Air-sea open ocean CO2 flux measurements have been made using the Eddy Covariance (EC) technique onboard the weathership Polarfront in the North Atlantic between September 2006 and December 2009. Flux measurements were made using an autonomous system ‘AutoFlux’. CO2 mass density was measured with an open-path infrared gas analyzer. Following quality control procedures, 3938 20-minute flux measurements were made at mean wind speeds up to 19.6 m/s, significantly higher wind speeds than previously published results. The uncertainty in the determination of gas transfer velocities is large, but the mean relationship to wind speed allows a new parameterisation of the gas transfer velocity to be determined. A cubic dependence of gas transfer on wind speed is found, suggesting a significant influence of bubble-mediated exchange on gas transfer.
 Evaluating the air-sea flux of CO2 is an essential part of understanding climate. The flux of a trace gas such as CO2, is commonly parameterised in terms of a transfer velocity coefficient, k, as:
where K0 is the solubility of CO2, and ΔpCO2 is the air-sea partial pressure difference. The air-sea flux of a slightly soluble trace gas such as CO2 is rate limited by molecular transfer across a thin aqueous-phase interfacial layer. The transfer velocity incorporates the effects of numerous kinetic factors affecting transfer across this layer. The diffusivity in seawater of a gas species, D, is incorporated into the transfer velocity via a Schmidt number, Sc, dependence:
where ν is viscosity of seawater and the exponent n depends on assumptions made about the interfacial layer dynamics. The exponent is typically assumed to be in the range ≤ n ≤ with n = 1/2 thought appropriate for wavy surfaces.
 Transfer velocity is commonly parameterised in terms of wind speed. Proposed gas transfer to wind speed relationships differ significantly, particularly at high wind speeds. At winds of 7 m/s published relationships differ by 50%, and at 15 m/s the relationships differ by 100% [e.g., Woolf, 2005]. Wind speeds of 15 m/s or more occur infrequently over the global ocean but due to the non-linear dependence of k on wind speed, they have a significant effect on the global flux [e.g., Takahashi et al., 2002]. There are very few measurements of k obtained at wind speeds above 15 m/s, and the derived relationships are extrapolated to higher wind speed values. Large uncertainties in gas transfer measurements make determining the form of the wind speed dependence difficult without measurements in high wind speeds.
 Estimates of gas transfer on large time (days to years) and spatial (kilometer to global) scales obtained via Dual Tracer Experiments (DTE) [e.g., Nightingale et al., 2000; Ho et al., 2006] and from the bomb radiocarbon inventory have been brought into good agreement [Sweeney et al., 2007]. The dependence of k on wind speed obtained via these methods is quadratic, and measurements have been obtained at wind speeds of up to 16 m/s [Ho et al., 2006]. However, the relationship determined from the radiocarbon budget implicitly assumes both a quadratic dependence, which is fit to one data point, and that n = 1/2. Around 50% of the scatter in the DTE results appears to be inherently due to experimental uncertainty [Asher, 2009]. The coastal locations used for some DTEs [e.g., Nightingale et al., 2000] may have less developed sea states and different surfactant concentrations to the open ocean, hence the results may not be widely applicable.
 Direct measurement of the turbulent CO2 flux using Eddy Covariance (EC) techniques allows the flux to be measured on shorter time scales similar to the variability of the various forcing factors. EC measurements are challenging to perform at sea due to a small signal, platform motion [Edson et al., 1998], distortion of the wind flow by platform superstructure (Yelland et al., 1998) and environmental sensor contamination [Prytherch et al., 2010]. The first successful open ocean experiment found a stronger, cubic dependence of k on wind speed [McGillis et al., 2001, hereafter M01]. There have been relatively few reported open ocean EC gas flux measurements, especially at high wind speeds (>15 m/s). Some air-sea EC experiments have found a quadratic wind speed dependence. One such experiment [Weiss et al., 2007] reported results for average wind speeds of up to 17.5 m/s, from a coastal location with low salinity (less than 9 psu) and relatively short fetch (order 100 Km). Hence, the results may not be directly applicable to the open ocean. There remains significant uncertainty in the dependence of k on wind speed.
 This paper presents a large dataset of open ocean EC CO2 flux measurements made in the North Atlantic during the High Wind Air-Sea Exchanges (HiWASE) experiment. A new parameterisation of the gas transfer velocity in terms of wind speed is developed.
2. Experimental Setup
 For the UK-SOLAS project HiWASE [Brooks et al., 2009], between September 2006 and December 2009 the Norwegian weather ship Polarfront was equipped with the autonomous turbulent flux measurement system ‘AutoFlux’ [Yelland et al., 2009]. The principle components of ‘AutoFlux’ include a Solent R3A sonic anemometer and two LICOR 7500 open-path Infrared Gas Analyzers (IRGA) measuring CO2 and H2O. The flux sensors were mounted on the Polarfront’s foremast, with one LICOR projecting to fore and one to starboard. Latent heat and momentum fluxes were measured using the Inertial Dissipation (ID) [Yelland et al., 1994] technique, and EC measurements were made of the latent heat, sensible heat, momentum and CO2 fluxes.
 Ship motion was measured using a Systron Donner MotionPak and corrections applied to the EC measurements [Edson et al., 1998]. The LICOR data were corrected for sensor head deformation effects due to ship motion by relating the results from a shrouded sensor to the MotionPak data and deducing a correction for that sensor when not shrouded [Yelland et al., 2009]: the correction is checked periodically to ensure that the shrouded “flux” values are not significantly different from zero. A system for measuring the surface water and atmospheric CO2 partial pressure [Pierrot et al., 2009] was installed on Polarfront by the Bjerknes Center for Climate Research (BCCR). It is calibrated every 3.5 hours with a zero gas and three secondary standards, which themselves have been calibrated against reference standards.
 The Polarfront operated year-round at Station M (66°N, 2°E), coming into port for 8 hours once per month, and for a 1-week refit once per year. For the majority of its time on station the Polarfront drifted beam on. The data presented here were obtained at Station M between September 2006 and December 2008. Data from 2009 were excluded due to instrument failures.
3. CO2 Flux Results
 EC measurements were made at 20 Hz, and fluxes were calculated from 20-minute sample periods. Measurements of CO2 molar density from the IRGAs were converted to mixing ratio using 20 Hz measurements of air pressure and humidity, avoiding the need for an additional flux dilution correction [Webb et al., 1980]. The CO2 fluxes calculated in this manner were compared to those calculated using the flux dilution correction and found to agree closely (R2 = 0.99) as expected.
 The initial flux results were typically about 10 times higher than would be expected using accepted values for the transfer velocity. This is a similar result to other reported measurements using open-path instruments [e.g., Smith and Jones, 1985; Kondo and Tsukamoto, 2007]. The cause of this error is thought to be a cross-sensitivity to water vapor due to contamination of the IRGA lens by hydroscopic particles from sea spray [Kohsiek, 2000]. A recently determined similarity theory-based iterative correction, the so-called PKT correction, was applied to all the EC CO2 fluxes to remove the cross-sensitivity error [Prytherch et al., 2010].
 In the available dataset there were 28,717 20-minute sampling periods with corresponding flux measurements, ΔpCO2 values and auxiliary data (i.e., mean meteorological, salinity and navigation data). Of these, 15,479 were omitted due to the relatively small size (<40 μ atm) of the air-sea ΔpCO2, which occurred during winter months. Several on station periods obtained exceptionally scattered flux measurements, possibly due to problems with instrument setup or data transfer, and measurements from these on station periods (2733 measurements) were removed. Quality control criteria were applied automatically to the remaining 10,505 sampling periods.
 To remove extreme outliers, periods were rejected if the transfer velocity was outside a cutoff value of ±900 cm/hr (1163 periods). This removed about 10% of the data: the remaining data all lay within ±3 standard deviations of the mean. Increasing the cutoff value made no significant change to the mean transfer velocity to wind speed relationship (a cutoff of ±1100 cm/hr caused a 2% decrease in k at a wind speed of 7 m/s and an increase in k of 2% at 15 m/s). Decreasing the cutoff value caused a larger change in the mean relationship (a cutoff of ±700 cm/hr caused an 18% decrease in k at a wind speed of 7 m/s and a 13% decrease at 15 m/s).
 Periods were rejected by the automated quality control if the crosswind momentum flux was larger than the along wind flux (710 periods) or if the wind direction was within 60° of the stern (853 periods). These periods are thought to be strongly affected by flow distortion. Periods were also rejected when the PKT correction did not converge (653 periods). The automated quality control procedures rejected a total of 6567 periods. The results discussed in the remainder of this paper are based on the remaining 3938 measurements. Discounting winter months when the ΔpCO2 was small, this represents approximately 30% of the total measurements. For comparison, quality control procedures on a recent long term EC CO2 flux experiment on a fixed platform in the Baltic Sea passed approximately 34% of the available periods (7820 30 minute periods passed from a 16 month long experiment [Weiss et al., 2007]).
 The HiWASE gas transfer velocities, averaged by 10-metre neutral wind speed, U10n in 1 m/s bins and normalised to a Schmidt number of 660 via:
where Sc was determined from sea surface temperature [Jähne et al., 1987] and n was assumed to equal 0.5, are shown in Figure 1 (tabulated results are available as auxiliary material). Also shown is the mean relationship and wind-averaged EC transfer velocities of M01, and the mean relationship of Sweeney et al. . Error bars show standard error: for the measurements of M01, standard error has been estimated from the published standard deviations, experiment length and assumption of a Rayleigh distribution of wind speeds [e.g., Wanninkhof et al., 2002]. If the Schmidt number exponent is chosen to be 2/3 instead of 1/2, then the transfer velocity is increased by approximately 5% at 7 m/s and 6% at 15 m/s. The Schmidt numbers measured in HiWASE were typically in the range 900 to 1300. Schmidt number values for tracers used in DTEs typically differ by a greater amount (at 20°C and a solubility of 35, Sc for 3He is 144 and for SF6 is 992). Hence the uncertainty in n is of greater importance in DTEs.
 The flux measurements from the HiWASE experiment are more scattered than those of M01. This is unsurprising: measurements were made using open-path sensors and in an opportunistic manner on a weathership rather than during a dedicated research cruise. Following the method of Fairall et al. , individual flux measurement uncertainty for a 20-minute sampling period is estimated at about 55%. Quality control procedures were applied in automated fashion rather than manual examination of each spectrum, and random error from sources such as bow thruster flumes and platform effects is likely to remain. Additionally, the PKT correction, whilst removing a large source of bias, could introduce significant additional variability through its dependence on the accuracy of the temperature and humidity fluxes. Application of the PKT correction procedure to sonic temperature measurements, in a manner analogous to the CO2 flux correction [Prytherch et al., 2010] increased the temperature flux variability by a factor of 5, although the mean flux results agreed to within 7%. A similar increase in uncertainty could therefore be expected when applying the correction to CO2 fluxes. However, application of the PKT correction led to an increase of only 3% in the variability of k for the majority of the wind speed bins. Salt contamination of the IRGA lens therefore introduces increased variability as well as bias into the CO2 flux measurements.
 A possible source of error in EC flux measurements is flow distortion by platform superstructure affecting both the turbulent components of the flow and the mean speed and height of the flow [Yelland et al., 1998]. The effect of flow distortion on the turbulent flow at exposed sensor positions and minimally disturbed wind directions is expected to be smaller for scalar fluxes than for momentum fluxes as they are dependent on only the vertical component of the wind vector [Pedreros et al., 2003]. To investigate the impact of flow distortion effects on the HiWASE flux results, latent heat fluxes measured on Polarfront using both the EC and ID methods were compared with bulk estimates. ID latent heat fluxes agreed well with bulk estimates [e.g., Smith, 1988] and the EC fluxes were low by about 5%, possibly due to the effect of flow distortion on the turbulent components of the flow. Hence any bias in the EC flux results is small compared to the existing uncertainty in k in the results presented here.
4. Wind Speed Dependence of k
 The HiWASE transfer velocity results include measurements at higher wind speeds than previously published for the open ocean. The highest wind speed measurement was at U10n = 19.6 m/s. The highest bin averaged wind speed, centered on 18.5 m/s, is based on 12 points. The very high variability of this average means it must be treated with caution. However, we have no particular reason to distrust these measurements. The previously reported highest wind speed result for open ocean EC measurements (made in the North Atlantic using a closed-path IRGA) was obtained at 15.5 m/s: this was based on only 4 points (M01).
 Assuming the same functional form as chosen by M01 (k = a + bU10nn), a cubic least squares fit to the binned measurements was found to best describe the HiWASE transfer velocities (Table 1). A quadratic least squares fit obtained nearly as high correlation with the measurements, but resulted in an unrealistic negative intercept and systematically overestimated k in the well-sampled moderate wind speed range (7 to 12 m/s). Both the quadratic and cubic fits are shown in Figure 1. The cubic fit is given by:
A fit to the individual data gives a similar cubic relationship (k660 = 7.62 + 0.034U10n3). Due to the high variability of the data, the correlation of this fit is very low and hence the fit to the averaged data is more robust. A variable-exponent fit to the binned data (k660 = a + bU10nn) determined an exponent of 3.1 (Table 1). Equation (5) is similar to, but higher than the fit determined from the data of M01 (k660 = 3.3 + 0.026 U10n3).
Table 1. Coefficients of Least Squares Fit to Wind Speed Averaged Transfer Velocitiesa
Coefficients calculated for the relationship k660av = a + bU10navn in a least squares fashion, where k660av is the wind speed averaged (ΔU10n = 1 m/s) gas transfer velocity, normalised to Sc = 660 and U10nav is the mean wind speed in each bin. Parameter uncertainties are the standard error. The r-squared correlation has been calculated between the least squares fit and k660av.
−45.3 ± 16.74
11.16 ± 1.54
−9.66 ± 8.93
0.6 ± 0.057
5.29 ± 7.02
0.034 ± 0.003
14.49 ± 6.91
0.002 ± 0.0002
Variable, n = 3.07 ± 0.6
6.03 ± 9.7
0.028 ± 0.048
 Uncertainty in the choice between a quadratic and cubic gas transfer dependence on wind speed leads to uncertainties in the global CO2 flux of order 70% [Takahashi et al., 2002]. Both quadratic and cubic wind speed relationships are capable of satisfying the global radiocarbon budget constraint (M01). However, the results reported here are higher than those of M01 (37% higher at a U10n of 7 m/s, 32% higher at 15 m/s). Conditions at the measurement site, the influence of factors other than wind speed, such as sea state and bubbles, or measurement error, may explain this discrepancy.
 Some proportion of the variability in k is due to the dependence of gas transfer on kinetic factors other than wind speed. Bubbles, primarily the result of wave breaking, have been shown to exert an influence on gas transfer by both providing an additional medium through which transfer can occur, and by disrupting the interfacial layer at the sea surface [e.g., Woolf, 1997]. The concentration of bubbles near the surface, commonly described in terms of fractional coverage of whitecaps, W, is often found to scale as the cube of the wind speed [e.g., Monahan and Spillane, 1984].
 A gas transfer model including a dependence on both wind speed and W was applied to a relatively small sample of open ocean whitecap measurements for which coincident, EC measurements of k were also available [Asher et al., 2002]. The W incorporating model agreed well with cubic wind speed dependence of the measurements. However, the bubble-mediated exchange component of the model accounted for less than 25% of the total k at the wind speeds encountered (up to 16 m/s), and is too small to explain the disparity between published quadratic and cubic wind speed based parameterisations of k. A different k model, incorporating wave-breaking effects via a fetch dependence, was tuned to encompass the spread of published parameterisations [Woolf, 2005], but this requires validation from simultaneous sea state and flux measurements.
 Bubble-mediated gas exchange implies an inverse dependence of gas transfer on gas solubility [Woolf, 1997]. EC field measurements of Dimethyl Sulfide (DMS) have shown a lower transfer velocity than usually obtained from EC CO2 flux measurements, as might be expected since DMS has a solubility about an order of magnitude larger than CO2 [Huebert et al., 2010]. Simultaneous flux measurements of gases with differing solubilities would improve understanding of bubble-mediated exchange.
5. Conclusions and Implications
 The measurements here form the largest reported set of directly-measured air-sea CO2 flux data obtained over the open ocean (Figure 1). The data includes measurements at higher open ocean wind speeds than have previously been obtained: 159 flux measurements were made at winds of over 15 m/s. A new parameterisation of the gas transfer velocity as a cubic function of neutral wind speed at 10m has been determined (equation (5)). The measurements have a high degree of variability, and two of the averages (at 7 and 16 m/s) are not well represented by the cubic relationship. Despite the large scatter in these measurements, they support the argument that the open ocean transfer velocity dependence on wind speed is stronger than quadratic at high wind speeds, and so imply a significant role for wave breaking and bubble mediated exchange in gas transfer. This makes the applicability of methods such as DTE that use a simple Schmidt number relationship to relate the transfer velocity of one gas to another, problematic at higher wind speeds [Asher and Wanninkhof, 1998].
 A stronger nonlinear dependence of gas transfer on wind speed increases the errors in CO2 fluxes from time averaging of winds. Thus the assumption of a Rayleigh distribution of wind speeds can cause significant overestimation of the global flux when calculated using global wind products [Wanninkhof et al., 2002]. In addition, wind products differ in the mean wind speed by over 1 m/s, leading to differences in global flux of 43% based on a quadratic wind speed dependence for gas transfer velocity, and 71% for a cubic dependence [Wanninkhof et al., 2009].
 It is worth noting that the results of this study are similar to those of M01: both were obtained in open ocean conditions using the EC method. The results of Weiss et al.  were also obtained using the EC method but from a coastal location where the fetch was relatively short (order 100 Km) and the salinity was very low (9 psu), conditions which are thought to lead to reduced wave breaking and whitecap coverage. At moderate and high winds the wind speed averaged results found by Weiss et al. are significantly lower than those found in this study and by M01, and agree more closely with the quadratic relationship of Sweeney et al. . The Weiss results agree with those predicted for a 100 Km fetch by Woolf’s  model which was tuned to reproduce the spread of previously published gas transfer results. Similarly, the open ocean results are similar to those predicted by the model for fetches of order 1000 Km. The difference between the coastal and open ocean EC flux results again lends weight to the hypothesis that a significant fraction of the open ocean gas transfer may be due to bubble-mediated mechanisms.
 This work was supported by the Natural Environment Research Council (grants NE/F007442/1, NE/C001826/1, NE/C001869/1, NE/C001834/1, NE/G000115/1, NE/G000123/1, NE/G003696/1, and Oceans 2025). We thank: the crew of Polarfront; the Norwegian Meteorological Institute for use of the ship; Jeff Hare (University of East Anglia) for his motion-correction algorithms and Peter K. Taylor for suggesting the PKT correction method.