Wind Speed and Sea State Dependencies of Air-Sea Gas Transfer: Results From the High Wind Speed Gas Exchange Study (HiWinGS)

Abstract

A variety of physical mechanisms are jointly responsible for facilitating air-sea gas transfer through turbulent processes at the atmosphere-ocean interface. The nature and relative importance of these mechanisms evolves with increasing wind speed. Theoretical and modeling approaches are advancing, but the limited quantity of observational data at high wind speeds hinders the assessment of these efforts. The HiWinGS project successfully measured gas transfer coefficients (k₆₆₀) with coincident wave statistics under conditions with hourly mean wind speeds up to 24 m s⁻¹ and significant wave heights to 8 m. Measurements of k₆₆₀ for carbon dioxide (CO₂) and dimethylsulfide (DMS) show an increasing trend with respect to 10 m neutral wind speed (U_10N), following a power law relationship of the form: and . Among seven high wind speed events, CO₂ transfer responded to the intensity of wave breaking, which depended on both wind speed and sea state in a complex manner, with increasing as the wind sea approaches full development. A similar response is not observed for DMS. These results confirm the importance of breaking waves and bubble injection mechanisms in facilitating CO₂ transfer. A modified version of the Coupled Ocean-Atmosphere Response Experiment Gas transfer algorithm (COAREG ver. 3.5), incorporating a sea state-dependent calculation of bubble-mediated transfer, successfully reproduces the mean trend in observed k₆₆₀ with wind speed for both gases. Significant suppression of gas transfer by large waves was not observed during HiWinGS, in contrast to results from two prior field programs.

Key Points

• Large data set of coincident gas transfer and wave measurements under high wind conditions
• COAREG bulk gas transfer model simulates observed gas transfer coefficients
• No evidence for significant suppression of gas transfer in the presence of large waves

1 Introduction

Air-sea exchange is an important process in the global budgets of many trace gases, with significant implications for climate, biogeochemical cycles, and pollution transport. Quantifying and modeling carbon dioxide (CO₂) exchange, for example, has been the focus of theoretical, laboratory, and field investigations for at least four decades. The current state of understanding and the remaining challenges are summarized in a review by Wanninkhof et al. (2009).

Modeling air-sea gas fluxes requires an accurate description of the air-sea concentration gradient and the transfer rate coefficient (transfer velocity). The gradient in atmospheric surface layer and surface seawater gas concentration is the driving force for the flux. The transfer coefficient specifies the effects of physical diffusive mechanisms that facilitate gas transfer. Gas concentrations can be estimated from global gridded climatological extrapolations based on historical data sets (e.g., Kettle et al., 1999; Takahashi et al., 2009) or computed with output from ocean biogeochemical models and atmospheric chemical transport models. The transfer coefficient can be represented as a simple empirical function of the primary forcing factor, wind speed, based on laboratory or field measurements, or computed from a parametric description of the physical mechanisms utilizing a broader set of primary forcing factors. Error in the flux estimate arises from limitations in the models and uncertainties in the bulk parameters (see Signorini & McClain, 2009). The analysis presented in this paper focuses on the nature and significance of physical forcing factors and on improvements to the parametric models that specify the transfer coefficient.

In the simplest terms, air-sea flux of a conserved (i.e., nonreactive) gas may be described as a product of the transfer coefficient and concentration gradient:

(1)

where k, without subscript, is the total transfer coefficient and is the departure of bulk concentrations from equilibrium conditions defined by dimensionless solubility: . k is conveniently conceptualized as the reciprocal of total transfer resistance over the distance defined by the reference depth of C_water to the reference height for C_air. For gases of low to intermediate solubility, the majority of the transfer resistance is localized in the water-side surface microlayer. By definition, when and the bulk concentration gradient is at saturation. The sign of F_c is determined by , where a positive flux is out of the ocean. Other forms of equation 1 are common, depending on the units for F_c and . For CO₂ fluxes at sea, partial pressure or fugacity units are widely used and , where is solubility in mol m⁻³ Pa⁻¹, in SI units. Typical units for k are cm h⁻¹, which we assume throughout this discussion.

One complication to equation 1 is the asymmetry in gas exchange resulting from bubble injection by breaking waves (Keeling, 1993; Woolf & Thorpe, 1991). Submerged bubbles are subjected to increased hydrostatic pressure, driving additional gas transfer into the liquid phase. The smallest bubbles are transported to the greatest depth and may completely dissolve. Submerged bubbles therefore serve to enhance gas invasion and suppress evasion. The effect is most significant for low-solubility gases, becoming the major component of gas flux when is close to equilibrium, leading to, for example, supersaturation of N₂ and Ar (Emerson & Bushinsky, 2016; McNeil & D'Asaro, 2007). The following form of equation 1 has been proposed to accommodate the invasive flux from bubble dissolution (Woolf, 1997; Woolf & Thorpe, 1991):

(2)

where is the fractional equilibrium supersaturation level due to dissolving bubbles. This adjustment for supersaturation is gas species specific and necessarily dependent on factors such as air volume injection rate, bubble size distribution and lifetimes, injection depth, etc., but is more conveniently parameterized as a function of wind speed.

The importance of to CO₂ flux is somewhat uncertain. The model of Woolf and Thorpe (1991) predicts that does not rise to 0.01 until wind speeds reach 49 m s⁻¹. The study by Liang et al. (2013) looks at the issue in greater detail using coupled LES turbulence and bubble population models, but is focused on very low-solubility gases (N₂, Ar). Their estimates of are considerably larger than Woolf and Thorpe (1991), but may be an overestimate because the model omits consideration of gas transfer equilibrium in bubbles. Nevertheless, based on their estimates, if is as large as 0.005 (0.5%) at m s⁻¹ and CO₂ = 20 μAtm, the contribution of supersaturation effects would yield a 10% increase in total flux, decreasing proportionally for larger values of CO₂. This may be geophysically significant in regions where CO₂ is close to equilibrium, but with current measurement technology it would be a challenge to resolve fluxes to better than 10% precision at high wind speeds. Therefore, we will not consider the supersaturation effect in this report, except to note that it is very important for highly insoluble gases and a necessary component in a universal gas transfer model.

In physical gas transfer models, the total transfer coefficient, k, is conveniently separated into components representing turbulent-diffusive transport on the air-side and water-side of the interface as a two-layer model of series resistances (after Liss & Slater, 1974):

(3)

where is approximately the same for all gases but exhibits a strong dependence on gas solubility and diffusivity in seawater. The water-side resistance, , is by far the largest term for sparingly soluble gases. is the major fraction of total resistance for highly soluble gases.

is further separated into interfacial and bubble-mediated mechanisms, each with a different functional dependence on the primary physical forcing factors. Because these resistances are in parallel, the transfer coefficients sum directly.

(4)

The water-side interfacial component, , accounts for the effects of near-surface turbulence from tangential wind stress or cool-skin buoyancy effects, and the current understanding of these mechanisms is reasonably well-established (e.g., Fairall et al., 2000; Soloviev, 2007; Soloviev & Schluessel, 1994). k_b quantifies the rate of gas transfer between injected bubbles and bulk seawater. The details of bubble-mediated transfer in breaking waves are more complex, but the general concepts have been described. Physical characteristics such as the air volume injection rate, bubble size distribution, bubble plume density, penetration depth, surfactant effects (i.e., “clean” or “dirty” bubbles) and gas solubility all influence the net transfer rate between injected bubbles and bulk seawater. Several historical publications present a review of the issues (e.g., Keeling, 1993; Memery & Merlivat, 1986; Woolf, 1993, 1997; Woolf et al., 2007). Other mechanisms could be included in the specification of , for example, to account for the near-surface turbulence effects of the breaking wave and rising bubble plume (Asher & Wanninkhof, 1995; Asher et al., 2002; Monahan & Spillane, 1984; Soloviev, 2007).

A purely physical algorithm encompassing all transfer mechanisms related to wave breaking is not currently feasible. Many of these processes are very difficult to study in the open ocean and many critical quantities and dependencies are unknown. The current approach is empirical modeling of individual transfer mechanisms in terms of parameters closely related to wave breaking, such as whitecap fraction, wind speed, friction velocity or turbulent energy dissipation.

2 Project Details

2.1 Experimental Design

The HiWinGS project was specifically conceived to address the paucity of direct gas transfer observations under high wind speed conditions. The physical mechanisms of air-sea gas exchange, momentum transfer, and heat transfer evolve with increasing wind speed and with the development of breaking waves. A variety of theoretical frameworks and parameterizations exist to describe the physical mechanisms of air-sea interaction, but very few direct field observations are available to validate these approaches at high wind speeds. The principal objective of HiWinGS was to deploy direct measurements of trace gas, heat, and momentum fluxes together with a suite of wave physics observations under extreme weather conditions. In this respect, the goals are similar to those of the 2008 Southern Ocean Gas Exchange experiment (SO GasEx, Ho et al., 2011) but with an emphasis on maximizing the quantity and quality of direct eddy covariance measurements. The HiWinGS experimental design highlights the value of simultaneous flux measurements for trace gases spanning a broad solubility range. The relative importance of interfacial and wave breaking transfer mechanisms depends significantly on gas solubility; parallel flux observations of gases such as DMS and CO₂, for example, differentiate between these various mechanisms.

The HiWinGS field operational plan met several objectives: (1) a location with a high frequency of mesoscale and synoptic-scale storm systems with high wind speeds; (2) a region and season with sufficient air-sea gas concentration gradients for measurable fluxes; and (3) a deployment strategy maximizing the time dedicated to simultaneous flux and wave physics observations. The Labrador Sea in October–November 2013 was selected as the optimal compromise of the first two objectives. In the fall season, this region is subject to frequent storms and is a well-known sink for atmospheric CO₂, with CO₂ gradients typically greater than 30 μAtm—a level sufficient to yield 30% precision in the flux measurement over 1 h using a Cavity Ring-Down Spectrometer (CRDS) and air dryer (see Blomquist et al., 2014). Sea surface DMS concentrations are declining in the N Atlantic at this time of year but still sufficient for precise flux observations with the Atmospheric Pressure Ionization Mass Spectrometer (APIMS) (Blomquist et al., 2010).

High quality eddy covariance flux measurements require the ship to remain hove-to, bow-to-wind. The wave physics measurements utilized drifting buoys. Therefore, to meet the third objective, ship operations focused on identifying a location of maximum predicted wind speeds in an approaching weather system, positioning the ship ahead of the storm, deploying the wave measurement buoys, and remaining hove-to throughout the event while drifting with the buoys. The buoys were recovered in calm periods between storms before transit to the location of the next forecast wind event.

Convenient temporal spacing between storms contributed to the success of this approach, and a series of seven stations were occupied for intensive observations following a southwesterly course toward a final destination at Woods Hole, MA. Figure 1 shows a map of the cruise track, indicating the location of each station and the sea surface temperature (SST) along the track. Appendix Appendix A presents a detailed summary of conditions at each station throughout the cruise.

Figure 1

Cruise track from Nuuk, Greenland to Woods Hole, MA, showing locations of intensive observation Stations 1–7 and hourly mean sea surface temperature.

2.2 CO₂ and DMS Flux Methods

Flux methods for CO₂ with the CRDS and for DMS using the APIMS have been detailed in prior publications and will not be reviewed here (see Blomquist et al., 2010, 2014). Both instruments incorporate a Nafion air dryer (PD-200T-24-SS, Perma Pure LLC, Toms River, NJ) to remove water vapor interferences and eliminate the need for density corrections (Webb et al., 1980). A closed-path LI-COR infrared gas analyzer (model LI-7200) with a Nafion air dryer was used for duplicate CO₂ flux measurements. Results for the LI-7200 were comparable to the CRDS, but with a lower flux detection limit and reduced precision. These results will not be discussed further in this report. A future publication is planned to analyze CO₂ flux methods employed during HiWinGS.

pCO₂ measurements were conducted by the Ocean Carbon group at NOAA Pacific Marine Environmental Laboratory (PMEL) using methods described by Wanninkhof and Thoning (1993) and Feely et al. (1993). Seawater was sampled from the ship's clean distribution line from a depth of 5 m and, for computation of CO₂, the air sample was drawn from the bow tower. Partial pressures were further corrected to fugacity. A comprehensive overview of PMEL ocean carbon measurement methods and a description of quality control procedures was published by Pierrot et al. (2009).

Underway seawater DMS measurements were obtained with a mass spectrometer fabricated at the University of Hawaii (UH) as a smaller version of the APIMS instrument used for the atmospheric DMS flux measurements (Blomquist et al., 2010). A continuous flow of seawater from the ship's clean distribution line was sampled with an equilibrator similar to that described by Xie et al. (2001). A peristaltic pump and liquid flowmeter (Omega FMG-201) delivered seawater to a 15 m equilibration loop of 0.25 in. OD FEP Teflon tubing at a flow of 110 − 130 cm³ min⁻¹. A parallel flow of deuterated DMS (d3-DMS) in dry nitrogen was injected with the seawater sample at a flow rate of 120 cm³ min⁻¹. The equilibrator loop was immersed in a bucket of flowing seawater for temperature control. Equilibration of natural and deuterated DMS between liquid plugs and gas bubbles occurs rapidly in the Teflon loop; laboratory tests indicate the 15 m length was at least a factor of three longer than required for efficient gas-liquid equilibration. An air-liquid separator at the outlet of the loop directed the equilibrated gas sample to the mass spectrometer for determination of the DMS•H⁺ isotopomer ratio (the ratio of natural mass 63 intensity to deuterated mass 66 intensity) at a frequency of 1 Hz. The seawater DMS concentration is computed using the measured isotopomer ratio, the gas and seawater flow rates, and the known concentration of the d3-DMS gas standard. A subsequent correction for DMS contamination originating in the ship's seawater system is described in Appendix Appendix B.

Trace gas fluxes are computed from the covariance of motion-corrected turbulent vertical wind velocity and gas concentration ( ) over 10 min segments, as described in Blomquist et al. (2010, 2014). A synchronization pulse and DMS blank measurement are automatically executed during the first 2 min of each hour, so the first 5 min of data are discarded in computing the flux. Over the remaining 55 min, 10 min flux segments are defined with 50% overlap, yielding 10 flux estimates per hour.

Quality-control criteria are applied to select valid 10 min periods, which are averaged to yield hourly mean fluxes and cospectra. A minimum of three valid segments are required to compute an hourly average. The basic quality-control criteria used during HiWinGS are: (1) relative wind direction within ±75° of the bow and (2) standard deviation in relative wind direction less than 10°. In addition, CO₂ fluxes were filtered for the rate of change in mean concentration and the magnitude of horizontal turbulent flux: (1) CO₂/ 5 ppm per 10 min, and (2) ppm m s⁻¹ (see Blomquist et al., 2014). No criterion limiting the range of valid CO₂ was applied. The magnitude of CO₂ generally exceeded 20 μAtm throughout the cruise and flux sensitivity for the CRDS instrument is typically sufficient under these conditions. Application of a lower limit criterion for CO₂ did not significantly change the observed trends in k₆₆₀ or the conclusions with respect to CO₂ transfer characteristics. In past projects, we have used additional criteria based on ship speed and changes in heading, but the vast majority of data from HiWinGS were obtained with the ship stationary, on-station, and these additional criteria were unnecessary. The ±75° relative wind direction criterion had little effect for the same reason.

A correction for high frequency signal attenuation in the inlet tubing was computed for both gases from the hourly synchronization pulses (see Blomquist et al., 2014). The vertical turbulent wind component was corrected for ship motion following methods in Edson et al. (1998). Further cospectral corrections for residual motion interference are described in Appendix Appendix C.

2.3 Wave Measurements

Wave physics measurements utilized two buoy systems: a Datawell Waverider^® (model DWR-G4) for directional wave spectra at wavelengths >1 m, and a custom-fabricated spar buoy from the UK National Oceanography Centre, Southampton, instrumented with wave wires and inertial sensors for 1-D wave spectra measurements to 40 Hz. Both systems were deployed at each station. The spar was always free-floating. The Waverider^® was mostly free-floating except at Stations 1 and 4, where a 200 m polypropylene line was used to tether the buoy to the ship. The intended procedure was to maintain slack in the buoy tether, minimizing any interference to wave measurements, but this was not always possible, leading to a few periods with data gaps. Measurements from the Waverider^® were used in conjunction with a hindcast run of the WAVEWATCH-III^® model, version 3.14 (WW3, Tolman, 2016) to assess 2-D wave spectra throughout the cruise. Additional 1-D wave measurements were obtained with a Riegl DL90 laser rangefinder mounted to the ship's bow mast.

The spar buoy carried a suite of bubble instruments, including a bubble camera (1 Hz) for large bubble size distributions at 2 m depth (Al-Lashi et al., 2016, 2017), a bubble resonator for small bubble size distributions at 4 m depth (Czerski et al., 2011; Farmer et al., 1998) and an upward-looking sonar at 8 m depth (Imaginex Multibeam Sonar, model 837A Delta T, 260 kHz). Bubble measurements were power-limited, operating for 40 min intervals every 3 h for up to 48 h in one deployment. Spar buoy measurements were hindered by technical problems at early stations, but data coverage from later stations was nearly complete.

3 Results

HiWinGS meteorological data, sea state, eddy correlation flux measurements, and gas transfer coefficients for CO₂ and DMS will be presented in this section. We show summary plots of supporting measurements as necessary, but for additional detail the reader is directed to other HiWinGS publications: Yang et al. (2014, 2016) have previously reported measurements and model results for methanol and acetone fluxes, sensible heat flux, and wind stress; Kim et al. (2017) present results for air-sea emissions of biogenic organic compounds and their influence on aerosol size distributions; and Brumer et al. (2017) report on the wind and sea state dependencies of whitecap fraction. Additional papers detailing empirical gas transfer parameterizations, 2-D wave statistics and bubble methods and measurements are in preparation.

3.1 Meteorological Setting, Sea State, and Flux Measurements

The project time series for meteorological variables, heat fluxes, CO₂ and DMS fluxes, bubble injection volume, significant wave height, and inverse wave age are shown in Figures 2-4. Wind speed is plotted in all figures for comparative purposes. It is conventional to adjust measured wind speeds to the 10 m neutral stability equivalent speed (U_10N), which for this study is done with the COARE bulk flux model, version 3.5 (Edson et al., 2013). Hourly mean U_10N exceeds 15 m s⁻¹ 19% of the time and exceed 10 m s⁻¹ 63% of the time. Over the course of the cruise, a succession of synoptic low-pressure systems propagated W-to-E across the Labrador Sea at roughly 4–5 day intervals. Wind speeds in excess of 15 m s⁻¹ were recorded at six of seven stations (all except Station 3), so the wind speed range 15–20 m s⁻¹ is well-sampled, representing a variety of sea state and hydrographic conditions. Throughout development of the St. Jude's Day storm on October 25 (Station 4), hourly U_10N remained above 20 m s⁻¹ for 14 continuous hours. Other periods of extended high wind speeds occurred at Station 2 near the southern tip of Greenland and at Station 5 in the aftermath of the 25–26 October storm.

Figure 2

HiWinGS time series of wind speed, air-side friction velocity ( ), pressure, temperatures, and heat fluxes. The timing and duration of seven on-station intensive measurement periods are shown as black bars at the top. Wind for periods of neutral-to-slightly stable atmospheric conditions shown as red points in the upper plot ( ). Heat fluxes, friction velocity and 10 m neutral wind speeds were computed with the COARE 3.5 bulk flux model.

Figure 3

HiWinGS time series of wind speed, trace gas fluxes, and trace gas air-sea concentration gradients. The timing and duration of seven on-station intensive measurement periods are shown as black bars at the top. Dashed black lines are the computed CO₂ and DMS fluxes from the COAREG 3.5 gas transfer model with . Gas fluxes and concentrations are reported in units consistent with the majority of prior CO₂ and DMS air-sea transfer studies, where CO₂ is the air-sea gradient of CO₂ fugacity in µAtm.

Figure 4

HiWinGS time series of wind speed, column-integrated bubble volume, significant wave height ( ) and inverse wave age ( ). Bubble volume is on a log scale and the lower limit of detection (2.3 × m³ m⁻²) is indicated by the dashed line. for the swell and wind-sea components are computed from 2-D spectra obtained with the Datawell Waverider^® buoy. from the WAVEWATCH III^® (WW3) hindcast is for the wind-sea component (red trace) and total (1D) wave spectrum (black dashed trace). Inverse wave ages are computed for the wind-sea components of the buoy measurements and the WW3 hindcast. is from COARE 3.5. The approximate inverse wave age for fully-developed wind-sea conditions is shown as a dotted line at ; inverse ages above the dashed line represent “young” or developing seas.

The sea surface was generally warmer than the overlying marine boundary layer yielding weakly unstable conditions, except at Stations 2, 3, and 6, where neutral to weakly stable conditions were observed for extended periods ( , where z is measurement height and the Obukhov length, L, is computed with the COARE bulk flux model). Even in stable conditions wind speeds generally exceed 10 m s⁻¹, so flux detection limit and precision are not adversely affected. See Blomquist et al. (2014) for a discussion of stability effects on the CO₂ eddy correlation flux detection limit.

The magnitude of CO₂ was greater than 30 µAtm for most of the cruise, with brief periods at Stations 2 and 5 where it fell below 20 µAtm. In the region bounded by 307°E–317°E longitude and 50°N–60°N latitude (roughly the Labrador Sea), the mean HiWinGS seawater fCO₂ was 348 ± 10 µAtm with a range of 328–377 µAtm, which is under-saturated with respect to the atmosphere, as expected, but not quite as under-saturated as the mean October value from the SOCAT database for seven cruises passing through this area in between 2007 and 2015 (333 ± 2 µAtm) (Bakker et al., 2016) or in comparison to the Takahashi et al. (2009) gridded mean pCO₂ climatology for October in this area (307–332 µAtm). The slightly elevated partial pressures are reasonable because we specifically target high wind speed conditions; significant quantities of bubbles are injected by breaking waves and net CO₂ flux into the ocean is increased, so the fCO₂ measurements are not unusual or unexpected.

Seawater DMS concentrations were quite low at 0.4–0.6 nM over most of the cruise, which is also not unusual for the fall season of rapidly declining ocean productivity and mixed layer deepening. Mean surface layer chlorophyll from CTD casts was 0.66 mg m³ with a maximum of 1.06 mg m³ at Station 3 and a minimum of 0.44 mg m³ at Station 2. Over 43 CTD casts, thermocline depth varied from 40 to 110 m with a mean depth of 50 m.

The wind sea component of the wavefield was dominant at most locations when wind was rising or steady at speeds greater than 10 m s⁻¹. The exception is at Station 4 following passage of the low-pressure system when a very large counter-swell component was superimposed on a large wind sea in wind speeds exceeding 15 m s⁻¹.

An estimate for the total column-integrated volume of injected bubbles over 40 min intervals was computed from spar buoy deployments at Stations 4, 6, and 7 for breaking events with bubble penetration depth of at least 2 m. Volumes were interpolated from the observed depth-resolved size distributions and summed over the 40 min interval. The estimated lower limit of detection is m³ m⁻² but results at this limit do not necessarily indicate an absence of bubbles, merely that they do not penetrate below 2 m. Bubble volumes for periods at the detection limit are therefore somewhat uncertain. A total of 31 integrated bubble volume estimates were obtained and of these, nine periods are at the detection limit.

3.2 Gas Transfer Velocity

Transfer velocities for DMS and CO₂ were computed from the observed 10 min fluxes (F_c) and air-sea concentration gradients ( ) as in equation 5, then filtered and averaged to hourly values as described in section 2.2. Measurement units for CO₂ flux (mol m⁻² y⁻¹) and DMS flux (µmol m⁻² d⁻¹) follow the convention of prior studies. Similarly, CO₂ concentration is given as fugacity in µAtm and DMS concentration is in µmol m⁻³. Appropriate conversion factors are applied to obtain the transfer coefficient in units of cm h⁻¹.

(5)

The observed transfer velocities are adjusted to a reference Schmidt number (Sc = 660, equation 6) to normalize for temperature effects on diffusivity, where Sc is defined as seawater kinematic viscosity divided by molecular diffusivity of the gas ( ).

(6)

Here we make the usual assumption that n = 1/2 for open-ocean conditions. However, this normalization strictly applies to the water-side component of the observed transfer coefficient, , only. For DMS, makes a significant contribution to (up to 5–10%), so the Sc normalization from equation 6 will be slightly biased. A further complication arises from the moderately high solubility of DMS compared to CO₂ ( 10–25 over SST of 4–25°C; 0.7–1.1 over the same SST range). Woolf (1997) discusses the asymptotic limits of k_b with respect to gas solubility and diffusivity; for an insoluble gas and at the high solubility limit. DMS is closer to the high solubility asymptote, therefore has a temperature dependence related to solubility which is not normalized by the Schmidt number dependence in equation 6 (see Yang et al., 2011). In this report, we retain the standard Sc normalization for to be consistent with the existing literature. Appendix Appendix D discusses methods for a full temperature normalization of . We note that for this project, a complete temperature normalization increases k₆₆₀ by up to 20% under conditions of low SST and high wind speeds.

Because wind is the most significant factor driving air-sea gas transfer, empirical parameterizations for k₆₆₀ traditionally take the form of a power law in U_10N. These are presented in Figure 5 for both gases. For CO₂, the best fit is significantly less than quadratic ( ) but this may be slightly influenced by k₆₆₀ observations at low wind speeds, which are higher during HiWinGS than comparable measurements from prior projects. Omitting these, a fit to measurements at m s⁻¹ yields a power law coefficient of 1.77. For DMS the fit is closer to linear: .

Figure 5

HiWinGS k₆₆₀ for DMS and CO₂ versus the 10 m neutral wind speed, U_10N. A power law fit of the form is shown for each gas. The best fit for CO₂ is slightly less than quadratic and for DMS much less so.

3.3 Sea State Effects

There is a subtle trend in the observed CO₂ transfer coefficients with wave age (or significant wave height) but less evidence of a similar trend in DMS transfer. Figure 6 shows k₆₆₀ versus U_10N for both gases, where symbol color represents inverse wave age ( ) of the total (1-D) wave spectrum, as determined from in situ measurements with the Waverider^® buoy, and where atmospheric friction velocity, , is computed using the COARE bulk flux model.

Figure 6

Wind speed and inverse wave age dependence of k₆₆₀. Wave age is from coincident, in situ observations with the Waverider® buoy. An inverse wave age of 0.38 represents wind-wave equilibrium and larger values (yellow and red colors) indicate high wind stress with limited sea state development (i.e., young seas).

Fully developed seas were most often encountered at wind speeds of 10–16 m s⁻¹. The largest transfer coefficients for both gases were observed in the presence of large waves in nearly fully developed seas. The largest values of inverse wave age correspond to the initial stage of the St. Jude's Day storm on 24–25 October (i.e., the greatest wind stress and least wave development, shown in Figure 6 as red and orange points). The somewhat lower magnitude of k₆₆₀ for these points is consistent with the limited development of breaking waves in high wind, young sea state conditions. As the event progressed and sea state developed, subsequent observations at lower wind speeds yield comparable or larger transfer coefficients (green-yellow colors). However, a strong relationship between sea state and transfer velocity is not evident in this data set.

A detailed inspection of the 24–25 October event further illustrates the relationship between wind, sea state, and gas transfer characteristics. Figure 7 shows a time series of inverse wave age, significant wave height, bubble volume, wind speed, and k₆₆₀ during the 24–25 October storm. As the low-pressure system approached, hourly mean wind speeds increased to 19 m s⁻¹ with limited wave development. The CO₂ transfer coefficient increased with rising wind but did not exceed values of 100 cm h⁻¹. During the quiescent period, as the center of the low passed over the ship, transfer coefficients for both gases decreased significantly. At this time, inverse wave age indicates a declining sea; visually, whitecaps had largely vanished. This is clear in the bubble trace which goes to the detection limit at this time. Shortly thereafter, wind direction shifted by roughly 180° and hourly mean wind speed increased rapidly to 25 m s⁻¹, with 10 min means approaching 30 m s⁻¹. The initially chaotic sea state gradually developed into a pure wind sea and grew to more than 8 m over the following 8 h. At the peak development of the sea state, from 12:00 to 18:00 on 25 October, reached the largest values measured during the cruise, cm h⁻¹, as did bubble volume. Thereafter, wind speeds gradually declined and inverse wave age trended toward equilibrium conditions in the presence of large waves, but remained elevated compared to the initial, young sea state conditions. For example, by 12:00 on 26 October, wind speed had decreased to well below 15 m s⁻¹ but remained significantly greater than 100 cm h⁻¹. This behavior is consistent with a low-solubility gas sensitive to the effects of breaking waves and bubble injection.

Figure 7

Time series of inverse wave age, wave height, 40 min column-integrated bubble volume, wind speed and gas transfer coefficients during the 24–26 October St. Jude's Day storm event. Wave data are shown for both the wind sea and total (1-D) components of the wavefield from in situ Waverider^® measurements and the WW3 hindcast model. The Waverider^® was tethered to the ship at this station, causing occasional drop-outs. Note, k₆₆₀ DMS is multiplied by 2 for scaling purposes. Modeled transfer coefficients are from COAREG 3.5, incorporating , as discussed in section 4.1.

DMS transfer velocities show much less relationship to sea state development, increasing smoothly as hourly mean wind speed climbs to 25 m s⁻¹ ( 1.3 m s⁻¹) with scant evidence of significant enhancement or suppression in the presence of large waves. For example, from 08:00 to 18:00 on 25 October, remains relatively flat, as does wind speed (23–25 m s⁻¹) while grows from 4 to 8 m.

An analysis of measurements in warm SST conditions (Station 7) reveals another case where sea state appears to affect the relative transfer velocities of CO₂ and DMS. The HiWinGS cruise was fortunate to sample a wide range of sea surface temperatures, from 6 to 11°C at the first six stations and 20°C at the last station. Equation 7 is the more general form of equation 6, specifying the temperature dependence of k with respect to diffusivity.

(7)

The adjustment to k for T₁ = 6°C and T₂ = 20°C from equation 7 is about a factor of two for both gases. Figure 8 shows and observations at ambient conditions (i.e., unnormalized) for all stations versus U_10N, where symbol color indicates SST. While shows the expected enhancement in warm water of about a factor of two compared to measurements in colder water, it is interesting that does not.

Figure 8

(top and bottom left plots) Hourly gas transfer coefficients and significant wave height for the wind sea versus U_10N; (bottom right plot) versus column-integrated bubble volume. Transfer coefficients are at ambient SST (i.e., without Sc normalization) and SST is indicated by symbol color in all plots. are for times with coincident observations. Bubble volume results are for Stations 4, 6, and 7 only with circle markers indicating bubble data coincident with and triangles for interpolated bubble estimates covering hours between successive measurements. (top left) shows the expected warm water enhancement at wind speeds from 10 to 15 m s⁻¹ while (top right) does not. was significantly lower at the warm water location (Station 7) and bubble volumes were very small, with many periods at the detection limit). Wind sea statistics are presented here to emphasize the breaking wave component of the sea state.

Hydrographic and sea state conditions at Station 7 were distinct from other sites, with much warmer SST and short-fetch offshore winds from the northwest. Waves corresponding to the wind sea were smaller, as shown in the bottom left plot of Figure 8. Visually, the breaking crests at Station 7 appeared smaller with less vigorous bubble plume penetration. The bottom right plot clearly shows a correlation between elevated and bubble volume and that bubble volumes at the warm water station were very low, with several periods below the detection limit, despite wind speeds of 10–15 m s⁻¹. These conditions, which contribute to reduced k_b, are the most likely explanation for the observed absence of enhancement to at the warm water station. In any case, observations at Station 7 highlight the divergent character of air-sea transfer for these two gases and the subtle effects of sea state.

4 Discussion

4.1 The COAREG Representation of Gas Transfer

The COAREG bulk model for gas transfer specifies the transfer coefficient as a combination of air-side and water-side resistances, and , in series (from equation 3):

(8)

where the water-side resistance, , is composed of turbulent-molecular resistance at the air-sea interface, , and bubble-mediated transfer resistance, , in parallel:

(9)

Note that r as computed in COAREG is resistance multiplied by (i.e., nondimensional), hence the introduction of in both these equations. Specific details on the derivation and functional form of and are presented in Fairall et al. (2000) and subsequent publications (Fairall et al., 2011; Hare et al., 2004).

Two empirical adjustment factors, A and B, are included in the specification of and k_b, respectively, to tune the model output to observations. The A coefficient adjusts the molecular sublayer contribution in . Ideally, A and B will be identical for all gases; A = 1.6 and B = 1.8 have been used in COAREG 3.0 to fit CO₂ and DMS observations from prior projects. Yang et al. (2014, 2016) find A = 1.6 provides a reasonable fit to observed transfer coefficients of gas-phase controlled compounds methanol and acetone. The magnitude of B will depend strongly on the functional dependence of whitecap fraction in the parameterization of k_b (equation 10). The value of 1.8 was tuned to the wind speed only formulation of Monahan and O'Muircheartaigh (1980), which is now considered an overestimate and yields a poor fit to high wind whitecap observations from recent programs.

COAREG specifies k_b after Woolf (1997) as an empirical fit to the output of a simplified gas transfer simulation of clean bubbles rising in quiescent water. The k_b model is formulated in terms of three physically relevant quantities: gas solubility ( ), whitecap fraction ( ), and diffusivity (Sc):

(10)

As described in Woolf (1997), this form exhibits the expected asymptotic limits with respect to solubility: and . Here k_b is driven entirely by , which is a difficult parameter to measure and for which existing wind speed relationships show considerable scatter and imprecision. In general, a specification of leads to steeply increasing transfer coefficients with wind speed, which is a poor fit to field observations at m s⁻¹. Furthermore, this approach reduces the gas transfer model to a pure wind speed dependency, ignoring the expected effects of sea state. An obvious adjustment is to derive from a parameter related to wind and sea state properties, as proposed by Zhao and Toba (2001) and subsequent authors (Woolf, 2005; Zhao et al., 2003).

The methodology for observations has improved with the development of digital image processing algorithms. Wind speed- dependencies from recent field programs are in better agreement compared to earlier studies (Anguelova & Webster, 2006; Callaghan et al., 2008a, 2008b; Callaghan & White, 2009). Nevertheless, reliable observations at high wind speeds are scarce. Brumer et al. (2017) have analyzed measurements from the HiWinGS and SO GasEx projects, examining goodness of fit for with wind, sea state, and composite parameters. Here we will focus on the “wave-wind” Reynolds number (Woolf, 2005):

(11)

where is the significant wave height of the total (1-D) wave spectrum and is the kinematic viscosity of seawater. This parameter encompasses the effects of wind stress ( , computed with COARE) and sea state development ( ).

As discussed in Brumer et al. (2017), a power law fit of to exhibits better agreement between projects compared to other wind or sea state parameters:

(12)

Here is total whitecap coverage, which includes both the breaking crest and surface foam. Because bubble lifetime and foam persistence has a known dependence on SST and surfactants, there is some ambiguity in the association of total with the wave breaking characteristics most directly related to gas transfer. In equation 10, for example, the factor is an estimate of the air volume injection rate of the breaking crest. Intuitively, the breaking crest fraction of whitecap coverage (Stage A or ), which is more directly related to energy dissipation, might be a better surrogate for bubble-mediated gas transfer. But is difficult to measure and Scanlon and Ward (2016) find it has a poor correlation to wind speed or Reynolds numbers. We will retain the use of total whitecap coverage in this analysis with the recognition that the best representation of wave breaking effects for gas transfer is an ongoing subject of debate and observational efforts.

Equation 12 is easily implemented within the existing COAREG code, replacing the older wind speed-dependent whitecap function. Adjustable constants A and B are then tuned to provide the best overall fit to observed k₆₆₀ for both gases. COAREG output incorporating this modification (which we will refer to as COAREG version 3.5) is plotted with observed k₆₆₀ versus U_10N in Figure 9. In this case, is computed from the WW3 estimate for total (1-D) because the hindcast data set provides a complete time series. In tuning the model, we do not find one set of coefficients that minimizes RMS error between hourly model estimates and observations for both gases, but A = 1.2 and B = 3.8 come very close, yielding cm h⁻¹ and cm h⁻¹. From inspection of Figure 9, this adjustment provides a reasonable fit to observations.

Figure 9

(left) Hourly k₆₆₀ (Eddy correlation and COAREG 3.5) versus U_10N and (right) COAREG components of k₆₆₀ versus U_10N for CO₂ and DMS. COAREG 3.5 output is computed with specified as a function of using WW3 hindcast values of for the total (1-D) wave spectrum and COAREG parameters A = 1.2 and B = 3.8. COAREG results for the 25–26 October event from Figure 7 are indicated by red diamonds. Wind speed power law fits from Figure 5 are shown as black traces. The interfacial transfer component, , is computed as in equation (13), without k_b. is the same for both gases and the two curves are superimposed in the right plot.

In Figure 9, scatter in COAREG 3.5 transfer velocities versus wind speed illustrates the impact of implementing a sea state-dependent calculation of . Furthermore, the large degree of scatter in modeled illustrates an important point; natural sea state variability at a given wind speed leads to considerable variability in the transfer rate for a sparingly soluble gas. In contrast, COAREG 3.5 , which is less influenced by breaking waves, shows much less scatter at a given wind speed. Thus, we should also expect considerable scatter in eddy correlation observations at a given wind speed arising from sea state variability. Although the RMSE for COAREG 3.5 and for the wind speed power law model are roughly equivalent, it is noteworthy that COAREG 3.5, with a sea state-dependent calculation of , simulates both the mean trend and a significant fraction of the variance in k₆₆₀ for both of these gases with respect to wind speed; in m s⁻¹ wind speed bins over the range 10–20 m s⁻¹, model variance is 16% of eddy correlation variance and 27% of measurement variance.

As shown in Figure 7, COAREG 3.5 overestimates after 16:00 on 25 October, at the height of sea state development during the St. Jude's Day storm, then underestimates observed transfer after 06:00 on 26 October, as conditions approach a fully developed wind sea with a large counter swell component. Data from this period are indicated in the left plot of Figure 9 as red diamonds increasing monotonically over the wind speed range 13–25 m s⁻¹. Figure 7 shows COAREG 3.5 does a much better job simulating over this same period. Model bias in may be an artifact of using total (1-D) in the computation of , leading to excessively large and k_b estimates. Wind sea was significantly less than total for much of this period (see Figure 4) and sea state was further complicated by counter swell, pointing to possible conditions where the relationship between and is poorly constrained. We have investigated the use of wind sea in the computation of in COAREG 3.5, with a generally less successful outcome. It appears swell is an important factor in gas transfer, but computed from total may not adequately capture the relevant wind and wave characteristics.

The right plot of Figure 9 shows COAREG 3.5 nonbubble and bubble-mediated components of k₆₆₀ for both gases. To illustrate the mean trend, scatter in model output apparent in the left plot is removed by bin averaging. All components are normalized to Sc = 660. Here we define the nonbubble transfer coefficient, , as in equation 13, omitting k_b. As before, is computed from WW3 total (1-D):

(13)

is almost identical for both gases and in this plot the two traces fall on top of each other. for DMS is less than the nonbubble component over much of the wind speed range, and only exceeds at wind speeds well above 18 m s⁻¹. In contrast, for CO₂ increases rapidly, and at wind speeds above 10 m s⁻¹ it represents the major fraction of k₆₆₀. In the mean, agreement between COAREG 3.5 and the wind speed only fit of k₆₆₀ to U_10N is very good for both gases, but at low wind speeds seems to be an overestimate.

There are known deficiencies in the COAREG algorithm. The model currently considers enhancements to molecular transfer from smooth flow viscous stress and from direct bubble injection, but does not explicitly specify contributions from incipient microbreaking wavelets as described by Csanady (1990). Current plans for the next update involve a more complete description of sea state dependencies of the drag and gas transfer coefficients in COARE and COAREG.

4.2 Other k-Parameterizations

In this section, we will examine several gas transfer models representing alternative approaches to estimating the effects of breaking waves and bubbles. The k-model developed by Asher and colleagues (Asher & Wanninkhof, 1995, 1998, hereafter A98; Asher et al., 1996) differentiates between physical mechanisms of interfacial transfer driven by surface turbulence from external forcing ( ), transfer via enhanced surface turbulence from the breaking wave ( ) and transfer via direct bubble exchange ( ). These transfer coefficients specify water-side (parallel) resistances and are thus additive. The focus of this model is on low-solubility gases, therefore air-side resistance is not considered explicitly but is probably implicitly included in :

(14)

(15)

(16)

(17)

Note, we have changed the symbolic notation in these equations compared to the published version for consistency with notation in this report. Contributions from wave breaking, and , are both proportional to . The constant 47 in equations 15 and 16 is determined from a global budget analysis of the air-sea invasion rate of (Asher & Wanninkhof, 1998) and the constant in equation 16 is determined from wave tank studies (Asher et al., 1996). is a linear function of wind speed, and both interfacial terms, and the additional nonbubble term , are proportional to . Direct bubble transfer, specified by , has a more complex empirical dependence on both solubility and diffusivity; the coefficients in equation 17 are obtained from wave tank studies reported in Asher et al. (1996) but differ depending on the direction of the flux: for evasion and for invasion. One caveat mentioned by the authors is that this formulation applies only to conditions where is far from equilibrium, which is often the case in field studies because large air-sea concentration gradients are a desired condition for the flux measurements.

The model of Liang et al. (2013) (hereafter L13) is derived from coupled LES turbulence and bubble population simulations of the ocean mixed layer. for partially dissolved bubbles is given as an empirical power law fit to the coupled model output in terms of water-side friction velocity (equation 18), where :

(18)

For , L13 employ the COAREG formulation (equation 13). L13 develop additional relationships for the supersaturation effects of hydrostatic pressure and bubble dissolution. As mentioned in section 1, this is a small component of total bubble transfer under conditions of large and we omit it in this discussion. Also, the L13 model is specific to low-solubility gases so equation 18 cannot be applied to DMS.

A recent paper by Goddijn-Murphy et al. (2016) (hereafter GM16) presents two approaches to account for the interfacial and bubble-mediated transfer mechanisms. Here, we focus on their “independent bubble model” which omits consideration of bubble plume void fraction effects (Woolf et al., 2007). In this “hybrid” model, is computed as the linear fit of DMS k₆₆₀ observations to over the range 2–13.5 m s⁻¹ (equation 19), where the bubble contribution to is assumed to be negligible (Goddijn-Murphy et al., 2012). k_b is computed using the Woolf (1997) model, as in equation 10, but without the B coefficient:

(19)

From a budget analysis of noble gases at the Bermuda Atlantic Time series Study (BATS) site spanning more than three years, Stanley et al. (2009) (hereafter S09) derive independent terms for gas flux from completely dissolved bubbles ( ) and partially dissolved, transient bubbles ( ):

(20)

(21)

where a cubic wind speed dependence is assumed and the empirical coefficients, and , are determined with an inverse approach using a 1-D vertical upper ocean model. Trace gas partial pressures , and refer to the atmosphere, bubbles, and bulk seawater, respectively; D is the diffusion coefficient; is a unity constant; and is the Bunsen solubility: . is computed as a function of injection depth as:

(22)

where X is atmospheric mole fraction, is atmospheric pressure, g is gravitational acceleration, and is seawater density. The mean effective bubble injection depth, , is computed according to Graham et al. (2004) as:

(23)

k_b can be estimated from the sum of and divided by , as in equation 5, and then adjusted to .

Figure 10 compares the COAREG interfacial and wave breaking k-components with k-components from the other models, all computed using HiWinGS observed bulk parameters and bin-averaged in U_10N. is obtained from as in equation 12. To compute normalized values from equations 14 to 17 we set Sc = 660 and use at 20°C and at 27°C. Here for A98 is the sum of and , although does not strictly specify bubble effects.

Figure 10

, and total k₆₆₀ versus U_10N for several k-models, as identified by trace color. The L13 model is not species specific but should best approximate CO₂ transfer. is equivalent for both gases, so only one set of curves is shown, and a trace for L13 is not included as it is identical to COAREG. For A98, the solid red curves include the component, while dashed red curves do not. For S09, only is computed. Wind speed power law curves from Figure 5 are shown as solid black lines in the lower two plots for comparison.

Both A98 and GM16 produce higher estimates for than COAREG, and this is not surprising in the case of GM16 given is a fit to field observations of k₆₆₀ DMS, which include some bubble contribution. Based on HiWinGS measurements, this may be a significant overestimate, as the result from equation 19 is slightly higher than the best fit to measurements from Figure 5.

Differences in are more significant, however. Because COAREG and GM16 both employ the Woolf (1997) model, the larger estimate from COAREG is entirely due to the B = 3.8 factor in equation 10. from A98 is very large for both gases and, for DMS, clearly wrong. The surface turbulence term, , is the largest contribution to k_b; normalized to Sc = 660 it is nearly the same for CO₂ and DMS. Omitting , the A98 result for DMS is much closer to both COAREG and observed , and for CO₂ is only slightly less than the COAREG result, with offsetting differences in the and components. The error in A98 may arise from the application of wave tank calibrations to open ocean conditions, especially in equation 16. COAREG does not explicitly consider surface turbulence from rising bubble plumes, but the B adjustment can be viewed as an implicit compensation for additional wave breaking turbulence since the net effect scales with . The L13 result roughly approximates direct measurements of , but the nearly cubic power law dependence is too extreme and a poor fit to the observed trend.

Within the 3–13 m s⁻¹ wind speed range of the BATS budget analysis, the k_b result from S09 is comparable to GM16 for DMS but quite low for CO₂ compared to other models. Some of this difference may be attributable to differences in bubble lifetimes and size distributions in Labrador Sea compared to the subtropical Sargasso Sea site. However, the noble gas analysis is in general more sensitive to dissolving bubbles (supersaturation effects) and less sensitive in the determination of fluxes related to transient bubbles, especially for gases where the equilibration time scale is less than or comparable to bubble lifetime. CO₂ is at least an order of magnitude more soluble than the noble gases in the budget analysis, which amplifies potential errors in the application of this model to HiWinGS results.

None of these models fit HiWinGS k₆₆₀ observations as well as the tuned version of COAREG 3.5 presented in section 4.1. L13 comes close for CO₂ because the power law parameterization of k_b is within 20 cm h⁻¹ of the observations over most of the wind speed range, diverging significantly above 20 m s⁻¹. For GM16, applying the B factor to k_b would obviously bring the “hybrid” model in rough agreement with both the observations and COAREG for CO₂, but for DMS this leads to a significant overestimate. As is, the GM16 result is close to the observations because opposing trends in and k_b nearly cancel. A consistent result for both gases with GM16 could be achieved applying the B factor to k_b with a more reasonable definition of . The bias in A98 stems from a large overestimate in the nonbubble effects of breaking waves, and omitting this term improves the comparison significantly for both gases.

4.3 Comparison to Other Field Projects

SO GasEx was conducted in the spring of 2008 near South Georgia Island (Ho et al., 2011). Results for DMS and CO₂ flux measurements are detailed in Yang et al. (2011) and Edson et al. (2011), respectively. Here we will focus on DMS. WW3 wave statistics for SO GasEx (3 h, 0.5° resolution) were obtained from the database archive of the French Research Institute for Exploitation of the Sea (ftp://ftp.ifremer.fr/ifremer/ww3/HINDCAST/GLOBAL/2008_ECMWF/). Fields were interpolated first in space onto the ship's track and then in time to match gas transfer velocities.

As shown in the left plot of Figure 11, observations from SO GasEx are lower at moderate wind speeds compared to HiWinGS, and remarkably low during the single event where wind speeds exceed 15 m s⁻¹. The right plot of Figure 11 shows that COAREG, tuned to HiWinGS results, slightly overestimates the SO GasEx observations at wind speeds below 15 m s⁻¹. There is insufficient wave and whitecap information during the storm event to compute from , as in section 4.1, but using the combined HiWinGS-SO GasEx wind speed only model (Brumer et al., 2017) for the period of the storm yields the k₆₆₀ result shown in Figure 11, which is a factor of 3 or 4 greater than the observed k₆₆₀ at U > 15 m s⁻¹.

Figure 11

Hourly average DMS transfer coefficient, k₆₆₀, versus U_10N. The left plot compares HiWinGS and SO GasEx observations. The right plot compares the SO GasEx observations to COAREG 3.5, where k_b is computed as in equations (10)–(12) with constants A = 1.2 and B = 3.8, as for Figure 9. For m s−¹ during SO GasEx, was estimated from a wind speed dependent model because wave data is unavailable.

The differences in between these projects may relate to specific characteristics of sea state and wind. Figure 12 summarizes inverse wave age, wave height, and wind speed, where wave statistics are computed from the 1-D spectrum of the WW3 hindcast. It is apparent from Figure 12 that HiWinGS sampled many more high wind speed events with wave heights in excess of 5 m. SO GasEx shows a large fraction of measurements in old sea state conditions, possibly related to a persistent background of long-period swell in the Southern Ocean. Still, the SO GasEx high wind event is not clearly distinct from similar events during HiWinGS with respect to wave age, wave height, wind speed or directional spread between the wind and wavefields. On the basis of sea state statistics, we cannot identify a cause for the large decrease in observed DMS transfer velocity during the SO GasEx storm event.

Figure 12

(left) Hourly average inverse wave age ( ) versus significant wave height ( ) for HiWinGS and (right) SO GasEx. Symbol color indicates 10 m neutral wind speed. The dashed line at is the approximate inverse age for wind-sea equilibrium, or a fully developed sea state. Inverse wave ages above the line are “young” or developing seas; inverse ages below the line are “old” or decaying seas, often dominated by swell, with or without a smaller wind sea component.

Figure 13 compares HiWinGS gas transfer coefficients to another recent field project, Knorr 2011 (Bell et al., 2013, 2017). We also show the mean observations from previous cruises by the UH group and the mean result from three previous GasEx cruises (GasEx98, McGillis et al., 2001; GasEx-2001, McGillis et al., 2004; and SO GasEx, Edson et al., 2011). Two empirical k-models are shown, plotted to a limit of 15 m s⁻¹, as validity above that wind speed is uncertain. Results are binned by wind speed for clarity.

Figure 13

DMS and CO₂ k₆₆₀ from several projects, binned by wind speed for clarity. For comparison purposes, results from selected empirical gas transfer parameterizations are also shown. Note the difference in vertical scaling between the two plots. Error bars are the standard error of the mean in each wind speed bin. Bin means and medians are shown for HiWinGS k₆₆₀ CO₂ to illustrate the effect of large waves during periods of moderate winds.

In the mean, HiWinGS (red diamonds) are consistent with previous measurements by the UH group (orange diamonds) with the exception of the one high wind event during SO GasEx mentioned in the previous section (orange squares). As noted earlier, HiWinGS bin-means at lower wind speeds exceed those from other projects but are similar to the mean GasEx result at moderate wind speeds. In this case, higher mean at 5–10 m s⁻¹ results from a few very large transfer velocities at these wind speeds coincident with large waves and declining winds (see EC measurements plotted in Figure 9). The bin-medians, shown in Figure 13 as red circles, are in substantial agreement with GasEx and Knorr 2011 results over this wind speed range. GasEx measurements above m s⁻¹ are more uncertain.

The contrast with results from Knorr 2011 is remarkable. While HiWinGS data and most prior measurements by UH follow a nearly linear increasing relationship with wind speed, the binned Knorr 2011 observations, largely from a single storm event, fall off significantly at wind speeds above 11 m s⁻¹ (blue triangles) and are more generally consistent with SO GasEx, especially the anomalous high wind event. It is also notable that k₆₆₀ for both DMS and CO₂ on Knorr 2011 are 30 cm h⁻¹ lower than the HiWinGS result in the highest wind speed bin (19 ± 1 m s⁻¹), and this offset is relatively constant for at all wind speeds above 15 m s⁻¹. The reduction in SO GasEx in Figure 11 is of the same magnitude. Because both gases are affected equally, this implies a suppression of , but seems too large to be solely a reduction in interfacial transfer because 30 cm h⁻¹ is comparable to the total value of estimated by the various models in Figure 10.

The comparison of these three cruises suggests specific conditions contributing to a suppression of transfer for DMS and CO₂ during the high wind event on Knorr 2011 (Station 191), and for DMS during the comparable event on SO GasEx, and that these conditions did not occur during HiWinGS. We note that at other stations during Knorr 2011 (e.g., Station 184) appears to be in general agreement with the trend in HiWinGS and other projects (see Figure 4, Bell et al., 2013). So the inferred gas transfer suppression from these projects is largely derived from two storm events.

The interfacial transfer model of Soloviev (2007) incorporates a wave age dependence that acts to reduce surface renewal and gas transfer in the presence of large waves, but these effects should apply equally to conditions on all these projects and on that basis does not provide a satisfying explanation of the observed differences. Considering factors other than sea state, the one condition which may have been different during HiWinGS relates to biological productivity. The Knorr 2011 cruise was staged in early summer during the North Atlantic bloom, with much larger DMS concentrations and fluxes than those encountered during HiWinGS (Bell et al., 2013). SO GasEx was conducted during the Austral autumn, following the summer bloom, but targeted on an area of enhanced productivity to maximize CO₂ fluxes. Based on MODIS data, the SO GasEx study area experienced a large bloom just prior to the start of the project (see Figure 2, Lance et al., 2012). In contrast, HiWinGS occurred during North Atlantic autumn, well after the summer bloom, during a time of rapidly declining productivity and deepening mixed layer. As noted by Bell et al. (2013), this suggests that a speculative explanation for the observed reduction in gas transfer during SO GasEx and Knorr 2011 may relate to the presence of surfactants in the ocean mixed layer.

Finally, one recent and notable study details a lengthy campaign of eddy correlation CO₂ flux measurements in the Southern Ocean and Antarctic marginal ice zone (Butterworth & Miller, 2016). Wind speeds were not as extreme as for HiWinGS but several measurements above 15 m s⁻¹ are reported. In this study, the mean relationship between and U_10N in open water is in substantial agreement with the global mean from the most recent evaluation of the ¹⁴C inventory (purple trace, Figure 13, Wanninkhof, 2014) and thus significantly lower than the mean trend from HiWinGS and GasEx shown in Figure 13. This suggests HiWinGS experienced a greater frequency of large breaking waves than is typical of the global mean condition or the conditions prevalent during the Southern Ocean study. As with the other cruises, surfactant levels are probably unknown and may be significant, especially during spring/summer blooms in the marginal ice zone. Fetch may also be a factor for winds off the Antarctic continent or sea ice. Sea state conditions may be available from the hindcast model and in future work it will be valuable to combine the Southern Ocean observations with the other projects as a challenge to physical gas transfer model development.

Several laboratory studies have investigated the effects of surfactant films (e.g., Bock et al., 1999; Frew, 1997) and suppression of microscale breaking and gas transfer under conditions of organic enrichment was demonstrated in a coastal field study at wind speeds less than 10 m s⁻¹ by Frew et al. (2004). Salter et al. (2011) demonstrate a similar reduction in gas transfer for an artificial surfactant release in the open ocean. However, to our knowledge, there have been no published reports of these effects at high wind speeds. Interfacial transfer inhibition through the “barrier” effect of insoluble surfactants in the sea surface microlayer is unlikely, except at very low wind speeds. But, there are two potential mechanisms which may be important at moderate-to-high wind speeds: (1) the “dirty bubble” effect which acts to reduce the contribution of bubble-mediated transfer from breaking waves, and (2) the suppression of microscale breaking caused by the scavenging and transport to the surface of soluble surfactants by bubble plumes. The latter process could have a significant impact on interfacial exchange, leading to reduced transfer of both DMS and CO₂. Furthermore, to the extent surfactants enhance the persistence of foam on the ocean surface, total as measured from image analysis will increase, driving -dependent k-models to over-predict transfer under conditions where transfer is actually suppressed. Brumer et al. (2017) show the best fit of to wind speed for SO GasEx is slightly steeper than for HiWinGS , which at least does not contradict this hypothesis.

Unfortunately, we do not have the information to meaningfully evaluate the importance of surfactants on these projects. The potential effects have been acknowledged and discussed for many years but have yet to be seriously addressed, especially for wind speeds above 10 m s⁻¹ in the open ocean. The experimental challenges are formidable, but physical, chemical, and biological measurements to evaluate these issues should be considered in planning future gas transfer studies.

5 Summary and Conclusions

A dedicated air-sea gas exchange research cruise, HiWinGS, was conducted in the fall of 2013 in the Labrador Sea, focussing on direct eddy correlation flux measurements and in situ observations of wave properties in high wind speed conditions. The project successfully sampled several severe weather events and represents the largest set of coincident gas transfer and sea state observations to-date under these conditions. Transfer coefficients were determined for gases spanning a wide range of solubilities. Results for methanol and acetone were reported in an earlier study (Yang et al., 2014). This submission analyzes results for CO₂ and DMS, revealing a large difference in the transfer characteristics of these two gases with respect to breaking waves, supporting similar observations from prior projects. In general, k₆₆₀ for CO₂ shows greater sensitivity to wave breaking and bubble-mediated transfer mechanisms, with a wind speed dependence of , while for DMS .

The observed influence of sea state on gas transfer was not as drastic as inferred from two prior field programs. There is clear evidence CO₂ transfer is enhanced under conditions of fully developed seas at high wind speeds compared to young, undeveloped seas at a comparable wind speed. However, differences between HiWinGS observations and those from the SO GasEx and Knorr 2011 cruises are difficult to rationalize. These prior data sets show evidence of significant gas transfer suppression in the presence of large waves and HiWinGS does not. At this point, we can only speculate on the reasons for this apparent discrepancy.

The COAREG bulk flux model with a sea state-dependent calculation of wave breaking transfer mechanisms successfully reproduces both the mean trend and as much as 27% of the variance in HiWinGS eddy correlation k₆₆₀ measurements in the wind speed range 10–20 m s⁻¹. Specifically, the implementation of a sea state-dependent and wind speed-dependent calculation of whitecap fraction as a function of the “wave-wind” Reynolds number, , was used in the computation of the bubble-mediated transfer component, k_b. While generally successful, there is evidence this formulation may not be sufficient in all conditions. In particular, the relationship of wind sea and swell components of the wavefield to gas transfer mechanisms is unclear, as is the appropriate definition for whitecap fraction as either the breaking crest or total coverage. Future development of the COARE and COAREG models will focus on representing the effects of sea state on the drag and gas transfer coefficients using an advanced wave model (e.g., Banner & Morison, 2010).

Comparisons with other physical gas transfer models were less successful, but in some cases there are clear modifications which would improve their performance. For continued development of gas transfer models, detailed knowledge of breaking wave and bubble mechanisms is a critical deficiency, as is a quantitative model of surfactant effects. There are large uncertainties in the current understanding of air injection rates, bubble size distributions, penetration depth and lifetimes, the influence of swell on breaking wave development, the sea state dependence of incipient, microscale breaking, and the best approach to representing these factors in terms of more accessible parameters like wind speed, whitecap fraction or statistics of the wave spectrum. As usual, modeling innovations are ahead of observations. In facilitating model development, results from HiWinGS and other recent programs clearly illustrate the value of coincident gas transfer and wave physics observations and the utility of including gases covering a broad range of solubilities.

Acknowledgments

The authors gratefully acknowledge support from NSF grants AGS-1036062, AGS-1036006, AGS-1444294, and OCE-1537890; the NOAA Climate Program Office, Climate Observation Division; and the UK Natural Environment Research Council grants NE/J020893/1, NE/J020540/1, and NE/J022373/1. Processed data from the HiWinGS project are available via anonymous ftp from ftp1.esrl.noaa.gov/psd3/cruises/HIWINGS_2013/Collective_Archive. Finally, we extend heartfelt thanks to Captain Kent Sheasley and the crew of R/V Knorr for critical support and assistance during the HiWinGS cruise, without which these results would not have been possible.

Appendix A: Cruise Overview

The following notes are a brief description of wind and sea state conditions at each station shown in Figure 1. Wind speeds are hourly average U_10N, computed from measured winds using the COARE bulk flux algorithm, version 3.5 (Edson et al., 2013).

Station 1 (59°N 50°W, 11–13 October). This station was characterized by strong northwesterly winds, building and then declining over 2 days, remaining in excess of 15 m s⁻¹ for approximately 12 h over 11–12 October. Significant wave height ( ) peaked above 6 m with little contribution from background swell, achieving nearly full development.

Station 2 (58.5°N 45°W, 14–17 October 14–17). This location commonly experiences intense low-level winds known as the Greenland “tip-jet.” Northeasterly wind speed exceeded 15 m s⁻¹ for 36 h on 14–16 October leading to development of 6 m waves in less-than-fully developed sea state conditions.

Station 3 (54.1°N 46°W, 18–21 October). This station is notable for a gradual increase in northeasterly winds over 18–19 October with coincident development of a wind sea, peaking on 20 October with approximately 24 h of wind speeds in excess of 13 m s⁻¹, followed by a reduction in both wind and waves through 21 October. The gradual increase in wind speed over 48 h allowed the sea state to remain in approximate equilibrium with wind throughout the event.

Station 4 (53.5°N 45.4°W, 24–27 October). This station is characterized by the passage of a strong low-pressure system, with a minimum sea level pressure of 960 hPa at 04:00 on 25 October (the “St. Jude's Day” storm). From 12:00 23 October into 24 October, as the low approached, wind veered from southerly to easterly, increasing gradually to 19 m s⁻¹. As the eye of the storm passed over the ship, pressure reached a minimum and winds decreased to 8 m s⁻¹ in foggy conditions. Then, very rapidly, from 07:00 to 08:00 on 25 October, westerly wind strengthened to 25 m s⁻¹. This transition led to an initially chaotic sea state, subsequently developing in excess of 8 m. Wind dropped below 20 m s⁻¹ just after 00:00 on 26 October and declined further over the course of the day, but waves remained large. Over 26–27 October a significant wind-sea, driven by strong westerly winds, was superimposed on a larger northeasterly swell component propagating from the northern lobe of the low-pressure system as it moved in a northeasterly direction toward Europe, yielding a chaotic mixed sea state.

Station 5 (53.5°N 45.4°W, 28–31 October). For this station, wave buoys were repositioned to the starting location of Station 4 and measurements continued under strong westerly winds, which persisted in excess of 15 m s⁻¹ for more than 48 h. The mixed sea state continued with a large westerly wind-sea component (6 m) and occasional cross-swell from the north.

Station 6 (52°N 50°W, 1–3 November). This station was set just off the continental shelf to the east of Newfoundland in cooler, fresher water, east of the main core of the Labrador Current. Southwesterly winds grew to 15 m s⁻¹ for most of 2 November, developing 3–4 m waves in young sea state conditions with southerly swell.

Station 7 (41.45°N 64°W, 7–12 November). The final deployment was located just beyond the continental shelf south of Nova Scotia, in warmer waters near the North Atlantic Current (SST 20°C). Wind speeds were 10–17 m s⁻¹. On 8 November, a cold front passed and wind speed declined rapidly, veering northerly and then strengthening again over the course of the day. Station 7 is notable for atmospheric instability behind the cold front, as air temperature dropped to 10°C over a much warmer ocean surface, leading to numerous squalls with hail and rain during 8–9 November. Over 10–11 November winds grew to 15 m s⁻¹ and then decreased over 24 h as a second cold front moved through the region.

Appendix B: Corrections to Seawater DMS

A 10 L sample of surface seawater at 2–3 m depth was collected during twice daily CTD rosette casts and analyzed for DMS immediately (within 5 min) using the underway system. To minimize DMS loss in the CTD sample, 20 L of water were delivered into the bottom of a 10 L carboy without introducing bubbles. Excess volume was allowed to overflow, then the carboy was sealed to prevent air exposure and taken to the laboratory for immediate analysis. Results from the CTD samples are therefore the best measure of surface DMS concentration.

Figure B1 shows the time series of underway and CTD data for the entire cruise. Comparison of the CTD and underway data revealed the ship's seawater line was contributing a DMS background. Figure B2 shows a clear linear relationship between the two measurements but the slope is significantly different from one. An attempt to clean the ship's lines with chlorine tablets following Station 1 was largely unsuccessful.

Figure B1

Project time series of seawater DMS measurements (nmol L⁻¹). Raw underway data (red) were corrected (blue) for contamination contributed by the ship's seawater system by comparison with manually analyzed CTD surface samples (triangles). CTD samples were obtained twice daily at all stations.

Figure B2

Seawater DMS from the CTD samples versus underway measurements. The underway measurement is the 10 min mean from the continuous flow system at the time the surface water sample was collected by the CTD. The regression yields an adjustment to correct for sample line artifacts in the ship:

A correction factor from the linear regression (Figure B2) was applied to the raw measurement to obtain the best estimate of the seawater DMS time series. Because the artifact is proportional to the ambient DMS concentration, this contamination may be due to phytoplankton cellular disruption or cell lysis in the ship's pump or plumbing. A definite cause was not identified. Because the CTD and underway measurements are obtained using the same instrument and standard, and within 5 min of each other, we can be certain the origin of the artifact is with the ship's plumbing and not the analytical system. Adjusted to account for the observed bias, the underway data represent the best estimate of the concentration for periods between CTD samples. The limited degree of scatter in the relationship between underway and CTD measurements shown in Figure B2 supports this assessment.

The bias in DMS measurements from the ship's seawater system is disappointing and unique in relation to other cruises we have done, which generally show very close agreement between underway and CTD measurements. Underway seawater DMS measurements during SO-GasEx were verified with discrete CTD samples and compared quite well (Yang et al., 2011). Similar comparisons were done during Knorr2011 (Bell et al., 2013). We will also note that DMS concentrations during HiWinGS were very low and even a small contamination artifact leads to significant bias.

Appendix C: Corrections to Trace Gas Cospectra

A careful review of cospectra ( versus ) revealed many hours with an obvious artifact at 0.03–0.3 Hz, especially during periods with large waves and extreme ship motion. The CRDS analyzer used for CO₂ flux measurements has a motion sensitivity in the cavity pressure control valve (see Blomquist et al., 2014). Decorrelation procedures were applied to remove as much of this interference as possible. Nevertheless, a correction to hourly mean cospectra was necessary to obtain the best flux estimate. In cases where spikes at Hz were greater than twice the magnitude of any other point in the binned cospectrum, a fit to the empirical neutral stability form of the scalar cospectrum was applied (equation C1), which is a rearrangement of the normalized form given in Kaimal et al. (1972) (equation C2),

(C1)

(C2)

where the surface normalized frequency .

Two fit parameters in equation C1, measurement height (z) and relative wind speed ( ), were fixed at the observed values and the total flux parameter (F_c) was subjectively adjusted for the best approximation to a smooth fit through the high and low frequency portions of the cospectrum, with the expectation that the measured cospectrum will be attenuated at the highest frequencies by inlet tubing. Spectral points over the frequency range 0.025–0.4 Hz in the raw, unbinned cospectrum were replaced with the fit result. The patched cospectrum was integrated to obtain a corrected flux estimate.

It should be noted this procedure is only successful when the hourly mean cospectrum has sufficient signal-to-noise that a clear cospectral shape is recognizable. The fit is not attempted in cases where the entire cospectrum appears to be noise (i.e., the CO₂ flux is near zero or below the limit of detection). Corrections were applied to 58% (405 of 693) of the hourly CO₂ fluxes and 9% (66 of 728) of hourly DMS fluxes.

Figure 1 shows the mean normalized raw and corrected cospectra of vertical turbulent wind velocity and CO₂ during the 24 h period of extreme ship motion at Station 4. The normalized neutral-stability scalar cospectrum (equation C2) has an expected peak value of 0.25 at n = 0.1 Hz. The raw cospectrum clearly shows the effects of extreme motion on the flux measurement. When the motion artifact is successfully removed, the corrected spectrum will closely approximate the theoretical form given by equation C2 across the entire range of frequencies. Corrected fluxes from this procedure are on average 11% greater than raw fluxes. For the extreme conditions illustrated in Figure C1, the correction to CO₂ flux is 19%.

Flux loss at frequencies above n = 0.3 Hz in Figure C1 is caused by signal attenuation in the gas inlet tubing. (Note, this is normalized frequency. Actual roll-off in response due to inlet effects occurs at measurement frequencies above 1 Hz.) The hourly nitrogen pulse injection at the inlet tip produces a negative square wave signal response in the gas analyzers, from which we derive a frequency attenuation correction factor (for details see Bariteau et al., 2010; Blomquist et al., 2014). Both gas analyzers draw air from the same inlet manifold, so the attenuation correction is applied to all DMS and CO₂ fluxes. The attenuation correction is rather small at low to moderate wind speeds, averaging 6% for the entire project and 11% for the period of high wind speeds at Station 4.

Fluxes corrected for motion artifacts and signal attenuation provide the best estimate of air-sea flux under difficult sampling conditions. The net effect on is an increase of up to 30% at the highest wind speeds. In the future, improvements to measurement technology should reduce the magnitude of these corrections, though the motion artifact may not be solely an instrumental sensitivity. We have argued previously that vertical motion of the sample inlet through a near-surface gradient in gas concentration should not interfere with the flux measurement because the motion and concentration gradient are out of phase by 90° (Blomquist et al., 2010). This is usually evident from a peak at motion frequencies in the quadrature spectrum. In fact, the phase angle will not be exactly 90° and some leakage of the vertical gradient artifact is likely to appear in the cospectrum. This may be particularly true for DMS since positive fluxes (surface emissions) yield a steeper surface concentration gradient than negative (deposition) fluxes.

Figure C1

Mean normalized raw and corrected cospectra of vertical turbulent wind velocity and CO₂ during the 24 h period of extreme ship motion at Station 4. The red trace is corrected for motion interference by fitting an idealized scalar cospectrum over the frequency range 0.025–0.4 Hz. The normalized Kaimal et al. (1972) neutral-stability scalar cospectrum from equation (C2) is shown as the black trace.

Appendix D: Temperature Normalization of

For moderately soluble gases, k_b has a temperature dependence that is not removed by the usual Schmidt number normalization procedure (Yang et al., 2011). For DMS, the Schmidt number reaches a value of 660 at 27.4°C, so a full temperature normalization of to Sc = 660 requires an adjustment of solubility effects to that temperature, in addition to the usual diffusivity normalization. For observations at low SST in high winds (when k_b is most significant), this additional adjustment can be large.

Normalizing to the reference state requires a model specifying the solubility dependence of k_b and a method of separating the interfacial and bubble-mediated components of . The simplest approach is to use the COAREG model to compute a correction factor. From the observed bulk meteorological parameters, COAREG produces an estimate for at ambient conditions (unnormalized) and for via equation 6. By setting the bulk SST to 27.4°C, leaving other input variables unchanged, a second estimate for the unnormalized transfer coefficient, , is computed at a reference state where , including any solubility effects to k_b. The ratio the two values, , is an adjustment factor for the eddy correlation transfer velocities computed with equation 6, correcting for the additional solubility temperature dependence of k_b.

Figure 1 is a plot of versus SST for HiWinGS. At an SST of 20°C the correction is 5%, but at 4°C the correction is approaches 15% in moderate wind speeds. The effects of wind speed are evident in the broad range of at a given SST, approaching a 20% correction for high wind speed events during HiWinGS. In this case, COAREG is configured with , A = 1.2 and B = 3.8 (as in Figure 9).

Figure 2 compares the usual Sc normalization of to the estimated “true” temperature-normalized value after applying . For binned results, the corrected value of k₆₆₀ at the highest wind speeds is 17% greater than the value computed from equation 6. Note that these adjustments are in general larger than the other recognized error of applying the Sc normalization to the observed rather than component alone. The full temperature normalization reduces scatter in the hourly k₆₆₀ observations, but in this case only slightly; for wind speed bins from 10 to 15 m s⁻¹ the relative standard deviation in k₆₆₀ is reduced from 25.5% to 24.2%.

Of course, the accuracy of this correction depends on having a reasonable model of k_b specifying the diffusivity and solubility dependence. Somewhat different results could be expected with another physical model or from a different configuration of COAREG. Except for Yang et al. (2011), this adjustment has not been applied in previous DMS transfer studies.

A full temperature normalization of from SO GasEx and HiWinGS does not resolve the large difference in observations at high wind speeds. SST was similar in both of these projects, and applying increases k₆₆₀ by roughly equal amounts. However, caution is advised in comparing from field studies at widely different temperatures, as the usual Sc normalization will not collapse observed to a well-defined reference state.

Figure D1

The correction factor for observed DMS , as a function of SST and wind speed. The magnitude of the correction can reach 20% for observations at high wind speeds in cold conditions.

Figure D2

A comparison of HiWinGS temperature normalization methods. The blue trace is the standard Sc normalization to 660 (equation (6)). The green trace is an estimate for the “true” k₆₆₀, using the COAREG physical model to compute the effects of solubility temperature dependence in k_b. Error bars are standard error of the mean in each bin.