GUIDE WAVE ANALYSIS AND FORECASTING - WMO

5.1 Introduction
National Meteorological Services in maritime countries
have experienced a rapidly growing need for wave forecasts
and for wave climatology. In particular the offshore
oil industry needs wave data for many purposes: design
sea states, fatigue analysis, operational planning and
marine operations. Furthermore, consulting companies
operating in the maritime sector have an increasing need
for wave information in their projects.
To meet this growing requirement for wave information,
wave conditions must be estimated over large
tracts of ocean at regular intervals, often many times a
day. The volume of data and calculations makes computers
indispensable. Furthermore, measured wave data
are often sparse and not available when and where they
are desired. Using wind information and by application
of the basic physical principles that are described in
Chapter 3, numerical models have been developed to
make the required estimates of wave conditions.
In wave modelling, we attempt to organize our
theoretical and observational knowledge about waves
into a form which can be of practical use to the forecaster,
engineer, mariner, or the general public. The most
important input to the wave models is the wind at the sea
surface and the accuracy of the wave model output is
strongly dependent on the quality of the input wind
fields. Chapter 2 is devoted to the specification of marine
winds.
In the WMO Handbook on wave analysis and forecasting
(1976), one particular model was described in
detail to exemplify the structure and methodology of
numerical wave models. Since then new classes of
models have appeared and were described in the WMO
Guide to wave analysis and forecasting (1988). Rather
than giving details of one or a few particular models, this
chapter will give general descriptions of the three model
classes that were defined in the SWAMP project
(SWAMP Group, l985). A short description of the “third
generation” WAM model developed by an international
group of wave modellers is added.
The basic theory of wave physics was introduced in
Chapter 3. In this chapter, Section 5.2 gives a brief introduction
to the basic concepts of wave modelling. Section
5.3 discusses the wave energy-balance equation.
Section 5.4 contains a brief description of some elements
of wave modelling. Section 5.5 defines and discusses the
most important aspects of the model classes. The practical
applications and operational aspects of the numerical wave
models are discussed in Chapter 6.
CHAPTER 5
INTRODUCTION TO NUMERICAL WAVE MODELLING
M. Reistad with A.K. Magnusson: editors
5.2 Basic concepts
The mathematical description of surface waves has a
large random element which requires a statistical
description. The statistical parameters representing the
wave field characterize conditions over a certain time
period and spatial extent. Formally, over these scales, we
need to assume stationarity (steadiness in time) and
spatial homogeneity of the process describing the sea
surface. Obviously, no such conditions will hold over the
larger scales that characterize wave growth and decay.
To model changing waves effectively, these scales (timestep
or grid length) must be small enough to resolve the
wave evolution, but it must be recognized that in time or
space there are always going to be smaller scale events
which have to be overlooked.
The most used descriptor of the wave field is the
energy-density spectrum in both frequency and direction
E(f,θ), where f is the frequency, and θ the direction of
propagation (see Section 1.3.7). This representation is
particularly useful because we already know how to
interpret what we know about wave physics in terms of
the spectral components, E(f,θ). Each component can be
regarded as a sinusoidal wave of which we have a
reasonably well-understood theory. From this spectrum,
we can deduce most of the parameters expected of an
operational wave model, namely: the significant wave
height, the frequency spectrum, the peak frequency and
secondary frequency maxima, the directional spectrum,
the primary wave direction, any secondary wave directions,
the zero-crossing period, etc. (see Chapter 1).
Not all models use this representation. Simpler
models may be built around direct estimation of the
significant wave height, or on the frequency spectrum,
with directional characteristics often diagnosed directly
from the wind.
There is a reasonable conception of the physical
processes which are thought to control wave fields. To
be of general use in wave modelling, these processes are
described by the response of wave ensembles, i.e. they
are translated into terms of useful statistical quantities
such as the wave spectrum. Not all the processes are yet
fully understood and empirical results are used to varying
degrees within wave models. Such representations
allow a certain amount of “tuning” of wave models, i.e.
model performance can be adjusted by altering empirical
constants.
Although models for different purposes may differ
slightly, the general format is the same (see Figure 5.1
for a schematic representation).