GUIDE WAVE ANALYSIS AND FORECASTING - WMO

The CH class may include many semi-manual
methods. The parametric approach allows empirical relationships
for the evolution of spectral parameters to be
used. These may often be evaluated without the assistance
of a computer, as may the characteristics of the
swell.
5.5.3 Coupled discrete (CD) models
The problem of swell/wind sea interaction in CH models
may be circumvented by retaining the discrete spectral
representation for the entire spectrum and introducing
non-linear energy transfers. In the models in operational
use today these interactions are parameterized in different
ways. The number of parameters are, however, often
limited, creating a mismatch between the degrees of
freedom used in the description of the spectrum (say for
example 24 directions and 15 frequencies) and the
degrees of freedom in the representation of the nonlinear
transfer (e.g. 10 parameters).
In CD models a source function of the Miles type,
Sin = B.E is very common, as in DP models. However,
the factor B is strongly exaggerated in the DP models to
compensate for the lack of explicit Snl. A Phillips’
forcing term may also be included so that Sin = A + B.E,
but the value of A is usually significant only in the initial
spin-up of the model.
The difference between present CH and CD
models may not be as distinct as the classification
suggests. In CD models the non-linear transfer is sometimes
modelled by a limited set of parameters. The
main difference can be found in the number of degrees
of freedom. It should also be noted that the CD models
usually parameterize the high-frequency part of the
spectrum.
The non-linear source term, Snl, may be introduced
in the form of simple redistribution of energy according
to a parameterized spectral shape, e.g. the JONSWAP
spectrum. Another solution can be to parameterize Snl in a similar way to the spectrum. This approach is
generally limited by the fact that each spectral form
will lead to different forms of Snl. This problem may be
avoided by using an Snl parameterized for a limited
number of selected spectral shapes. The shape most
resembling the actual spectrum is chosen. Further
approaches include quite sophisticated calculations of
Snl, such as the discrete interaction approximation of
Hasselmann and Hasselmann (1985) and the two-scale
approximation of Resio et al. (1992), and the near exact
calculations which result from numerical integration of
Equation 3.4.
The individual treatment of growth for each
frequency-direction band in CD models provides a
certain inertia in the directional distribution. This allows
the mean wind-sea direction to lag the wind direction
and makes the models more sensitive to lateral limitations
of the wind field or asymmetric boundary
condition. The CD models also develop more directional
fine structure in the spectra than CH models.
INTRODUCTION TO NUMERICAL WAVE MODELLING 65
5.5.4 Third generation models
A classification of wave models into first, second and
third generation wave models is also used, which takes
into account the method of handling the non-linear
source term S nl:
• First generation models do not have an explicit S nl
term. Non-linear energy transfers are implicitly
expressed through the S in and S ds terms;
• Second generation models handle the S nl term by
parametric methods, for example by applying a
reference spectrum (for example the JONSWAP or
the Pierson-Moskowitz spectrum) to reorganize the
energy (after wave growth and dissipation) over the
frequencies;
• Third generation models calculate the non-linear
energy transfers explicitly, although it is necessary
to make both analytic and numerical approximations
to expedite the calculations.
Results from many of the operational first and
second generation models were intercompared in the
SWAMP (1985) study. Although the first and second
generation wave models can be calibrated to give reasonable
results in most wind situations, the intercomparison
study identified a number of shortcomings, particularly
in extreme wind and wave situations for which reliable
wave forecasts are most important. The differences
between the models were most pronounced when the
models were driven by identical wind fields from a
hurricane. The models gave maximum significant wave
heights in the range from 8 to 25 m.
As a consequence of the variable results from the
SWAMP study, and with the advent of more powerful
computers, scientists began to develop a new, third
generation of wave models which explicitly calculated
each of the identified mechanisms in wave evolution.
One such group was the international group known as
the WAM (Wave Modelling) Group.
The main difference between the second and third
generation wave models is that in the latter the wave
energy-balance equation is solved without constraints on
the shape of the wave spectrum; this is achieved by
attempting to make an accurate calculation of the S nl
term. As mentioned in Section 3.5 a simplified integration
technique to compute the non-linear source term,
S nl, was developed by Klaus Hasselmann at the Max
Planck Institute in Hamburg. Resio et al. (1992) has also
derived a new method for exact computation of this
term. The efficient computation of the non-linear source
term together with more powerful computers made it
possible to develop third generation spectral wave
prediction models (e.g. the WAM model, WAMDI
Group, 1988).
Third generation wave models are similar in structure,
representing the state-of-the-art knowledge of the
physics of the wave evolution. For the WAM model the
wind input term, S in, for the initial formulation was
adopted from Snyder et al. (1981) with a u * scaling