Dissipation function of wind seas and wave parameterization of whitecap coverage

Wind-generated waves are the ocean surface roughness. Mass, momentum and energy passing through the air-sea interface under a given wind condition are modified by surface wave conditions. A useful parameter of wind waves in the study of air-sea exchange is the dissipation function because it quantifies the work done by the wind to the ocean. In many situations detailed wave spectral information is not available, and parameterization of energy dissipation with some global representation of surface waves, such as the significant wave height and dominant wave period, is of great value. In particular, satellite remote sensing using scatterometers, radiometers, altimeters and synthetic aperture radars is now approaching the stage of providing global coverage of wind speed, significant wave height and dominant wave period. A parameterized energy dissipation equation can be used to generate a synoptic estimation of the energy input at the air-sea interface, which is an important upper boundary condition of ocean fluid dynamics. Source function measurement is one of the most challenging tasks in wind wave research. The dominant source terms of ocean surface waves are wind input, breaking dissipation, and nonlinear wave-wave interaction. Nonlinear interaction exchanges energies between wave spectral components and does not contribute to the overall energy gain or loss of the wave field. The fetchor duration-limited growth laws can be used to derive a resultant source function, that is, the net growth rate of wind waves [e.g., Hasselmann et al., 1973; Donelan, 1998]. Using the independently derived wind generation functions [e.g., Snyder et al., 1981; Hsiao and Shemdin, 1983; Donelan et al., 2006], the equivalent wind input term can be derived from integrating wind generation function over the whole spectrum. The difference between the integrated wind input and the net wave growth, therefore, represents the integrated energy dissipation. Because net growth rate is only about five percent or less of wind input [Hasselmann et al., 1973; Donelan, 1998], for practical purposes, the integrated dissipation function can be approximated with the integrated wind input function. The detailed discussion is presented in Section 2. In Section 3, the derived dissipation function is applied to whitecap observations that also reported wave measurements. Over the years, extensive observations of whitecaps have led to the conclusion that the powerlaw wind speed dependence remains the most robust empirical relation describing the whitecap coverage in the ocean despite the consensus that wave parameters somehow play a role because whitecaps are caused by wave breaking, thus it should be related to wave energy dissipation [e.g., Monahan, 1971; Toba and Chaen, 1973; Ross and Cardone, 1974; Monahan and O’Muircheartaigh, 1986; Wu, 1988; Zhao and Toba, 2001; Lafon et al., 2004, 2007; Anguelova and Webster, 2006]. With the analytical expression of the integrated dissipation function, it becomes clear that wave energy dissipation is proportional to the cubic power of wind speed and the explicit dependence on wave parameters is 3.3 * * ω η , which, for a wide range of wave growth conditions is almost constant. This offers a plausible explanation on why it is so difficult to establish a reliable dependence of whitecap coverage on wave parameters up to this date. A summary is presented in Section 4.