The interpretation of these observations can be made using the classical aerodynamic bulk relationship, which for the evaporative mass flux (Bye 1996), is,
where F = pE, in which p and pa are respectively the densities of freshwater and air, KE is the drag coefficient for water vapour, qs = qs(T) is the saturated specific humidity at the sea surface where T is the sea surface temperature (SST), rs = qi0/qs is the 10 m relative humidity with respect to T (which reduces to the relative humidity at 10 m for T = T10), and u = | u10| is the surface wind speed at 10 m. On taking the (natural) logarithm of (1) we obtain the expression, lnE = ln[paKB/p] + lnu + lnqs + ln(1 - rs) (2)
where es is the saturated vapour pressure, p is the atmospheric pressure and e = 0.622 is the ratio of the molecular weight of water to that of dry air. On using the Clausius-Clapeyron relation, ln es = - [e L/ (RT) ] + constant (3b)
where T(K), L = 2.5 106 J kg-1 is the latent heat of evaporation and R = 287 J kg K-1 is the specific gas constant for dry air (Gordon et al. 1998), and differentiating (2) with respect to T, we obtain approximately, dlnu/dT « dlnE/dT-eL/(RT2) (4)
in which the variation of the first and fourth terms on the right hand side of (2), with respect to T, which is relatively insignificant, has been neglected, as discussed in Bye and Keay (2006).
Equation (4) is the central working relation for our study. Firstly, evaluating the second term on the right hand side for a sea surface temperature of 15°C (which is representative of the subtropics), yields, e L/(RT2) = 0.065 K-1. Hence, since from Figs. 1 and 2, the mean slope (d ln E/dT) in the subtropics is approximately 0.065 K-1, it is clear that the variation of wind speed with sea surface temperature is of relatively small account. Here the evaporation gradient is controlled almost completely by the Clausius-Clapyron relation. The match of the observed and theoretical slopes is particularly good in the maritime southern hemisphere In the subpolar regions (which are not considered here) and in the tropics other factors become important. Our focus turns now exclusively to the situation in the tropics.
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