Detection and measurement of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 112

between wavelet-approach detection and the measurements. The results of these final counts
of the breaking cases are shown in Figure 2.4 and discussed in Section 2.4 .
Thus, the wavelet transform provides an opportunity to look at each individual wave
crest in a time series of wave data and assess whether or not it might be a breaking wave.
In Liu & Babanin ( 2004 ), the approach was shown to be capable of producing the same
breaking statistics as field measurements of wave-breaking conditions based on detection
of whitecaps at a fixed point of observations.
The Liu & Babanin ( 2004 ) approach uses the classical limiting downward-acceleration
concept, developed primarily for monochromatic waves (e.g. Longuet-Higgins , 1969a ).
With wavelet transform as a time-frequency analysis method, this concept can now be
extended to spectral dominant waves when an instantaneous wave spectrum is replaced by
an instantaneous characteristic wave (3.35) - (3.38) , and applied to actual sea-wave meas-
urements. The results can be interpreted through basic wave physics and a limiting value
of the acceleration has been obtained from available field measurements. The approach is
applicable to both deep-water and finite-depth environments.
3.8 Statistical methods for quantifying breaking probability and dissipation
The statistical methods for quantifying breaking probability and whitecapping dissipation,
described in this section, are not actually based on direct or even indirect detection and
measuring the breaking events as such. Based on some assumptions and, as is usual in
wave-breaking studies, on some theoretical/empirical criteria, they try to interpret statis-
tical properties of the wave fields in order to figure out a contribution of breaking waves
to this statistics. It is argued that these properties prior to the breaking (or rather in the
absence of breaking) are known theoretically, and therefore the differences observed are
due to the breaking. In this regard, such statistical methods do not deal with either detection
or the measurement of wave breaking, which is the topic of this chapter, but we thought it
would be logical to place a brief description in the current chapter because these methods
do appeal to measurements of the waves and, based on these measurements, infer breaking
probabilities and severity, as with the other methods described in this chapter.
The first analytical approach of this kind was a probability model suggested by Longuet-
Higgins ( 1969a ) and further developed by Yuan et al. ( 1986 ), Hua & Yuan ( 1992 ) and Yuan
et al. ( 2008 , 2009 ). All of these studies used the Gaussian distribution of surface elevations
to predict the appearance of wave heights exceeding the limiting steepness of the Stokes
wave (2.47) , or its limiting orbital velocity (2.49) , or its limiting acceleration at the crest
(2.50) . In this regard, the models are based on sound physical principles.
Statistical approaches to surface elevation, or wave-height, or wave-crest probability
distributions are now a textbook subject and we refer the reader to such topics for details
(e.g. Young , 1999 ; Holthuijsen , 2007 ). The surface elevation is often treated as having
a normal/Gaussian probability distribution, and although obvious deviations from such
distributions are reported (e.g. Babanin & Polnikov , 1995 ), the Gaussian probability