The Central Baltic Air-Sea Exchange Experiment (CenBASE; EMB 295) was conducted in summer 2022, immediately after the phytoplankton bloom season, to capture strong air–sea gas exchange signals (Parard et al., 2016; Bittig et al., 2024). The research cruise on the R/V Elisabeth Mann Borgese (EMB) departed from Rostock, Germany, on 2 July and returned on 18 July, with the primary study area located in the Gotland Basin (Fig. 1A).

Eddy covariance (EC) CO2 flux observations (Sect. 2.2) and the 3He/SF6 dual-tracer experiment (see Appendix A1) were performed simultaneously to determine gas transfer velocities, representing the second successful joint deployment of these two approaches after GasEx-98 (Ho and Wanninkhof, 2016; McGillis et al., 2001). Surfactant samples were collected from both the microlayer and underlying water (see Appendix A2). Wave parameters were extracted from the ERA5 hourly reanalysis data product (0.5° × 0.5°) (Hersbach et al., 2020) based on the cruise track's spatiotemporal coordinates. Additional measurements included fCO2, sea surface properties, and meteorological variables to support the analysis.

The EC technique allows for direct measurements of air–sea CO2 flux using the following equation: 2F=ρw′c′‾ where ρ is the mean molar density of dry air (in molem-3), w is the vertical wind velocity (in ms-1), and c is the dry air mole fraction of CO2 (in ppm or µmolmol-1). The primes denote the fluctuations from the mean, and the overbar indicates time averaging. Due to the dynamic nature of the marginal sea environment, a 10 min averaging interval was chosen, shorter than the 20–30 min typically used in the open ocean (e.g., Blomquist et al., 2017). The CO2 transfer velocity (K660_CO2) is derived by combining Eqs. (1) and (2). The EC momentum flux is similarly calculated as ρw′u′‾, where u is the horizontal wind component. The friction velocity (u∗) is then derived as the square root of the momentum flux divided by the air density.

Most components of the EC system were mounted on a custom-built tower at the bow of the ship to minimize the flow distortion (Fig. 1B). The tower extended 5 m above the deck, reaching a height of 14 m above mean sea level (a m.s.l.). A three-dimensional (3D) sonic anemometer (CSAT3B, Campbell Scientific) was installed on the starboard arm to measure the wind fluctuations, with a backup unit on the port side (CSAT3). An Inertial Measurement Unit (IMU, SBG Systems), housed in a meteorological box at the top of the tower, recorded ship motion. The IMU was positioned 66 cm from the starboard sonic and 173 cm aft of it. CO2 fluctuations were measured using a LI-7200 gas analyzer. The sampled air was dried with a Nafion dryer operating in “reflux” mode (Perma Pure LLC). Air was drawn from the port-side inlet through a ∼ 10 m Teflon tube (3/8” inner diameter) at a stable flow rate of 33.2 ± 0.3 Lmin-1, which results in turbulent flow within the tube. The 20 Hz signal from the sonic anemometer, IMU, and LI-7200 was logged by a datalogger (CR6, Campbell Scientific).

Data processing and quality control procedures followed those described in Dong et al. (2021). Briefly, motion corrections were applied to the wind (Edson et al., 1998; Miller et al., 2008) and CO2 signals (Miller et al., 2010) to remove contamination from ship motion. A nitrogen puff test revealed a 0.3 s e-folding response time, which is used to correct the high-frequency attenuation (Blomquist et al., 2014). The time delay (∼ 2.5 s) between the inlet and the gas analyzer was assessed via the maximum covariance method. Flow distortion was minimized by mounting the EC tower arms beyond the ship's hull.

The partial pressure of CO2 in surface water was measured at 1 min intervals using the Mobile Equilibrator Sensor System (MESS) paired with two off-axis integrated cavity output laser spectrometers (oa-ICOS, Los Gatos Instruments) (Sabbaghzadeh et al., 2021). Seawater was continuously drawn from the ship's inlet at a depth of ∼ 3.3 m. Atmospheric CO2 was measured daily using an air inlet mounted on the ship's foremast at 13.5 ma.m.s.l. These air CO2 data are compared to the absolute CO2 values measured by the EC gas analyzer (LI-7200, LI-COR, Inc.) to generate the 10 min time series of atmospheric CO2. Sensor calibration was performed almost daily using standard gases from the Central Analytical Laboratories of the European Integrated Carbon Observation System (ICOS RI). Mean wind measurements were obtained from a sonic anemometer mounted 17 ma.m.s.l. on the ship's foremast to minimize flow distortion (O'Sullivan et al., 2013). Residual distortion was corrected using the ERA5 reanalysis wind product and nearby station records (see Appendix A3). Atmospheric pressure and temperature at ∼ 13.5 ma.m.s.l. were recorded by the onboard weather station. Surface seawater temperature and salinity were monitored by the ship's underway system and calibrated against CTD (conductivity, temperature, and depth) casts. A spar buoy equipped with cameras and sensors for temperature, salinity, and dissolved oxygen was deployed at several stations to characterize upper-ocean bubble and water column dynamics.

In addition, EC air–sea CO2 flux observations from previous open-ocean cruises (Yang et al., 2022) are also used for comparison with the CenBASE results. Wave parameters were extracted from the ERA5 analysis wave product according to these open-ocean EC cruise tracks (see Yang et al., 2022) and the CenBASE cruise. The COARE model is used to estimate the bulk u∗ (Edson et al., 2013). For the open-ocean scenario, environmental variables from the corresponding cruises are used as inputs to the COARE model (Yang et al., 2022). The environmental parameters observed during the CenBASE cruise are used to estimate the Baltic Sea u∗ in the COARE model.

During CenBASE, winds predominantly originated from the west to north sector (Fig. 2A), with an effective fetch of approximately 50–300 km in the main study area (Fig. A1, Appendix). The wind speed ranged from 1 to 12 ms-1 (Fig. 2A). Water depth across the central Baltic Sea study site ranged from ∼ 50 to 250 m. Surface water was generally warmer than the overlying air (Fig. 2B), resulting in an unstable boundary layer. Surface salinity remained consistent at approximately 7.3 throughout the study region (Fig. 2C). The cruise took place shortly after a summer phytoplankton bloom, resulting in remarkably low sea surface fCO2 (∼ 120 µatm; Fig. 2D). Atmospheric fCO2 remained constant at ∼ 403 µatm, creating a strong air–sea gradient (ΔfCO2≈ -280 µatm on average; Fig. 2D) that generated strong ocean CO2 uptake signals.

Surface microlayer surfactant activity (SA), expressed as Triton-X-100 equivalents, was relatively constant at 0.54 ± 0.08 mgL-1 (Fig. 2E), significantly higher than typical open-ocean values (0.1–0.2 mgL-1; Mustaffa et al., 2020; Sabbaghzadeh et al., 2017). Modeled significant wave height (Hs) remained below 1.5 m (Fig. 2E), lower than expected for comparable wind speeds in the open ocean (Fig. A2). Bulk CO2 fluxes estimated from the measured ΔfCO2 and an open-ocean dual-tracer K660 parameterisation (Ho et al., 2006) were higher than observed EC fluxes under high wind speeds and lower than observed EC fluxes under low wind speeds (Figs. 2F and A3). During the tracer-tracking period (8–14 July), frequent ship heading changes reduced EC flux quality, leading to most valid EC measurements being obtained from outside this period (Fig. 2F, light-gray shading). Nevertheless, as both EC and dual-tracer were collected in the same study area, the K from both methods can be reasonably considered simultaneous measurements.

The friction velocity is a key parameter characterizing near-surface turbulence. Observed values of u∗ from EC momentum fluxes during CenBASE were 10 % higher than modelled open ocean u∗ at the same wind speeds (Fig. 3A), likely reflecting fetch-related differences. The wave field in the central Baltic Sea is much younger than in the open ocean, with wave age ∼ 60 % lower at the same wind speed (Fig. 3B). The waves are shorter and steeper than in the open ocean (Fig. A2). This wave field enhances sea surface roughness and elevates u∗ relative to the open sea. u∗ predicted by the COARE3.6 model, when forced with observed environmental and extracted wave parameters during CenBASE, broadly agrees with measurements (Fig. 3A). This suggests that the COARE model remains applicable in fetch-limited marine environments when wave information is included, despite being developed primarily from open-ocean observations (Edson et al., 2013). Given that u∗ is an indicator of surface wind-induced turbulence, this elevated u∗ is expected to enhance CO2 transfer velocity (see Sect. 3.4).

The CO2 transfer velocity (K660_CO2) was derived from EC air–sea CO2 flux and ΔfCO2 observations using Eq. (1). After quality control, 301 valid 10 min K660_CO2 data points were retained (Fig. 4). The large |ΔfCO2| (∼ 280 µatm) ensured accurate K660_CO2 derivations, with hourly uncertainties of ∼ 20 % (Fig. A4), substantially lower than typical cruise-based uncertainties (e.g., ∼ 30 % during the HiWinGS cruise; Blomquist et al., 2017). The cool skin correction (reduces ΔfCO2 by ∼ 2 µatm; Woolf et al., 2016) is negligible relative to the observed ΔfCO2 and was therefore ignored. K660 from the DT experiment is summarized in Appendix A1.

The EC dataset offers high temporal resolution (∼ 10 min), enabling investigation of small-scale processes influencing gas exchange. The EC observations span a broad range of wind speeds (1 to 12 ms-1, Fig. 4A), providing a robust constraint of K660_CO2 under low-to-moderate wind conditions. In contrast, DT-derived K660 represents daily averages, in which short-term extremes (i.e., low and high wind conditions) are smoothed, resulting in seven observations concentrated at U10N of 5–9 ms-1 (Fig. 4A). Within this wind range, DT-and EC-derived K660 values are in good agreement, with the former on average being only slightly (∼ 8 %) lower than the latter (Fig. 4).

DT-derived K660 values during CenBASE also generally agree with the open-ocean DT-based parameterisation of Ho et al. (2006) under equivalent wind speeds (orange dashed line in Fig. 4A), with the former on average being only ∼ 7 % lower than the latter. However, EC-derived K660_CO2 values deviate systematically from this open-ocean relationship (Ho et al., 2006), being higher at low wind speeds (1–7 ms-1, +12 %) and lower at high wind speeds (7–12 ms-1, -18 %) (Fig. 4A). This divergence does not contradict the agreement between the DT-and EC-based K660 observations, as this agreement falls within the 5–9 ms-1 range (where the DT data concentrate). Fitting K660_CO2 with U10N reveals a weaker wind speed dependence than the open ocean DT-based parameterisation (Fig. 4A). It is worth noting that including a constant term in the K660_CO2-U10N fitting function (i.e., K660_CO2=aU10Nb+c, R2 = 0.48) improves the fit compared to a purely power-law form (i.e., K660_CO2=aU10Nb, R2 = 0.42) (Fig. A5), suggesting a non-zero CO2 exchange (∼ 3 cmh-1) under calm conditions. This is unsurprising, since the chemical enhancement (Cole and Caraco, 1998; Fairall et al., 2022; Yang et al., 2022) and likely buoyancy flux sustain CO2 transfer at low wind speeds (McGillis et al., 2004; Wanninkhof et al., 2009).

Notably, the DT data collected during CenBASE provide only limited constraints at wind speeds below 5 ms-1 and above 9 ms-1, and the K660-U10N relationship derived from these data is sensitive to the chosen functional form (Fig. A5). Moreover, the DT-based open-ocean K660 estimates are lower than the EC CO2-based estimates across the wind speed range observed during CenBASE (Fig. 4A), likely reflecting differences in methodology. Because the CenBASE DT data are interpreted elsewhere (Dobashi et al., 2026), and, more importantly, because the EC measurements resolve finer-scale processes and ensure methodological consistency, the subsequent section focuses on comparing EC CO2 observations in the Baltic Sea with those in the open ocean.

The EC-derived K660_CO2 during CenBASE was generally lower than open-ocean EC CO2 transfer velocities (Yang et al., 2022; 2024) (Fig. 4A and B), indicating a substantial suppression of CO2 exchange in the Baltic Sea. To explain this reduction, we partition the total gas transfer velocity (K660) into interfacial (Ki660) and bubble-mediated (Kb660) components (i.e., K660=Ki660+Kb660). Ki660 is primarily driven by wind stress or u∗, whereas Kb depends on both the wind forcing and sea state. A machine-learning analysis of 15 open ocean datasets identified significant wave height (Hs, including both windsea and swell) as a key proxy for sea state that strongly affects K660_CO2 (Yang et al., 2024). Based on this analysis, Yang et al. (2024) express the K660 as (Fig. 4B, black line): 3K660=Ki660+Kb660=55u∗+10u∗Hs Because Kb depends on solubility, normalizing it using the Schmidt number (i.e., converting Kb to Kb660) may not be strictly appropriate. However, the sensitivities of the CO2 transfer velocity to Sc-1/2 and α-1 are nearly identical (see Fig. A1 in Dong et al., 2025). Therefore, normalization using either Sc or α produces almost the same gas transfer velocities. For simplicity and consistency, we adopt the Sc-1/2-based normalization in this study.

The observed EC K660 during CenBASE averaged 14.9 cmh-1. To compare this value with open-ocean conditions at equivalent wind speeds, we apply the wind-speed observations from the CenBASE cruise (i.e., wind speed values shown in Fig. 4A) to Eq. (3) to estimate open-ocean K660, yielding average values of Ki660 = 15.1 cmh-1, Kb660 = 7.0 cmh-1, and K660 = 22.1 cmh-1. This means that the observed K660 during CenBASE was 33 % (7.2 cmh-1) lower than the open-ocean K660 estimate.

Equation (3) implies a linear dependence of K660_CO2 on u∗. Regression of the observed K660_CO2 against u∗ indeed yields an approximately linear relationship (Fig. 4B), consistent with prior findings at low-to-moderate winds (Landwehr et al., 2018; Yang et al., 2022). Additionally, the K660_CO2-u∗ fit (R2 = 0.59) outperforms the K660_CO2-U10N fit (R2 = 0.48), confirming that u∗ better captures variability in gas transfer velocity than U10N (Jähne et al., 1987; Landwehr et al., 2018; Yang et al., 2022). As shown in Fig. 3A, the observed u∗ during CenBASE was ∼ 10 % higher than open-ocean values under equivalent wind speeds, implying a ∼ 10 % enhancement in K660_CO2 due to fetch-related increases in shear stress (Vickers and Mahrt, 1997). It is important to note that the observed 33 % reduction in K660_CO2 includes this enhancement, suggesting that CO2 exchange was suppressed even more, by ∼ 43 % (9.2 cmh-1) relative to open-ocean conditions.

According to Eq. (3), Kb is linearly dependent on Hs. Due to the limited fetch, the Hs during CenBASE was 57 % lower than in the open ocean at the equivalent u∗ (Fig. 5A, Table 1), and this reduction is expected to cause a comparable decrease in Kb. Using the extracted Hs values from ERA5 for CenBASE, the parameterised Kb660 decreases on average from 7.0 to 4.0 cmh-1, corresponding to an 18 % suppression on the total K660_CO2 (Fig. 5B; Table 1), explaining about half of the observed suppression during CenBASE.

Surfactants inhibit both interfacial (e.g., Frew, 1997) and bubble-mediated gas exchange (e.g., Woolf, 1993), and their concentrations in the Baltic Sea are substantially higher than in the open ocean. We assume that all residual suppression of K660_CO2 during CenBASE, which cannot be explained by fetch effects, is caused by surfactants. Under this assumption, the residual 25 % suppression (i.e., 5.4 cmh-1; Fig. 5B and Table 1) reflects the impact of elevated surfactant levels. This effect is not captured by the Yang et al. (2024) parameterisation, which is based primarily on open-ocean observations characterized by low surfactant concentrations (Wurl et al., 2011; Fig. A6).

The resulting suppression fraction (sf) is consistent in magnitude with previous field-based estimates (Fig. 6; Mustaffa et al., 2020; Salter et al., 2011; Yang et al., 2021) within uncertainty (see Sect. 3.5). The constrained sf is generally smaller than laboratory-derived values (Fig. 6A), likely due to challenges in extrapolating laboratory conditions to the field. Notably, previous studies report conflicting relationships between sf and surfactant concentration. Some show increasing sf with increasing concentration (Mesarchaki et al., 2015; Pereira et al., 2018; Ribas-Ribas et al., 2018), whereas others identify a threshold concentration above which sf shows little change (Mustaffa et al., 2020; Schmidt and Schneider, 2011) (Fig. 6A). Because surfactant concentrations were nearly constant during CenBASE, we cannot assess this relationship here.

Several studies also show that sf decreases with wind speed (Fig. 6B; Bock et al., 1999; Mesarchaki et al., 2015; Salter et al., 2011; Yang et al., 2021), and the sf constrained here aligns well with these findings, especially those from field observations. Fitting sf as a function of u∗ yields a correction factor (i.e., 1-sf) that can be applied to Eq. (3) to account for surfactant effects, generating the updated parameterisation: 4K660=(1-0.38e-1.25u∗)(55u∗+10u∗Hs) This parameterisation reflects conditions during CenBASE, where the surfactant concentration was relatively stable at ∼ 0.5 mgL-1. If a SA concentration-dependent sf is needed, one option is the published linear relationship sf=0.32SA+0.025 (Pereira et al., 2018). However, this formulation maybe physically inconsistent because it predicts a non-zero suppression even when SA=0, whereas sf should theoretically approach zero in surfactant-free conditions. To address this, we re-evaluated the same dataset used in the original study (Pereira et al., 2018) and fitted a proportional relationship that passes through the origin: sf=0.38SA. The goodness-of-fit (R2 = 0.49) is only marginally lower than the original relationship (0.51, Pereira et al., 2018), indicating that the proportional form captures the data nearly as well while remaining physically realistic. For the mean CenBASE surfactant concentration (SA = 0.54 mgL-1), this relationship yields sf = 0.21. Applying this SA-dependent suppression to the wind-dependent correction in Eq. (4) results in the combined parameterisation: 5K660=1-0.38SA0.79(1-0.38e-1.25u∗)(55u∗+10u∗Hs) Previous studies have suggested that water-side convection may influence gas exchange in both open-ocean (McGillis et al., 2004) and Baltic conditions (Rutgersson and Smedman, 2010). During CenBASE, a small spar buoy recorded oxygen, temperature, and salinity at depths of 1.2 and 2.9 m. Dissolved oxygen exhibited small-scale variability with similar patterns at both depths (Fig. A7), indicating coherent near-surface structure over 5–20 m scales, likely driven by wind-induced turbulence intermittently exposing surface patches to the atmosphere. In contrast, no corresponding variability was observed in temperature or salinity (Fig. A7), suggesting that convection played a negligible role in gas exchange under the observed conditions. This supports our assumption that the deviation in K660_CO2 between the Baltic Sea and the open ocean can be fully attributed to the combined effects of limited fetch and elevated surfactant levels.

The quantification results shown above are not free from uncertainty. First, we use the Kb∝u∗Hs relationship for the bubble component, which fits best with the EC-based K660_CO2 observations (Yang et al., 2024). However, alternative formulations have been proposed, such as Kb∝u∗1.67Hs0.67 (Deike and Melville, 2018) and Kb∝u∗0.9Hs0.9 (Brumer et al., 2017a; Fairall et al., 2022). These different exponents indicate that the relative contributions of u∗ and Hs to gas exchange may vary slightly, introducing parameterisation uncertainty. Yang et al. (2024) reported that the R2 for the fit (i.e., Eq. 3) is ∼ 0.75, indicating that ∼ 25 % of the variance in the observed K remains unexplained by the parameterisation. We therefore assign a 25 % uncertainty to the parameterisation given in Eq. (3). This uncertainty propagates through the suppression estimates. For instance, the uncertainty in the u∗-related K enhancement estimate is approximately 0.6 cmh-1 (i.e., 2.2 cmh-1 × 25 %). The suppression analysis uses Hs data derived from ERA5 reanalysis, which likely carries an uncertainty of about 30 % in the Baltic Sea (Giudici et al., 2023). Consequently, the uncertainty in the Hs-related suppression estimate is ∼ 1.6 cmh-1 (i.e., (4.0×25%)2+(4.0×30%)2 cmh-1). The uncertainty associated with the surfactant-related suppression is substantially larger because it is not directly determined but inferred as a residual after accounting for other components. Combining the propagated uncertainties from the parameterised total K and from two fetch-induced suppression estimates yields an uncertainty of 5.8 cmh-1 (i.e., (22.1×25%)2+0.62+1.62 cmh-1), corresponding to approximately 110 % of the estimated suppression value (Table 1).

Furthermore, it is worth noting that the two corrections in Eq. (5) (i.e., the SA-sf correction and the u∗-SA correction) are implicitly assumed to be independent. However, potential interactions between u∗-dependent SA variation and the SA influence on sf may introduce additional uncertainty into Eq. (5).

The CenBASE cruise took place during the summer bloom (July), when chlorophyll a (Chl a) is high (Pitarch et al., 2016) and fCO2w is strongly reduced by primary productivity (e.g., Parard et al., 2016; Bittig et al., 2024). To upscale these results, we adopt a fCO2w product from Bittig et al. (2024) to examine how fetch and surfactants shape the climatological CO2 flux of the Baltic Sea. This climatological fCO2w product is derived by combining observations and model patterns. The fCO2w indicates a CO2 sink in summer and a source in winter (Fig. 7A). However, weaker summer winds and stronger winter winds suggest that the magnitudes of uptake and outgassing may be similar. Seasonal cycles of u∗ and Hs closely follow wind speed (Fig. 7B), while Chl a peaks during the spring-summer bloom and remains low in winter (Fig. 7C). We estimate monthly surfactant concentrations by scaling the July CenBASE value (0.54 mgL-1) with monthly Chl a concentrations following the idea of Wurl et al. (2011) and using the formula 0.54 × Chl a/Chl aJuly mgL-1. Equation (5) is then used to compute the corresponding suppression of gas transfer, 1-1-0.38SA0.79(1-0.38e-1.25u∗). The resulting sf reflects the seasonal Chl a cycle and modulations by u∗, yielding ∼ 25 % suppression in summer and ∼ 10 % in winter (Fig. 7C). However, surfactant concentrations are not solely determined by Chl a; for example, humic acids also act as surfactants (e.g., Klavins and Purmalis, 2010), and the Baltic Sea is known for elevated humic acid levels due to significant terrestrial inputs (Hammer et al., 2017). Therefore, estimating surfactant levels solely from Chl a has inherent limitations.

We estimate K660 using three parameterisation schemes: the conventional open ocean DT-based U10N formulation (Ho et al., 2006), the open ocean EC CO2-based u∗-Hs formulation (Eq. 3; Yang et al., 2024), and the Baltic Sea EC CO2-based u∗-Hs-SA formulation (Eq. 5). Although all these schemes reproduce similar seasonal patterns, their magnitudes differ (Fig. 7D), reflecting sea state and surfactant effects as well as methodological differences. The u∗-Hs-SA parameterisation yields lower values than the u∗-Hs scheme because it incorporates surfactant-induced suppression from the surfactant. This suppression is especially strong in summer when SA concentrations are highest, leading to the largest discrepancies between the estimated climatological K660 from the u∗-Hs-SA and the u∗-Hs schemes. As shown in Sect. 3.4, K660 during CenBASE has been reduced by 33 %. Notably, this reduction is relative to open-ocean EC-based estimates. However, compared with the open ocean DT-based U10N formulation, however, this reduction occurs only at wind speeds above ∼ 7 ms-1. At lower wind speeds, the EC-based K660 observations during CenBASE exceed the DT-based estimates (Fig. 4A). Because climatological Baltic Sea wind speeds are typically below 7 ms-1 in Spring, Summer, and Autumn (Fig. 7A), the u∗-Hs-SA parameterisation produces higher K660 than the U10N formulation in these seasons. In winter, despite higher wind speeds, the u∗-Hs-SA scheme still exceeds the U10N-based estimates due to modulation of the surfactants. The SA concentration in winter is estimated to be three times lower than during the summer CenBASE cruise (Fig. 7C), resulting in much weaker suppression.

Overall, relative to the conventional U10N formulation (Ho et al., 2006), the u∗-Hs-SA parameterisation increases K660 in all seasons, enhancing both summer CO2 uptake by ∼ 10 % and winter outgassing by ∼ 30 %, and amplifying the seasonal cycle by ∼ 40 %. These opposing seasonal effects are expected to largely compensate, resulting in only a modest change in the annual mean CO2 flux.