Gas transfer velocities measured with He/SF6 during the Sou

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, C00F04, doi:10.1029/2010JC006854, 2011

Toward a universal relationship between wind speed and gas exchange: Gas transfer velocities measured with 3He/SF6 during the Southern Ocean Gas Exchange Experiment David T. Ho,1 Rik Wanninkhof,2 Peter Schlosser,3,4,5 David S. Ullman,6 David Hebert,6,7 and Kevin F. Sullivan2,8 Received 8 December 2010; revised 1 April 2011; accepted 15 April 2011; published 28 July 2011.

[1] Two 3He/SF6 dual‐gas tracer injections were conducted during the Southern Ocean

Gas Exchange Experiment (SO GasEx) to determine gas transfer velocities. During the experiment, wind speeds of up to 16.4 m s−1 were encountered. A total of 360 3He and 598 SF6 samples were collected at 40 conductivity‐temperature‐depth (CTD) rosette casts and two pumped stations. The gas transfer velocity k was calculated from the decrease in the observed 3He/SF6 ratio using three different approaches. Discrete points of wind speed and corresponding k were obtained from the change in 3He/SF6 ratio over three time intervals. The results were also evaluated using an analytical model and a 1‐D numerical model. The results from the three approaches agreed within the error of the estimates of about ±13%–15% for Patch 1 and ±4% for Patch 2. Moreover, 3He/SF6 dual‐tracer results from SO GasEx are similar to those from other areas in both the coastal and open ocean and are in agreement with existing parameterizations between wind speed and gas exchange. This suggests that wind forcing is the major driver of gas exchange for slightly soluble gases in the ocean and that other known impacts are either intrinsically related to wind or have a small effect ( 0.01 kg m−3). Note that the cost function defined by equation (6) is formally equivalent to the definition in equation (5) (i.e., F = N × rRMSE2). As discussed previously, the uncertainties in the measured gas concentrations are expressed as relative errors, so that the uncertainty in the observed tracer ratio is proportional to its magnitude. Therefore, normalization of the differences

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HO ET AL.: UNIVERSAL GAS EXCHANGE RELATIONSHIP

Table 1. Summary of Ship Wind Speeds and k(600) From SO GasEx Schmidt Numbers

Wind Speeds, u10N (m s−1) Stations

Date Range (Yearday)

Mean

Range

sa

u210 /u10 2

Numberb

Temperature

Salinity

2–10 16–28 28–51

70.20–74.09 82.12–86.56 86.56–96.03

8.9 11.2 8.2

3.9–14.3 3.1–16.4 1.5–14.6

1.7 2.8 2.8

1.04 1.06 1.11

555 638 1365

5.6 4.8 4.7

33.8 33.7 33.7

Gas Transfer Velocities, k(600) (cm h−1)

He

SF6

Meanc

Enhancement Corrected

Error

270.8 281.5 282.9

2182.6 2284.6 2298.5

25.8 30.1 21.0

25.0 28.3 18.9

2.9 3.0 1.3

3

a

Standard deviation. Number of 10 min averaged measurements used to calculate the wind speed statistics in each interval. c Integrated k(600) over the entire period. b

in the numerator of equation (6) by the observed ratio is equivalent to weighting by the inverse of the observational errors, known as chi‐square fitting [Press et al., 1992]. The cost function (equation (6)) was minimized using a simplex direct search method (Nelder‐Mead) [Press et al., 1992].

3. Results and Discussion 3.1. Wind Speed [25] Ship wind speed during Patch 1, which consists of 555 measurements of 10 min averaged winds, ranged from 3.9 to 14.3 m s−1, with a mean of 8.9 m s−1 and a standard deviation of 1.7 m s−1. Wind speeds during Patch 2, consisting of 2003 measurements, ranged from 1.5 to 16.4 m s−1, with a mean of 9.2 m s−1 and a standard deviation of 3.1 m s−1 (Table 1 and Figure 1). The corresponding QuikSCAT wind speeds for Patch 1 from 502 measurements ranged from 2.4 to 14.5 m s−1, and had a mean of 8.7 m s−1 and a standard deviation of 2.1 m s−1. Patch 2 ranged from 1.4 to 20.8 m s−1, with a mean of 9.4 m s−1 and a standard deviation of 3.7 m s−1. The QuikSCAT and ship wind speeds averaged between CTD stations (ca. every 12 h) compared well (R2 = 0.84), with QuikSCAT winds being higher than ship winds by up to 2 m s−1 at u10 > 12 m s−1 (Figure 2). However, considering that the QuikSCAT winds cover a larger region and are based on 2–4 overpasses per day rather than continuous measurements, and because the

ship winds are averaged over ca. 12 h, this should be considered a good agreement. The ship winds are thus assumed to be representative over the entire patch. 3.2. SF6 Patch [26] The center of the tracer patch at the completion of the first injection on 9 March 2008 (yearday 69) was at 50.6042°S, 38.6308°W. SF6 concentrations as high as 440 fmol L−1 were measured during the initial survey following tracer injection. The final CTD performed before leaving the study area for the vicinity of South Georgia Island was Station 10 on 14 March 2008 (yearday 74) at 50.8620°S, 38.2394°W, and the surface SF6 concentration at this location was 29 fmol L−1. The tracer patch advected approximately 40 km over the six days of the survey [see Ho et al., 2011, Figures 16 and 17]. [27] After 4 days at South Georgia Island, the ship returned to survey in the vicinity of the MAPCO2 buoy that was deployed in the tracer patch. Low SF6 concentrations of 10 fmol L−1 were detected near the buoy. A CTD station was conducted at the approximate center of the residual patch at 51.0401°S, 37.6988°W before moving on to locate a site for a second tracer injection. Because there were no high temporal resolution wind speed measurements made at the patch location when the ship was at South Georgia Island, the change in 3He/SF6 during this period was not used in the analysis here.

Figure 1. Histograms of wind speeds encountered during SO GasEx for (a) Patch 1 and (b) Patch 2. 5 of 13

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approximately 78 km over the 15 days after the second injection. 3.3. The 3He and SF6 [29] For the CTD casts in the tracer patches, the SF6 concentrations were mostly uniform throughout the mixed layer (Figure 3). For a few of the casts, the surface concentrations were lower than the mixed‐layer average, but still well above background SF6 concentration. Over the 10.5 days during which CTD casts were done in the first tracer patch (which includes time away at South Georgia Island), the SF6 in the mixed layer in the center of the patch decreased to about 6% of the initial concentration but remained over two times higher than background concentrations. [30] The initial SF6 concentrations in the second patch were more than 4 times greater than the first patch. Over the 14 days CTD casts were done on the second tracer patch, the mixed‐layer SF6 concentrations decreased to less than 2% of the initial concentration but remained over almost three times higher than background concentration. Figure 2. Comparison between QuikSCAT and ship wind speeds for Patches 1 and 2. [28] The second tracer patch, created on 21 March 2008 (yearday 81) was centered on 51.1442°S, 38.4042°W. The maximum SF6 concentration following the injection was 999 fmol L−1. The final CTD performed in Patch 2 was on 5 April 2008 (yearday 96) and located at 51.4650°S, 37.4072°W. The surface SF6 concentrations located at this location were ∼6 fmol L−1. The second patch advected

3.4. SF6 and 3He/SF6 Depth Profiles [31] The large number of samples and duration of the study offers a unique opportunity to further investigate the basic assumptions of the dual gaseous deliberate tracer approach. In particular, we assess the issues of mixed‐layer homogeneity and mixed‐layer depth, which are both critical for calculating k3He. In some previous studies [e.g., Wanninkhof et al., 2004], the mixed‐layer depth for gas transfer is assumed to be a classically defined mixed layer based on temperature or density criteria. Here we show that in SO GasEx, the layer exchanging gas with the atmosphere

Figure 3. Profiles of normalized SF6, 3He/SF6, and temperature for (a) Station 5 (Patch 1) and (b) Station 47 (Patch 2). Normalization of SF6 (solid squares) and 3He/SF6 (open squares) is to mixed‐layer concentrations, and that for temperature (thin black line) is to the difference of the mixed‐layer average and the temperature at depth where the measured [SF6] ≈ 0. The red line is the mixed‐layer based on density criteria, where r (z)−r (5 dbar) ≤ 0.01 kg m−3, while the blue line is based on a ventilation criteria of 0.5 × [SF6]20m, where [SF6]20m is the average concentration in the upper 20 m of the water column. 6 of 13

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Figure 4. Comparison between 3He/SF6 ratios measured during SO GasEx and those derived using the analytical model described by equation (4) for (a) Patch 1 and (b) Patch 2. Six commonly used parameterizations between wind speed and gas transfer velocity are used in the analytical model. as determined from a constant 3He/SF6 ratio is often deeper. This is attributed to the longer characteristic time scales of gas transfer, expressed as h/k, of order of a week, compared to the short time scale (12 m s−1). If the comparison is limited to the wind speed range below 12 m s−1, then Wanninkhof and McGillis [1999] are able to explain about 37% of the variance. Like that of Wanninkhof and McGillis [1999], another cubic parameterization derived from eddy covariance CO2 measurements during GasEx 98 is that proposed by McGillis et al. [2001a]. This parameterization was derived from the same data set but assumed a nonzero intercept and predicts k(600) that are 10–15% lower than that of Wanninkhof and McGillis [1999] between u10 of 12 and 20 m s−1. The result is that it is able to explain 48% of the variance in the 3He/SF6 data set over the entire wind speed range. 3.10. The Future of 3He/SF6 Dual‐Tracer Experiments [46] One of the reasons that short time scale measurements like eddy covariance measurements of CO2 often produce these higher‐order dependencies (i.e., cubic versus

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quadratic) that are not reflected in the 3He/SF6 data might be because on these time scales (i.e., minutes to hours), the fluxes are indeed very high at the near surface. However, because vertical mixing cannot keep pace with the fluxes, the full water column is not impacted and therefore the higher‐order dependence is not reflected in techniques that utilize full water column mass balances. However, the 3 He/SF6 is an integrative approach that yields robust estimates of total gas exchanged in the mixed layer over periods ranging from days to weeks. This is often the relevant parameter in biogeochemical cycling whereas the micrometeorological techniques are discrete, and sometimes discontinuous, measurements with an appreciable uncertainty in each discrete value. The deviation between 3He/SF6 dual‐ tracer and CO2 eddy covariance measurements is most pronounced at higher wind speeds (i.e., > 12 m s−1) (e.g., Edson et al., submitted manuscript, 2011) where the eddy covariance values are higher. Simultaneous 3He/SF6 dual‐ tracer and CO2 eddy covariance measurements at high wind speeds, along with natural tracers of gas exchange and surface water residence time such as and 222Rn and 7Be [Kadko and Olson, 1996], and detailed physical mixed‐layer measurements are expected to help us resolve the conflict between these two leading techniques. [47] The 3He/SF6 tracer release experiments conducted in the ocean have demonstrated the power of deliberate tracers to quantify gas exchange over a period of several days or more, and spatial scales of a few tens of kilometers. However, because of the global 3He shortage [Cho, 2009], future 3 He/SF6 experiments could be jeopardized. At the moment, no alternative tracer with the properties that make 3He the perfect companion to be used with SF6 (i.e., inert, low background, similar solubility, very different diffusivity) has emerged. A concerted effort should be made to obtain 3He for these experiments, and/or to find alternative deliberate tracers to quantify air‐sea gas exchange. Since there is no other volatile tracer with a Schmidt number as low as 3He and as large a dynamic range over which it can be measured, the likely candidate is a nonvolatile tracer. The innovative application of bacteria spores used by Nightingale et al. [2000b] is an option but has a limited dynamic range for large‐scale open ocean experiments. Dyes such as Rhodamine WT measured by HPLC with fluorescence detection [e.g., Hofstraat et al., 1991; Suijlen et al., 1994] hold some promise, as demonstrated by Upstill‐Goddard et al. [2001], but losses due to absorption and photobleaching need to be properly quantified [Smart and Laidlaw, 1977].

4. Conclusions [48] During the Southern Ocean Gas Exchange Experiment (SO GasEx), two 3He/SF6 injections were made to quantify gas transfer velocities. The experiment had the largest number of 3He samples collected during a 3He/SF6 dual‐tracer experiment, and concurrent eddy covariance measurements of CO2 and DMS were made [see Yang et al., 2011; Edson et al., submitted manuscript, 2011]. [49] The 3He/SF6 results from SO GasEx show that the recently proposed parameterizations based on dual‐tracer or other water column mass balance approaches reasonably describe the relationship between wind speed and gas transfer velocity, and that results from SO GasEx are similar

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to those from other ocean basins. The important implications of these results are as follows. [50] 1. Within 20%, the wind speed/gas exchange parameterizations obtained in one location can be applied to another, so, for example, the measurements made during SAGE or SO GasEx should be applicable to other parts of the Southern Ocean. [51] 2. Field experiments, like SO GasEx, can produce valuable data for determining the relationship between wind speed and gas exchange and allow us to verify existing parameterizations. However, because of their similarities in results they cannot distinguish the functional form of these parameterizations, since these relationships are empirical and within a certain wind speed range, different functional forms will share similar features. [52] 3. Wind speed, while not the direct mechanism responsible for enhancing gas exchange, is generally recognized to be a major forcing and is perhaps the best correlate to use, considering its wide spread measurement and ease of implementation in both simple calculations and in global biogeochemical models. Furthermore, while the parameterizations of Liss and Merlivat [1986], Wanninkhof [1992], and Wanninkhof and McGillis [1999] can describe the relationship between wind speed and gas exchange in certain wind speed ranges, they fail to predict gas transfer velocities derived from the dual‐tracer method over the entire range from 0 to 16 m s−1. [53] Acknowledgments. We acknowledge M. Reid and P. Schmieder for assistance with tracer injection, sampling, and measurement; S. Archer, G. Lebon, S. Purkey, and M. Rebozo for assistance during tracer injection; C. McNally for 3 He extraction; R. Friedrich for 3 He measurements; J. Edson for providing the ship wind speed data; H. Czerski, S. Eggleston, and L. Larsen for help with data processing; and J. Triñanes for providing the QuikSCAT data from http://podaac.jpl.nasa.gov/PRODUCTS/p286. html. Funding was provided by the National Oceanic and Atmospheric Administration through NA07OAR4310113 and NA08OAR4310890 (D.T.H. and P.S.), GC07–136 (R.W. and K.F.S.), and NA07OAR4310105 (D.H. and D.S.U.). This is LDEO contribution 7466.

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