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 =

 

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

 

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.

 

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

 

    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= ,Wµwave relationship is needed.}