In this study, we investigate the role of waves and bubble mechanisms in modulating the ocean's biogeochemical response by comparing the control simulation (B–CTL) with the coupled POP2–waves model within the CESM1.2.2 framework (Fig. 1). The CESM simulation was conducted using a fully coupled component set over a 30-year period, with well-mixed greenhouse gases (CO₂, CH₄, N₂O, etc.), ozone, and aerosols fixed to year-2000 values (the B_2000_CAM5 compset). The framework features a horizontal resolution of 1.9°×2.5° for both the Community Atmosphere Model 5.3 (CAM5.3) and the Community Land Model version 4 (CLM4). In contrast, the ocean component (POP2; configured with 60 vertical layers) and the prognostic Los Alamos Sea Ice Model (CICE) share a nominal 1° horizontal resolution. State fields and fluxes are exchanged across these differing grids via the coupler (CPL) (Hurrell et al., 2013). POP2 is forced by CAM5.3 through CPL via four primary fields: (1) momentum fluxes (zonal and meridional wind stress and friction velocity), (2) heat fluxes (net shortwave radiation, sensible heat flux, longwave radiation, and heat flux from snow/ice melt), (3) freshwater fluxes (precipitation, evaporation, river runoff, and ice melt), and (4) surface winds (10 m zonal and meridional wind speeds). Furthermore, POP2 interacts with the Biogeochemical Elemental Cycling (BEC; Moore et al., 2013) module to regulate carbonate chemistry and air–sea CO₂ fluxes. This interaction is mediated via ocean dynamics (currents and sea surface height), the K-profile vertical mixing, and tracer transport, with wave-induced processes providing additional physical constraints. Within the BEC module, variations in DIC and nutrients (NO₃, PO₄, and Fe) are primarily controlled by biological processes: photosynthesis consumes DIC and nutrients, whereas respiration and remineralization return organic carbon to the DIC pool. Together with the wave module, these biogeochemical and physical processes jointly regulate the carbon cycle.

The control simulation (B–CTL), which served as the baseline for air–sea CO₂ flux and seawater acidification, utilized Eq. (1) with the gas transfer velocity parameterization from Wanninkhof (1992) (Eq. 2). Both the B–CTL and POP2–waves experiments were integrated under a present-day scenario (starting from the year 2000) to estimate air–sea CO₂ flux and pH variations. This experimental design allows us to isolate the impact of wave effects on carbonate chemistry and directly compare our results with the NOAA CT2022 data assimilation system. For the POP2–waves experiment, the wave module (Mellor et al., 2008) from the POM was online-coupled with POP2. This configuration incorporated bubble-mediated gas transfer – computed from a mechanistic model for air bubble entrainment at the breaking-wave scale (Deike and Melville, 2018) – and was integrated with the POP2 marine biogeochemistry module.

Specifically, the POP2–waves experiment adopts the advanced parameterization framework expanded by Reichl and Deike (2020), and Deike (2022). In this framework, both the non-bubble and bubble-mediated gas transfer velocity are explicitly resolved as a function of the ocean surface friction velocity (u*, m s⁻¹) and significant wave height (Hs, m). This parameterization effectively captures the main wave effect, as well as solubility and diffusivity. To standardize the formulation for CO₂, the total gas transfer velocity is expressed relative to a Schmidt number of 660. Following Deike and Melville (2018), it is calculated as the sum of the non-bubble (kwNB,660) and bubble (kwB,660) components: 3kw,660=kwNB,660+kwB,660=ANBu*Sc660-1/2+ABk0RT0(u*)5/3gHs2/3Sc660-1/2 where ANB is an empirical, nondimensional coefficient set to 1.55×10-4, AB is a dimensional fitting coefficient (1.2×10-5 s² m⁻²), R is the ideal gas constant (0.082 L atm mol⁻¹ K⁻¹), T0 is the sea surface temperature (SST, in K), and g is gravitational acceleration (9.806 m s⁻²). Section 3.3 examines the relative contributions of the non-bubble and bubble components in simulating the air–sea CO₂ flux.

The marine carbonic acid system is a nonlinear, coupled system governed by CO₂ dissolution equilibrium, CO2aq+H2O⟷KHH2CO3(aq), where the Henry's constant (KH) for CO₂ in water at 25 °C is approximately 3.4×10-2 (m atm⁻¹), two-step dissociation reactions, and the conservation of the total dissolved inorganic carbon (DIC) and total alkalinity (TA), ultimately determining pH and the distribution of carbonate species. Carbonic acid (H₂CO₃) has two hydrogen ions and dissociates in two steps: 4H2CO3⟷Ka1H++HCO3-Ka1=4.4×10-75HCO3-⟷Ka2H++CO32-Ka2=4.7×10-11 The DIC can be expressed as 6DIC=H2CO3+HCO3-+CO32-=KHpCO2w+Ka1KHpCO2wH++Ka1Ka2KHpCO2wH+2=KHpCO2w1+Ka1H++Ka1Ka2H+2=KHpCO2wH+2+Ka1H++Ka1Ka2/H+2 The marine carbonate system describes the distribution of DIC among its chemical species in seawater and is jointly governed by TA and pH. From Eq. (6), if the oceanic pCO2w and pH are known, the DIC can be determined; conversely, pCO2w can be derived from DIC. Following Dickson (1981), TA represents the net proton-neutralizing capacity of weak acid anions in seawater and is expressed as TA = [HCO3-] + 2[CO32-] + [B(OH)4-] + [OH⁻] + [HPO42-] + 2[PO43-] + [SiO(OH)3-] + [NH₃] + [HS⁻] - [H⁺] - [H₃PO₄]. In the POP2–waves framework, TA, DIC and biogeochemical processes are used to calculate pH and pCO2w.

When TA increases, seawater becomes more alkaline, leading to a higher CO32- concentration and enhanced buffering of hydrogen ions. Consequently, [H⁺] decreases, causing pH to rise and boosting the ocean's capacity to absorb CO₂. Conversely, when TA decreases, the buffering capacity weakens, [H⁺] increases, and pH drops, rendering the ocean more acidic with a reduced capacity for CO₂ uptake.

Except for the ocean component, all other components adhere strictly to the CESM1.2.2 framework. The wave module is forced by variables exchanged through the coupler, POP2, and a dedicated input initialization file. Specifically, in addition to the baseline component interactions in CESM1.2.2, the framework passes the zonal and meridional 10 m winds, along with surface friction velocity (u*, accounting for both open-ocean and sea-ice fractions) from the CPL to evaluate the wave properties and the associated gas transfer velocity. To drive the wave module calculations, key physical variables are retrieved from POP2; this involves interpolating depth-variable currents from POP2 z-coordinates (60 levels of zonal and meridional horizontal velocities) onto POM (waves) sigma-coordinates (21 vertical levels). This vertical mapping is required to compute both the depth-dependent wave radiation stresses and the specified spectrum. Additionally, spatial grid configurations in the x, y, and z directions, along with time-step settings, are exchanged. The wave module further integrates external variables (F1–F4), which represent the spectrally averaged wave radiation stress components used to force the momentum equation.

Following Mellor et al. (2008), the significant wave height (Hs) used in calculating wave radiation stresses represents the total wave energy integrated over the full spectrum, which inherently encompasses both locally wind-generated seas and remotely generated swells. During the simulation of wave energy and propagation, improper handling of parallel boundary formulations within the domain decomposition can induce artificial wave energy accumulation at the subdomain interfaces. To address this issue, this study mirrors the parallel computing infrastructure of the POP2 Message Passing Interface (MPI) protocol. Key physical and prognostic variables – including the zonal and meridional 10 m winds, wave radiation stress, subsurface momentum, and wave radiation and energy densities – are explicitly exchanged across processor subdomains to establish a robust, scalable online-coupling framework.

We evaluate the simulated spatial patterns of the air–sea CO₂ flux from both the uncoupled control simulation (B–CTL) and the coupled POP2–waves simulation against estimates from the NOAA CT2022 data assimilation system. Unlike our forward, ocean-centric modeling frameworks, CT2022 optimizes the system from an atmospheric perspective, utilizing a top-down approach to infer net surface CO₂ fluxes by assimilating observed atmospheric CO₂ mole fractions. Consequently, this product captures the integrated signature of both anthropogenic emissions and natural carbon cycle variability to provide continuous global flux estimates spanning from 2000 to 2020.

Following the inversion framework established by Jacobson et al. (2007), NOAA CT2022 partitions the global ocean into 30 distinct basins to capture large-scale circulation and biogeochemical dynamics. This basin-based approach groups regions characterized by coherence in physical processes – such as major current systems, upwelling zones, and boundary mixing layers – as well as shared biogeochemical characteristics, including air–sea CO₂ exchange rates and biological productivity. Moreover, because numerous observational datasets and ocean carbon products are resolved at regional scales, a basin-scale aggregation ensures greater methodological consistency. We evaluate the seasonal variability and mean state of global air–sea CO₂ fluxes, specifically excluding regions characterized by seasonal flux sign reversals – a feature that can introduce substantial artifacts during model–data comparisons. Instead, our analysis focuses primarily on regions exhibiting robust, clear oceanic CO₂ flux signals. Recognizing that inherent uncertainties in atmospheric inversions stem from sub-grid-scale anthropogenic emissions and localized sea-ice melt, we follow the protocols of Fay et al. (2024) and exclude both the coastal ocean and high-latitude marginal ice zones from our model–data evaluation.

Based on the spatial patterns of oceanic CO₂ outgassing, uptake, and low-flux regimes characterized in the Pacific (Fig. 2c), this study delineates 12 key regions exhibiting high air–sea CO₂ flux variability as identified by NOAA CT2022 (Fig. 2d). These are selected from the 30 ocean basins defined in the CT2022 model documentation (Jacobson et al., 2023) for optimizing flux inversions. These oceanic domains are categorized into three major basins: (1) the Pacific Ocean, (2) the Indian Ocean, and (3) the Atlantic Ocean (Table 1). Within the Pacific basin, specific labels denote regions exhibiting the most pronounced oceanic CO₂ outgassing (the Equatorial Eastern Pacific, EEP) and uptake (the Northeastern Pacific, NEP).

We utilize the traditional air–sea CO₂ flux bulk formula (Eq. 1) in CESM1.2.2 while also incorporating wave- and bubble-mediated effects via a gas transfer velocity parameterized by u*, SST, and Hs (Eq. 3). A comparison of the climatological means and monthly standard deviations indicates that the spatial distribution of the model-simulated air–sea CO₂ fluxes is broadly consistent with NOAA CT2022, with regional differences generally remaining below 0.5 mol m⁻² yr⁻¹ across most analyzed sub-basins (Fig. 2a–f). Notably, the Pacific CO₂ outgassing and uptake regions simulated by the POP2–waves experiment show smaller range-normalized relative biases (Table 3) against NOAA CT2022 than the B–CTL baseline across most selected regions. This improvement occurs despite POP2–waves having a higher monthly SD across both the Pacific and Indian Oceans.

To ensure an objective and reproducible classification, the 12 ocean regions were categorized into two distinct groups based on rigid statistical criteria, requiring either seasonal phasing consistency or model–data absolute bias magnitudes relative to the NOAA CT2022 baseline to be met:

Seasonal phasing consistency (temporal alignment): Regulated by the Pearson correlation coefficient (r) between the simulated monthly flux cycles and NOAA CT2022. Regions assigned to Fig. 3 exhibit consistent seasonal phasing with significantly positive correlations (r≥0.50), whereas regions in Fig. 4 display prominent phase mismatches or anti-correlated trends (r<0.50 or statistically non-significant r).

Based on these thresholds, the eight regions in Fig. 3 exhibit coherent seasonal phasing and relatively small monthly model–data biases. In contrast, the four regions in Fig. 4 (including the South Atlantic Ocean with r=0.33) display clear structural discrepancies, such as inverted seasonal trends or weak temporal alignment. Importantly, these temporal phase misalignments tend to amplify the calculated monthly model–data biases, as the model and data fluctuate in opposing directions throughout the annual cycle. This phase mismatch contributes to larger relative monthly mean biases; specifically, the model–data biases averaged across the four regions in Fig. 4 (33.7 % in B–CTL and 32.6 % in POP2–waves) are markedly larger than those in the eight regions of Fig. 3 (26.4 % in B–CTL and 22.0 % in POP2–waves).

In terms of the regional mean values of air–sea CO₂ flux, the POP2–waves simulation generally demonstrates closer structural agreement with NOAA CT2022 compared to the uncoupled B–CTL baseline, showing improvements in seven of the eight analyzed regions (with the exception of the Northwest Pacific (NWP); Fig. 3). Nevertheless, despite this larger mean offset in specific regions such as the NWP, POP2–waves successfully captures the autumn transition of oceanic CO₂ from a sink to a source as depicted in NOAA CT2022 – a feature that remains unrepresented in B–CTL. Table 3 presents the range-normalized relative magnitudes of model–data biases across eight selected regions, providing a robust metric to evaluate the simulated seawater carbonate system, pH and flux field performance against the NOAA CT2022 atmospheric inversion baseline. Overall, the wave-coupled framework (POP2–waves) demonstrates a widespread reduction in systematic biases across the majority of the analyzed regions compared to the uncoupled control simulation (B–CTL). Specifically, the regional mean absolute deviation dropped noticeably in major ocean basins, with the most pronounced improvement captured in the Equatorial Eastern Pacific (EEP), where the relative bias was drastically attenuated by 25.0 % (from 71.5 % in B–CTL down to 46.5 % in POP2–waves). Notable bias reductions are also observed in the Northwest Pacific (NWP, down by 4.9 %), and South Indian Ocean Region 1 (SIO1, down by 4.1 %), confirming that incorporating wave-effect mechanisms successfully rectifies over- or under-estimations in air–sea carbon exchange dynamics. Conversely, the uncoupled baseline (B–CTL) exhibits slightly smaller biases in the Equatorial Atlantic Ocean (EAO) (11.9 % vs. 15.0 %), suggesting potential localized over-compensations in wave parameterizations within this sub-basin. Nonetheless, the reduction of relative biases across most other regions indicates that the online-coupled framework generally provides an improved representation of air–sea CO₂ fluxes.

The POP2–waves simulation generally exhibits a higher SD than B–CTL, reflecting an amplified seasonal variability (Figs. 3–4). Although these SD values typically remain below 3 mol m⁻² yr⁻¹, they peak during boreal winter, driven by intense oceanic CO₂ uptake in high-latitude regions of the Northern Hemisphere, such as the Northwestern and Northeastern Pacific, and the North Atlantic Ocean 1. In contrast, the Southern Hemisphere exhibits pronounced monthly SD along with clear oceanic CO₂ uptake during the austral winter (boreal summer), particularly across regions such as the South Pacific Ocean 1 (SPO1), South Indian Ocean 1 (SIO1), and South Atlantic Ocean (SAO). However, the monthly SD derived from NOAA CT2022 shows notable regional variations. In particular, both models underpredict the magnitude of variability observed in the Northwest Pacific (NWP), Equatorial Eastern Pacific (EEP), and North Atlantic Ocean 1 (NAO1).

Four specific sub-basins – South Atlantic Ocean (SAO), South Pacific Ocean Region 2 (SPO2), South Indian Ocean Region 2 (SIO2), and North Atlantic Ocean Region 2 (NAO2) – exhibit prominent model–data discrepancies when evaluated against NOAA CT2022 (Fig. 4). Notably, these systematic deviations are not attributable to wave-mediated processes or the parameterization of the CO₂ flux bulk formula. Within the NAO2, both the B–CTL and POP2–waves models simulate strong seasonal variations that mirror NAO1, characterized by substantial oceanic CO₂ uptake during the boreal winter; conversely, NOAA CT2022 displays the opposite seasonal trajectory in this sub-basin. A structurally similar mismatch is observed in the mid-latitude South Pacific (SPO2 and SIO2), where the simulated seasonal cycles of both models exhibit close synchronization with their respective low-latitude counterparts (SPO1 and SIO1) but differ noticeably from the inverse trend captured by the NOAA CT2022 atmospheric inversion framework.

To demonstrate that the sea-state-dependent gas transfer velocity (Deike and Melville, 2018) provides a more suitable estimate of air–sea CO₂ flux than the wind-only formulation (Wanninkhof, 1992) under high-wind conditions (U10>10 m s⁻¹), we selected the Western Pacific (WP) and the Equatorial Pacific (EP) regions due to their contrasting wind regimes. The WP region experiences a high frequency of high-wind conditions (exceeding 30 %), whereas wind speeds in the EP region consistently remain below this threshold. Because both regions exhibit stable and significant oceanic CO₂ outgassing or uptake, they enable a clear comparative analysis of the correlation between kw,660 and U10 (Fig. 5a, b).

Generally, the B–CTL data shows higher R2 but lower kw,660 values compared to those in POP2–waves across both the WP and EP. The POP2–waves experiment exhibits a slightly lower R2 than B–CTL due to greater deviations between kw,660 and U10, particularly at higher surface wind speeds. This pattern is consistent with the findings of Gutiérrez-Loza et al. (2022) under conditions where Hs>1.5 m. The relationship between kw,660 and U10 was evaluated under two scenarios: baseline monthly climatological means (Hs<1.5 m) and high-resolution daily data filtered for Hs>1.5 m (enhanced conditions) aggregated into 30-year monthly averages. Notably, both approaches substantially diminish the differences in kw,660 at identical U10 values.

However, short-term (30 min) observations indicate that gas transfer velocity can be up to twice as high under similar wind speeds when Hs>1.5 m (Gutiérrez-Loza et al., 2022). Divergence between the models becomes significant when U10 exceeds 12 m s⁻¹ over the WP region (Fig. 5a), whereas over the EP region, the convergence of kw,660 estimates is most notable around U10=9 m s⁻¹ (Fig. 5b), suggesting that mid-range wind speeds dominate the EP flux signal.

As shown in Fig. 5c, the enhanced WP cases (Hs>1.5 m) have data available for all months except August and October, during these available months, their kw,660 values consistently exceed both the all-data POP2–waves and B–CTL averages. In contrast, the EP region exhibits Hs>1.5 m data only during the summer months (July to October), where corresponding kw,660 values also exceed both all-data POP2–waves and B–CTL averages. The monthly SD indicates no significant differences between the enhanced (Hs>1.5 m) data and the standard POP2–waves simulations over the WP, with the kw,660 discrepancies between the two datasets remaining minimal from January to May because the average Hs during this period consistently remains below 1.5 m. However, over the EP, a pronounced discrepancy is observed between the Hs>1.5 m condition and the all-data POP2–waves average from July to September.

The wind-only parameterization of gas transfer velocity tends to underestimate values under high-wind conditions (U10>10 m s⁻¹) or high significant wave heights (Hs>1.5 m) (e.g., Gutiérrez-Loza et al., 2022; Zhou et al., 2023). Under these high-wind conditions, the monthly mean air–sea CO₂ fluxes derived from the B–CTL and POP2–waves simulations diverge notably within the Western Pacific region (WP) (Fig. 6), highlighting key discrepancies between the wind-only and wave-modified kw,660 formulations. The data were filtered to include only grid points that met this high-wind threshold before being regionally averaged. Because not all months contained grid points satisfying the threshold, a final subset of 154 data points was utilized for the linear regression analysis. These high-wind conditions over the WP region occur primarily in winter (accounting for 42 % of the valid data), when the concurrent low sea surface temperatures further enhance CO₂ solubility. The slopes of the regression equations (-0.77 mol m⁻³ s yr⁻¹ for B–CTL and -1.40 mol m⁻³ s yr⁻¹ for POP2–waves) alongside the mean CO₂ fluxes (Yavg: -6.35 mol m⁻² yr⁻¹ for B–CTL and -6.97 mol m⁻² yr⁻¹ for POP2–waves) both indicate that POP2–waves exhibits a higher sensitivity to wind speed, leading to stronger oceanic CO₂ uptake across the WP domain under elevated wind speeds.

The correlation coefficient (R) of the POP2–waves simulation is higher than that of B–CTL, indicating that the sea-state-dependent kw,660 formulation provides a more realistic representation of the CO₂ flux than the wind-only kw,660 scheme under high-wind conditions. This finding aligns with the observations of Gutiérrez-Loza et al. (2022) and Zhou et al. (2023). The average air–sea CO₂ flux in B–CTL over the WP region during DJF and JJA is -0.021 and -0.004 mol m⁻² yr⁻¹, respectively. Meanwhile, POP2–waves exhibits only slight discrepancies relative to B–CTL during these respective seasons, with differences ranging between 0.001 and 0.002 mol m⁻² yr⁻¹ in CO₂ uptake (data not shown). This contrast indicates that under high-wind conditions, the episodic air–sea CO₂ flux is significantly greater than the seasonal baseline averages.

The spatial co-variations of sea level pressure (SLP), U10, and Hs underscore their combined role as key meteorological and wave drivers steering the regional kw,660 patterns (Fig. 7a, b). The region with Hs>1.5 m is generally situated where U10>8 m s⁻¹ and lies south of the high-SLP region. The spatial patterns of climatological U10 and Hs align closely with the findings of Reichl and Deike (2020) (Fig. 7a, b). Furthermore, a dominance of bubble-mediated transfer in the POP2–waves simulation, where the kwB,660/kw,660 ratio exceeds 0.5, primarily occurs in regions characterized by Hs>1.5 m (Fig. 7b). However, an elevated Hs does not always correspond to a higher kwB,660/kw,660 ratio in the POP2–waves simulation; this decoupling is explicitly observed in the North Pacific (Fig. 7b).

Deike and Melville (2018) demonstrated that the bubble contribution to CO₂ transfer exceeds 40 % when the U10≥10 m s⁻¹. In our POP2–waves simulation, the bubble fraction (kwB,660/kw,660) accounts for approximately 38 % of total gas transfer velocity, which is slightly higher than the ∼30 % reported by Reichl and Deike (2020). This discrepancy may be attributed to differences in the AB scaling coefficients (Eq. 3), which are derived from field data, where gas transfer velocity is estimated from eddy covariance flux measurements (Reichl and Deike, 2020; Brumer et al., 2017).

The structural differences in kw,660 (POP2–waves - B–CTL) reveal that the most pronounced discrepancies are primarily distributed in regions characterized by elevated Hs, particularly in the Southern and South Indian Oceans (Fig. 7c). Although U10 in the Indian Ocean and tropical Pacific is relatively low (<5 m s⁻¹; Fig. 7a), the kw,660 values simulated by POP2–waves remain approximately 9 cm hr⁻¹ higher than those in B–CTL. In these regions, this wave-driven enhancement of the total gas transfer velocity is predominantly governed by the non-bubble-mediated component (kwNB,660; Fig. 7d). Although Hs is also elevated in the Southern Ocean (Fig. 7b), it does not contribute substantially to the kw,660 difference between POP2–waves and B–CTL; this is because the high U10 in this region (Fig. 7a) already yields high gas transfer velocities through the empirical formulation of Wanninkhof (1992). The spatial patterns of both the B–CTL kw,660 and the wave-induced kw,660 discrepancies (POP2–waves - B–CTL) closely align with the findings of Reichl and Deike (2020) (Fig. 7c). Overall, the two simulations exhibit consistent geographic distributions, yielding 30-year domain-wide mean gas transfer velocities of 17.0 cm hr⁻¹ for B–CTL and 22.7 cm hr⁻¹ for POP2–waves, despite their reliance on distinct input parameters (U10 versus u* and Hs). Aside from the polar regions, the total gas transfer velocity in the POP2–waves coupled model exceeds that in B–CTL, with the most pronounced differences localized in the tropics (Fig. 7c). To elucidate the driving mechanisms behind this global enhancement, it is necessary to quantify whether the non-bubble (kwNB,660) or bubble-mediated (kwB,660) component dominates the total gas transfer velocity across the different ocean basins. This partitioning demonstrates that bubble-mediated processes dominate (kwB,660>kwNB,660) under high-Hs conditions, whereas non-bubble mechanisms prevail (kwB,660<kwNB,660) in light-wind zones where U10<7 m s⁻¹ (Fig. 7).

Integrating wave dynamics induces a pronounced spatial reorganization of both pCO2w and ocean surface pH over the 30-year climatological period (Fig. 8). Specifically, the baseline B–CTL simulation shows that high pCO2w is concentrated in the equatorial eastern Pacific (EEP), contributing to a larger oceanic CO₂ source (Fig. 8a). In contrast, low pCO2w is found in high-latitude regions of the Pacific and Atlantic (e.g., NWP, NEP, NAO1, and NAO2), driving strong oceanic CO₂ uptake (Fig. 8a). Over the study period, the climatological standard deviation of pCO2w in B–CTL ranges between 10 and 30 ppm (Fig. 8a).

In the CESM1 framework of the B_2000_CAM5 compsets, atmospheric pCO2a is held constant (367 ppm). The pCO2w in the Eastern Pacific exceeds 440 ppm, indicating an air–sea ΔpCO₂ greater than 73 ppm in B–CTL (109.8 and 92.7 ppm during DJF and JJA, respectively), whereas the pCO2w in the Western Pacific is below 320 ppm, indicating an air–sea ΔpCO₂ lower than -47 ppm (-53.4 and -31.4 ppm during DJF and JJA, respectively). Notably, POP2–waves reduces the high pCO2w by more than 10 ppm over the Eastern Equatorial Pacific and increases the low pCO2w in other regions (Fig. 8b). Consequently, in the oceanic CO₂ outgassing (uptake) regions, the POP2–waves coupled model decreases (increases) pCO2w, thereby reducing the magnitude of the air–sea ΔpCO₂. The climatological SD of the pCO2w discrepancy between POP2–waves and B–CTL displays marked spatial variability over the Eastern Equatorial Pacific, whereas changes across other regions remain relatively minor.

The biogeochemical module of POP2 (BEC) updates TA in each grid cell by solving a coupled transport–reaction equation (Moore et al., 2013). The average pH of the ocean is currently around 8.1 in oceanic CO₂ uptake regions (e.g., the Western Pacific) and 8.0 in outgassing regions (e.g., the Equatorial Pacific; Fig. 8c), reflecting slightly alkaline conditions. Within the DIC system, bicarbonate ions (HCO3-) are the dominant species because background seawater pH falls strictly between pKa1 and pKa2. However, continued uptake of atmospheric CO₂ drives a decline in pH – a process termed ocean acidification. Our study highlights that wave-induced kw,660 significantly influences the marine CO₂ system, altering alkalinity, pH, and carbonate speciation. These chemical shifts, in turn, provide a feedback mechanism that modulates the overall dynamics of the air–sea CO₂ flux. Consequently, wave-driven perturbations in kw,660 directly alter both ΔpCO₂ and net air–sea CO₂ fluxes within the Earth System Model framework.

Ocean pH and surface ocean pCO2w are strongly negatively correlated (Macovei et al., 2021). Consequently, low pH values are observed in the Equatorial Eastern Pacific (Fig. 8c), as a direct result of the elevated DIC and pCO2w concentrations characteristic of that region (Fig. 8a). Conversely, elevated pH conditions persist in domains with lower pCO2w, a signature most prominent throughout high-latitude waters in both the Pacific and Atlantic Basins. Rustogi et al. (2025) indicate that accelerated equilibration of oceanic pCO₂ in the wind–wave–bubble simulation, driven by enhanced gas exchange, ultimately reduces the magnitude of the air–sea ΔpCO₂. This pCO₂ feedback is strongest in the extratropics, where it suppresses CO₂ uptake. Our POP2–waves experiment reveals a consistent response, characterized by increases in both oceanic pCO₂ (Fig. 8b) and hydrogen ion concentration ([H⁺]), which are accompanied by a corresponding decline in pH (Fig. 8d) throughout the extratropical ocean basins. Accounting for wave effects results in simulated pH shifts of approximately +0.01 (-0.01) in oceanic CO₂ outgassing (uptake) regions (Fig. 8d). This suggests that incorporating this mechanism alleviates acidification in the equatorial Pacific, whereas it intensifies ocean acidification in the high-latitude domains of both the Pacific and Atlantic Oceans (Fig. 8d). Rustogi et al. (2025) also showed that the effects of Δkw (the difference between wave-induced kw,660 and kw,660 based on U10) and ΔpCO₂ (POP2–waves - B–CTL) partially offset each other. However, because the Δkw effect is generally 20 %–30 % stronger, it dominates the counteracting ΔpCO₂ effect, explaining the modest changes observed in both oceanic outgassing and uptake CO₂ fluxes within the wave-effect simulation.

Several investigations have parameterized the air–sea CO₂ flux using Eq. (1), yet current kw,660 parameterizations within prominent global frameworks still rely exclusively on the neutral 10 m wind speed (U10) as seen in models such as MPI-ESM1.2 (Mauritsen et al., 2019), CESM2 (Danabasoglu et al., 2020), NorESM2 (Seland et al., 2020), UKESM1 (Sellar et al., 2019), MIROC6 (Chikamoto and DiNezio, 2021), CMCC-ESM2 (Lovato et al., 2022), and CanESM5 (Sigmond et al., 2023) (Table 2). Concurrently, pioneering efforts have begun quantifying wave-induced effects on both air–sea CO₂ flux and long-term ocean carbon storage by incorporating coupled wind–wave–bubble gas transfer formulations into ocean general circulation models (OGCMs), such as MOM6–COBALTv2 (Rustogi et al., 2025) and NEMO–PISCES (Wu et al., 2025). Importantly, Wu et al. (2025) emphasize that integrating these wave-mediated boundary layer dynamics into fully coupled Earth System Models is crucial to reducing systemic uncertainties in global carbon cycle projections.

Several studies have incorporated wave effects following the parameterization of Deike and Melville (2018), utilizing the Surface Ocean CO₂ Atlas (SOCAT) database (Bakker et al., 2016) to calculate diagnostic air–sea CO₂ fluxes. In these offline configurations, however, the computed air–sea CO₂ flux is treated independently of pCO2w dynamics and surface pH evolution, lacking any interactive feedback mechanisms between the atmosphere and the upper-ocean carbonate system.

Rustogi et al. (2025) utilized an ocean-biogeochemistry system forced by offline atmospheric reanalysis and wave model outputs. While comprehensive, such an offline-forced setup is limited in its ability to capture high-frequency, episodic, and synchronous interactions between physical wave states and surface water chemistry during rapid weather transitions. In contrast, our study implements an online coupling framework. The key added value of our setup is its capacity to simulate step-by-step interactive feedbacks where wave properties dynamically alter the gas transfer velocity (kw,660) and physical mixing in real-time. The coupled behavior of POP2–waves includes ΔpCO₂-driven negative feedbacks, which fundamentally differs from traditional obs-based products that treat wave-induced kw,660 and ΔpCO₂ as independent variables when estimating air–sea CO₂ flux (e.g., Reichl and Deike, 2020). This online coupling mechanism also contrasts with global ocean models forced offline by atmospheric reanalysis and wave model outputs (e.g., Rustogi et al., 2025), where such interactive feedbacks are often omitted. This approach enables our model to resolve non-linear, high-resolution modulations of air–sea CO₂ exchange during rapid dynamic events – effects that are typically muted in offline configurations.

To evaluate which driver exerts the most direct control on air–sea CO₂ flux, Fig. 9 displays the spatial distributions of the linear regression coefficients (LRCs) derived from univariate (one-on-one) linear regressions between the flux and various standardized variables: air–sea ΔpCO₂ (Fig. 9a), kw,660 (Fig. 9b), SST (Fig. 9c), and pH (Fig. 9d). To remove the confounding artifacts of differing physical units and enable a direct comparison on a common scale, both the air–sea CO₂ flux and the independent variables were standardized into anomalies (with a mean of 0 and a standard deviation of 1) prior to the regression analysis. The statistical significance of these regressed relationships was subsequently evaluated using a Student's t-test at the 95 % confidence level. Because each standardized regression was performed individually with a single independent variable, the resulting LRCs are equivalent to Pearson correlation coefficients (r), constraining their values strictly between -1 and +1. Here, we do not delve into the intricate chemical and biochemical feedback mechanisms governing carbonate species. Nevertheless, it is worth noting that the collective influence of carbonate composition – specifically TA and dissolved inorganic carbon (DIC) – on pCO2w variability has been shown to outweigh that of solubility changes driven by sea surface salinity and SST (e.g., Koseki et al., 2023).

Among these drivers, air–sea ΔpCO₂ and air–sea CO₂ flux exhibit the strongest positive LRCs, with coefficients ranging from 0.6 to 0.8 across the global ocean; this underscores the ocean's role as a net CO₂ source or sink depending on the sign of the air–sea ΔpCO₂ gradient. Additionally, wave effects increase the LRCs by approximately 0.1 to 0.2, particularly within regions of intense oceanic CO₂ outgassing or uptake. Clear positive (negative) LRCs exist between kw,660 and the air–sea CO₂ flux in oceanic CO₂ outgassing (uptake) regions. Furthermore, wave effects reduce the absolute LRCs between kw,660 and air–sea CO₂ flux in both oceanic CO₂ outgassing (uptake) regions (Fig. 9b). This indicates that once interactions between the modeled CO₂ flux and the ocean carbonate–pH system are considered, the wave-influenced CO₂ flux becomes less correlated with kw,660 and more closely linked to air–sea ΔpCO₂. This shift can be attributed to the limitations of wind-only parameterizations; as indicated by Zhou et al. (2023), wind-only formulas tend to underestimate gas transfer velocities when U10 exceeds 10 m s⁻¹, where intense wave breaking and high significant wave height substantially boost air–sea gas exchange. Furthermore, Johansson et al. (2022) reported that Hs generally increases with wind speed, but the relationship is strongly modulated by wind direction and regional conditions, leading to spatially variable and nonlinear wind–wave coupling.

In contrast to the former, there are clear positive (negative) LRCs between SST and CO₂ flux in oceanic CO₂ uptake (outgassing) regions (Fig. 9c). A negative correlation exists between kw,660 and SST, reflecting the latitudinal gradient where colder, high-latitude waters are characterized by more intense sea states and elevated kw,660 values. This pattern occurs because lower temperatures at high latitudes increase CO₂ solubility, thereby enhancing oceanic uptake. From a thermodynamic perspective, higher SST enhances molecular diffusion while lowering seawater viscosity, thereby reducing the Schmidt number (Sc=ν/D, defined as the ratio of kinematic viscosity (ν) to the molecular diffusion coefficient (D)). Because kw,660 is parameterized as a function of Sc^−0.5, a decrease in Sc theoretically elevates kw,660. Separately, Fay et al. (2024) attributed the regional discrepancies and variations in air–sea CO₂ fluxes to a combination of factors, including choices in wind speed products, SST datasets, biological carbon uptake, and the parameterization of gas transfer velocity. Wave effects only slightly reduce the LRCs between SST and the air–sea CO₂ flux – by approximately 0.1 – within the tropics, with negligible impacts observed in other regions. The strong negative correlation between ocean pH and pCO2w is dictated by the acid dissociation equilibria of the marine carbonate system (Fig. 8a, c), which govern the fundamental relationship between dissolved CO₂ and hydrogen ion concentration (Williams et al., 2017). As seawater pH decreases, the resulting increase in hydrogen ion concentration ([H⁺])reacts with carbonate ions (CO32-). This consumption of carbonate ions reduces the ocean's buffering capacity for CO₂ uptake, causing seawater pCO2w to increase. Because atmospheric pCO2a is fixed at 367 ppm in the CESM1.2.2 configuration, this rise in surface ocean pCO2w narrows the air–sea partial pressure gradient ΔpCO₂ in uptake regions (where seawater pCO2w is below atmospheric levels), thereby suppressing the air–sea CO₂ influx. Reflecting this mechanism, pH and air–sea CO₂ flux exhibit strong negative LRCs (less than -0.9) across most of the global ocean, with exceptions confined to the Eastern Equatorial Pacific and along the Arctic margins (Fig. 9d). Wave effects marginally attenuate this relationship in the Eastern Equatorial Pacific (EEP), reducing the LRCs by approximately 0.1.

Rustogi et al. (2025) indicate that as surface seawater pCO2w equilibrates with changes in DIC and alkalinity, the air–sea ΔpCO₂ gradient is partially attenuated. This induces a negative feedback loop whereby enhanced CO₂ uptake (or outgassing) is systematically damped by chemical re-equilibration within the marine carbonate system, a mechanism that is highly consistent with the findings of this study. To assess the uncertainty in CO₂ flux resulting from the absence of interactions between the flux and the ocean carbonate–pH system (i.e., the decoupling of the ΔpCO₂-driven negative feedback), we performed a series of sensitivity experiments. The air–sea CO₂ flux was reconstructed using the uncoupled ΔpCO₂ fields from the control simulation (B–CTL) and the wave-influenced kw,660 parameterization from the coupled wave simulation (POP2–waves). This experimental setup explicitly isolates the statistical mean and standard deviation of the flux under a scenario defined by the “lack of ΔpCO₂-driven negative feedback”. Only data showing a statistically significant air–sea CO₂ flux difference (at a 95 % confidence level) between “lack of ΔpCO₂-driven negative feedback” scenario and POP2–waves are presented in Fig. 10b. Compared to the baseline (Fig. 2b), the CO₂ flux under the “lack of ΔpCO₂-driven negative feedback” scenario is stronger than that in the POP2–waves simulation across both oceanic CO₂ outgassing and uptake regions, accompanied by a larger SD. The most pronounced discrepancies occur in the Pacific basin across both outgassing and uptake zones. However, certain mid-to-high latitude subregions – specifically the Northeastern Pacific (NEP), South Indian Ocean 2 (SIO2), and South Pacific Ocean 2 (SPO2) – do not reach the 95 % confidence threshold.

Rustogi et al. (2025) demonstrate that while wave-enhanced kw,660 accelerates local air–sea CO₂ exchange, it simultaneously attenuates the air–sea ΔpCO₂ gradient. In this study, we conceptualize this process as a manifestation of the ocean's buffering capacity, which encompasses the dynamic coupling between CO₂ flux (estimated via kw,660) and the marine carbonate–pH system. Within the coupled POP2–waves framework, incorporating wave effects alleviates surface acidification and reduces air–sea ΔpCO₂ over oceanic CO₂ outgassing regions; conversely, the resulting relatively higher pH levels systematically enhance the ocean's capacity to absorb atmospheric CO₂ within oceanic CO₂ uptake regions in the coupled POP2–waves model. In contrast, the simulation lacking the ΔpCO₂-driven negative feedback – which artificially omits realistic marine buffering effects – overestimates the air–sea exchange, yielding excess CO₂ outgassing into the atmosphere (>0.4 mol m⁻² yr⁻¹) over source regions. Concurrently, it amplifies excess CO₂ uptake (<-0.4 mol m⁻² yr⁻¹) within regions characterized by oceanic CO₂ uptake regions (Fig. 10b) compared to the coupled POP2–waves model.