In Search of Patagonian Dust: Atmospheric Deposition of Micronutrients to the Southern Atlantic

[1] Petelski and Piskozub [2006] have reported some novel and significant evaluations of the spray generation function that are based on measuring spray droplet concentration as a function of height near the sea surface. Their method for obtaining the spray generation function thus relies on the flux gradient relations common in micrometeorology. The more usual method for evaluating the spray generation function is to measure droplet concentration at a single height and to use a dry deposition model to infer the surface flux [e.g., Fairall and Larsen, 1984; Smith et al., 1993; Hoppel et al., 2002]. Because of the assumptions necessary in a dry deposition model, Petelski and Piskozub's method, though requiring instrumentation capable of resolving small differences in droplet concentration as a function of height, should potentially yield more accurate results. [2] I worry, however, that Petelski and Piskozub [2006] left the von Kármán constant (typically 0.40) out of their flux gradient relation for droplet concentration and consequently overestimated the spray generation function by a factor of 2.5. They also show plots of functions from the literature that are based on several different droplet-sizing conventions. The absence of a convention in marine aerosol science on how to report the size of a spray droplet that is continually changing size has been a bane to this field [cf. Andreas et al., 2001]. Although Petelski and Piskozub do not state how they standardized spray generation functions that were originally based on different sizing conventions, T. Petelski (personal communication, 2007) confirmed that they used the radius at a reference relative humidity of 80%, r80, following Petelski [2005]. [3] On including the von Kármán constant in Petelski and Piskozub's [2006] result and standardizing droplet size to the radius at formation, r0, as in my earlier review [Andreas, 2002], I show that Petelski and Piskozub's results actually agree better than they realized with the most reliable spray generation functions reported in the literature. [5] When the flow speed profile in (1) is multiplied by the fluid density and the appropriate turbulent diffusivity, the result should be τ. Thus the turbulent diffusivity clearly must be u*kz. [14] I thought at first that perhaps the absence of k in Petelski and Piskozub's [2006](12) and (14) was a typographical error rather than a mathematical oversight, but an earlier paper by Petelski [2003] includes the same two erroneous equations. Thus Petelski and Piskozub's evaluations of the spray generation function, which are based on (12) and (14) (rather than on the correct pair, (12) and (16)), are too large by a factor of 1/0.40 = 2.5. [17] As I mentioned, the variety of droplet sizing conventions has plagued attempts to reach consensus on the rate of spray generation. Petelski and Piskozub [2006] evidently used the droplet radius in equilibrium at a reference relative humidity of 80%, r80, for r in (18). In their Figures 9–11, however, they compare (18), henceforth denoted dF/dr80, and the data on which it is based to some spray generation functions that originally were referenced to the droplet radius at formation, denoted r0 and dF/dr0. [19] Andreas [2002] reviewed over a dozen published spray generation functions and concluded that the functions from Andreas [1992, 1998] and Fairall et al. [1994] had the most reasonable magnitudes and fit theoretical constraints best in the range of droplet sizes, r0, from about 1 to 500 μm. Furthermore, for their smallest sizes these three functions agree well with the function from Monahan et al. [1986], which is appropriate for r0 values from 0.8 to 20 μm and is well respected. [20] 1, 2–3 compare my version of the Petelski and Piskozub [2006] spray generation function, (19), with these four “recommended” functions. Figures 1 and 2, which are for wind speeds of 8 and 10 m/s, show that the revised Petelski and Piskozub function agrees quite well with the other four functions. For comparison, Petelski and Piskozub's [2006] Figure 9 suggests that for U10 = 8 m/s and r0 = 5 μm (equivalent to approximately r80 = 2.5 μm in their Figure 9) their spray generation function is 12 times larger than both the Monahan et al. [1986] and the Andreas [1998] functions. In my Figure 1, in contrast, the revised Petelski and Piskozub function is the same as the Andreas [1998] function at r0 = 5 μm and is only 1.7 times larger than the Monahan et al. [1986] function here. [21] Likewise, for U10 = 10 m/s, Petelski and Piskozub's [2006] Figure 9 suggests that for r0 = 5 μm (again, approximately r80 = 2.5 μm in their plot) their spray generation function is 2.5 and 6 times larger than the Monahan et al. [1986] and Andreas [1998] functions, respectively. In my Figure 2, on the other hand, my revised version of the Petelski and Piskozub function is 1.4 times smaller than both the Monahan et al. [1986] and the Andreas [1998] functions at r0 = 5 μm. [22] Finally, for Figure 10 (right) of Petelski and Piskozub [2006], where U10 = 13 m/s, for r0 = 5 μm (r80 = 2.5 μm in their Figure 10) their spray generation function is about 8 times larger than the Monahan et al. [1986] function and about 50 times larger than the Andreas [1998] function. In my Figure 3, however, for r0 = 5 μm the revised Petelski and Piskozub function is only about 3.5 times larger than the Monahan et al. [1986] function and about 8 times larger than the Andreas [1998] function. [23] Moreover, Petelski and Piskozub's [2006] data at U10 = 13 m/s may be biased high. Their Figure 7 shows that the a and exp(b) values (see my (18) and Table 1) used to create their plot for U10 = 13 m/s are significantly above the trends in these values at lower wind speeds. This bias could explain some of the remaining discrepancy in Figure 3. [24] A final curiosity about these comparisons is that if Petelski and Piskozub [2006] had standardized all the spray generation functions they showed in their figures to the dF/dr80 versus r80 convention, the comparative ranges between their plots and my plots would differ only by my multiplication by the von Kármán constant (see (19)). In the discussion of differences between their function and the Monahan et al. [1986] and Andreas [1998] functions above, however, the difference between their figures and my figures is not a constant factor of 2.5. [25] As an example of this perplexing result, for the U10 = 8 m/s plots, both the Monahan et al. [1986] and the Andreas [1998] functions are 12 times smaller than the Petelski and Piskozub [2006] function at r0 = 5 μm in their Figure 9. In my Figure 1, however, at r0 = 5 μm, the Monahan et al. [1986] function is 1.7 times smaller than the revised Petelski and Piskozub [2006] function, a factor of 7 (not 2.5) difference between their plot and mine. Likewise, the Andreas [1998] function in my Figure 1 is the same as the revised Petelski and Piskozub [2006] function, a factor of 12 (not 2.5) difference between their plot and mine. I cannot explain these discrepancies but know that I was careful in standardizing all the functions I plotted to the dF/dr0 versus r0 convention. [26] Because Petelski and Piskozub [2006] did not include the von Kármán constant in their flux gradient analysis of the spray generation function, they overestimated their spray generation function for wind speeds between 6 and 13 m/s and for droplet radii, r0, between 0.8 and 8 μm by at least a factor of 2.5. Their paper also is unclear as to whether they applied a uniform sizing convention to all the spray generations functions that they depict. [27] My (19) is a proper formulation for Petelski and Piskozub's [2006] spray generation function and should be used for future comparisons with their work. It includes the von Kármán constant and standardizes droplet radii to r0, the radius at formation. 1, 2–3 show that with these modifications, Petelski and Piskozub's results agree better with the most reliable spray generation functions than they had realized. Therefore, with their measurements, which were obtained with important new technology, we do seem to be narrowing the uncertainty in the magnitude of the spray generation function. [28] I thank Jacek Piskozub and Tomasz Petelski for insights into their measurements and for encouragement. I also thank two anonymous reviewers for helpful suggestions. The U.S. Office of Naval Research supported this work through awards N0001406MP20089 and N0001407M0142. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

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