3.1. Determination of Gas Transfer Velocities
[15] Airsea gas transfer rates were determined from the change in ratio of ^{3}He/SF_{6} over time. This method takes advantage of the large difference in diffusion coefficients between SF_{6} and ^{3}He. The concentration of the ^{3}He and SF_{6} will decrease over time due to dispersion and airsea gas transfer. Dispersion will decrease the concentration of both gases at the same rate, while the ^{3}He will be lost by gas exchange approximately 3 times faster than SF_{6} because of the diffusivity dependence of airwater gas transfer. The relative rate of gas transfer over the airwater interface is
where and are the gas transfer velocities of ^{3}He and SF_{6}, respectively. Sc is the Schmidt number defined as the kinematic viscosity of seawater divided aqueous diffusion coefficient of the gas and n is the Schmidt number exponent which is −2/3 for smooth (calm) surfaces and −1/2 for wavy surfaces [Jähne et al., 1987]. This Sc dependency breaks down in situations with bubble entrainment. Studies comparing SF_{6} and He exchange in wave breaking simulation tanks suggest that the dependency becomes less negative under breaking wave conditions. Initial studies [Wanninkhof et al., 1995] suggested a rapid increase (less negative) in the exponent in the presence of breaking waves, but subsequent laboratory studies and theoretical arguments suggest that for He and SF_{6} the Schmidt number exponent increases by <20% under extreme breaking wave conditions [Asher and Wanninkhof, 1998; Woolf, 1997].
[16] The known relative dependency of ^{3}He and SF_{6} transfer makes it possible to determine the absolute gas transfer velocity as shown by Wanninkhof et al. [1993],
where Δt is the time interval between t_{1} and t_{2}, and X_{t1}, X_{t2} are the ratio of ^{3}He and SF_{6} concentrations in the water sample corrected for background concentrations at t_{1} and t_{2}. In this formulation it is implicitly assumed that the concentration decreases due to dispersion and mixing are firstorder processes, and that the surface layer is well mixed on the timescale of concentration decrease due to gas exchange (≈days). Dilution processes by mixing and dispersion can be assumed to be firstorder processes if the samples are taken well within the tracer patch and if the dilution due to dispersion is of similar or smaller magnitude as loss due to gas transfer [Gulliver et al., 2002]. For the study in the southern patch of SOFex these conditions are fulfilled, except for the first few days when the streaks injected at 3m depth were spreading vertically and laterally to form a single patch. The concentrations of SF_{6} in the mixed layer with depth are reasonably homogeneous based on vertical profiles. The loss due to gas exchange can account for all of the concentration decreases in the latter part of the study, suggesting limited lateral spreading.
[17] Four to six colocated ^{3}He and SF_{6} samples were obtained in the mixed layer at each of the eight stations that were sampled. The concentration profiles for the five stations used in the analysis are shown in Figure 3. The gas transfer values were determined by averaging the ln(^{3}He/SF_{6}) values for the mixed layer samples for each station. The standard deviations of the 4 to 6 ln(^{3}He/SF_{6}) values varied from station to station but without clear correlation with mixed layer concentration or time (Figure 4). During the first 2 days of sampling immediately after the ^{3}He and SF_{6} injection, concentration ratios did not decrease systematically with time, likely because of heterogeneity caused by mixing of the injection streaks and low wind speeds. In the first days after injection the streaks coalesced, and the dilution of SF_{6} was probably not a firstorder process with respect to concentration decrease. The data from the stations sampled on the first 3 days were excluded from the analysis. During the following 8 days, the concentration ratio decreased with time, with larger drops in the ln(^{3}He/SF_{6}) occurring in stormy periods (Figure 4).
[18] The calculated gas exchange velocities of ^{3}He for each time interval after JD 28 were normalized to a Schmidt number of 660 (equivalent to that of CO_{2} in seawater at 20°C) and related to wind speeds obtained from the bow mast at 22 m above the water surface (u_{22}) normalized to a height of 10 m (u_{10}) using a constant drag coefficient of 1.2 × 10^{−3}, yielding u_{10} = 0.93 u_{22}. The results shown in Figure 5 as solid squares show a general trend of gas exchange with wind. Two frequently used relationships expressing gas transfer as a function of the square of the wind speed [Wanninkhof, 1992] and the cube of the wind speed [Wanninkhof and McGillis, 1999] are included for comparison. Two sets of curves are shown, those applicable to steady (or shortterm) winds and those for climatological winds. Although the time interval (0.5 to 2 days) would suggest that comparison with the shortterm relationships would be more applicable, the wind speed variability for each of the intervals was significant. The trend of the data favoring a strong (≈u^{3}) dependence of wind might be, in part, related to the k at 9.8 m s^{−1} falling below the trend. Since each k value was determined from ln(^{3}He/SF_{6}) measurements at adjacent times, any anomalously low k value would be followed by an anomalously high k value. Thus if ln(^{3}He/SF_{6}) values for JD 30.23 (station 25) are anomalously high, this biases the k value for 9.8 m s^{−1} low and the value for 11.3 m s^{−1} high. However, no artifacts in sampling or analysis of samples from station 25 are apparent. This station profile did show a middepth maximum in SF_{6} (Figure 3), but the ln(^{3}He/SF_{6}) values were constant in the mixed layer.
[19] The unique wind speed distributions for each time interval can account for some of the scatter of k versus u_{10} in Figure 5. Nonlinear dependencies yield higher gas transfer values for periods with greater wind speed variability. For each time period, this effect was assessed by determining k for instantaneous or steady winds, k_{inst}, assuming a particular relationship between gas exchange and wind,
R is the enhancement caused by the variability in the winds and is expressed as R = u_{10av}^{−x} where Σ(u_{10}^{x}) is the average of the sum of the 10min wind speeds squared (x = 2) or cubed (x = 3). The value for a_{x} is 0.34 when x = 2 and 0.0277 when x = 3. The values for R for each time period are shown in Table 1. They range from 1.12 to 1.24 for x = 2 and from 1.35 to 1.74 for x = 3. This implies that the variability in the wind “enhances” the gas exchange by 12–24% over each time period over which k is determined, compared with a steady wind situation if a quadratic dependency is assumed. A cubic dependency of k with wind leads to enhancements of 35–74%. The resulting k_{inst} values that account for variability are depicted in Figure 5 as crosses and open squares for quadratic and cubic dependencies, respectively. In each case, the k_{inst} values are closer to the steady wind speed relationships than the unnormalized values.
[20] To quantitatively determine the optimal coefficient for a quadratic or cubic dependency, a least squares difference was determined from the observed ln(^{3}He/SF_{6}) decrease over each time interval versus the decrease expected using a quadratic or cubic dependency with 10min averaged winds obtained from the ship's anemometer,
[21] The results shown in Figure 5 are weighted linearly with concentration decrease according to [ln(^{3}He/SF_{6})_{obs}–ln(^{3}He/SF_{6})_{modeled}]^{2} Δln(^{3}He/SF_{6})_{obs} to assign a greater weight for time intervals with greater concentration decrease. The minimum in the weighted squares of the difference is 0.34 and 0.0277 for a_{2} and a_{3}, respectively. The coefficient of 0.34 is higher than the coefficient of 0.31 for the quadratic dependency proposed by Wanninkhof [1992], while the coefficient of 0.0277 is similar to the coefficient of 0.0283 suggested for the cubic dependency by Wanninkhof and McGillis [1999]. The minima in the weighted least squares difference is similar for the cubic and the quadratic dependencies, suggesting that either fit is applicable.
[22] To further investigate if a quadratic or cubic dependence yields a better fit to the data, we focus on the time period with high winds when the difference would be most pronounced. Very strong winds were experienced during the middle part of the study from JD 30.2 to JD 31.4 with maximum 10min winds (U_{10}) reaching over 20 m s^{−1}. For this time interval there were also very low winds, further contrasting the dependencies. The optimal fit through the two points is accomplished for k = 0.403 u^{2} (660/367)^{0.5} and k = 0.02663 u^{3} (660/367)^{0.5}. The coefficient for the cubic dependence is close to the coefficient for the best fit of the entire experiment, while the coefficient for the quadratic dependence is 10% higher. This suggests that a cubic dependence, which implies a very weak dependency at low wind speeds and a strong dependency at high wind speeds, is an appropriate way to model the concentration decreases for this study.
[23] The difficulty in discerning whether a quadratic or cubic functional dependence is more appropriate for the study can be well illustrated from the modeled decrease in ln(^{3}He/SF_{6}) compared with the measured mixed layer ln(^{3}He/SF_{6}) over the course of the experiment following the approach of Kuss et al. [2004]. The concentration trends are shown in Figure 6 using 10min averaged wind speeds normalized to 10m height using cubic and quadratic relationships with the appropriate proportionalities. The initial modeled ln(^{3}He/SF_{6}) ratio at the start of the experiment was adjusted such that the modeled values would equal the value at JD 28. Since the winds at the start of the study were low, little change in modeled ln(^{3}He/SF_{6}) was noted for the first 2 days with any of the parameterizations. The modeled decreases in ln(^{3}He/SF_{6}) are very similar, illustrating the challenge of providing unique parameterizations with the limited data sets available from deliberate tracer studies. The modeled trends clearly show the effect of varying winds with very sharp decreases during periods of high wind and invariant ratios during quiescent periods. The modeled trends show that by the end of the study the use of different coefficients and dependencies yields differences in ^{3}He/SF_{6} of less than 10%, which is significantly smaller than the uncertainty in the measurements.
[24] The SF_{6} losses due to airsea gas exchange between injection and survey 1 (determined at the midpoint, JD 26.1), survey 2 (JD 30.3), and survey 3 (JD 33.5), based on the decrease in ^{3}He/SF_{6} ratio, are 5.7, 24.2, and 29.5 L of SF_{6} (STP). When these values are added to the estimated SF_{6} remaining in the patch, based on a volume integral of SF_{6} measured on the surveys, this accounts for 102, 125, and 110% of the total SF_{6} injected. Within the overall uncertainty of the gas exchange and water column inventories this suggests that all the SF_{6} is accounted for during the study.
3.2. AirSea CO_{2} Flux Estimates for the Southern Ocean
[25] The magnitude of the Southern Ocean CO_{2} sink is much debated, with significant discrepancies between estimates based on atmospheric and oceanic inverse models, and oceanic estimates based on ΔpCO_{2} [Gloor et al., 2003; Gurney et al., 2002]. Using the gas transfer parameterization described here, along with QuikSCAT wind data and the pCO_{2} climatology of Takahashi et al. [2002], an estimate of Southern Ocean fluxes is made for the region >34°S from August 2001 through July 2002. This estimate differs from Takahashi et al. [2002] in that it is for a different year and uses a different wind speed product, which includes an estimate of the influence of wind speed variability. The similarity is that the same ΔpCO_{2} field is used. Although the optimal coefficients for the gas exchange relationships derived here are slightly different from those proposed by Wanninkhof [1992] and Wanninkhof and McGillis [1999], we chose to use the published relationships since they fall well within the uncertainty range of our results. The satellite QuikSCAT wind product from August 2001 through July 2002 is used and compared with the climatological NCEP winds for 1995 or the 41year averaged NCEP winds used by Takahashi et al. [2002].
[26] The variability in the wind was assessed by determining the second and third moments of the wind product. The gas transfer velocities were determined according to
where u_{10av} is the average wind speed, a = 0.31 when x = 2, and a = 0.0283 when x = 3. The R is the enhancement caused by the variability in the winds and is expressed as R = u_{10av}^{−x} where is the average of the sum of the wind speeds squared or cubed. Note that Σ(u_{10}^{x})/n is the second or third moment if x = 2 or 3, respectively. For this analysis, monthly averaged winds over the 4° × 5° grid were determined along with the second and third moments of the wind using about 16 × 10^{3} observations per pixel per month for the QuikSCAT product. The resulting gas transfer velocities were applied to the 960 K pCO_{2} climatology of Takahashi et al. [2002], which is an update based on more data compared with the original study presented by Takahashi et al. [1997].
[27] To assess the agreement of wind products, the average and moments of the QuikSCAT winds are compared with the shipbased winds for the 2week study period. For the entire year, a blended product of QuikSCAT and special sensor microwave/imager (SMM/I) data are compared with the QuikSCAT record. The average, second, and third moments of the wind are determined from each satellite overpass for each 4° × 5° grid. Any particular point on the surface is sampled about twice a day with the QuikSCAT sensor. The large number of observations per month (≈1.6 10^{4}) for the QuikSCAT product is attributable to the 4° × 5° region in which the data are binned.
[29] The average, second, and third moments for QuikSCAT over the entire year are compared with the blended QuikSCAT and SMM/I data set. The SSM/I has a higher temporal coverage of up to 8 times a day and yields, on average, 5.7 10^{4} values per month. From this comparison, the effect of number of observations on the moments was determined. From August 2001 through July 2002, the QuikSCAT values for average wind, u_{10av}^{−2}, and u_{10av}^{−3} were 9.76 m s^{−1}, 1.15, and 1.46, respectively. For the blended product, the values were 10.6 m s^{−1}, 1.25, and 1.91. This suggests that the QuikSCAT observations miss an appreciable fraction of the variability over the annual cycle that is captured with the blended product. The combination of higher winds and greater variability of the blended product leads to 28% greater gas transfer velocities for quadratic dependencies and 67% greater gas transfer velocities for cubic dependencies, illustrating the importance of accurate and high fidelity wind speed measurements to constrain fluxes in this region. A more detailed study of wind speed variability and the effect on global airsea CO_{2} fluxes is forthcoming.
[30] Table 2 presents the fluxes for CO_{2} for both a cubic and quadratic dependence and compares the 41year averaged NCEP wind product, 1995 NCEP wind product, and QuikSCAT wind product for the period August 2001 through July 2002. The uptake for the quadratic and cubic relationship for QuikSCAT winds, including the second and third moments, ranges from 1.4 to 1.6 Pg C yr^{−1}. These values can be compared with estimates ranging from 1.4 to 2.6 Pg C yr^{−1} using the “longterm” wind equations of Wanninkhof [1992] and Wanninkhof and McGillis [1999], k = 0.39 u_{10av}^{2}, and k = 1.09 u_{10av} − 0.333 u_{10av}^{2} + 0.078 u_{10av}^{3}, respectively. The very high uptake of 2.6 Pg C yr^{−1} is, in part, due to the incorrect NCEP wind product used by Takahashi et al. [2002]. The good agreement of the quadratic relationship between this analysis and that of Takahashi et al. [2002] using the 1995 NCEP wind product is caused by the compensating effect of the 1995 NCEP winds being lower than the QuikSCAT winds, but the longterm relationship yielding a higher k.
Table 2. Summary of AirSea Fluxes in the Southern Ocean (>34°S)^{a}Formulation  Wind Product  Reference  u_{10av}, m s^{−1}  u_{av}^{−2}  u_{av}^{−3}  Uptake, Pg C yr^{−1} 


WLong  NCEP41  T2002  10.25    −1.72 
W&McGLong  NCEP41  T2002  10.25    −2.55 
WLong  NCEP95  T2002  9.26    −1.42 
W&McGLong  NCEP95  T2002  9.26    −1.92 
0.31 R u^{2}  NCEP95  this work  9.26  1.15   −1.29 
0.0283 R u^{3}  NCEP95  this work  9.26   1.54  −1.40 
0.31 R u^{2}  QuikSCAT  this work  9.76  1.15   −1.40 
0.0283 R u^{3}  QuikSCAT  this work  9.76   1.46  −1.59 
[31] Boutin et al. [2002] performed a global analysis of the influence of gas transfer parameterizations using ERS1 scatterometer winds. For the region >40°S they obtained values of 1.35 Pg C yr^{−1} and 1.51 Pg C yr^{−1} for the quadratic and cubic relationships, respectively, with the appropriate statistical estimates of variability, again suggesting that the overall effect of the difference between these two dependencies is small for the Southern Ocean. Our analysis shows an uptake of ≈0.3 Pg C yr^{−1} between 34°S and 40°S yielding an uptake of ≈1.2 Pg C yr^{−1} for >40°S, suggesting that the analysis of Boutin et al. [2002] with ERS1 winds yielded a slightly greater uptake.
[33] The results from the in situ gas exchange experiment do not suggest any significant difference in the gas exchangewind speed relationship in the Southern Ocean when compared with the established empirical relationships. The difference in resulting CO_{2} fluxes between the quadratic and cubic wind speed dependence is significantly less than previous analyses. The discrepancy of model derived CO_{2} fluxes and uptakes estimated from observations of ΔpCO_{2} must be sought elsewhere. It has been suggested that the lack of observations of ΔpCO_{2} for the entire Southern Ocean for the winter season negatively biases the ΔpCO_{2} values. Metzl et al. [2001] show that the ΔpCO_{2} in the Indian Ocean in the winter is less than that suggested by the Takahashi climatology. However, changes in Southern Ocean uptake values in the updated climatology of Takahashi et al. [2002], which substantially increased the amount of Southern Ocean observations, show only a modest decrease in the Southern Ocean sink from −1.65 to −1.42 Pg C yr^{−1} using the longterm quadratic relationship of Wanninkhof [1992].
[34] A key question arising from this analysis is how to capture the influence of variability in wind speed on the CO_{2} fluxes. Although the QuikSCAT winds provide a time series record of high accuracy, the two observations per day, on average, appear to be insufficient to characterize the full spectrum of variability over a full year. From a mechanistic perspective, this requires capturing the variability in wind at the frequency of the response of gas transfer to surface forcing. Windwave tank studies suggest that this is less than 10 min [Jähne et al., 1989], but the exact magnitude is not constrained in the natural environment.
[35] The first gas exchange determination in the Southern Ocean using the dual deliberate tracer approach suggests a clear dependence of gas exchange on wind speed that is similar to previous parameterizations by Wanninkhof [1992] and Wanninkhof and McGillis [1999]. The SOFex results show that during a period of high and variable winds the cubic dependence with the coefficient proposed by Wanninkhof and McGillis [1999] provides a slightly better fit than the quadratic dependence of Wanninkhof [1992]. Applying our derived gas exchange wind speed parameterization to the climatological ΔpCO_{2} field does not lead to significant differences in the Southern Ocean CO_{2} uptake estimate when compared with that of Takahashi et al. [2002]. However, the difference in flux between the quadratic and a cubic dependence of gas exchange on wind speed is significantly less because the variability in winds is better accounted for by using remotely sensed wind products. This analysis points to the importance of properly accounting for the effect of variable winds on gas transfer.