The Latitudinal Variation in the Wind-Speed Parameterization of Oceanic Whitecap Coverage: Implications for Global Modelling of Air-Sea Gas Flux and Sea Surface Aerosol Generation

��� In a recent publication Salisbury et al (2014) compared their estimates of oce= anic whitecap coverage, derived from microwave measurements taken by satellite-b= orne radiometers, with whitecap coverage deduced from the application of one of = the wind speed power-law parameterizations found in Monahan and O'Muircheartaigh (1980).� Specifically, they co= mpare their global maps of whitecap coverage with those determined using for n, t= he power-law exponent in Eq. 1, the value of 3.41, as obtained by Monahan and =

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�� W= _B =3D C Uⁿ, where U is the 10-meter elevation wind speed.� Eq.1

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O'Muircheartaigh via= the application of the technique of robust biweight fitting to = the whitecap data found in Monahan (1971) and Toba and Cha= en (1973).

A comparison between the whitecap coverage as deduced = at a microwave frequency of 37GHz and that deduced using Eq.1 above is found in = Fig. 3b of Salisbury et al (2014).� It is apparent from this figure of Salisbury et al that MM80 (their notation) overestimates whitecap coverage at both the high northern and high southern latitudes.� Those authors conc= lude that Eq.1 incorporates too high a wind speed dependence of whitecap coverag= e at such high latitudes.�� Th= is conclusion is consistent with the discussion found in Monahan and O'Muircheartaigh (1986) where, looking at the n's associated with 5 data sets, they dete= cted a diminution in n with decreasing surface sea water temperature (SST), and concluded that this was a reflection of the general decrease in SST with increase in latitude.� (MM86 a= ttributed this latitude dependence of n primarily on the latitudinal variation of the= characteristic duration of high wind speed events.)

��� The current authors have, in the work presented here, made use of 14 Stage B whitecap data sets (each resulting from the manual analysis of photographs), and 1 data set recently collected in the Southern Ocean involving high resolution digital i= mages (and the use of an automatic analysis protocol).

�� The initial test involved us= ing all of the non-null W_B,U data points from these 15 data sets, ha= ving first sorted them into two categories by temperature, i.e. SST > 15^{= 0}C and SST < 15⁰C.� The result is illustrated in Fig. 1, where the n(SST= > 15⁰) =3D 3.53, and the n(SST< 15⁰) =3D2.89.� It is noted that Monahan and O'Muircheartaigh(1980), analyzing only two W_{= b} data sets, for both of which SST > 15⁰C, by ordinary least squares fitting, had arrived at an n-value of 3.52.� It should also be noted that these n-values are all greater than the n-values obtained by Salisbury et al (201= 4) for their W₃₇(and W₁₀) power-laws.

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Figure 1.� ln W_B vs ln U, for SST > 15⁰ C and SST< 15⁰C.� Green dots: from high resolution d= igital imagery taken in the Southern Ocean.

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The slopes of these two lines on this log-log plot, i.e. the two n's, are significantly different (P =3D 0.01625).

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��� A further analysis was conducted using that subset of 8 W_B-data sets for which the curr= ent authors had information on the mean latitude of the observations. �A three-dimensional graphical summa= ry of these results is shown in Fig. 2.� Note here that�results from both hemispheres are plotted along the some branch of the x axis, i.e. what is plotted here is the absolute value of latitude. ��When one looks at the interse= ction of the gray�"data surface"�in this figure with the left-hand (high (absolute) Lat.) wall of this "data cube"�one sees that the slope of this intersection, i.e. the high Lat. n, is much less than the slope of the intersection of this "data surface" with the right-hand (low (absolute) Lat.) wall of this "data cube", i.e. t= he low Lat. n.� �Thus we see�that n does decrease with increasing (absolute) latitude.� It should be acknowledged that the �twist� with latitude of this "data surface" is only marginally significant, but it is consiste= nt with the findings illustrated in Fig. 1, where the difference between the "cold water" and "warm water" n's�is significantly different.&nbs= p;

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��Figure 2.ln U, where= U is the 10 m-elevation wind speed (y-axis); and lnW_B<=/sub>, where W_B is the simple fraction of the sea surface covered by decaying foam patches (z-axis). _�Key: BOMEX+ =3D black, BOMEX(Flip) =3D blue,= S. China Sea (Toba & Chaen= ) =3D green, JASIN =3D red, MIZEX83 =3D brown, MIZEX84 =3D gold, STREX (Doyle= ) =3D light blue, and Southern Ocean (Zappa) =3D magenta.�

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A series of air-sea gas transfer models, beginning with Monahan and Spillane (1984), ha= ve parameterized the gas transfer coefficient, or �friction velocityR= 21;, explicitly in terms of the fraction of the sea surface covered by Stage B (current usage) whitecaps.� If= such a model is to be evaluated where, of necessity, wind speed is being used as= a surrogate for W_B, then it is critical= that the latitude-appropriate exponent, n, be used in assessing W_B fr= om Eq. 1.� Most of the early stud= ies of k(trans. coeff.) as a function of W_B used photographs, or digital systems working in t= he visible portion of the E-M spectrum, to estimate W_B.� If W₃₇, or some other m= icrowave frequency measurement of whitecapping, is to be substituted in such parameterizations for k, a robust relationship, i.e. an inter-calibration, between W_B and W_{&mi= cro;wave} need be established.

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Grythe et al (2014) and others have recently concluded that the Monahan et al (1986) sea surface aerosol source function= is still �the most widely used source function�, and one of the te= rms in this function is W_B.� While clearly the substitution in this function, or in modifications= of it, of a climatologically derived W_B-expression, or W_{B-values from satellite-derived synoptic maps, is to be encouraged, but again a clea= rer understanding of the WB= ,W�wave relationship is needed. ��}