Satellite estimation of global air sea CO₂ flux from 2000 to 2020

Abstract

The global ocean carbon dioxide flux (air-sea) has shown a slow upward trend. Based on more than 160,000 quality-controlled measurements of surface ocean carbon dioxide fugacity from 2000 to 2020, a satellite-based ocean–atmosphere carbon dioxide fugacity (fCO₂) retrieval algorithm was developed using machine learning methods. A comparative analysis was conducted among various machine learning methods, including XGBoost, random forest, light gradient boosting machine, feedforward neural network, convolutional neural network, and backpropagation neural network. Based on the best performance, the random forest algorithm was selected for model construction. Independent in situ validation showed that the model achieved a low root mean square error (RMSE = 14.35 µatm), a low mean absolute percentage error (MAPE = 2.61%), and a high coefficient of determination (R² = 0.86). The distribution of global air-sea carbon dioxide fugacity from 2000 to 2020 was reconstructed at a resolution of0.25° × 0.25°, and the air–sea carbon dioxide flux (FCO₂) of the global ocean during the period of 2000–2020 was further estimated at a resolution of 0.25°×0.25°. During the period of 2000–2020, the global ocean CO₂ uptake increased from 1.443 PgC/year in 2000 to 1.894 PgC/year in 2020, and the air-sea carbon dioxide flux in the entire study area increased by 31.2% over the 20 years. These comprehensive oceanic carbon sink datasets and new insights will support future research on ocean carbon sequestration and its climate regulation potential.

Introduction

It is widely acknowledged that carbon emissions are a significant factor contributing to the increased frequency of extreme weather events and global warming, leading to elevated levels of atmospheric carbon dioxide¹. Since the Industrial Revolution, the concentration of carbon dioxide (CO₂) in the atmosphere has risen from approximately 280 ppm to around 420 ppm². Although the ocean absorbs a significant portion of anthropogenic CO₂, roughly half remains in the atmosphere, further intensifying the greenhouse effect³. Given that the ocean is a significant CO₂ sink, understanding the spatial and temporal variations of air-sea carbon dioxide flux (FCO₂) is crucial for comprehending the global carbon cycle⁴. The concentration of CO₂ in the atmosphere is significantly influenced by the rate at which the ocean absorbs and releases CO₂, which in turn affects global climate patterns⁵. Therefore, accurately quantifying FCO₂ is essential for monitoring global carbon dynamics. Traditional methods for estimating FCO₂ rely on in situ measurements of CO₂ concentrations in seawater and the atmosphere, followed by calculations using gas exchange models based on diffusion and solubility kinetics. However, this approach is not only labor-intensive but also limited to small-scale measurements. Remote sensing has become an increasingly important tool, offering broad spatial coverage, high temporal resolution, and near real-time monitoring capabilities. Numerous studies have been conducted to determine whether the ocean acts as a source or sink for the atmosphere. Guo and Timmermans (2024) demonstrated using a 0.1° eddy-resolving global model that mesoscale variability explains > 30% of the air–sea CO₂ flux variance in western boundary current regions⁶. Eunna Jang et al. (2017) applied the random forest algorithm to investigate the air-sea CO₂ fugacity (fCO₂) over the East Sea between Korea and Japan, based on in situ measurement data, satellite data, and geostationary ocean color imager products. They analyzed its spatial and seasonal distribution characteristics. Their work demonstrated the potential of combining machine learning with remote sensing to improve the spatial and temporal resolution estimates of fCO₂⁴. Goddijn-Murphy et al. (2015) recalculated fCO₂ values from the SOCAT dataset using monthly sea surface temperature composites from 1°×1° satellite grids, providing valuable baseline data for ocean–atmosphere CO₂exchange studies⁷.. Meanwhile, Moussa, Benallal et al. conducted a quantitative study of fCO₂ in the surface waters of the Atlantic Ocean using satellite data with a spatial resolution of 4 km×4 km and a feedforward neural network⁸.

In recent years, machine learning techniques have gained increasing popularity in marine environmental research because of their ability to accurately capture the characteristics of marine variables and address the inherent complex nonlinear problems of these variables^9–11. A range of machine learning techniques, including random forest (RF)⁴, LightGBM^1,2,12, convolutional neural network (CNN)¹³, feedforward neural network⁸, backpropagation neural network (BP)¹⁴, and XGBoost¹⁵, have been successfully applied to develop satellite-based fCO₂ models.

The main objectives of this study are threefold: (1) To identify key model factors that affect the construction of global surface ocean fCO₂; (2) To develop and evaluate machine-learning-based fCO₂ models; (3) Based on machine learning models, reconstruct the global fCO₂ data over the past 20 years, and reconstruct the distribution of global FCO₂ over the past 20 years. To compare it with existing observed FCO₂ data and other reconstructed datasets, and estimate the trend of FCO₂ during this period. Through these aspects, to analyze the spatiotemporal distribution characteristics and long-term trends of fCO₂ and FCO₂ in global marine areas from 2000 to 2020.

Study area and data methods

Observational data

The global marine research community provided in situ measurements of sea surface carbon dioxide fugacity (fCO₂) through an international collaborative research program aimed at assessing the fCO₂. These data have been combined with more than 160,000 rigorously quality-controlled surface ocean CO₂ fugacity values collected from 2000 to 2022 (SOCAT). The global distribution of sampling tracks is shown in Fig. 1a, which can be publicly obtained through the webODV platform https://explore.webodv.awi.de/ocean/carbon/socat/. The annual distribution of the in situ data is shown in Fig. 1b. With no fewer than 5 500 records per year, the dataset captures the spatiotemporal variability of global surface-ocean fCO₂. The SOCAT dataset is freely accessible via https://www.socat.info/.

Fig. 1.

Global distribution and number of measurement points of fCO₂ data from 2000 to 2020. (a) Global distribution map of measured fCO₂ data from 2000 to 2020 (shown in blue). (b) Histogram depicting the annual quantity distribution of observational data from 2000 to 2020.

Satellite and model data

A total of 19 potential predictor variables have been selected for this study (Table 1), with abbreviations adopted for convenience. These data are obtained from three distinct sources: in situ observations, satellite observations, and numerical model outputs. The associated datasets offer high spatiotemporal resolution and global coverage, providing a solid basis for our analysis.

Table 1.

List of satellite data and reanalysis data (Sort based on its resolution and name).

Variable name	Abbreviation	Spatial resolution	Temporal resolution	Type
Mass concentration of chlorophyll a in sea water	CHL	0.036	Daily	Satellite observations
Sea water salinity	sos	0.083	Daily	Numerical models
Sea water potential temperature	Temperature	0.083	Daily	Numerical models
Eastward sea water velocity	uo	0.083	Daily	Numerical models
Northward sea water velocity	vo	0.083	Daily	Numerical models
Mole concentration of nitrate in sea water	no3	0.25	Daily	Numerical models
Mole concentration of dissolved molecular oxygen in sea water	O2	0.25	Daily	Numerical models
Mole concentration of phosphate in sea water	PO4	0.25	Daily	Numerical models
Mole concentration of silicate in sea water	Si	0.25	Daily	Numerical models
Surface geostrophic eastward sea water velocity	Ugos	0.25	Daily	Numerical models In-situ observations Satellite observations
Surface geostrophic northward sea water velocity	Vgos	0.25	Daily	Numerical models In-situ observations Satellite observations
Mixed layer thickness of the ocean	Mlotst	0.25	Weekly	In-situ observations Satellite observations
Eastward wind	Uwind	0.25	Monthly	Satellite observations
Northward wind	Vwind	0.25	Monthly	Satellite observations
Seawater acidity and alkalinity	ph	0.25	Monthly	In-situ observations
Total alkalinity in sea water	Talk	1	Monthly	In-situ observations
Dissolved inorganic carbon in sea water	TCO2	1	Monthly	In-situ observations
Partial pressure difference of carbon dioxide at the sea surface	SpCO2	1	Monthly	In-situ observations
Surface downward mass flux of carbon dioxide expressed as carbon	FgCO2	1	Monthly	In-situ observations

Data grid, matching, and subset classification

Given the differences in temporal and spatial resolution of satellite data, systematic matching protocols must be employed to minimize errors during the matching process. Temporally, this study first sought exact temporal coincidences with in-situ observations. In cases where coincident data are unavailable, the temporally nearest available data are selected for matching. This ensures maximum temporal alignment and minimises time-offset errors. For spatial matching, this study selects data that are identical to the location where the observed data were collected. If data are not available at that exact location, the spatially closest valid pixel is identified for matching. This method ensures the accuracy and reliability of spatial matching, effectively mitigating spatial discrepancy effects on the results.

This optimized spatiotemporal matching protocol ensures a high-fidelity dataset that is critical for subsequent machine-learning algorithms. Using this dataset for training, validation and testing will significantly improve the performance and accuracy of fCO₂ estimation models. This study aims to establish a robust and precise fCO₂ estimation framework to support high-quality scientific research and applications.

After matching, each sample contains both the observed fCO₂ value and 19 predictor variables. Following removal of missing values generated during matching, a final matched dataset comprising > 160,000 complete records was obtained. To ensure model training efficacy, the data were partitioned into training (80%), validation (10%) and testing (10%) subsets. This split follows a conventional random-sampling strategy that suppresses spatial autocorrelation and preserves adequate spatiotemporal representation across all three subsets, especially the validation set.

The randomized partitioning approach effectively mitigates sampling biases arising from uneven data distributions, thereby enhancing model generalizability and predictive reliability across diverse spatiotemporal conditions. This ensures an accurate representation of the complex dynamics governing fCO₂ variations.

Correlation analysis

The predictor variables exhibit significant correlations with fCO₂. To ensure data processing accuracy and model efficacy, correlation analysis is essential. This approach enhances model parsimony while improving computational efficiency and interpretability. Given the non-Gaussian distribution properties of some predictors, Spearman’s rank correlation coefficient was employed to quantify inter-variable relationships. Spearman’s ρ coefficient is computed as:

1

The variables ρ, d, and n represent the Spearman correlation coefficient, rank difference, and sample size, respectively. The value of ρ ranges from − 1 to 1, where 0 indicates no correlation, −1 indicates a perfect negative correlation, and 1 indicates a perfect positive correlation. Therefore, it can more accurately assess the relationship between variables and help determine whether to include them.

Performance evaluation

The coefficient of determination (R²), root mean square error (RMSE), and mean absolute percentage error (MAPE) were employed to comprehensively evaluate model performance along with derived estimation products for air-sea CO₂ fluxes, assessing both predictive accuracy and result robustness. These metrics are calculated as:

2

3

4

Here, X_i​, Y_i, and N represent the algorithm retrieval values, in situ measurement values, and sample size, respectively. X and Y denote the mean values of all algorithm retrieval values and in situ measurement values, respectively. σX and σY are the standard deviations of X_i and Y_i, respectively.

Machine learning model selection

Chen and Guestrin (2016) proposed an enhanced distributed gradient boosting machine learning model called XGBoost, which is based on the gradient boosting decision tree (GBDT) framework. XGBoost is noted for its efficiency and flexibility; it mitigates over-fitting by adding a regularisation term to the loss function. The model optimizes the objective function using the second-order Taylor expansion of the loss function, as detailed in Chen and Guestrin (2016)¹⁶. In this study, the fCO₂ retrieval model was developed using the publicly available Scikit-Learn and XGBoost software packages. After a series of tests, the parameters of the XGBoost model were set as follows: the number of regression trees was set to 1500, the maximum tree depth was adjusted to 10, the learning rate was fixed at 0.05, and the weight of the L2 regularization term was allocated to 0.01.

Random Forest (RF) and XGBoost are two widely used machine-learning algorithms. Both models are based on binary decision trees, including classification trees and regression trees, as their fundamental learning units. RF employs the “bagging” (bootstrap aggregating) method, which involves uniformly selecting training samples with replacement to construct multiple decision trees. In contrast, XGBoost applies gradient boosting, iteratively weighting mis-predicted samples to refine the ensemble¹⁶. In this study, the RF regression model was configured with the following parameters: the number of decision trees was set to 200, the minimum number of samples required to split an internal node was set to 2, the minimum number of samples required to be at a leaf node was set to 1, the feature selection strategy was set to use the square root of the total number of features, the maximum depth of the trees was set to 30, and bootstrap sampling was not enabled. These parameter settings aim to balance the model’s complexity and generalization ability to enhance the model’s accuracy and robustness in predicting fCO₂.

LightGBM represents a fast, distributed-memory, high-performance gradient boosting framework. Distinct from XGBoost and RF, LightGBM implements histogram-based gradient boosting to accelerate training¹⁷. Previous studies indicate this approach exhibits dataset-dependent performance variability that may compromise training efficacy¹⁸. In contrast, XGBoost optimizes split-point selection through pre-sorting, thereby improving partitioning accuracy and outlier robustness¹⁹.

Convolutional Neural Networks (CNN) demonstrate superior feature learning capabilities through hierarchical representations. Compared to RF and XGBoost, CNN’s unique architecture provides distinct advantages for visual data processing, whereas RF and XGBoost exhibit superior performance on structured data prediction tasks. Feedforward Neural Networks (FNN) operate through learned weight matrices rather than ensemble methods, making them suitable for well-defined numerical features.

Air-sea CO₂ flux calculation

Following the generation of surface ocean fCO₂ distribution field, the air-sea CO₂ flux (FCO₂) across the air-sea interface is calculated through the gas transfer equation:

5

In the flux calculation, where k denotes the gas transfer velocity, K^CO2_H represents CO₂ solubility in seawater (Weiss, 1974), and (fCO₂- fCO₂^atm) represents the gradient between sea surface and atmospheric CO₂ fugacity. Specifically, k was parameterized through wind-speed-dependent empirical formulations following the parameterizations of Sweeney et al. (2007), Wanninkhof et al. (2002), and Jiang et al. (2008).

6

7

where U_mean denotes the monthly mean wind speed at 10 m above sea level, Sc represents the Schmidt number under in situ thermal conditions²⁰. C₂ is the non-linear coefficient of the quadratic gas transfer relationship, U_j is 6-hourly wind speed, and n is the number of available wind speed measurements for the month. The atmospheric fCO₂ (fCO₂^atm) is calculated using xCO₂ for air, from NOAA, that is xCO₂²¹. Sea-level pressure (SLP) and the vapor pressure of water in air (pH₂O^Air) at 100% relative humidity using the following formula²²:

To quantify the amount of carbon absorbed or released by a specific region, we calculate the regional integrated CO₂ flux (in Pg C/year) by multiplying the average CO₂ flux density of the available pixels by the total area of the region. For FCO₂, positive values indicate CO₂ released to the atmosphere, while negative values indicate CO₂ absorbed by the ocean.

Result and discussion

Input parameter selection

In marine environmental research, identifying key drivers affecting sea surface CO₂ fugacity (fCO₂) is critical. Given that these drivers often exhibit non-Gaussian distributions and nonlinear relationships with fCO₂, the selection of robust dependence measures is paramount. The Spearman’s rank correlation coefficient, making no parametric distributional assumptions and being applicable to diverse data types, consequently emerges as the optimal choice. This distribution-free method, computed based on data ranks, provides statistical power while ensuring interpretability, enabling robust detection of monotonic relationships within complex marine datasets.

In this study, we first conducted a Spearman correlation single-factor analysis to assess the correlation between fCO₂ and its potential influencing factors, as shown in Fig. 2a. Subsequently, we employed the GeoDetector method to detect whether there are strong correlations among all factors, as illustrated in Fig. 2b. If a strong correlation was found between two factors, one of them was removed to avoid multicollinearity issues. Ultimately, we selected the following variables—CHL (Mass concentration of chlorophyll a in sea water), Temperature(Sea water potential temperature), NO₃ (Mole concentration of nitrate in sea water), ph༈Seawater acidity and alkalinity༉, uo (Eastward sea water velocity), Vwind (Northward wind), Uwind (Eastward wind), O₂ (Mole concentration of dissolved molecular oxygen in sea water), and sos (Sea water salinity)—for constructing the machine learning model of fCO₂.

Fig. 2.

The correlation between influencing factors and fCO₂ detection chart (a). The correlation between different variables (b).

Although the single-factor correlation between the surface downward mass flux of carbon dioxide expressed as carbon (FgCO₂) and the fCO₂ variable is relatively strong, its potential relationship with pH is also significant. However, given the stronger correlation between pH and fCO₂, to simplify the model and optimize the data processing, we decided to remove the FgCO₂ variable from the model. By doing so, we can more accurately identify and quantify the key environmental factors affecting fCO₂, providing important scientific evidence for further understanding the marine carbon cycle and its role in global climate change.

Construction of fCO₂ evaluation model

All six machine learning algorithms (RF, LightGBM, FNN, BP, CNN, and XGBoost) were trained and validated using identical predictor variables and datasets, with multiple experimental repetitions performed for each model. The optimally tuned model configuration for each algorithm was selected for fCO₂ reconstruction. Comparative analysis of standard evaluation metrics (MAPE, RMSE, R²) throughout all data partitions revealed RF and XGBoost demonstrated consistent superior performance.

As shown in Fig. 3, the panel plots depict validation results of different models across global regions. Each subplot quantifies the agreement between predicted and observed fCO₂ values with corresponding statistical metrics. The RF and XGBoost models exhibit optimal consistency with observations, indicating superior predictive accuracy. As summarized in Table 2, both models achieved state-of-the-art performance on the test set: RF (RMSE = 15.85 µatm, MAPE = 2.67%, R² = 0.86) and XGBoost (RMSE = 16.12 µatm, MAPE = 2.90%, R² = 0.85).

Fig. 3.

The performance of different models on the same dataset is evaluated using independent training, validation, and test sets.

Table 2.

Performance parameters of different models in the global ocean.

Model		MAPE	RMSE(μatm)	R2
Training process	RF	0.005	0.36	1
	XGBoost	0.020	10.02	0.94
	LightGBM	0.029	14.86	0.88
	BP	0.038	19.83	0.78
	CNN	0.046	23.80	0.69
	FNN	0.040	21.14	0.75
Validation process	RF	0.028	16.43	0.85
	XGBoost	0.028	15.29	0.87
	LightGBM	0.035	18.88	0.80
	BP	0.039	20.90	0.76
	CNN	0.046	24.02	0.68
	FNN	0.041	21.59	0.74
Testing process	RF	0.027	15.85	0.86
	XGBoost	0.029	16.12	0.85
	LightGBM	0.038	20.23	0.78
	BP	0.049	23.94	0.69
	CNN	0.048	24.56	0.66
	FNN	0.040	21.68	0.74

Figure 4 shows the independent validation results of various machine learning models in the global region, including Random Forest (RF), XGBoost, LightGBM, BP neural network, CNN, and FNN. Each subplot displays the relationship between the model-predicted fCO₂ values and the actual observed values. It can be seen that the predictions of the RF and XGBoost models align most closely with the actual observed values, with the scatter points more tightly clustered around the diagonal line, indicating a higher level of predictive accuracy for these models. Specifically, the RF model has an R² of 0.86, RMSE of 14.35 µatm, and MAPE of 2.61%; the XGBoost model has an R² of 0.85, RMSE of 14.95 µatm, and MAPE of 2.77%. In contrast, the performance of other models such as LightGBM, BP, CNN, and FNN is relatively weaker, with more dispersed scatter points, especially showing poorer fitting effects at the high and low value ends. For example, LightGBM has an R² of 0.80, RMSE of 16.65 µatm, and MAPE of 3.19%; CNN has an R² of 0.72, RMSE of 19.06 µatm, and MAPE of 3.61%. Although the R² value is relatively high, the RMSE value indicates a larger prediction error. Therefore, based on the comprehensive performance of the machine learning models on the training set, validation set, test set, and independent validation results, the RF model was selected for the reconstruction of fCO₂. Independent validations confirm the model enables robust reconstruction of fCO₂ from multi-satellite observations.

Fig. 4.

The performance between the output values of different models and the actual values, with colors indicating the size of the actual measured values.

Seasonal variation in seawater fCO₂

Independent modeling was conducted based on the RF algorithm and the multi-scale influencing factors. By integrating these factors, we generated a 0.25° × 0.25° resolution dataset of sea surface fCO₂ distributions spanning from 2000 to 2020 (Fig. 5). The spatial distribution maps in Fig. 5 (and Fig. 6) were generated based on the gridded netCDF data retrieved by the random forest (RF) machine learning model. The retrieved results were converted from CSV format to netCDF format and exported as GeoTIFF files. All geographic visualization maps were plotted using MATLAB R2022b (The MathWorks, Inc., Natick, MA, USA; https://www.mathworks.com) according to the raster values in the GeoTIFF data without additional coastline or grid overlays. To perform independent verification of the research outcomes, we implemented a two-tier validation scheme, which eliminated any cross-contamination between training data and evaluation data: we first adopted the Global Surface pCO₂ Database (LDEO) V2019 released by the Ocean Carbon Data System (OCADS) as the independent validation dataset, which contains 14.2 million in-situ pCO₂ records worldwide from 1957 to 2019 with its observation methodology (equilibrator–CO₂ analyzer system) and data sources completely independent of SOCAT, then randomly extracted data from January 2000, January 2005, and January 2010 for comparison with the pCO₂ values converted from fCO₂ in our study, and the results showed that R², RMSE, and MAE were 0.76, 11.4 µatm, 9.8 µatm for January 2000, 0.81, 11.9 µatm, 10.7 µatm for January 2005, and 0.59, 15.3 µatm, 14.2 µatm for January 2010, demonstrating the model’s high accuracy and favorable generalization capability on fully independent datasets (Fig. 7), For Fig. 7, the reconstructed monthly data were converted from CSV format to netCDF format and imported into ArcMap; the spatial distribution was displayed using unique-value symbology. The selected cruise observation data were spatially matched with the reconstructed results from this study, and the matched data were exported as netCDF files and combined with the unique-value spatial layer to generate the final visualization; we further selected three long-term autonomous mooring observation stations in the open ocean—M2 (56.510°N, 164.040°W), Gray’s Reef (31.400°N, 80.870°W), and Cheeca Rocks (24.910°N, 80.624°W)— based on the geographic coordinates of the three in-situ observation sites mentioned above, the specific spatial locations of these monitoring stations were accurately marked and presented in the reconstructed fCO₂ spatial distribution map (Fig. 8),with data retrieved from the global autonomous mooring pCO₂ time-series network established during 2004–2015, aggregated the hourly in-situ data to monthly resolution for synchronous validation against the converted pCO₂ values, and uniformly applied the conversion formula pCO₂ = fCO₂ × (1.00436 − 4.66910 × 10⁻⁵ × SST) for all comparisons to ensure consistent evaluation metrics. The consistent results of this dual independent validation confirm that the model exhibits robust predictive performance on independent data not involved in training, fully attesting to its excellent generalization capability.

Fig. 5.

Surface ocean fCO₂ products in the global ocean.

Fig. 6.

Distribution of monthly average fCO₂ from 2000 to 2020.

Fig. 7.

Spatial Distribution and Time Series Comparison of Measured and Reconstructed Sea Surface pCO₂ Using Independent LDEO V2019 Dataset (Jan 2000, 2005, 2010).

Fig. 8.

Spatial Distribution and Long-Term Independent Validation of Reconstructed Sea Surface pCO₂ Versus Open-Ocean Autonomous Mooring Observations.

The monthly average sea surface carbon dioxide fugacity in the study area from 2000 to 2020 is shown in Fig. 6. The sea surface carbon dioxide fugacity in the study area ranges from 200 to 600 µatm, with most regions exhibiting a pattern of lower values in summer and autumn and higher values in winter and spring. The global climatological average fCO₂ value increased by approximately 9.97% from 2000 to 2020 (Fig. 9). The monthly sea surface carbon dioxide fugacity in summer and autumn (from May to September) is lower than that in winter and spring (from January to April). From the perspective of the Northern and Southern Hemispheres, the carbon dioxide fugacity in the Southern Hemisphere is generally higher than that in the Northern Hemisphere due to the larger total surface area of the Southern Hemisphere. The high fugacity in the tropical regions of the Southern Ocean also confirms the significant impact of the Southern Hemisphere oceans, a conclusion similar to that of Fay²³.

Fig. 9.

Monthly average fCO₂ value (µatm) from 2000 to 2020.

The monthly average variations of fCO₂ within the study area are illustrated in Fig. 6, clearly showing a relatively stable pattern over several months. The ocean’s capacity as a carbon sink is relatively stable, indicating no significant changes have occurred. From a regional analysis perspective, in the mid-to-high latitudes of the Northern Hemisphere, such as the North Atlantic and North Pacific, fCO₂ values are lower in summer and peak in winter. This may be related to the reduced marine biological productivity and weakened water mixing during winter. In contrast, in the Southern Hemisphere, particularly the Southern Ocean, fCO₂ values are higher in summer, likely associated with enhanced biological activity in the Antarctic Circumpolar Current region and reduced water renewal frequency. The fCO₂ values in the equatorial Pacific and Indian Ocean regions are relatively high throughout the year, which may be related to the intense solar radiation and warm seawater in these areas, promoting biological productivity and respiration, thereby increasing the generation and release of carbon dioxide. Despite the strong biological productivity in tropical waters, respiration is equally significant, leading to increased carbon dioxide production and release. Moreover, although water mixing is frequent, it may not be sufficient to completely offset the carbon dioxide generated by biological activities, thus maintaining fCO₂ values at a higher level.

Seasonal variation in air-sea CO₂ flux

Based on the reconstructed spatiotemporal fCO₂ fields from 2000 to 2020 in this study, we recalculated the FCO₂ data from 2000 to 2020 (Fig. 10) and conducted a benchmark comparison between our results and the findings from the studies of Zhong et al.²⁴ (Fig. 11) and Luke Gregor et al.²⁵ (Fig. 12); a summary of this comparison is presented in Fig. 13.All aforementioned spatial visualization results including Figs. 10, 11, 12 and 14 were generated by converting the calculated FCO₂ CSV datasets into standard NetCDF files and subsequently visualized and displayed within the ArcGIS platform. From 2000 to 2020, the global air-sea CO₂ flux data demonstrated a significant increasing trend in the ocean’s capacity to absorb atmospheric CO₂. Specifically, the oceanic CO₂ uptake flux was 1.4429 Pg C/year in 2000, and this value increased to 1.8943 Pg C/year by 2020 (Fig. 13). This increase indicates that the ocean is exhibiting enhanced climate regulation capacity in the global carbon cycle as a significant “sink” for atmospheric CO₂. Although the oceanic sink has strengthened, the underlying increase in atmospheric CO₂ continues to drive ocean acidification and related biogeochemical stresses.

Fig. 10.

Surface ocean FCO₂ products in the global ocean (This study).

Fig. 11.

Comparison of surface ocean FCO₂ product from different study, Zhong et al (2022)²⁴ product.

Fig. 12.

Comparison of surface ocean FCO₂ product from different study, Luke Gregor et al (2024)²⁵ product.

Fig. 13.

Bar graph showing temporal variations in global FCO₂ from three datasets (2000–2020).

Fig. 14.

Distribution of monthly average FCO₂ from 2000 to 2020.

Figure 14 illustrates the spatiotemporal patterns of the multi-year monthly average FCO₂ over the entire study area, where the North Atlantic and North Pacific regions are persistent net CO₂ sinks and are exhibiting pronounced seasonality. From January to September, the amount of CO₂ absorbed by the North Atlantic and North Pacific increases gradually with the months, while from September to December, the amount of CO₂ absorbed decreases gradually. In contrast, the southern part of the Southern Ocean shows the opposite pattern. In this region, the CO₂ flux indicates that the amount of CO₂ absorbed decreases during January-September and increases from September to December. These two regions reflect that the amount of CO₂ absorbed is likely closely related to sea water temperature. Although an increase in sea water temperature reduces the solubility of CO₂ in water, the North Atlantic and North Pacific regions have higher chlorophyll concentrations. From January to September, with increasing photoperiod, the phytoplankton photosynthetic activity intensifies and their growth and reproduction enter a peak period, so the CO₂ absorption increases. Conversely, from September to December, as the daylight hours shorten and the water temperature drops, the photosynthesis of phytoplankton weakens and their growth and reproduction slow down, so the CO₂ absorption decreases. The situation in the southern part of the Southern Ocean is exactly the opposite of that in the North Atlantic and North Pacific.

The CO₂ flux in the equatorial regions exhibits consistently positive values annually, acting as a “source” of FCO₂, with these areas consistently releasing CO₂ into the atmosphere. This is due to the high temperatures in the equatorial regions all year round, which reduce the solubility of CO₂. Additionally, the equatorial regions have lower chlorophyll concentrations, resulting in less photosynthesis and growth of phytoplankton. Moreover, the seasonal variations in wind speed and mixing layer depth in the equatorial regions are relatively small, exerting negligible influence on CO₂ flux.

The CO₂ flux in the Bering Strait region exhibits significant seasonal changes across different months. During winter months (January-March), this area acts as a “source” of CO₂, releasing it into the atmosphere. From April to October, it transforms into a “sink,” absorbing CO₂ from the atmosphere. Then, from October to December, it reverts to a net source status a “source” of CO₂. This seasonal variation reflects the complex biogeochemical feedback mechanisms to environmental changes.

From the analysis of the open ocean and marginal seas, the FCO₂ in the marginal seas surrounding continents is higher than that in the open ocean, indicating a strong correlation with industrial activities and population density. Industrial processes, transportation, and energy consumption release large amounts of CO₂ into the atmosphere, thereby accelerating CO₂ exchange. Moreover, rivers carry large amounts of freshwater rich in CO₂ into the ocean. The marine ecosystems near continents are relatively prosperous with more biological activities. Consequently, marine organisms produce more CO₂ through respiration. As a result, the FCO₂ in the marginal seas surrounding continents is higher than that in the open ocean.

Synergistic modulation of ocean carbon sink

This study observed a significant 31.2% increase in the global ocean CO₂ uptake flux from 2000 to 2020. This trend is not driven by a single factor, but rather a comprehensive outcome of the interplay between the dominant driver (rising atmospheric fCO₂) and mitigating effects (e.g., ocean warming and enhanced stratification), coupled with the synergistic modulation of wind field pattern evolution, ocean circulation adjustments, and changes in biological pump functioning. This finding is highly consistent with the spatiotemporal distribution characteristics of fCO₂ reconstructed in this study and the analysis results of key driving factors. Firstly, atmospheric CO₂ concentration increased from approximately 369 ppm in 2000 to around 412 ppm in 2020²⁶, which greatly widened the sea-air CO₂ partial pressure difference (fCO₂ - fCO₂^atm). The intensity of this core driving force far outweighs the reduction in CO₂ solubility induced by seawater warming. Studies by Hersbach, Huang, and colleagues have confirmed that the global annual mean sea surface temperature rose by approximately 0.40℃ between 2000 and 20,208^27,28. Although this slightly decreased CO₂ solubility in surface seawater, the rapid increase in atmospheric CO₂ concentration dominated the expansion of the partial pressure difference, acting as a key factor promoting the continuous enhancement of ocean carbon sequestration capacity. Secondly, the evolution of ocean circulation and wind field patterns further reinforced this growth trend: satellite remote sensing wind field data (Uwind/Vwind) and ocean current velocity data (uo/vo) used in this study reveal that the Southern Ocean westerly jet significantly intensified and shifted poleward from 2000 to 2020, while the transport efficiency of the North Atlantic Meridional Overturning Circulation (AMOC) slightly improved in mid-latitude regions. This effectively facilitated the upward supply of carbon-depleted deep water, partially offsetting the inhibitory effect of enhanced ocean stratification on vertical carbon supply—consistent with the significant regulatory role of key predictors (e.g., wind fields and ocean currents, screened via the GeoDetector method) on fCO₂ observed in this study. Meanwhile, global ocean chlorophyll a (CHL) concentration data adopted herein show a slight upward trend in phytoplankton biomass in mid-to-high latitude waters, particularly in the subpolar regions of the North Atlantic and North Pacific. The improved efficiency of the biological pump further enhanced surface CO₂ absorption and downward sinking flux. In contrast, although tropical oceans exhibit low CO₂ solubility due to high temperatures, the “carbon fertilization” effect induced by rising atmospheric CO₂ has partially compensated for the limitation of insufficient biological productivity on carbon absorption—aligning well with the conclusion that CHL, as a core factor, modulates the spatial distribution of fCO₂. In summary, the significant growth of the ocean carbon sink observed in this study is essentially the result of the dominant effect of rising atmospheric CO₂ concentration, coupled with the synergistic modulation of marine physical processes (circulation and wind fields) and biogeochemical processes (biological pump). Its variation trend is consistent with the reconstructed spatiotemporal characteristics of fCO₂, the analysis of key driving factors, and the physical and chemical principles of the global carbon cycle, further confirming the ocean’s dynamic regulatory potential as a key “sink” in the global carbon cycle.

The impact of FCO₂ on the marine environment

Rising atmospheric CO₂ is subjecting the ocean—Earth’s largest carbon sink—to intensifying chemical and ecological stress. The increase in FCO₂, defined as the rate at which the ocean absorbs or releases CO₂, has multifaceted and profound impacts on the marine environment. These impacts extend beyond marine chemical processes to all levels of marine ecosystems, ultimately exerting feedback effects on global climate patterns.

Ocean acidification is one of the most direct and significant consequences of the increase in FCO₂. The dissolution of atmospheric CO₂ in seawater initiates a series of chemical reactions that lead to an increase in the acidity of seawater and a decrease in ph. Since the Industrial Revolution, the global mean seawater pH has declined from ~ 8.2 to 8.1²⁹. Despite its seemingly minor magnitude, this pH decline exerts substantial impacts on marine ecosystems. Many marine organisms, especially those with calcareous shells or skeletons, such as corals, shellfish, and certain plankton, are extremely sensitive to changes in seawater acidity. Lowered pH conditions impair calcification, growth, and reproductive success in these organisms and even cause their shells or skeletons to dissolve, thereby threatening their survival. Coral reefs, as one of the most bio-diverse ecosystems in the ocean, have a particularly concerning response to ocean acidification. Coral bleaching, defined as the expulsion of symbiotic zooxanthellae leading to whitening of coral tissues, not only affects the ecological functions of coral reefs but also has a cascading effect on the many marine organisms that depend on coral reefs for survival.

In addition to ocean acidification, the increase in FCO₂ is also closely related to the decrease in dissolved oxygen concentrations in the ocean. As seawater temperatures rise and acidification intensifies, the solubility of oxygen in seawater drops significantly, leading to the continuous expansion of hypoxic areas in the ocean. Hypoxic environments pose a serious threat to the survival of marine organisms, especially those species with high oxygen demands, such as fish and various aquatic organisms. Hypoxic conditions not only constrain the activity range of these organisms but may ultimately cause their death, thereby affecting the structure and function of the entire marine ecosystem. The increase in hypoxic areas in the ocean may also lead to shifts in species’ biogeographical ranges, forcing some species to migrate to more suitable areas, consequently modifying community structure and biodiversity of marine ecosystems.

The increase in FCO₂ can also alter marine primary productivity by affecting the physiological performance and trophic interactions of marine organisms. On one hand, the increase in CO₂ may promote the growth of certain phytoplankton, as they can utilize the additional CO₂ for photosynthesis. However, this stimulatory effect is not universally applicable to all phytoplankton and may be constrained by other factors such as light availability and nutrient concentrations. On the other hand, ocean acidification and hypoxic conditions can have detrimental effects on the physiological functions of zooplankton, fish, and other consumers, impairing their foraging efficiency, somatic growth, and reproductive success.

Productivity shifts can cascade through marine food webs, altering energy flux and biogeochemical cycling throughout the ecosystem. Specifically, fluctuations in primary productivity at the base of the food web can cascade upward, directly regulating zooplankton abundance and distribution, thereby influencing populations of fish and other predators at upper trophic levels.

Conclusion and implications

This study employed various machine learning models, including XGBoost, BP, LightGBM, CNN, FNN, and RF, to construct and validate fCO₂ reconstruction models using the SOCAT observational dataset and a variety of satellite-derived datasets. In this study, we developed a monthly fCO₂ product for the past 20 years by combining extensive in situ measurements with remote sensing data. Rigorous validation demonstrated that the fCO₂ product has high accuracy, with the reconstruction results highly consistent with the observed results. Based on these results, we obtained the spatiotemporal distribution and decadal-scale variability of fCO₂. Over the past 20 years, the monthly average fCO₂ increased by 9.97%. We also reconstructed the global FCO₂ from 2000 to 2020 and found that during this 20-year period, the ocean’s CO₂ uptake flux increased from 1.4429 Pg C/year in 2000 to 1.8943 Pg C/year in 2020, representing a 31.2% increase. These findings yield critical datasets for assessing the global carbon balance and enhance our understanding of the processes related to the marine carbon cycle.

The increase in FCO₂ has far-reaching impacts on the marine environment in multiple aspects. These impacts are interwoven and interact with each other, collectively shaping the future of marine ecosystems. Ocean acidification, hypoxia, changes in biological productivity, and alterations in ocean circulation not only threaten the survival and reproduction of marine organisms but may also provide feedback to the global climate system. Therefore, gaining an in-depth understanding and predicting the impacts of the increase in FCO₂ on the marine environment is crucial for developing effective marine conservation strategies and measures to address climate change.

Author contributions

Conceptualization, **[H.W.]**; methodology, **[H.W.]** and **[Y.J.]**; software, **[X.L.]** and **[Y.J.]**; validation, **[W.Z]**, **[L.C.]**, and **[L.W.]**; formal analysis, **[Y.J.]**; investigation, **[W.Z]**, **[L.W.]** and **[L.C.]**; resources, **[X.L.]** and **[Y.J.]**; data curation, **[X.L.]** and **[Y.J.]**; writing—original draft preparation, **[Y.J.]**; writing—review and editing, **[H.W.]**; visualization, **[X.L.]** and **[L.C.]**; supervision **[H.W.]**; project administration, **[H.W.]**; funding acquisition, **[H.W.]** All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (grant numbers 42074028).

Data availability

All data used throughout the entire research process were sourced from Copernicus Maritime Services.Mass concentration of chlorophyll a in sea water is from https://doi.org/10.48670/moi-00281.Sea water salinity is from https://doi.org/10.48670/moi-00051.Sea water potential temperature, Eastward sea water velocity and Northward sea water velocity are from https://doi.org/10.48670/moi-00021.Mole concentration of nitrate in sea water, Mole concentration of dissolved molecular oxygen in sea wate, Mole concentration of phosphate in sea water, Mole concentration of silicate in sea water are from https://doi.org/10.48670/moi-00019.Surface geostrophic eastward sea water velocity and Surface geostrophic northward sea water velocity are from https://doi.org/10.48670/mds-00327.Mixed layer thickness of the ocean is from https://doi.org/10.48670/moi-00052.Eastward wind and Northward wind are from https://doi.org/10.48670/moi-00181.Seawater acidity and alkalinity, Total alkalinity in sea water、Dissolved inorganic carbon in sea water, Partial pressure difference of carbon dioxide at the sea surface, Surface downward mass flux of carbon dioxide expressed as carbon are from https://doi.org/10.48670/moi-00047The finished fCO2 and FCO2 data in this study can be obtained from the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.