Detection and measurement of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 52

also Section 5.3.4 ), but most importantly agree with the recently found threshold behaviour
of breaking onset. These days, the threshold is expressed in terms of the characteristic
steepness of the wave field rather than in terms of the wind speed, which makes a differ-
ence in cases of complicated wave fields, or wave fields ambiguously coupled with the
local wind ( Banner et al. , 2000 ; Babanin et al. , 2001 , 2007a ). See, however, discussions of
the low-wind breaking threshold in Sections 5.3.4 and 9.1.1 .
Furthermore, we can mention that Cardone ( 1969 ) suggested an analytical model for
whitecap-coverage dependence on the wind by assuming that the whitecaps are a mani-
festation of wave-energy dissipation which balances the energy input to the waves from
the wind. This idea was to be followed by a great many studies in subsequent decades
(e.g. Wu , 1979 ; Zhao & Toba , 2001 ; Guan et al. , 2007 ).
The apparent quantitative differences between the early observations were not unex-
pected for both technical and physical reasons. On the technical side, variations in the
accuracy and methodology of wind measurements were pointed out by the authors of
early studies themselves ( Monahan , 1971 ). The shortcomings of the manual techniques
of processing photographic images became clearer once digital methods were developed
(see, e.g. Stramska & Petelski , 2003 ). For example, the manual methods did not take into
account the geometry difference between the near-field and far-field in oblique photogra-
phy, and as a result the whitecapping coverage of the former was overestimated and of the
latter underestimated. This would bring about discrepancies between observations taken
at different angles of incidence and introduce scatter and bias, particularly significant at
low wind speeds where the presence or absence of a breaking event in the near-field could
essentially distort the overall statistics.
Physical processes that can affect the size and duration of the persistence of whitecaps in
different environmental circumstances are very many, and they could certainly contribute
to the quantitative disagreements too. The early researchers were aware of at least some of
these, and here we refer to a recent update by Stramska & Petelski ( 2003 ):

“For example, wind history, local hydrodynamic conditions such as currents and swell, directionality
of the wave field, presence of biological surfactants, and variations of the water temperature and
atmospheric stability all can contribute to variability in the W versus U 10 relationship”

(see also Bortkovskii , 1997 , 1998 ).
The envelope of dependence of the fractional whitecap coverage W on wind speed U 10
at 10m height above mean sea level (i.e. experimental fit through the highest-coverage
values at various wind speeds) was suggested by Monahan ( 1971 ) for ocean whitecapping
as follows:

00135 U 3 . 4 W = 0 .

10 .

(3.1)

Monahan ( 1971 ) reviewed the earlier observations and found, as we have just discussed,
that available parameterisations were qualitatively similar, but quantitative deviations were
essential.