Asymmetric bubble-mediated gas transfer enhances global ocean CO₂ uptake

Abstract

Sea-air carbon dioxide (CO₂) flux is typically estimated from the product of the gas transfer velocity (K) and the CO₂ fugacity difference between the ocean surface and atmosphere. Total gas exchange comprises interfacial transfer across the unbroken surface and bubble-mediated transfer from wave breaking. While interfacial transfer is symmetric for invasion and evasion, bubble-mediated transfer theoretically favours invasion due to hydrostatic pressure, though field evidence has been lacking. Here we provide direct field evidence of this asymmetry and develop an asymmetric flux equation. Applying the asymmetric equation reduces bias in K, and increases global oceanic CO₂ uptake by 0.3-0.4 Pg C yr^-1 (~15% on average from 1991 to 2020) relative to conventional estimates. Further evasion data are needed to better quantify the asymmetry factor. Our study suggests that the ocean may have absorbed more CO₂ than previously thought, and the asymmetric equation should be used for future CO₂ flux assessments.

Field evidence reveals that bubble-mediated CO2 transfer favors invasion. The authors introduce an asymmetric bulk flux equation, suggesting that the global ocean may absorb ~15% more CO2 than previously estimated.

Introduction

The global ocean is a major sink of anthropogenic carbon dioxide (CO₂), and accurate quantification of the sea-air CO₂ flux is critical for projecting the future climate and developing climate mitigation strategies¹. The exchange of CO₂ between sea and air is a significant component of the global carbon cycle. Sea-air CO₂ fluxes vary regionally and seasonally between uptake (invasion) and outgassing (evasion), leading to a net global ocean CO₂ uptake of ~3 Pg C yr⁻¹ during the last decade².

The sea-air exchange of sparingly soluble gases such as CO₂ is controlled by processes immediately below the sea surface³. Wind is the major forcing factor for surface turbulence in the open ocean, driving gas exchange across the sea-air interface⁴. The sea-air gas flux (Flux, e.g., in mol cm⁻² h⁻¹) is often estimated by a bulk equation:

$$Flux=K\left(C_{\mathrm{w}}-C_{\mathrm{a}}\right)$$ 1

Total gas transfer velocity K (cm hr⁻¹) is often normalised to a reference Schmidt number (Sc) to account for variability due to temperature and salinity (i.e., K = K₆₆₀ (Sc/660)^−0.5, with Sc equal to 660 at 20 °C seawater for CO₂) and then parametrized as a simple function of wind speed (U₁₀). C_w–C_a (= ΔC) is the gas concentration difference between the seawater (C_w) and the sea-air interface (C_a) that is equilibrated with the lower atmosphere. For CO₂, ΔC is often expressed as the sea-air CO₂ fugacity difference (i.e., ΔfCO₂ = fCO_2w–fCO_2a, in μatm) multiplied by the gas solubility (α, e.g., in mol cm⁻³ μatm⁻¹). We refer to Eq. (1) as a “symmetric” bulk formula because the flux is proportional to ΔC, regardless of the flux direction.

Wind stress leads to wave formation and development. Wave breaking entrains air into the water, creating bubbles and providing a separate pathway for gas transfer^5,6. The total gas transfer can be mechanistically separated into interfacial transfer and bubble-mediated transfer. The interfacial transfer is symmetric for invasion and evasion fluxes, and is independent of gas solubility because it occurs at sea level air pressure with an effectively infinite air volume. In contrast, bubble-mediated transfer: (1) depends on solubility because bubbles have limited volume and lifetime⁷, and (2) is asymmetric because the internal gases within submerged bubbles are over-pressured⁸.

Different gases in a bubble have different characteristic equilibration times. Relatively soluble gases equilibrate faster, which limits the total gas transfer that can occur via bubbles. Thus, bubble-mediated transfer has a solubility dependence and is relatively more important for less soluble gases^7,9. Furthermore, bubble-mediated transfer is more efficient for invasion than evasion^8–10. This “asymmetric” bubble effect occurs primarily due to hydrostatic pressure. Subsurface pressure compresses a bubble, causing a concentration increase in all gases within the bubble and encouraging net transfer from the bubble into the ocean. The pressure can also drive out nitrogen and oxygen, shrinking the bubble, increasing trace gas concentrations, and encouraging additional gas transfer into the ocean. Some small bubbles may dissolve entirely, forcing the contents into the ocean completely.

Due to this asymmetric effect, an asymmetric bulk equation has been proposed for calculating the sea-air gas flux that accounts for the over-pressure effect in bubbles⁸:

$$Flux=K\left[C_w-C_a\left(1+{\mathrm{\Delta }}_s\right)\right]$$ 2

where ∆_s is an asymmetry factor, representing the “average” fractional enhancement in the gas concentration in contact with the sea due to bubbles¹¹ (see “Methods” section for details). If the overall gas transfer (K) is mechanistically separated into the interfacial transfer component (K_int) and the bubble-mediated transfer component (K_bub)⁷, Eq. (2) can be expressed as:

$$Flux=K_{int}\left(C_w-C_a\right)+K_{bub}\left[C_w-C_a\left(1+\delta \right)\right]$$ 3

The first term in the right side of Eq. (3) represents the interfacial transfer process, which is symmetric, whereas the second term corresponds to the bubble-mediated transfer process, which is asymmetric (represented by the over-pressure factor, δ). Note that δ and ∆_s have different meanings: δ is only related to the bubble process, while ∆_s captures the combined effects of both bubble and interfacial processes. By combining Eqs. (2 and 3), ∆_s and δ can be related as:

$${\mathrm{\Delta }}_s=\delta K_{bub}/\left(K_{int}+K_{bub}\right)$$ 4

Field observations, such as the supersaturation of noble gases¹², typically reflect ∆_s, since the natural measurements integrate both interfacial and bubble processes. δ can be simulated by bubble dynamic models based on the near-surface bubble size distributions^11,13.

The asymmetric transfer of highly insoluble gases, such as noble gases, is well-evidenced by observations of their supersaturation state in the field¹² and laboratory¹⁴. However, the saturation state cannot be used to evaluate the asymmetric transfer of CO₂ because of the effect of biological activity and seawater CO₂ buffering capacity. Previous research suggested that asymmetric bubble transfer accounts for more than 20% of the total oceanic CO₂ uptake based on a CO₂ supersaturation factor scaled from oxygen¹⁵. The asymmetry results of very poorly soluble gases provide an upper limit; however, extrapolating from these gases to infer asymmetric effects on CO₂ is likely unreliable. Alternatively, asymmetric bubble transfer can be estimated using numerical models coupled with bubble dynamic observations^11,13,16. For sparingly soluble gases (e.g., CO₂), this asymmetry is mainly driven by large bubbles near the sea surface⁹. While a study argued that the asymmetric effect is insignificant for CO₂⁸, more recent research inferred a substantial asymmetry in CO₂ transfer from measurements of large bubbles near the sea surface¹¹. However, no results or analysis have thus far demonstrated direct evidence of asymmetric CO₂ transfer.

Direct flux measurements by the eddy covariance (EC) technique can be used with gas concentration observations to derive K from Eqs. (1 and 2). In this study, field evidence of asymmetric bubble-mediated CO₂ transfer is observed in a re-analysis of a large EC dataset. The impact of asymmetric transfer on global ocean CO₂ flux estimates is then assessed by comparing fluxes calculated using the symmetric bulk equation (Eq. (1)) with those calculated using the asymmetric bulk equation (Eq. (2)).

Results

Evidence of asymmetric CO₂ transfer

A large EC CO₂ flux and ΔfCO₂ dataset (4082 h, 17 cruises, Fig. S1A) is used to evaluate asymmetric sea-air CO₂ transfer. The dataset contains flux observations with strong invasion (ΔfCO₂ ≤ −20 µatm), weak invasion (−20 < ΔfCO₂ ≤ 0 µatm), weak evasion (0 < ΔfCO₂ < 20 µatm), and strong evasion (ΔfCO₂ ≥ 20 µatm). Each scenario includes data collected from multiple cruises (Fig. S1B, C). High wind speeds (U₁₀ > 12 m s⁻¹) were observed within all four scenarios (Fig. S2). If asymmetry has a negligible effect on CO₂ exchange, the transfer velocity derived from EC CO₂ fluxes using the symmetric bulk equation (K_{_Sy}, Eq. (1)) should be consistent regardless of whether the CO₂ flux is invasive or evasive. In contrast, if the asymmetric effect is important for CO₂ transfer, the CO₂ transfer velocity computed using the symmetric bulk equation will be biased, causing K_{_Sy} to differ between invasion and evasion conditions, i.e., K_{_Sy} (weak invasion) > K_{_Sy} (strong invasion) > K_{_Sy} (strong evasion) > K_{_Sy} (weak evasion). From theory, this bias is expected to be largest when ΔfCO₂ is small and wind speed is high (see Supplementary Information, Section 1, Eq. S4).

Traditionally, K is derived by dividing the EC flux by the ∆C (i.e., K = Flux/ ∆C), and then parameterising K against wind speed (one-dimensional (1D) fitting method). However, under weak invasion or evasion conditions (i.e., |ΔfCO₂|<20 µatm), this method often fails because the large relative uncertainties in the EC flux and ΔfCO₂ lead to unreliable derivations of K. Therefore, many authors have chosen to exclude low-ΔfCO₂ data from their analysis¹⁷ (“Methods”). However, although the relative uncertainty in EC fluxes under these conditions is large, the absolute uncertainty is small¹⁸. Moreover, the asymmetric effect is expected to be more pronounced under the weak invasion/evasion conditions (Eq. S4), making these data valuable. This study uses an innovative two-dimensional (2D) method to fit the CO₂ flux directly as a function of both wind speed and ∆C, avoiding the K derivation process (see “Methods”). This method enables inclusion of small-ΔfCO₂ data in the parameterisation. The bulk flux derived from the 2D fitting approach generally replicates the hourly EC flux observations across various conditions (Fig. S3).

The 2D fit is first run using the symmetric bulk equation. The results show that there is a notable divergence between the parameterised K (K^2D_{_Sy}) for invasion and evasion conditions (Fig. 1A). These divergences agree with theory that the asymmetry is important for CO₂ exchange (i.e., weak invasion > strong invasion > strong evasion > weak evasion), and the discrepancies are largest at high wind speeds (Fig. 1A). Statistical analysis indicates that the discrepancies at wind speeds above 10 m s⁻¹ are significant (p-value < 0.05, Fig. S4A), except in the weak evasion case, where limited data reduce confidence in the result.

Fig. 1. Gas transfer velocity (K₆₆₀) parameterisations with 10-meter neutral wind speed (U₁₀).

Parameterisation of gas transfer velocity derived from hourly eddy covariance (EC) sea-air CO₂ observations and the 2D method with: A the symmetric bulk equation (Eq. 1, K^2D_{_Sy}); and B the asymmetric bulk equation (Eq. 2, K^2D_{_Asy}). Red-solid lines, Weak Invasion (−20 < ΔfCO₂ ≤ 0 µatm, mean = −11 µatm, R² = 0.26, N = 617 h). Blue-dashed lines, Strong Invasion (ΔfCO₂ ≤ −20 µatm, mean = −68 µatm, R² = 0.63, N = 2889 h). Purple-dot-dashed lines, Strong Evasion (ΔfCO₂ ≥ 20 µatm, mean = 29 µatm, R² = 0.41, N = 236 h). Orange-dot lines, Weak Evasion (0 < ΔfCO₂ < 20 µatm, mean = 9 µatm, R² = 0.014, N = 340 h). Here, the R² refer to the fits in (A); those for panel B are similar (see Table S1). The 95% confidence intervals (CI) are added to each parameterisation curve, using corresponding colours.

To verify whether accounting for asymmetric transfer can reconcile the difference between invasion and evasion shown in Fig. 1A, the 2D fit process is repeated using K computed from the asymmetric bulk equation (K^2D_{_Asy}, Eq. (2)). Before the fitting process, the asymmetric factor (Δ_s) in Eq. (2) should first be determined. Here, we use two approaches to estimate Δ_s: reanalysis of the EC CO₂ data and derivation from existing gas transfer velocity parameteristions. The detailed procedures for determining and parameterising Δ_s using both methods are described in the “Methods” section, and here, we provide only a brief overview. Both approaches require prior knowledge of δ and K_int. This study adopts the recent estimate of δ for CO₂ from a bubble dynamic model (δ = 0.0132¹¹), and employs the K_int parameterisation based on the EC DMS (dimethylsulfide) observations¹⁹. In the first method, we re-analyse the EC datasets to estimate Δ_s, which is then fitted against wind speed (Fig. S5). This yields the following parameterisation:

$${\mathrm{\Delta }}_s=0.0132\left(1-1.37U_{10}^{-0.37}\right),U_{10}\ge 5{\mathrm{m\; s}}^{-1}$$ 5

The alternative way to determinate Δ_s is by linking Δ_s with the fractional contribution of bubble-mediated gas transfer velocity to the total K (see Eq. (4)). If the widely-used ¹⁴C-based parameterisation²⁰ is adopted to represent the total K, Δ_s can be derived as:

$${\mathrm{\Delta }}_s=0.0132\left(1-2.95U_{10}^{-0.67}\right),U_{10}\ge 5{\mathrm{m\; s}}^{-1}$$ 6

For wind speeds below 5 m s⁻¹, Δ_s is set to zero for both parameterisations because bubble contributions are negligible under this condition. The Δ_s values from Eqs. (5 and 6) diverge at wind speeds below 10 m s⁻¹, but they converge at high wind speeds (10−20 m s⁻¹), with differences of less than 10%. Both parameterisations yield comparable results for the subsequent analysis within this section; therefore, only results based on Eq. (5) are presented in the figures below.

When the asymmetric equation (Eq. (2)) is used for the 2D fit, the invasion transfer velocity decreases, especially for the weak invasion group, while the evasion transfer velocity increases. K^2D_{_Asy} show much less divergence and are mostly collapsed onto a single curve (Fig. 1B). There is no statistically significant difference between K^2D_{_Asy} across the different flux regimes (Fig. S4B). The weak evasion group in Fig. 1B remains an outlier (lower K^2D_{_Asy} than the other three groups), which may well be attributable to the large relative uncertainty in these observations and fewer data points (8% of the total data points). K^2D_{_Asy} is less dependent on flux direction and magnitude, suggesting that the asymmetric model more consistently reflects the underlying physical processes across varying flux conditions. It is important to emphasize that the improvement offered by the asymmetric equation is not primarily demonstrated through a better statistical fit (e.g., R²) to noisy field data, but rather through the reduction in the systematic divergence between the four K^2D_{_Sy} groups (as evidenced by the difference between Fig. 1A, B). The robustness of the 2D method is evaluated in detail in the “Methods” section.

These results support the use of the asymmetric equation (Eq. (2)) rather than the symmetric formulation (Eq. (1)) for interpreting EC observations and calculating bulk fluxes. Previous research has tended to use the symmetric equation to derive K and then parameterise with wind speed using the 1D fit approach (i.e., K^1D_{_Sy})²¹. Our analysis shows that this method has overestimated K (especially at high wind speeds, Fig. S6) because most of the existing observations were collected under invasive scenarios. The bulk flux estimated using the asymmetric equation and the 2D fit method agrees better with observed EC CO₂ fluxes compared to bulk fluxes estimated using the conventional symmetric equation and the 1D fit method (Fig. S7), indicating that the asymmetric equation is more appropriate for bulk CO₂ flux estimates.

K^2D_{_Asy} based on all EC data is consistent with the K₆₆₀-U₁₀ parameterisation constrained by the global ¹⁴C inventory²⁰ (Fig. S8). We note that K₆₆₀ derived from the ¹⁴C inventory is insensitive to the asymmetric bubble transfer because the ocean is in large disequilibrium with respect to radiocarbon in the atmosphere²².

The over-pressure factor (δ) of 0.0132¹¹ is needed to determine ∆_s. The small fraction of remaining divergence shown in Fig. 1B suggests that δ may be slightly underestimated. If δ is increased to 0.018, K_{660_CO2} derived from the asymmetric bulk equation fully collapses the parameterisations for the weak invasion, strong invasion, and strong evasion groups (Fig. S9). However, uncertainty in the EC data could lead to overfitting, especially when using a small dataset (e.g., two evasion groups). The published value of δ = 0.0132 is thus used for the rest of this study, and Eqs. (5 and 6) are applied accordingly, as this value is based on independent evidence. If δ is better constrained in the future, Eq. (5 and 6) can be readily updated by replacing the coeffient 0.0132 with the revised value.

Impact of asymmetry on large-scale CO₂ flux estimates

Accurate global sea-air CO₂ flux estimates are crucial for the Global Carbon Budget (GCB) assessment². The GCB calculates sea-air CO₂ flux using the symmetric bulk equation, but previous results provide evidence of bubble-induced asymmetry in gas exchange^11–13,16, and our results further support that this asymmetry is important for sea-air CO₂ transfer. Here, we assess the impact of the asymmetric bubble transfer on global sea-air CO₂ flux estimates. The CO₂ flux from 1991 to 2020 is recalculated using the asymmetric bulk equation (Eq. (1)) and compared with the results using the symmetric bulk equation (Eq. (2)) (see “Methods”); their difference yields ΔFlux (i.e., asymmetry-induced flux). To ensure comparability, all flux estimates use the ¹⁴C-based K₆₆₀-U₁₀ parameterisation²⁰, with coefficients scaled to the ERA5 wind speed²³. Both Δ_s parameterisations are used for this global ocean assessment. The global mean value of Δ_s is estimated to be 0.004 (i.e., 0.4%) using Eq. (5) and 0.003 (0.3%) using Eq. (6).

The global ocean CO₂ uptake computed using the asymmetric equation is 0.33–0.41 Pg C yr⁻¹ greater than using the symmetric equation on average from 1991 to 2020, corresponding to ~15% increase in the oceanic CO₂ sink estimates. Equation (5) produces higher Δ_s under typical oceanic wind conditions (5–10 m s⁻¹; Fig. S5) and thus yields a larger ΔFlux magnitude (0.41 Pg C yr⁻¹) than Eq. (6) (0.33 Pg C yr⁻¹). This difference highlights the uncertainty associated with quantifying Δ_s. The impact of the asymmetry on sea-air CO₂ flux is ubiquitous, but is most evident in the Southern Ocean (South of 35°S) and relatively minor in the tropics (Fig. 2A). The Southern Ocean accounts for about half of the asymmetry-induced flux increase in the global ocean. The spatial variability of ΔFlux is primarily driven by wind speed (Fig. 2B), as stronger winds enhance wave breaking and bubble formation, thereby amplifying asymmetric bubble-mediated transfer. Notably, the impact of ΔFlux is always negative (i.e., enhanced ocean CO₂ uptake) because the bubble over-pressure always favours gas invasion. Over the past three decades, ΔFlux has shown a strengthening trend in a rate of ~3 Tg C yr⁻¹ per decade (Fig. 2C). This trend is primarily driven by the rising atmospheric CO₂ concentration. In addition, hemispheric ΔFlux varies seasonally, with greater asymmetrical fluxes in winter and smaller fluxes in summer (Fig. 2D). The seasonal variability is primarily driven by seasonal wind variation and sea surface temperature changes.

Fig. 2. Impact of asymmetric transfer on the sea-air CO₂ flux estimate (∆Flux).

A Map of ∆Flux; B 1°-latitude mean of ∆Flux and ERA5 wind speed; C Temporal trend in annual mean ∆Flux; D Seasonal variations of ∆Flux in northern (green) and southern (purple) hemispheres (1–12 corresponding to January-December). The results shown here represent the ensemble mean ∆Flux estimated from two different ∆_s parameterisations (Eqs. 5 and 6). The ∆Flux shown in (A, B, and D) is averaged from 1991 to 2020. A negative ∆Flux means enhanced ocean CO₂ uptake.

Note that Fig. 2 does not consider the upper ocean temperature effects²⁴ in the calculation of global sea-air CO₂ flux. Recent studies provide relatively direct evidence that the cool skin effect does affect the bulk sea-air CO₂ flux estimates^25,26. The cool skin effect has been estimated to increase oceanic CO₂ uptake by ~0.4 Pg C yr^{−1 27,28}. All previous cool skin studies apply the correction to the total gas transfer velocity, but the cool skin effect theoretically only influences interfacial transfer, whereas bubbles bypass the cool skin. We have re-evaluated the cool skin correction by only considering interfacial transfer (see “Methods”). Our results suggest a smaller cool skin correction (CO₂ uptake increase by ~0.25 Pg C yr⁻¹ on average from 1991 to 2020, ~2/3 of previous estimates). The Surface Ocean CO₂ Atlas (SOCAT)-based flux in the 2023 GCB using the symmetric flux formula suggests that ~65% of the global surface ocean has net CO₂ invasion². Applying asymmetric transfer along with updated temperature effects increases the area of net invasion to ~75% (Fig. S10) regardless of whether Δ_s is estimated using Eqs. (5 or 6). The change in sign from evasion to invasion primarily occurs in the high-latitude Southern Ocean and in oligotrophic waters. The updated climatological flux estimate shows that the global ocean is generally a CO₂ sink, with CO₂ outgassing only occurring in regions with upwelling (e.g., near the equator and the coast, Fig. S10).

The GCB reports global ocean CO₂ uptake using both SOCAT-based contemporary flux estimates and Global Ocean Biogeochemistry Models (GOBMs)-based anthropogenic fluxes². The anthropogenic ocean CO₂ uptake is defined as the contemporary net sea-air CO₂ flux adjusted for the riverine CO₂ flux to the ocean (0.65 Pg C yr⁻¹ with large uncertainties²⁹). Note that the asymmetric effect and the updated cool skin-induced flux corrections correspond to SOCAT-based flux, which cannot be directly applied to GOBMs³⁰. Both the cool skin effect and the asymmetric transfer effect increase the net invasion flux in the upper mixing layer, but only a fraction of the additional CO₂ can be transported to the deeper ocean in the model because of the slow vertical ocean circulation. This results in an accumulation of carbon in the mixing layer (i.e., an increase in C_w) and thus dampens the flux enhancement. It has been estimated that ~2/3 of the impact of the cool skin effect on global CO₂ flux will be dampened within a GOBM³⁰, and we assume the same damping magnitude for the impact of the asymmetric transfer. After accounting for asymmetric transfer and updating the cool skin effect as well as incorporating another temperature correction (warm bias²⁸), GOBMs-based ocean CO₂ uptake is ~2.4 Pg C yr⁻¹ (on average from 1991 to 2020), which is 1 Pg C yr⁻¹ (30%) lower than the SOCAT data-based estimates (Table 1).

Table 1.

Corrections and revisions to the estimate of global ocean anthropogenic CO₂ uptake

Oceanic CO2 uptake estimates	GCB 2023	Corrections			Revised flux
		Asymmetric effect	Cool skin effect	Warm bias
Based on SOCAT data	2.60	0.37	0.25	0.17	3.39
Based on models	2.23	0.12	0.08	–	2.43

Two independent oceanic CO₂ uptake estimates are made in the Global Carbon Budget (GCB) 2023². The values in the “asymmetric effect“ column represent the ensemble mean of the flux corrections using two Δ_s parameterisations (Eqs. 5 and 6). The correction to the model-based flux estimate is assumed to be ~1/3 of the correction to the data-based flux estimate³⁰. The warm bias correction is taken from ref. ²⁸. All numbers in the table are in Pg C yr⁻¹ and represent the average from 1991 to 2020.

Discussion

This study uses EC sea-air CO₂ flux observations with both invasion and evasion scenarios to present direct evidence that asymmetric bubble-mediated transfer is significant for CO₂ exchange, especially at high wind speeds (Fig. 1). The evidence is broadly in line with the concepts proposed in a previous study¹¹. The asymmetric bulk equation (Eq. (2)), with ∆_s from Eqs. (5 or 6), is recommended for sea-air CO₂ flux estimates and for EC sea-air CO₂ flux-based K₆₆₀ analyses. Published EC-based K₆₆₀ data (e.g., a synthesis study²¹) contain biases due to the use of the symmetric bulk equation to derive K₆₆₀. The bias is larger for cruises with high wind speeds and weak invasion/evasion fluxes^19,31, and smaller for cruises with strong invasion/evasion flux signals and low-medium wind speeds³². The observed asymmetry is further evidence that bubble-mediated transfer is important for sea-air CO₂ flux, consistent with the large differences between the gas transfer velocities of CO₂ and DMS^19,33–35 and the sea state dependence of CO₂ transfer velocities³⁶.

Using the constrained asymmetric factor, the asymmetric effect results in an additional oceanic CO₂ uptake of 0.3–0.4 Pg C yr⁻¹ (1991 to 2020 average) compared to the uptake calculated with the symmetric bulk equation. The asymmetric flux has wind-driven regional and seasonal variations, and is relatively large in the Southern Ocean and during winter (Fig. 2). The influence of asymmetric bubble transfer on sea-air CO₂ flux has increased over the past decades due to ever-rising atmospheric CO₂ concentration (Fig. 2C). The revisions to global climatological CO₂ flux increase the ocean areas with net CO₂ invasion from ~65% to ~75%, leaving only the upwelling regions with net CO₂ evasion. The revisions also widen the gap between the SOCAT-based flux estimates and the GOBMs-based flux estimates (from 0.4 Pg C yr⁻¹ to ~1.0 Pg C yr⁻¹). Reconciling the difference between model-based and SOCAT data-based sea-air CO₂ flux estimates is a major challenge to the community. Resolving possible model biases due to inadequate simulation of ocean circulation and oceanic buffer capacity has been proposed³⁷. With respect to the observations, the sparsity of SOCAT data has been identified as a major source of uncertainty in SOCAT-based sea-air CO₂ flux estimates³⁸. Moreover, reducing the uncertainties associated with the riverine flux is also critical for understanding the discrepancy between model and data-based flux estimates³⁹.

This study provides observational evidence of asymmetric CO₂ transfer using a large dataset (N = 4082 h). The EC sea-air CO₂ flux dataset is dominated by measurements in net invasion conditions (86%, N = 3506 h), whereas there are fewer net evasion observations (N = 576 h), which limits our confidence in the global asymmetry-adjusted ocean CO₂ uptake estimate. ∆_s estimates from two different approaches are similar under high wind speeds (U₁₀ > 10 m s⁻¹), but differ substantially at lower wind speeds. This difference results in large variations in the estimated impact of bubble-induced asymmetry on global ocean CO₂ uptake, highlighting the need to reduce uncertainties in the ∆_s estimates. Nevertheless, the value of ∆_s (0.3–0.4% on average) estimated in this study is consistent with existing evidence. Field noble gas observations indicate Xenon (Xe) supersaturation of ~1% under typical ocean conditions¹². The solubility of Xe (α ~ 0.1 at 20 °C) is lower than that of CO₂ (α ~ 0.7 at 20 °C), meaning that the ∆_s of CO₂ is expected to be less than 1%. Another independent estimate uses a bubble dynamic model designed for low solubility gases, and extrapolates a ~ 0.7% supersaturation factor for CO₂¹³. Still, more direct sea-air CO₂ flux measurements are needed to reduce the uncertainty associated with the bubble-induced supersaturation factor, and strengthen and improve the asymmetric parameterisations proposed here. Future observations should target CO₂ evasion as a priority at high wind speeds and over a wide range of sea states. A mixture of methodologies that encompass evasion, invasion, and a range of gases with different solubilities would provide even stronger evidence of asymmetric bubble-mediated transfer (e.g., wintertime in the Bering Sea, or the summer monsoon season in the Arabian Sea). In the long term, expanding EC sea-air CO₂ flux observations using autonomous platforms such as a buoy⁴⁰, Saildrone, and/or Wave Gliders will provide an essential reference for bulk flux estimates.

Methods

Two-dimensional analysis of the CO₂ flux

A recent study²¹ presents a synthesis of high-quality EC sea-air CO₂ flux and ΔfCO₂ measurements made over the last ~15 years (2698 h). These data were collected from 11 research cruises conducted in the North Atlantic Ocean^17,19,34, the Southern Ocean^35,41,42, the Arctic Ocean³², and the Tropical Indian Ocean³¹. There were both net invasion and net evasion observations in this synthesis dataset (ΔfCO₂ ranges from −273 µatm to 76 µatm). A further six EC sea-air CO₂ flux and ΔfCO₂ datasets are included in this analysis, two during the Atlantic Meridional Transect cruises (732 h)¹⁸ and four in the Southern Ocean (652 h)²⁵. All of the datasets (17 research cruises, see Fig. S1) are combined to investigate the bubble-induced asymmetry. The EC system setup for different cruises, data quality control, and data processing are presented in a synthesis study²¹ and the literature referenced therein. The Atlantic Ocean and the Southern Ocean datasets are described in related literatures^18,25.

The EC-based K is traditionally computed as “EC flux/ αΔfCO₂” and then fitted with wind speed after Schmidt number normalisation (i.e., one dimensional fitting method, K^1D). However, K derived in this way becomes unreliable when ΔfCO₂ is close to 0, and thus data with small absolute ΔfCO₂ (typically |ΔfCO₂|<20 μatm) are often excluded from analysis. The excluded near-saturation data are useful because the influence of asymmetric transfer is expected to be relatively large (see Eq. S4). A recent study demonstrated that EC flux observations are still reliable even when the sea-air CO₂ flux is ~0 and the small EC fluxes often contain small absolute uncertainties¹⁸. To make use of the low flux signal data, an alternative two-dimensional (2D) fit method is employed for analysis. Rather than fitting the derived K as a function of wind speed, flux data are fit as a function of both concentration difference and wind speed with the following functional structure:

$$Flux={\mathrm{\Delta }C}_{660}\left(a{U}_{10}^b\right)$$ 7

where ΔC₆₆₀ is equal to (C_w–C_a)(Sc/660)^−0.5 if using the symmetric bulk equation, and [C_w - (1 + ∆_s)C_a](Sc/660)^−0.5 if using the asymmetric bulk equation. The wind speed dependence of the gas transfer velocity with the 2D fit (K^2D) has an assumed structure, with free parameters “a” and “b”. The fit is to the flux, meaning that the error minimisation is on the predicted flux (i.e., a “least squares” fit to flux; see Supplementary Information, Section 2).

The EC data is separated into four groups according to ΔfCO₂ (see the caption of Fig. 1). The 2D fit is applied to each data group, and also to a combined group of strong evasion and strong invasion data, and to the entire dataset. The direct 1D fit between K₆₆₀ and U₁₀ is only applied to the strong evasion and invasion groups, as well as the combined group containing strong evasion and invasion data. Coefficients “a” and “b” and the R² for each fit are reported in Table S1.

Estimation of the asymmetry factor ∆_s

The asymmetry factor (∆_s) in Eq. (2) is a key parameter in this study. We estimate ∆_s using two approaches. Both methods rely on the independent estimates of the over-pressure factor (δ), the interfacial transfer velocity (K_int) and the total gas transfer velocity (K) (see Eq. 4). For CO₂, δ is primarily driven by the hydrostatic pressure and is directly related to the effective penetration depth of the bubble plume, which has been shown to remain largely unchanged with wind speed^9,43. Accordingly, we adopt a fixed δ value of 0.0132, simulated from a bubble dynamic model-based on near-surface bubble observations¹¹. For K_int, we use transfer velocity parameterisations based on EC DMS observations¹⁹ (Fig. S8), as the high solubility of DMS minimises the contribution of bubbles to its exchange. Based on the way to represent K, two approaches are proposed to estimate ∆_s.

In the first approach, hourly EC sea-air CO₂ flux measurements are treated as the total CO₂ exchange in the estimate of estimate ∆_s. However, these EC CO₂ fluxes inherently include the effect of chemical enhancement (CE), which is absent in EC DMS observations that are being used for K_int. While CE is negligible at high wind speeds, it becomes relatively important under low wind conditions. Given that ∆_s is sensitive to the treatment of K at low wind speeds, CE contribution should be removed from the observed EC CO₂ transfer velocities. To account for this, we applied a CE correction ratio derived from analytical and numerical models^6,44. We then combine Eqs. (2 and 4) to derive ∆_s for each corresponding flux using an iterative method (see Supplementary Information, Section 3). The resulting ∆_s increases with the wind speed and asymptotically approaches the value of δ when the bubble-mediated exchange dominates the total gas exchange (Fig. S5). Given that ∆_s =  δK_bub/K = δ(K – K_int)/K, and K and K_int can be expressed as a₁U₁₀^b1 and a₂U₁₀^b2, respectively, ∆_s can thus be parameterised as ∆_s = δ(1 – a₃/U₁₀^b3). Fitting the bin averages of ∆_s for U₁₀ between 5 and 20 m s⁻¹ yields Eq. (5).

Alternatively, the widely used ¹⁴C inventory-based parameterisation²⁰ can represent the total K (Fig. S5A). Thus, ∆_s can be directly calculated using the existing parameterisations of K and K_int, which yields Eq. (6). If the recent K parameterisation based on the synthesis of the EC sea-air CO₂ data²¹ is used to represent the total gas transfer velocity, the derived Δ_s will be similar to Eq. (5) (Fig. S5B), and thus is not shown in the main text. It should be noted that the ¹⁴C inventory-based parameterisation of K does not include chemical enhancement²⁰ and therefore require no correction, whereas the K parameterisation derived from EC CO₂ data²¹ does include this chemical effect and thus necessitates a correction.

Robustness test of the 2D fitting method

To assess the robustness of the 2D fitting approach, we performed several sensitivity tests.

First, we applied a bootstrapping test by systematically excluding one or more cruises from the entire dataset (Fig. S11). The divergence between invasion and evasion groups observed in the symmetric equation consistently merges (Fig. S11A), and the asymmetric equation continues to reduce this divergence across all subsets (Fig. S11B). This consistency demonstrates that the observed pattern is not driven by a few specific cruises or one specific research group, and supports the stability of the asymmetric equation and the 2D fitting method. We note that the weak evasion is always an outlier due to less data and high uncertainty as shown in Fig. 1 and discussed in the main text.

Second, the results shown in Fig. 1 do not consider the cool skin effect, which can also lead to bias in the derived K₆₆₀. However, the cool skin effect is relatively more substantial at low wind speeds and relatively weak and consistent at intermediate and high wind speeds⁴⁵. Inclusion of the cool skin effect in the derivation of K^2D does not collapse any divergences shown in Fig. 1A (see Fig. S12). Other processes, such as sea spray and rainfall (both of which often occur during stormy conditions), may also induce asymmetric gas transfer. Sea spray tends to enhance evasion relative to invasion⁴⁶, which is opposite to the pattern observed in Fig. 1. Sea spray-related asymmetries remain highly uncertain⁴⁷ and are beyond the scope of this study. Rain events may also promote asymmetric CO₂ uptake^48,49, but rain intensity is generally independent of wind speed and thus unlikely to explain the wind speed-dependent divergence observed in Fig. 1.

For the 2D fit, we limit the form of K₆₆₀ to aU₁₀^b (Eq. 7) with zero intercept, and it was plausible that this form forced most of the divergence into the high wind speeds. To check this, we relaxed the constraint in Eq. 4 and adopted a more flexible formulation (aU₁₀^b + c), allowing for a non-zero intercept. The results confirm that the collapse between invasion and evasion at high wind speeds persists (Fig. S13), further supporting the robustness of the 2D fitting approach.

Global ocean CO₂ flux estimates

The global ocean CO₂ flux is estimated using the asymmetric bulk equation and the symmetric bulk equation. The difference between these two fluxes is considered the additional flux due to asymmetric bubble-mediated transfer. The global bomb-¹⁴C inventory-based K_{660_CO2} parameterisation^20,22 is used to make the flux estimate. ∆_s in Eq. (2) is estimated from ERA5 wind speed²³ when U₁₀ is higher than 5 m s⁻¹ (Fig. S5) and set as zero when U₁₀ < 5 m s⁻¹ since bubble-mediated transfer should be minimal at low wind speed³⁴. For the revised cool skin correction, the K_int parameterisation based on the EC observations of DMS transfer¹⁹ (Fig. S8) is used to calculate the interfacial CO₂ flux. For the interfacial flux with cool skin correction, ΔC is calculated as α_subskin fCO_2w–α_skin fCO_2a, while the flux without cool skin correction uses ΔC = α_subskin fCO_2w–α_subskin fCO_2a. Here, α_subskin and α_skin are the CO₂ solubility calculated using subskin and skin seawater temperature, respectively²⁸. ERA5 wind speed data from 1991 to 2020 are used to estimate the transfer velocity for the global ocean at a 1° × 1°, monthly resolution. The ensemble mean of seven SOCAT-based fCO_2w products (1° by 1°, monthly)² is used as the fCO_2w product. Global atmospheric CO₂ fugacity (fCO_2a) data is calculated from NOAA ESRL marine boundary layer CO₂ mole fraction⁵⁰. The CCI SST v2.1 data product⁵¹ is used to estimate Schmidt number²⁰ and α_subskin⁵² for the global ocean.

Author contributions

Y.D. and T.G.B. came up with the initial idea. M.Y., D.K.W., T.G.B. and Y.D. conceived the study. M.Y., C.A.M. and T.G.B. provided most of the EC data. D.K.W. contributed to the reanalysis method of the EC data, and M.Y. proposed the 2D analysis method. Y.D. and M.Y. performed the data analysis with help from all other authors. Y.D. wrote the initial draft, and all coauthors contributed to the writing.

Peer review

Peer review information

Nature Communications thanks Steven emerson and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

Open Access funding enabled and organized by Projekt DEAL.

Data availability

All data needed to evaluate the results in the paper are present in the paper and/or the Supplementary Information. SOCAT-based data products and Global Ocean Biogeochemistry Models: https://zenodo.org/records/10222484; ERA5 wind speed: https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=form; The data to directly produce Figs. 1 and 2 are provided in the Supplementary Information/Source Data file. The reanalysed EC data generated in this study have been deposited in the Figshare database under accession code: 10.6084/m9.figshare.29903636.

Code availability

The code to produce the figures are provided in the Supplementary Information/Source Data file.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-66652-5.