmosphere. Depending on the direction of this exchange, the ocean can act as either a sink or a source of atmospheric CO₂. The flux is calculated as follows (Wanninkhof, 2014):

k represents the gas transfer velocity, and a is an empirical coefficient. U is the wind speed (ms^-1) at a height of 10 m, and Sc is the schmidt number, representing the temperature-dependent rate of molecular diffusion. K₀ denotes the solubility of CO₂ in seawater per 1 atm of pressure. The term pCO_2,sea is the pCO₂ of the sea surface, while pCO_2,air is the atmospheric pCO₂.

For the pCO_2,sea, the output from this study’s algorithm was used. For pCO_2,air, the atmospheric xCO₂ from NOAA’s CarbonTracker CT2022 product was used (available online: https://gml.noaa.gov/aftp/products/carbontracker/co2/CT2022/molefractions/; accessed on 25 Jul 2026). The pCO_2,air was calculated using SLP and pH₂O based on the method of Weiss and Price (1980).

Long-term trends and inter-annual variability were analyzed by removing seasonal cycles from the air-sea CO₂ flux. Pixel-wise flux anomalies were derived by subtracting the monthly climatological mean (2003–2023) from the original time series, effectively removing local seasonal amplitudes. These anomalies were spatially averaged for each regime (CW and TW) and smoothed using a 12-month rolling mean to highlight structural shifts. The statistical significance of these trends was assessed using the Mann-Kendall test (Mann, 1945; Kendall, 1975) to determine whether the sink or source intensity has significantly changed over the study period.

3 Results

3.1 Model selection and interpretation

3.1.1 Model selection and validation

To select the optimal algorithm, the performance of five machine learning methods across ten variable combinations (Exp. 1–10) was evaluated on the validation dataset (Table 2). The evaluation revealed that most algorithms performed best with Exp. 7 (see Supplementary Table S2 for detailed metrics and hyperparameter settings for each Exp). Specifically, the CatBoost model demonstrated the highest performance on the validation data, achieving the best predictive accuracy (R² = 0.91, p < 0.001) and the lowest errors (RMSE = 16.78 µatm, MAE = 9.74 µatm) (Table 3). XGBoost also showed robust performance with Exp. 6 (RMSE = 17.09 µatm). Conversely, SVM and MLP exhibited significantly lower accuracy (RMSE > 37 µatm). The ablation study (Exp. 8–10) highlighted the differing sensitivities of the algorithms to specific environmental predictors. For the CatBoost model, the inclusion of the regime-aware variable (Water Case) proved critical, as its exclusion (Exp. 9) caused the RMSE to increase to 17.16 µatm. Removing SSS from the optimal combination (Exp. 8) substantially increased the CatBoost RMSE to 19.35 µatm. Additionally, comparing Exp. 7 to a combination without the thermodynamic background variable (pCO_2,baseline, Exp. 5, RMSE = 18.20 µatm) showed an error reduction of approximately 7.8%. Interestingly, the RF model achieved its best performance with Exp. 9 (RMSE = 17.78 µatm), which excludes the Water Case variable, slightly outperforming its Exp. 7 counterpart (RMSE = 18.38). Despite this algorithm-specific variation, the CatBoost model paired with the full variable set (Exp. 7) remained the most accurate approach overall.

Figure 2 illustrates the performance of the optimal CatBoost algorithm across the training, validation, and test datasets. The model demonstrated an excellent fit on the training data (Figure 2a), the model maintained robust performance across the different water regimes. For CW, it achieved an R² of 0.84, RMSE of 14.69 µatm, and MAE of 9.28 µatm. For TW, the performance was R² = 0.83, RMSE = 32.69 µatm, and MAE = 21.01 µatm, culminating in a total validation R² of 0.91 and RMSE of 16.78 µatm. To definitively confirm the model’s generalization capability, we evaluated it using a spatially independent test dataset. This dataset was strictly isolated during both the training and validation processes (Figure 2C). The overall results for this test set (R² = 0.86, RMSE = 16.55 µatm, MAE = 10.49 µatm) were highly consistent with the validation outcomes. Notably, the total RMSE actually slightly decreased from 16.78 µatm (validation) to 16.55 µatm (test), and the error in the complex TW regime also improved (RMSE decreased from 32.69 µatm to 22.01 µatm). Although the TW dataset contains substantially fewer observations than the CW dataset, our stratified spatial block splitting (Section 2.3.4) ensured that these observations were proportionally represented and spatially independent. Consequently, the regime-specific statistics (Figure 2) robustly demonstrate that the model successfully captures the inherently large pCO₂ variability within the TW regime, without its performance being overshadowed by the CW majority. This consistency provides evidence that our early stopping strategy prevented overfitting to the training data. The model proves reliable predictive capabilities for unseen spatial regions, rather than simply memorizing localized noise. Therefore, the CatBoost model with Exp. 7 configuration was adopted as the final algorithm for the subsequent spatiotemporal analysis of pCO₂.

Figure 2

3.1.2 Analysis of variable importance using XAI

To ensure the reliability of the reconstructed pCO₂ time series, we evaluated the performance of the pCO₂ estimation algorithms. We utilized Shapley Additive Explanations (SHAP) analysis to quantify the relative importance of input variables and to interpret how the developed models utilize these environmental features for pCO₂ estimation (Figure 3).

Figure 3

To assess variations in feature importance across different water masses, the analysis was conducted separately for CW (Figure 3a) and TW (Figure 3b). In both regimes, the thermodynamic effect (pCO_2,baseline) emerged as the most dominant predictor, contributing approximately 37.6% in CW and 23.5% in TW. This indicates that thermodynamic forcing plays a primary role in regulating sea surface pCO₂ variability across the ECS. Furthermore, the algorithms effectively distinguished the distinct oceanographic characteristics of each regime, exhibiting a clear divergence in variable importance. For CW, the model placed relatively higher importance on physical variables, particularly SSS (13.5%) and SST (8.5%). In contrast, for TW, optical properties represented by R_rs bands were identified as critical predictors. Specifically, R_rs 555 (17.9%) and R_rs 488 (16.8%) emerged as the second and third most important variables, respectively. These R_rs bands, derived from optical sensors, serve as key proxies for bio-optical properties (Jang et al., 2017). Together with Chl-a, K_d490, and PAR (contributing 5.3%, 4.8%, and 7.8% in CW and 8.4%, 6.5%, and 3.6% in TW, respectively), these variables effectively capture biological processes and suspended particle dynamics. Interestingly, the categorical Water Case variable itself showed a substantially higher contribution in TW (8.7%) compared to CW (2.2%). This further validates that explicitly feeding regime information helps the model navigate the highly complex and optically variable turbid plume areas, leading to improved spatial adaptability.

3.2 Spatiotemporal variability of sea surface pCO₂

Based on the validated algorithm, we reconstructed the spatiotemporal distribution of sea surface pCO₂ in the ECS. From 2003 to 2023, the overall mean pCO₂ in the ECS was 369.87 ± 42.89 µatm.

The monthly climatology of surface pCO₂ concentrations is shown in Figure 4. The seasonal patterns of pCO₂ in the ECS are characterized by a pronounced seasonal cycle, exhibiting a minimum in spring (March–May) and a maximum in autumn (September–November). Specifically, the ECS-wide mean pCO₂ reached its lowest value in April (342.56 ± 28.30 µatm) and gradually increased during the warming season, peaking in terms of monthly mean in September (397.63 ± 39.87 µatm). Notably, while the mean values peaked in September, the absolute maximum concentrations were recorded in July (758.95 µatm).

Figure 4

Spatially, a distinct cross-shelf gradient was observed, characterized by generally higher pCO₂ values in the coastal waters compared to the offshore region.

However, the intensity of this gradient varied significantly by season. During winter (December–February) and early spring, the spatial distribution was relatively homogeneous. For instance, in January, the difference in mean pCO₂ between the coastal (369.71 ± 15. 14 µatm) and offshore (343.59 ± 8.32 µatm) was relatively small (approximately 30 µatm). The maximum values observed during this period were also comparable between the two regimes (January Max: 400.39 µatm in offshore vs. 414.56 µatm in coastal). In contrast, this spatial heterogeneity intensified drastically during summer (June–August). While the offshore maintained moderate mean levels (< 380 µatm; in July and August), the coastal exhibited a rapid increase in pCO₂, reaching a monthly mean maximum of 509.18 ± 58.71 µatm in July. Furthermore, the extreme nature of the coastal waters is highlighted by the maximum values, which surged to 758.95 µatm in July and 695.46 µatm in August. These extremes stand in stark contrast to the offshore region, where the maximum values remained significantly lower (609.25 µatm and 538.65 µatm) during the same period. Consequently, the steepest cross-shelf gradient was observed in July, with a difference of approximately 128 µatm in mean values between the two regimes.

Over the two-decade study period, the surface pCO₂ concentration of the entire ECS exhibited a significant increasing trend of approximately 0.73 µatm yr^-1 (y = 0.73x + 360.40, p < 0.01). Decomposed by optical regimes, CW showed a similarly significant but slightly slower increasing trend of 0.66 µatm yr^-1 (y = 0.66x + 351.01, p < 0.01). In contrast, the TW exhibited a much steeper increasing rate of 1.11 µatm yr^-1 (y = 1.11x + 428.30). However, unlike the CW, the trend in TW did not reach statistical significance (p = 0.06). This lack of statistical significance, despite the steeper slope, is attributed to the substantial spatiotemporal variability inherent to the turbid coastal zone, as evidenced by the wide standard deviation bands (red shaded area) in Figure 5.

Figure 5

3.3 The key factors of surface pCO₂ changes

Statistical analyses were conducted to identify the dominant controls on the spatiotemporal variability of surface pCO₂, using correlation analysis and decomposition analysis. To understand how these environmental differences drive pCO₂, we examined the relationships using a seasonal pair-grid analysis (Figure 6). In CW, pCO₂ is positively correlated with SST (r = 0.61) but shows negligible correlations with SSS and Chl-a. TW exhibits a complex multi-driver structure, with pCO₂ showing a stronger correlation with SST (r = 0.78) and a positive relationship with Chl-a.

Figure 6

Table 4 summarizes the statistical differences between the two regimes. The independent t-test and Cohen’s d analysis confirm that the optically classified CW and TW are fundamentally distinct biogeochemical provinces (p < 0.001). nL_w555 (d = -6.40) validates the optical threshold. TW is characterized by significantly lower salinity (d = 1.40) and higher Chl-a (d = -1.54). Notably, the non-thermal component of pCO₂ shows opposite signs (d = -0.75).

The temporal dynamics of dominant drivers are further quantified in Figure 7. In the CW regime (Figure 7a), the magnitude of the thermal effect (ΔpCO_2,therm) generally exceeds that of the non-thermal effect (ΔpCO_2,non-therm) throughout the year, confirming a thermodynamically controlled system. The contribution of the non-thermal component remains relatively moderate across most months, ranging from approximately 31% to 47%, with the exception of a brief shift in November where it accounts for 54% of the variability.

Figure 7

In contrast, the TW regime (Figure 7b) reveals not only substantially larger absolute anomalies but also a significantly amplified non-thermal influence. Unlike the CW, the non-thermal effect in the TW frequently rivals or even surpasses the thermal effect. This non-thermal dominance is most pronounced during the transitional and early winter months, peaking heavily in May (62%) and November (68%). The thermal effect regains dominance during the mid-summer to early autumn period, accounting for 57% to 68% of the variability from July to October. Nevertheless, the overall annual pattern highlights that the TW is a highly dynamic, multi-driver system where non-thermal processes play a critical, and often leading, role in dictating pCO₂ variability.

3.4 Spatiotemporal variability and trends of air-sea CO₂ flux

The air-sea CO₂ fluxes are estimated to quantify the role of the ECS as a carbon sink or source. To evaluate the actual impact of oceanic pCO₂ changes on this regional carbon budget over the long term, we calculated the fluxes across the entire 21-year study period (2003–2023). The fundamental thermodynamic driving force governing this air-sea exchange is the partial pressure gradient (ΔpCO₂^sea-air). Figure 8 illustrates the long-term temporal variations of this gradient for each regime (CW and TW).

Figure 8

The atmospheric CO₂ concentration increased at a rate of 2.41 µatm yr^-1. However, the oceanic pCO₂ in both regimes increased at much slower rates than the atmosphere (CW: 0.66 µatm yr^-1; TW: 1.11 µatm yr^-1; Figure 5). Because the atmospheric growth outpaced the oceanic pCO₂ rise, the ΔpCO₂^sea-air exhibits significant negative trends in both regimes. In CW (mean -37.15 µatm), this growing disparity resulted in a negative gradient (-1.69 µatm yr^-1). Conversely, the TW maintains a positive ΔpCO₂^sea-air state (mean +44.85 µatm), its overall source potential is gradually weakening (-1.43 µatm yr^-1) due to the overwhelming accumulation of atmospheric CO₂.

To determine the actual impact of these thermodynamic trends on air-sea exchange, we estimated the seasonal and annual CO₂ fluxes (Table 5). CW occupies the majority of the study area, accounting for 82.82% of the annual mean coverage. Consequently, it functions as a dominant perennial sink throughout the year (with an annual mean flux of -3.11 mmol m^-2d^-1). The strongest uptake in the CW occurs in winter (-7.40 ± 2.85 mmol m^-2 d^-1).

In contrast, the TW exhibits dynamic seasonal shifts. During summer and autumn, the TW acts as a significant CO₂ source, with a summer mean of 8.55 ± 6.43 mmol m^-2 d^-1 (autumn of 7.40 ± 4.07 mmol m^-2 d^-1). However, its impact on the overall budget is limited because it covers only 6.10% (Autumn: 14.28%) of the area during this season. A distinct transition occurs in winter. The TW turns into a net sink (-3.96 ± 3.22 mmol m^-2 d^-1) and simultaneously expands to its maximum extent of 29.04%. This expansion, combined with the intense uptake in the CW, drives the entire ECS to its peak sink intensity in winter (-6.39 ± 3.35 mmol m^-2 d^-1). Ultimately, on an annual basis, the TW functions as a net CO₂ source (+0.40 ± 6.66 mmol m^-2 d^-1).

We further analyzed the inter-annual variability of flux anomalies to capture structural shifts over the 21-year study period (Figure 9). In CW (Figure 9a), the flux anomaly shows a statistically significant decreasing trend with a slope of -0.182 mmol m^-2 d^-1 yr^-1 (where Z denotes the standardized Mann-Kendall test statistic; Z = -5.405, p < 0.001), indicating an enhancement of the CO₂ sink capacity. The TW (Figure 9b) also exhibits a highly significant decreasing trend with a slope of -0.166 mmol m^-2 d^-1 yr^-1 (Mann-kendall test, Z = -4.460, p < 0.001). This confirms that although the TW acts as a net carbon source, its overall source capacity has steadily weakened over the study period.

Figure 9

4 Discussion

This study evaluates the reconstructed surface pCO₂ fields and air–sea fluxes based on predictive skill and mechanistic consistency. The reconstructed results align well with the observed magnitudes and seasonal patterns across the ECS, accurately reproducing the distinct regime characteristics and effectively capturing the realistic coastal–offshore contrast between the CW and TW. Evaluation against the spatially independent test dataset further demonstrates that the learned relationships generalize robustly across unseen regions, rather than merely memorizing localized patterns. Consequently, the reconstructed climatology (Figure 4) and long-term trends (Figure 8, 9) can be confidently interpreted in a process consistent manner.

4.1 Performance superiority of the regime-specific pCO₂ model and necessity of optical separation

Model performance was benchmarked against three representative algorithms developed for comparable coastal environments: MeSAA of Yu et al. (2023) and the multivariate statistical algorithm of Chen et al. (2016), and the multiple non-linear regression (MNR) approach by Liu et al. (2023b). To ensure a rigorous and fair comparison, all algorithms were evaluated using a test dataset to match available data time-scales (2003–2019). Inputs were implemented following each model’s original protocol (Chen et al., 2016; Liu et al., 2023b; Yu et al., 2023). Specifically, the MeSAA algorithm by Yu et al. (2023) was applied in its original form without retraining to evaluate its native structural performance, whereas the coefficients of Chen et al. (2016) were recalibrated using the training dataset to optimize parameterization for the study domain.

Taylor diagrams and error metrics (Figure 10) confirm a clear advantage of our regime-specific framework. In the TW, our model drastically reduced the error (RMSE = 23.33 µatm), corresponding to relative RMSE reductions of ~81%, ~65%, and ~52% compared to Liu et al. (2023b); Yu et al. (2023), and Chen et al. (2016), respectively. In the CW, our model also demonstrated superior accuracy, translating to error reductions of ~55% and ~42% compared to Yu et al. (2023) and Chen et al. (2016), respectively. To visually demonstrate spatial robustness, we compared the in-situ and retrieved pCO₂ distributions along representative cruise tracks across the four seasons (Figure 11). The model reproduces the intricate localized coastal-to-offshore gradients, particularly the sharp transitions between the TW and CW. As explicitly shown in the spatial difference maps and annotated statistics (Figure 11, right column), the estimated pCO₂ values closely match the in-situ observations. The RMSE values for these representative cruises ranged from 9.95 to 30.68 µatm, with overall minimal mean biases (ranging from -6.92 to 3.17 µatm). This statistical performance and the overall spatial patterns confirm that our regime-aware framework effectively captures the seasonal variation. Furthermore, a dual-evaluation using the static geographic partitioning of Liu et al. (2023b) (e.g., Domains 1, 2, and 3 corresponding to inner, middle, and outer shelves) (Supplementary Figure S1) revealed that while their model is effective in stable offshore waters, it exhibits massive uncertainties in the highly variable inner shelf. The methodological differences between static partitioning and dynamic tracking are visually evident in the reconstructed spatial distributions (Supplementary Figure S2), demonstrating that our dynamic approach consistently achieves the lowest errors across all geographic domains.

Figure 10

Chen et al. (2016) (grey triangles), and Liu et al. (2023b) (yellow diamonds).

Figure 11

The superior performance of our model likely stems from CatBoost’s structural advantages. Unlike traditional frameworks, CatBoost utilizes ordered boosting and symmetric trees to mitigate gradient bias and prediction shift, effectively preventing overfitting and ensuring generalization stability even with sparse coastal pCO₂ data. While the available in-situ observations in the TW regime are inherently limited, this performance confirms that the current framework effectively maximizes the utility of the existing dataset. This generalization strongly supports the plausibility of our quantitative estimates regarding the TW CO₂ source. Moreover, this algorithmic robustness synergizes with our regime-specific framework (uniquely optimized for categorical features), CatBoost internally processes the Water Case predictor without information loss, effectively partitioning the decision-making logic between CW and TW regimes. These gains align with the nL_w555-based optical separation. Although summer CDW has a slightly higher median nL_w555 (0.51) than CW (0.42), it remains well below the 1.5 threshold. By comparison, TW exhibits a markedly elevated median of 3.17, indicating extreme turbidity (Table 4). This gap reflects winter wind-driven sediment resuspension exceeding summer CDW SPM levels (Yuan et al., 2008). Biogeochemically, CDW acts as a strong sink (331.4 ± 45.2 µatm) compared to the CW mean (361.2 ± 30.8 µatm), while TW functions as a strong source (415.1 ± 63.7 µatm) driven by positive non-thermal anomalies (+28.09 µatm; Table 4). Misclassifying CDW into TW based solely on turbidity mixes opposing drivers, risking systematic underestimations (~30 µatm) in high-pCO₂ waters (Chen et al., 2016). Feature attribution (Figure 3b) further confirms this, identifying R_rs bands and Water Case as critical predictors that successfully discriminate sediment-associated source signals from biologically driven sinks (Li et al., 2015).

Beyond statistical improvements, this regime-specific framework significantly alters the estimated regional carbon budget. A quantitative comparison against the algorithm framework of Yu et al. (2023) for the period 2003–2019 reveals that conventional approaches can significantly overestimate CO₂ uptake, particularly in turbid nearshore waters. While the Yu et al. (2023) model estimated a strong net sink of -5.50 mmol m^-2 d^-1 in the TW region, our regime-specific model yielded a weak net source of +0.78 mmol m^-2 d^-1. This discrepancy results in a massive difference of ~4.04 Tg C yr^-1 within the TW domain alone (+0.50 Tg C yr^-1 net release vs. 3.54 Tg C yr^-1 net uptake). Across the entire ECS (8.55 × 10⁵ km²), our study estimated an annual overall uptake of 8.05 Tg C yr^-1, which is approximately 46% lower than the 14.80 Tg C yr^-1 reported by Yu et al. (2023). This indicates that a substantial portion of the shelf-scale overestimation in previous studies originates from the turbid domain, highlighting how the exclusion of localized nearshore dynamics can propagate into massive uncertainties in regional carbon accounting. Overall, optical regime separation is a necessary condition for achieving both low error and physically interpretable pCO₂ variability in the ECS coastal zone.

To quantitatively confirm that this significant discrepancy in the regional carbon budget is robust against inherent estimation errors, we performed a Monte Carlo uncertainty analysis (10,000 iterations). We propagated the principal uncertainties from the gas transfer coefficient (10%; Wanninkhof, 2014), wind speed (RMSE = 1.5 m s^-1), SSS (RMSE = 1.41 psu), and the regime-specific predictive errors of our model (Test RMSE = 15.64 and 22.01 µatm for CW and TW, respectively).

The simulation yielded a total ECS uptake of 8.64 ± 0.92 Tg C yr^-1 and a TW budget of +0.63 ± 0.06 Tg C yr^-1. The slight increase in the mean magnitudes compared to our deterministic estimates (8.05 and +0.50 Tg C yr^-1, respectively) inherently stems from the non-linear dependence of the gas transfer velocity on wind speed, where the addition of Gaussian noise systematically amplifies the time-averaged flux. Even at the upper bound of our 95% confidence interval (10.44 Tg C yr^-1), our total estimate remains lower than the 14.80 Tg C yr^-1 reported by Yu et al. (2023). Furthermore, the simulated TW budget (+0.63 ± 0.06 Tg C yr^-1) indicates a net source, which provides a contrasting perspective to the strong net sink (3.54 Tg C yr^-1) estimated by conventional approaches. This uncertainty analysis supports our conclusion that previous shelf-scale estimations might have significantly overestimated the ECS carbon sink (by approximately 41.6% ± 6.2%), reaffirming that optical regime separation is critical for accurate coastal carbon accounting.

4.2 Importance of key predictors and model generalization

Our variable sensitivity analysis demonstrated the critical importance of specific environmental predictors in estimating pCO₂ within the ECS. Notably, when SSS was excluded (Exp. 8), model performance degraded substantially, underscoring its indispensable role in capturing complex spatial salinity gradients and their related biogeochemical dynamics in coastal regions. Although algorithms exist to derive salinity directly from satellite refectance (Kim et al., 2020; Son and Choi, 2022; Liu et al., 2023a), their broad application across extreme coastal turbidity gradients still requires further regional optimization. Furthermore, the significant error reduction achieved by adding the thermodynamic background variable (pCO_{2, baseline}) confirms that establishing a baseline thermodynamic effect is crucial for optimizing model stability before resolving non-thermal biological variations.

Beyond these continuous variables, the categorical regime-aware approach proved structurally essential. While deriving a categorical feature (Water Case) from continuous optical data might raise concerns about redundancy, it serves a distinct algorithmic purpose. In tree-based models, relying solely on continuous optical predictors often causes the extreme, minority signals of the coastal plume to be overshadowed by the vast offshore data. The Water Case explicitly acts as a structural regime-switching node, contributing significantly more to predictions in the highly variable TW (8.7%) compared to the stable CW (2.2%). A controlled ablation experiment confirmed this necessity: removing the Water Case (Exp. 9) severely degraded the model’s ability to capture extreme pCO₂ dynamics, causing the test RMSE in the highly variable TW to surge from 22.01 to 26.62 µatm and introducing localized instability (Supplementary Figure S3).

Because CatBoost is highly optimized for categorical feature processing, it successfully minimizes these errors while maintaining robust spatial adaptability. However, a slight performance gap between the training dataset (R² = 0.96, RMSE = 9.64 µatm) and the independent test dataset (R² = 0.91, RMSE = 16.55 µatm) was still observed. This discrepancy must be interpreted in the context of our 0.1° spatial block partitioning strategy. While this configuration is mathematically essential to capture fine-scale cross-shelf gradients without triggering data starvation in the narrow TW, it is slightly smaller than the 14.3 km decorrelation length. Nevertheless, sensitivity analyses using larger grids confirmed that the overall predictive performance on the independent test set was not significantly altered, proving that our validation-based early stopping successfully mitigated severe overfitting.

4.3 Spatiotemporal climatology and biogeochemical control mechanisms

The monthly climatology of surface pCO₂ (Figure 4) reveals a pronounced seasonal cycle superimposed on a persistent coastal–offshore gradient. Rather than imposing artificial physical boundaries, our model explicitly utilizes the optical classification (CW and TW) as a structural element to recognize the different biogeochemical mechanisms operating across this continuum. By doing so, the framework avoids the spatial smoothing common in conventional regressions and accurately captures the steep cross-shelf gradients essential to the ECS carbon cycle. The plausibility of these derived spatiotemporal patterns is quantitatively supported by distinct control mechanisms, as evidenced by correlation analysis (Figure 6) and thermodynamic decomposition (Figure 7).

In the CW, waters exhibit comparatively modest variability. CW shows only a negligible pCO₂–SSS correlation (r = 0.04), consistent with limited freshwater influence outside the summer plume period and relatively low variability of salinity (1.41 psu) (Takahashi et al., 1993; Zou et al., 2024). During spring, the ECS generally exhibits a low pCO₂ state with weakened spatial gradients, reflecting early biological uptake and a reduced dominance of resuspension-driven supply. However, pronounced spatial heterogeneity emerges in summer, revealing localized sink-like conditions associated with the CDW extension. Here, the pCO₂ plummets to 150–250 µatm over the central shelf. This intense biological drawdown is driven by nutrient-rich freshwater input combined with strong solar radiation under stratified conditions (Chou et al., 2009; Tseng et al., 2011; Guo et al., 2015; Choi et al., 2021; Ye et al., 2025), which is consistent with previous studies reporting bloom-driven surface pCO₂ drawdown of 150–300 µatm (Shim et al., 2007; Guo et al., 2015). Mechanistically, this is confirmed by an annual mean non-thermal anomaly of - 23.15 µatm, indicating net biological buffering on average. While the summer thermal component tends to increase pCO₂, this non-thermal contribution increases substantially, accounting for 47% of the total variability (Figure 7a) and driving the mean pCO₂ in summer CDW (331.4 ± 45.2 µatm) well below the overall CW average (361.2 ± 30.8 µatm; Table 4).

In contrast, TW exhibits stronger month-to-month changes and sharper cross-shelf gradients. TW shows a clear negative pCO₂–SSS correlation (r = - 0.49). This indicates that freshwater influence is generally associated with higher pCO₂. Such a pattern is consistent with riverine inputs containing elevated DIC/DOC and nutrients (Choi et al., 2021; Yang et al., 2025). In summer, the model resolves extreme contrasts where pCO₂ exceeds 900 µatm near the Yangtze Estuary. Although higher biomass co-occurs with nutrient-rich plume waters (pCO₂–Chl-a relationship = 0.52), pCO₂ remains exceptionally high because Changjiang discharge can introduce water with elevated pCO₂ (Zhai et al., 2007) and warming strengthens thermodynamic forcing. Notably, mean summer SST is higher in CW (28.39 °C) than in TW (26.26 °C), indicating strong thermal pressure in both regimes, but divergent outcomes due to opposing non-thermal dominance (+28.09 µatm annual mean non-thermal anomaly in TW; Table 4).

The distinct nature of TW is further highlighted during autumn and winter, where boundaries effectively trace the frontal zones near 125°E. Despite significant cooling, coastal pCO₂ remains elevated, implying a massive non-thermal contribution (46–51%) to total variability. In the ECS, nearshore waters can become even more turbid in winter than in summer due to intense wind-driven sediment resuspension (Yuan et al., 2008). This strong physical forcing not only elevates turbidity but also drives CO₂ release from remineralized carbon stored in seabed and pore waters (DeMaster et al., 1985; Li et al., 2015; Bartl and Thrush, 2025). Coupled with turbidity-induced light limitation (Dong et al., 2011; Lin et al., 2024), these factors suppress biological uptake and maintain the TW as a strong CO₂ source. Ultimately, the agreement among climatological patterns (Figure 4), correlation structures (Figure 6), and thermodynamic decomposition (Figure 7) indicates that the mapped variability is mechanistically coherent rather than a statistical artifact. Collectively, the opposing sign and seasonality of non-thermal controls justify the regime-specific modeling strategy and explain why a pCO₂–environment relationship is unlikely to be robust across both regimes.

4.4 Long-term air-sea CO₂ exchange trends and drivers

Before discussing long-term air-sea CO₂ exchange trends, it is important to clarify the interpretation of pCO₂ variability in the TW regime. Although a positive pCO₂ increase is estimated in TW, this trend did not reach statistical significance over the full study period (2003–2023; p = 0.06; Section 3.2). While this requires cautious interpretation of the oceanic trend in isolation, the resulting long-term air-sea flux trends remain robust. As detailed below, the resolution to this paradox lies in understanding how the dominant atmospheric CO₂ climate forcing interacts with and ultimately overpowers the localized variance of the coastal ocean.

Long-term trends in air–sea CO₂ exchange provide critical insights into the evolving carbon sink capacity of the ECS. As presented in Section 3.4, the 21-year (2003–2023) atmospheric CO₂ growth rates (+2.41 µatm yr^-1) significantly outpaced the surface pCO₂ increases in both the CW (+0.66 µatm yr^-1) and TW (+1.11 µatm yr^-1).

In the CW, the persistently lower oceanic pCO₂ maintains a robust carbon sink (mean ΔpCO₂^sea-air of -37.15 µatm; annual mean flux of -3.11 ± 4.00 mmol m^-2 d^-1; Table 5). Furthermore, the disparity in their growth rates continuously intensifies this negative ΔpCO₂^sea-air gradient (-1.69 µatm yr^-1; Figure 9). This intensified thermodynamic driving force mechanically explains the statistically significant strengthening of the carbon sink capacity observed in the flux anomaly (-0.182 mmol m^-2 d^-1 yr^-1, p < 0.001; Figure 9a). Interestingly, our analysis reveals that wind speed anomalies in the CW experienced no significant long-term change (-0.0004 ms^-1 yr^-1, 95% CI: [-0.0123, 0.0115], p = 0.976). This implies that the intensified carbon sink is overwhelmingly driven by the thermodynamic gradient rather than accelerated physical gas transfer. Furthermore, the CW exhibits a statistically significant warming trend in SST anomalies (+0.0325 °C yr^-1, 95% CI: [0.0118, 0.0532], p = 0.014), which thermodynamically decreases CO₂ solubility. However, as demonstrated by the decomposition analysis (Figure 7a), although the CW is fundamentally a thermally-driven system, this warming effect is effectively offset. This behavior aligns with previous studies indicating that ocean pCO₂ over many continental shelves rises more slowly than atmospheric CO₂, thereby enhancing coastal uptake (Lohrenz et al., 2018), and reinforces the continental shelf pump concept within the ECS (Tsunogai et al., 1999).

The TW presents a highly dynamic yet coherent scenario. Unlike the CW, which operates as a perennial sink, the TW inherently functions as a net carbon source characterized by a predominantly positive mean ΔpCO₂^sea-air state (+44.85 µatm) and massive biogeochemical noise (SD = 63.67 µatm). When evaluated using monthly averages, this extreme localized variance masks the long-term oceanic pCO₂ trend, rendering the slow increase (+1.11 µatm yr^-1) statistically nonsignificant (p = 0.06).

However, the long-term trajectory of the air-sea CO₂ flux is ultimately dictated by the overarching atmospheric climate signal. Because the rapid atmospheric CO₂ growth (+2.41 µatm yr^-1) fundamentally outpaces the noisy oceanic pCO₂ rise, the thermodynamic driving force (ΔpCO₂^sea-air) is forced into a systematic negative trajectory, diverging by approximately -1.43 µatm yr^-1. This shrinking thermodynamic gradient physically explains the steady weakening of the TW outgassing capacity. When the massive seasonal and episodic non-thermal noise is smoothed using a 12-month moving average, this atmosphere-driven systematic decrease in the flux anomaly emerges as highly significant (-0.166 mmol m^-2 d^-1 yr^-1, p < 0.001). Furthermore, despite a strong localized warming trend (+0.0422 °C yr^-1, p = 0.005) that would typically amplify natural outgassing by decreasing solubility, the overwhelming accumulation of atmospheric CO₂ effectively suppresses this temperature-driven release. Consequently, the atmospheric forcing successfully overrides the immense non-thermal variance inherent to the turbid zone, gradually stifling the coastal carbon source.

Regarding these dynamics, a notable observation in the retrained model is the underestimation bias for pCO₂ values exceeding 500 µatm within the TW regime (Figure 2). Importantly, this bias is observed across the training, validation, and test datasets. This shared performance characteristic suggests that the model is not overfitting to localized noise or specific subsets; rather, it reflects a robust, generalized response to the inherent sparsity of extreme in-situ observations in the highly variable coastal zone. Because the TW regime currently functions as a carbon source (Table 5), this inherent underestimation implies that the future role of the TW region as a CO₂ source might be far more significant than currently estimated. This finding underscores the critical need for expanded high-frequency monitoring of extreme events in coastal RiOMars.

4.5 Global applicability to River-dominated Ocean Margins (RiOMars)

Quantitatively, CW exhibits an annual mean influx of -3.11 mmol m^-2 d^-1 (≈ -1.14 mol C m^-2 yr^-1), exceeding the global coastal ocean average of -0.68 ± 0.14 mol C m^-2 yr^-1 synthesized by Dai et al. (2022) and surpassing earlier estimates (-0.5 to -0.7 mol C m^-2 yr^-1) reported by Cai et al. (2006). Even the ECS-wide mean (-2.55 mmol m^-2 d^-1 or -0.93 mol C m^-2 yr^-1) suggests a stronger sink than typical open-ocean uptake (~ -0.5 mol C m^-2 yr^-1). This magnitude is comparable to the northern Gulf of Mexico (-1.1 ± 0.3 mol C m^-2 yr^-1), another major river-dominated shelf (Lohrenz et al., 2018). However, an important nearshore contrast is revealed: the coastal TW in the ECS acts as a weak net source of CO₂ annually (+0.40 mmol m^-2 d^-1 or +0.15 mol C m^-2 yr^-1), in stark contrast to the inner-shelf sink capacity reported for the Gulf of Mexico (-2.3 mol C m^-2 yr^-1).

This contrast emphasizes that optical classification is not merely a technical choice but a prerequisite for defensible carbon cycle attribution in heterogeneous coastal waters, because it isolates a light limited, resuspension-dominated regime from bloom-supporting waters and reduces bias introduced by averaging across incompatible controls.

The framework developed in this study provides a robust methodology that can be extended to other major River-dominated Ocean Margins (RiOMars) globally. The effectiveness of nL_w555 as a reliable optical proxy for identifying turbid river plumes has been demonstrated not only in the ECS but also in other complex coastal environments, such as the Oregon and Washington coasts (Saldías et al., 2012).

The necessity of a specialized approach for turbid waters is further supported by observations in major global estuaries. In the Mississippi River, Fichot and Benner (2014) reported high variability in pCO₂ driven primarily by terrestrial organic matter inputs, suggesting that conventional algorithm frameworks may struggle to resolve such localized and terrestrially influenced signals. Similarly, at the Amazon river mouth, Ward et al. (2015) high-lighted that high concentrations of suspended matter and terrestrial organic matter create a highly heterogeneous biogeochemical environment, playing a critical role in the transformation and production of particulate organic carbon (POC).

These findings suggest that in global RiOMars, the presence of high turbidity and terrestrial organic input creates biogeochemical regimes that are fundamentally distinct from the adjacent clear-water shelf. Therefore, the optical classification-based machine learning approach presented in this study offers a highly promising methodological foundation for resolving such inherent heterogeneity. However, as this framework was developed and validated solely within the ECS, its global applicability remains a hypothesis requiring future validation using in-situ datasets from diverse marine systems. While not yet a proven globally transferable framework, we anticipate that accurately accounting for the unique dynamics of turbid river plumes through similar regime-aware approaches can significantly reduce uncertainties in estimating regional carbon budgets and enhance our understanding of the global coastal carbon cycle.

5 Conclusions

This study demonstrates that an nL_w555-based optical regime separation provides a highly accurate framework for reconstructing surface pCO₂ and air-sea CO₂ fluxes in the East China Sea (ECS). By explicitly delineating Clear Water (CW) and Turbid Water (TW) regimes, our model reduced relative errors in turbid waters by up to 81% compared to conventional models, achieving outstanding overall accuracy on the independent test dataset (R² = 0.86, RMSE = 16.55 µatm). The 21-year reconstructed climatology (2003–2023) captures distinct regime dynamics: CW is dominated by summer biological drawdown, while TW functions as a highly variable CO₂ source driven by non-thermal forcing (+28.09 µatm). Over two decades, atmospheric CO₂ growth (+2.41 µatm yr^-1) significantly outpaced oceanic pCO₂ increases in both regimes. This thermodynamic disparity has driven a statistically significant strengthening of the CW carbon sink capacity (-0.182 mmol m^-2 d^-1 yr^-1), confirming the clear-water shelf as an intensifying CO₂ sink. Crucially, correctly identifying the TW region as a weak net CO₂ source (+0.50 Tg C yr^-1) rather than a sink reveals that conventional models overestimate the total ECS carbon uptake by approximately 46% (~4.04 Tg C yr^-1). This substantial discrepancy highlights that optical classification is a prerequisite for robust carbon-cycle attribution. This regime-aware framework demonstrates potential as a methodological foundation for other major River-dominated Ocean Margins (RiOMars), though its global transferability requires future validation across diverse marine systems.

While demonstrating robust performance, this work has specific caveats. Notably, the model exhibits a tendency to underestimate extreme high-pCO₂ values in highly variable TW, reflecting the inherent sparsity of in-situ observations in these dynamic zones. Additionally, reconstructing the 21-year climatology necessitated a partial dependence on reanalysis salinity products due to the limited temporal span of continuous satellite records. The 0.1° (~11.1 km) spatial block size is slightly smaller than the 14.3 km decorrelation length, though sensitivity analyses confirmed its impact is practically minimal. Future efforts must directly address these limitations by integrating continuous coastal observation data to better capture extreme non-thermal outgassing events, and by transitioning to satellite-derived salinity datasets as those records sufficiently mature.

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