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Reply to comment by X. Zhang on “Measurements of air-sea gas exchange at high wind speeds in the Southern Ocean: Implications for global parameterizations”

[1] We thank Zhang [2007] for recognizing the significance and importance of our work. In his comment, he questioned whether we have correctly assessed the wind speed/gas transfer velocity relationship derived from the NZ SOLAS Air-Sea Gas Exchange (SAGE) experiment [Ho et al., 2006]. Specifically, he assumes that we only analyzed the gas transfer velocity data from SAGE using a quadratic wind speed enhancement and not a cubic wind speed enhancement. In fact, we concluded that the quadratic fits of Wanninkhof [1992] and Nightingale et al. [2000] were more consistent with the SAGE data than the cubic relationship of Wanninkhof and McGillis [1999], on the basis of statistical comparisons using corresponding quadratic and cubic wind speed enhancements. Also, he has misinterpreted a sentence in the abstract of Ho et al. [2006]: “The results clearly reveal a quadratic relationship between wind speed and gas transfer velocity, rather than a recently proposed cubic relationship” to mean that the data derived from the SAGE Experiment excludes all cubic relationships, when in fact, we were merely assessing existing wind speed/gas exchange relationships. In the following, we respond to the comment by Zhang [2007] and address both of his misunderstandings.

2. Wind Speed Enhancement

[2] The assumption by Zhang [2007] that we used a quadratic wind speed enhancement when we conclude that the quadratic fits of Wanninkhof [1992] and Nightingale et al. [2000] were better than the cubic relationship of Wanninkhof and McGillis [1999] is incorrect. While Ho et al. [2006] did not present cubic enhancement–corrected gas transfer velocity data because of space constraints, a cubic enhancement correction was made when comparing the SAGE data to the cubic relationship of Wanninkhof and McGillis [1999]. The enhancement corrections were made following Wanninkhof et al. [2004, equation (3)], which was referenced. We compared the various published wind speed/gas exchange relationships to the SAGE data based on the χ^{2} values of the respective fits, and the χ^{2} values for the quadratic fits of Wanninkhof [1992] (χ^{2} = 1354) and Nightingale et al. [2000] (χ^{2} = 666) were a factor of 5 and 10 smaller, respectively, than that for the Wanninkhof and McGillis [1999] (χ^{2} = 7059) cubic relationship. While space constraints did not permit us to show all the details, a more comprehensive discussion is in preparation for publication elsewhere as stated by Ho et al. [2006].

[3] Furthermore, a significant portion of Zhang [2007] deals with deriving an approximation for the cubic wind speed enhancement factor. This is an interesting exercise that would be of benefit where wind speed data are not available. However, it is not necessary for SAGE and other gas exchange experiments where direct time series measurements of wind speed are obtained.

3. Cubic Relationships

[4]Zhang [2007] also misinterprets a sentence in the abstract by Ho et al. [2006]: “The results clearly reveal a quadratic relationship between wind speed and gas transfer velocity, rather than a recently proposed cubic relationship” to mean that the data derived from SAGE excludes all cubic relationships. Ho et al. [2006] compared the SAGE data to existing relationships between wind speed and air-sea gas exchange and stated that the SAGE data are inconsistent with the recently proposed cubic relationship of Wanninkhof and McGillis [1999]. This is clearly apparent here [Ho et al., 2006, p. 3]:

Number of hours covered by the 3 stations used to calculate k(600).

b

Number of measurements used to calculate the mean wind speed in each interval.

7.5

7.4

1.13

1.11

25.6

23.1

0.5

23

276

84

9.8

8.9

1.21

1.14

15.3

13.4

10.1

24

232

114

10.5

9.0

1.09

1.15

35.9

31.2

9.0

24

195

114

10.7

7.7

1.22

1.24

19.1

15.4

10.4

24

248

105

11.0

11.3

1.16

1.10

33.3

30.3

17.5

22

248

86

11.4

11.5

1.04

1.03

29.5

28.6

15.7

24

232

106

11.5

10.4

1.02

1.05

30.6

29.2

4.7

24

234

92

12.4

8.7

1.08

1.25

31.9

25.5

5.7

34

358

152

12.9

10.8

1.02

1.04

38.5

37.0

6.6

25

234

102

15.3

15.5

1.05

1.03

52.4

50.9

3.4

50

458

206

16.1

16.0

1.03

1.03

80.8

78.4

4.3

59

574

246

[7]Zhang [2007] argues that if nonzero intercepts were used, then there is no statistical difference between the quality of a quadratic or a cubic fit to the SAGE data. We can confirm this, as we find a_{2} = 0.242 (χ^{2} = 587, r^{2} = 0.822) and a_{3} = 0.013 (χ^{2} = 562, r^{2} = 0.832), with b_{0} = 3.8 and 9.7 for the quadratic and cubic fits, respectively (Figure 1).

[8] However, the analysis of Zhang [2007] was based solely on statistical methods to determine the quality of fit to the SAGE data, without considering real world applications and constraints. Although it has similar fitting statistics to an unconstrained quadratic fit, an unconstrained cubic fit to the SAGE data might not represent the relationship between wind speed and gas exchange in the real world. While the relationship that Zhang [2007] is advocating shows that k(600) is ca. 10 cm h^{−1} at u_{10} = 0 [see Zhang, 2007, Figure 1], existing data suggest that a gas transfer velocity this high is not reached until u_{10} > 5 m s^{−1}. A zero intercept has been used for all previous wind speed/gas exchange parameterizations because for global CO_{2} update calculations, it makes very little difference whether the intercept at u_{10} = 0 was zero or slightly above zero (although it does create significant regional differences). If zero intercepts were used for the fits to the SAGE data, then a quadratic fit to the quadratic wind speed enhancement corrected data (a^{2} = 0.266, χ^{2} = 622, r^{2} = 0.811) is a slightly better fit than a cubic fit to the cubic wind speed enhancement corrected data (a^{3} = 0.017, χ^{2} = 979, r^{2} = 0.707).

[9] It is important to note that the cubic fits described above are substantially different from that proposed by Wanninkhof and McGillis [1999] (Figure 1). The analysis that we have included here, and the analysis by Zhang [2007], both show that the SAGE data are inconsistent with the cubic relationship proposed by Wanninkhof and McGillis [1999]. This is important because the Wanninkhof and McGillis [1999] parameterization has been used to generate alternate budgets of the global ocean carbon uptake, which yields a significant and important difference from other frequently used parameterizations and has significant implications for prediction of future climate change. Using the delta pCO_{2} disequilibrium method to calculate global mean ocean CO_{2}, the unconstrained cubic fit described above would yield an uptake for 1995 of 1.0 pgC y^{−1}, while Wanninkhof and McGillis [1999] would yield an uptake of 1.9 pgC y^{−1}.

5. Future

[10] These frequently used wind speed/gas exchange parameterizations [e.g., Wanninkhof, 1992; Nightingale et al., 2000] are semiempirical because the function forms are determined a priori. The main contribution of Ho et al. [2006] is that by obtaining measurements of gas transfer velocities from a range of wind speeds from the open ocean, and especially the first measurements at high wind speeds (>15 m s^{−1}), these parameterizations can now be evaluated. Zhang [2007] has misinterpreted aspects of Ho et al. [2006], but we are in agreement that the field of air-sea gas exchange study needs more measurements of k(600) from various parts of the open ocean so that we can further evaluate these existing wind speed/gas exchange parameterizations and so that we can determine whether a universal relationship exists between wind speed and air-sea gas exchange.