Effects of Langmuir circulation parameterization on seasonal air–sea CO₂ exchange in the Bering Sea

Abstract

Intensified ocean mixing can alter both the vertical temperature profile and biogeochemical states. Using a physical–biogeochemical coupled ocean model, we examine the impact of parameterized Langmuir circulation (LC) on the ocean carbon system in the Bering Sea. While LC has limited influence in summer, it significantly enhances turbulent mixing in winter, leading to an average wintertime mixed-layer deepening of about 11%. In the presence of a winter temperature inversion, LC-driven mixing enhances the entrainment of warmer subsurface water into the surface, increasing the surface ocean partial pressure of CO₂ (pCO₂). Concurrently, intensified vertical mixing entrains carbon-rich deep water into the surface layer, further elevating wintertime surface pCO₂. By decomposing pCO₂ into thermal and non-thermal components, we find that changes in dissolved inorganic carbon (DIC) supply exert a stronger influence than temperature-driven change, increasing the non-thermal pCO₂ by up to 8.5 µatm in March and amplifying the seasonality of non-thermal processes. The thermal component also increases pCO₂ by about 4.3 µatm in March, but its contribution to the seasonal amplitude is relatively small. These results demonstrate that enhanced vertical mixing combined with a winter temperature inversion can substantially alter pCO₂ and air–sea CO₂ fluxes in high-latitude regions; in regions without such inversions, thermal and non-thermal LC effects are likely to offset one another.

1 Introduction

The Bering Sea, a semi-enclosed marginal sea, is a corridor connecting the North Pacific to the Arctic. It can be divided into two regions by the shelf break with a distinct biogeochemical characteristics: a biologically active shelf to the northeast (Bates et al., 2011; Springer et al., 1996) and a High-Nutrient Low-Chlorophyll basin to the southwest (Tyrrell et al., 2005; Shiomoto et al., 2002). These regions show contrasting patterns in air-sea CO₂ exchange - the shelf acts as a net annual sink of atmospheric CO₂, whereas the basin serves as a net source (Zhang et al., 2023). In addition to spatial heterogeneity, the region exhibits strong seasonal variability, particularly in sea surface temperature (SST) (Shevchenko et al., 2024) and mixed layer depth (MLD) (Hayden and O’Neill, 2024; Johnson and Stabeno, 2017).

These seasonal changes drive biogeochemical temporal processes, influencing the seasonal variability of air-sea CO₂ fluxes. Observation-based estimates indicate that the subpolar region of the North Pacific acts as a source of CO₂ to the atmosphere in winter and a sink in summer (Rodgers et al., 2023), consistent with findings in the Bering Sea, where estimates reveal seasonal CO₂ flux variability linked to changes in SST, MLD, and chlorophyll-a (Zhang et al., 2023). Many ocean biogeochemical models, however, struggle to accurately capture this seasonal cycle (McKinley et al., 2006; Lerner et al., 2021; Rodgers et al., 2023; Carroll et al., 2020). For instance, Lerner et al. (2021) reported that the NASA-GISS model simulates a seasonal CO₂ flux pattern opposite to that inferred from observations. Similarly, most CMIP6 models reproduce reversed seasonal CO₂ fluxes in the subpolar North Pacific (Rodgers et al., 2023). This misrepresentation also persists in data assimilation products that incorporate both physical and biogeochemical observations. Despite generally good agreement with observed fluxes globally, they fail to reproduce the correct seasonal CO₂ exchange in this region (Carroll et al., 2020), likely due to unresolved physical processes that affect upper-ocean biogeochemistry.

Refinements in physical processes within ocean models can improve biogeochemical simulations. Multiple physical drivers influence the air-sea CO₂ exchange, including mesoscale features resolved by high-resolution ocean models (Guo and Timmermans, 2024; Ford et al., 2023; Kim et al., 2022), freshwater-driven stratification (Ahmed et al., 2020; Dong et al., 2021), SST changes linked to marine heatwaves (Edwing et al., 2024), topographically modulated upwelling (Fiechter et al., 2014), and current-wind interaction (Kwak et al., 2021). In particular, surface vertical mixing can have a significant impact on air-sea CO₂ flux. For example, vertical mixing induced by near-inertial waves can enhance DIC concentrations, thereby decreasing the CO₂ uptake in austral summer (Song et al., 2019). In contrast, Langmuir turbulence contributes to enhanced carbon uptake, adding approximately 0.07–0.1 PgC/year of extra CO₂ absorption globally (Smith et al., 2018). Tak et al. (2023) applied a LC parameterization to an ocean model in the Southern Ocean and showed deepening of the mixed layer, increasing sea-ice fraction, and improving the simulation of air–sea CO₂ flux.

We hypothesize that the bias in the Bering Sea’s air–sea CO₂ exchange may stem from biases in vertical mixing. Enhanced vertical mixing can influence CO₂ flux through both thermal and non-thermal processes. Thermally, mixing tends to lower SST by bringing cooler subsurface water to the surface, which decreases surface pCO₂. Non-thermally, mixing can elevate surface DIC concentrations by entraining DIC-rich subsurface water, which increases surface pCO₂. These opposing effects can offset each other, which dampens net change on air–sea CO₂ exchange. However, in high-latitude regions such as the Bering Sea, where wintertime thermal inversions are present (i.e., subsurface waters are warmer than the surface), LC-driven enhanced vertical mixing may produce a distinct effect on CO₂ exchange.

This study evaluates the impact of LC parameterization on air–sea CO₂ exchange in the Bering Sea using a physical-biogeochemical coupled model. As a first step, we decompose pCO₂ into thermal and non-thermal components, clarifying the relative contributions of temperature-driven and biogeochemical processes. Next, we conduct a DIC budget analysis to investigate the mechanisms driving DIC changes under LC parameterization and to determine when and why LC-enhanced vertical mixing affects DIC redistribution and air–sea CO₂ exchange.

2 Method

2.1 Langmuir circulation parameterization

LC refers to wind-driven, counter-rotating vortices aligned parallel to the wind direction (Langmuir, 1938). This circulation can erode near-surface stratification and thereby enhance vertical mixing in the upper ocean (Thorpe, 2004). The impact of LC on vertical mixing has been investigated using Large Eddy Simulations (LES), which show significant effects under weakly stratified conditions (Noh et al., 2011). To account for these effects in coarse-resolution global ocean models, LC has been parameterized and incorporated into global climate models, resulting in improvements such as the mitigation of the shallow mixed layer bias, especially in the Southern Ocean (Noh et al., 2016; Tak et al., 2023).

Ocean models typically incorporate LC by extending vertical mixing schemes. A commonly employed approach parameterizes LC effects in the K-profile parameterization (KPP) by increasing the turbulent velocity scale (McWilliams and Sullivan, 2000; Smyth et al., 2002; Li et al., 2016; Reichl et al., 2016). Additionally, LC effect is parameterized in the energetics-based planetary boundary layer (ePBL) scheme by enhancing the entrainment buoyancy flux (Reichl and Li, 2019). In this study, the influence of LC on the air-sea CO₂ flux is investigated using a simple parameterization scheme presented in Tak et al. (2023). This LC parameterization modifies the turbulent kinetic energy (TKE) closure scheme by Gaspar et al. (1990) and Blanke and Delecluse (1993) where the vertical eddy viscosity is proportional to the turbulent mixing length scale (l_mix) and the square root of the TKE. The LC parameterization relaxes the near-surface constraint on l_mix by a factor of Γ (from local depth (z) to Γz), allowing larger l_mix near the surface to represent LC-enhanced vertical mixing. Γ is shown to depend on the Langmuir number (Γ increases as La decreases), where and are the friction velocity and the Stokes velocity at the surface, respectively (McWilliams et al., 1997). Belcher et al. (2012) reported that La is smaller than 0.35 roughly 70% of the time during the Northern Hemisphere winter (around 60% in summer). Also based on LES results, Figure 8 of Noh et al. (2011) shows that the amplification of the mixing length scale under Langmuir circulation is well represented by Γ = 10 when La = 0.32. Therefore, we use La = 0.32 and Γ = 10 as constant values following Noh et al. (2011, 2016), and Tak et al. (2023), which provide a reasonable and practical approximation for implementing LC effects under our wintertime Bering Sea conditions.

This scheme also includes the effects of Stokes drift into both the TKE equation and the Coriolis term in the momentum equation (Tak et al., 2023). The magnitude of this contribution depends on the vertical profile of the Stokes velocity, , which is formulated as . The surface Stokes velocity is estimated using the Langmuir number, , and the friction velocity, , where is the wind stress and is the water density. The wavelength of the monochromatic surface wave, m, is adopted following Noh et al. (2004).

2.2 Model configuration

The impact of LC on air-sea CO₂ flux in the Bering Sea is investigated using a global ocean configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) (Adcroft et al., 1997, 2004; Marshall et al., 1997b, a, 1998). This configuration has a horizontal resolution of approximately 1^° and shares many features with ECCO Version 4 (Forget et al., 2015). However, it includes key modifications, such as three additional vertical layers within the top 10 m of the ocean to better represent the effects of the LC parameterization.

The carbon cycle and air-sea CO₂ flux are represented by the DIC module, a simple biogeochemical model that simulates 6 tracers: DIC, alkalinity, dissolved organic phosphorus, phosphate, oxygen, and iron (Dutkiewicz et al., 2005; Parekh et al., 2005; Song et al., 2016a, 2019). The air-sea CO₂ flux () is given by

In Equation 1, k_w is the piston velocity for CO₂ weighted by the fraction of the sea-ice-free area within each grid cell. is the partial pressure of CO₂ in the surface ocean, which is determined by local values of DIC, alkalinity, SST and sea surface salinity (SSS). The atmospheric partial pressure of CO₂ () is prescribed as a fixed pre-industrial value of 278 µatm. Because is held constant, the surface ocean pCO₂ controls the direction of the air-sea CO₂ exchange (positive sign indicates oceanic uptake), and its magnitude depends on both k_w and ΔpCO₂. The surface DIC has two additional source/sink terms. The first accounts for changes due to biological production, estimated from phosphate consumption, which is converted to carbon consumption using the Redfield ratio. The second is the export of carbon to depth in the form of calcium carbonate shells. The biological production requires sunlight and nutrients, where sunlight exponentially decreases with depth and is further reduced by self-shading. Detailed information on the biological model configuration is available in the previous modeling study by Song et al. (2016b).

This physical-biogeochemical coupled model was first spun up for 600 years starting from the initial temperature, salinity and phosphate fields from World Ocean Atlas (https://www.nodc.noaa.gov/OC5/WOA09/pubwoa09.html), and DIC and alkalinity fields from GLODAP (Key et al., 2004) under the atmospheric forcing from Common Ocean-ice Reference Experiments version 2 (CORE-II) - “normal year” forcing dataset (Large and Yeager, 2004), which provides a repeat annual cycle representative of climatological conditions, and atmospheric iron deposition data from aeolian dust sources (Luo et al., 2008). The simulation bifurcates into two experiments after the spin up. The first experiment extends the simulation for an additional 100 years, serving as a baseline control (CTRL) where LC effects are excluded. The second experiment integrates 100 years with the LC parameterization to examine its impact on the air-sea CO₂ exchange. A detailed description of the experimental setup can be found in Section 3 of Tak et al. (2023). For the analysis presented here, model outputs from the final nine years of each simulation were averaged.

3 Results

3.1 Air-sea carbon exchange

We first describe the annually averaged air-sea CO₂ exchange in the Bering Sea. Figure 1 shows the annual mean in the Bering Sea, where the region is divided into the basin (deeper than 200 m) and shelf areas. The observation-based estimate of ΔpCO₂, derived from the self-organizing map feed-forward neural network (SOMFFN) approach (Jersild et al., 2017), suggests that the basin tends to emit CO₂, whereas the shelf takes up CO₂ (Figure 1A). The CTRL captures the basin-shelf contrast in pCO₂, and localized outgassing occurs in parts of the basin, but CO₂ uptake dominates overall (Figure 1C). This bias is reduced by incorporating LC effect, which eventually decreases CO₂ uptake, particularly in the western part of the basin (Figures 1B, D). Therefore, we focus on the basin region.

Figure 1

This improvement can be attributed to enhanced vertical mixing by the LC effect. Compared with the MLD climatology dataset v2023 (de Boyer Montégut et al., 2004; de Boyer Montégut, 2023), CTRL has a shallower MLD bias in the basin, which is mitigated in the LC simulation (Supplementary Figure S1). This deepening results from increased turbulent mixing due to the inclusion of the LC effect. The LC parameterization is expected to enhance the l_mix near the surface under weakly stratified conditions (Noh et al., 2016). Indeed, l_mix is significantly amplified in the LC simulation, particularly during winter and early spring, showing an increase of approximately 44% near 100 m compared to CTRL (Figure 2C). Consistent with this, the increase in TKE is also more pronounced during winter and early spring, extending beyond 100 m (Figure 2F), suggesting deeper and more sustained vertical mixing due to LC.

Figure 2

To investigate the variability of air-sea carbon exchange due to the LC parameterization, we focus on changes. The exhibits a wintertime minimum and summertime maximum (Figure 3), with the simulated maximum occurring about 5 months later than the observation-based estimate (Supplementary Figure S2). This is a rather common discrepancy that many global biogeochemical models have in the North Pacific high latitudes (e.g., Carroll et al., 2020; Rodgers et al., 2023).

Figure 3

To identify the cause of this mismatch, we decompose into thermal () and non-thermal () components using the approach of Takahashi et al. (2002).

In Equations 2 and 3, the overline indicates the spatiotemporal mean value over the Bering Sea basin region, and 0.0423 °C⁻¹ is the sensitivity coefficient of pCO₂ to SST (Takahashi et al., 1993). The accounts for the change induced by SST variations, and the is obtained by removing this SST effect from the total pCO₂. The pCO₂ decomposition reveals that the seasonal variability of is smaller than that of (Figure 3). This result contrasts with previous studies showing that in the Bering Sea, non-thermal effects play a dominant role over thermal effects in the seasonal variability of pCO₂ (Song et al., 2016c; Zhang et al., 2023), which is consistent with the observation-based decomposition of pCO₂ (Supplementary Figure S2). Consequently, the bias in seasonality largely accounts for the observed mismatch in total pCO₂.

Focusing on the differences between the two experiments, the LC effect increases pCO₂ and both of its components ( and ) during winter. In March, increases by 4.3 µatm due to the LC effect, which corresponds to approximately 13% of the seasonal standard deviation in CTRL . The LC effects on are minimal during summer, and this is consistent with the limited changes in vertical mixing, as indicated by little change in TKE and l_mix (Figure 2). Overall, the LC effect slightly reduces the seasonal amplitude of by about 1% compared to CTRL, indicating that the thermal contribution is small.

The also contributes to a wintertime increase in pCO₂. Among the factors that influence - namely DIC, salinity, and alkalinity - DIC has been identified as the primary driver of its seasonal variability in the Bering Sea (Gallego et al., 2018). In March, increases by 8.5 µatm, which is substantial given that its temporal standard deviation in the CTRL simulation is 17.12 µatm. As a result, the LC effect amplifies the seasonal amplitude of by 14% compared to CTRL.

The LC simulation exhibits that a large portion of the wintertime increase in pCO₂ is explained by the . Typically, intensified vertical mixing leads and to offset each other (e.g., Mahadevan et al., 2004); however, our results show both components amplify the wintertime pCO₂ increase. This atypical response is attributed to the Bering Sea’s vertical structure. In the following sections, we examine the vertical structure of temperature (thermal process) and DIC (non-thermal process), with particular focus on the winter season.

3.2 Vertical temperature profile

The Bering Sea is characterized by a temperature inversion (Miura et al., 2002, 2003; Ueno and Yasuda, 2005; Johnson and Stabeno, 2017). This inversion is well captured in the model simulations, which successfully reproduce the seasonal variation within the Bering Sea basin (Figures 4A, B). During winter, a temperature inversion emerges at the surface through surface cooling. In contrast, summertime surface heating suppresses temperature inversion near the surface, with the temperature inversion confined to the subsurface.

Figure 4

Figure 4C illustrates the seasonal variation of the MLD along with the potential temperature difference between the two simulations. Enhanced vertical mixing deepens the MLD and warms the near-surface layer down to approximately 50 m, resulting in a 0.1°C increase in March SST relative to the CTRL simulation. This warming increases wintertime . If the Bering Sea had followed a thermally stratified structure within the reach of the LC effects, intensified winter mixing would decrease . Therefore, the temperature inversion in the Bering Sea plays a pivotal role in regulating .

3.3 Dissolved inorganic carbon

Vertical mixing alters the DIC vertical structure in the Bering Sea, where DIC concentration generally increases with depth (Dubinina et al., 2024; Chen et al., 2014; Keppler et al., 2020). In order to quantify the impact of LC on DIC concentration, we conducted a monthly DIC budget analysis for the Bering Sea. The tendency of DIC is written as

In Equation 4, ADV_DIC represents the horizontal and vertical advection of DIC, MIX_DIC denotes its horizontal and vertical diffusion (the vertical diffusion being more than three orders of magnitude larger than the horizontal diffusion), BIO_DIC accounts for biological sources and sinks via inorganic and organic processes, and represents the air–sea CO₂ flux at the surface layer (0 to 2 m).

The DIC tendency has a seasonal variability within the MLD, increasing in winter and decreasing in summer in both experiments (Figures 5A, B), which is closely associated with the seasonal pattern of (Figure 3). Among the DIC budget, MIX_DIC is the key driver of this seasonality within the MLD, showing a positive contribution during winter when intensified turbulent mixing promotes upward DIC entrainment (Figures 5B, E, H, K). ADV_DIC also influences the DIC tendency, but its contribution is the opposite sign of MIX_DIC within the MLD (Figures 5E, H). BIO_DIC contributes to reducing DIC during the spring; however, its overall influence remains limited compared to MIX_DIC and ADV_DIC (Figures 5E, H, K).

Figure 5

The surface DIC budget is primarily controlled by three terms— , MIX_DIC, and ADV_DIC (Figures 5E, H, N). Between February and September, a DIC increase induced by MIX_DIC is largely compensated by ADV_DIC (Figures 5E, H), with varying seasonally, exhibiting oceanic uptake during winter and outgassing during summer (Figure 5N), balancing the DIC changes driven by physical processes.

The comparison between the two experiments highlights the importance of wintertime MIX_DIC (Figures 5C, F, I, L). In the LC simulation, increased vertical mixing during winter leads to intense upward entrainment from carbon-rich deep water to the surface. Consequently, the DIC supply through MIX_DIC in the LC simulation exceeds that in the CTRL by approximately 0.03 GtC/year within the upper 100 m in February, whereas this difference becomes negligible (−0.0002 GtC/year) in August (Figure 5I). The wintertime increase is mitigated by ADV_DIC and BIO_DIC (Figures 5F, L). ADV_DIC dominates the wintertime reduction in DIC, whereas BIO_DIC contributes a relatively small decrease in spring.

At the surface layer, the LC parameterization increases both vertical mixing (MIX_DIC) and advection (ADV_DIC) of DIC during winter, deviating from the typical compensatory relationship between these two terms (Figures 5F, I). In response to LC, wintertime CO₂ uptake decreases (Figure 5O), which helps to close the surface DIC budget. In the LC simulation, the surface ADV_DIC, responsible for the wintertime reduction of DIC, is weakened (Figure 5F) due to reduced horizontal outflow from the basin (Supplementary Figure S3), contributing to the increase in pCO₂. Therefore, the combination of enhanced supply through MIX_DIC and weakened decrease through ADV_DIC increases surface DIC, which reduces wintertime CO₂ uptake in the LC simulation relative to the CTRL (Figures 5F, I, O). In contrast, differences between the two simulations are considerably smaller in summer than in winter (Figure 5O). The suppressed CO₂ uptake persists except during summer, leading to a net decrease in annual CO₂ uptake (Figure 5O).

The LC response on pCO₂ in the Bering Sea exhibits a seasonal asymmetry. During winter, enhanced carbon supply elevates pCO₂, which suppresses oceanic CO₂ uptake. Increasing pCO₂ is supported by surface warming, but its effect is minor compared to DIC entrainment. In contrast with the winter response, the summer response shows small differences between the two simulations, indicating the limited impact of LC during this period. Consequently, the LC effect is important in winter, when enhanced DIC entrainment associated with non-thermal processes dominates the air–sea CO₂ exchange.

4 Summary and discussion

This study evaluates the impact of LC parameterization on vertical mixing and the carbon cycle in the Bering Sea basin using a physical–biogeochemical coupled ocean model. In the model experiments, LC is implemented to enhance turbulent mixing near the surface, and its impact is pronounced during winter. In this season, the Bering Sea can be characterized by a temperature inversion layer, with surface waters cooler than the underlying layers. Under such conditions, enhanced vertical mixing by LC raises SST, which in turn increases pCO₂. Simultaneously, the deepened mixed layer driven by intensified turbulence facilitates the upward entrainment of carbon-rich subsurface water. As a result, surface ocean pCO₂ increases during winter. This behavior contrasts with many other ocean regions, where enhanced vertical mixing typically cools the surface and reduces pCO₂, partially offsetting the upward entrainment of carbon-rich water (Mahadevan et al., 2011).

To evaluate the contribution of LC to the carbon cycle and the seasonal variability of pCO₂ in the Bering Sea, we decompose the LC-induced changes in pCO₂ into thermal and non-thermal components. The LC effect slightly increases the thermal component of pCO₂ throughout the year, resulting in a minor (1.4 µatm) reduction in its seasonal amplitude. A large portion of the wintertime pCO₂ increase comes from the non-thermal component, which is associated with enhanced upward entrainment of DIC. Specifically, the non-thermal effect of LC amplifies the seasonal amplitude of pCO₂ by 7.2 µatm. This increased seasonality brought by LC helps narrow the gap between the model results and observations.

In summary, parameterizing LC and applying it to a physical-biogeochemical coupled ocean model improves the seasonal variability of non-thermal effects. The existence of temperature inversion is vital for the clear expression of both thermal and non-thermal effects of LC. If a wintertime temperature inversion does not develop, LC leads to a decrease in SST, which offsets the non-thermal increase in pCO₂. Thus, the wintertime temperature inversion prevents the suppression of the LC-induced non-thermal amplification of pCO₂ in the Bering Sea basin.

In our study, both λ and Γ are prescribed as constant values, which is a reasonable assumption based on the previous studies. For example, Noh et al. (2016) showed that ocean general circulation model outputs are only weakly sensitive to the prescribed Γ and λ within typical observational ranges. When La is sufficiently small to ensure a large Γ, the LC-induced changes in MLD and SST remain largely unaffected by Γ variations, and the sensitivity to λ is also weak, with λ-induced MLD differences accounting for only about 6–7% of the difference between simulations with and without LC. Although the expected overall mean changes resulting from varied values for λ and Γ remain small, their cumulative biogeochemical influence over longer timescales may become non-negligible, necessitating further improvements in parameterization. Therefore, future work should investigate the potential effects of time-varying λ and Γ to better represent turbulent mixing processes and their associated biogeochemical responses, particularly those influencing the oceanic carbon cycle.

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