GUIDE WAVE ANALYSIS AND FORECASTING - WMO

4.1 Introduction
CHAPTER 4
WAVE FORECASTING BY MANUAL METHODS
L. Burroughs: editor
There are many empirical formulae for wave growth
which have been devised from large visually observed
data sets. There are also formulae, more recently
derived, which are based on wave measurements. These
formulae make no attempt to separate the physical
processes involved. They represent the net wave growth
from known properties of the wind field (wind speed and
direction, fetch and duration).
There are some inherent differences between
visually and instrumentally observed wave heights
and periods which affect wave prediction. In general,
the eye concentrates on the nearer, steeper waves and so
the wave height observed visually approximates
the significant wave height (H – 1/3), while the
visually observed wave periods tend to be shorter than
instrumentally observed periods. There are several
formulae which have been used to convert visual data
to H – 1/3 more accurately. For almost all practical
meteorological purposes, it is unlikely to be worth the
transformation. Operationally useful graphical presentations
of such empirical relations have existed since the
mid-1940s.
The curves developed by Sverdrup and Munk
(1947) and Pierson, Neumann and James (1955) (PNJ)
are widely used. These two methods are similar in that
the basic equations were deduced by analysing a great
number of visual observations by graphical methods
using known parameters of wave characteristics.
However, they differ fundamentally in the way in which
the wave field is specified. The former method describes
a wave field by a single wave height and wave period
(i.e. H – 1/3 and T – H1/3 ) while the latter describes a wave field
in terms of the wave spectrum. The most obvious
advantage of the PNJ method is that it allows for a
more complete description of the sea surface. Its major
disadvantage is the time necessary to make the
computations.
A more recent set of curves has been developed by
Gröen and Dorrestein (1976) (GD). These curves
comprise a variety of formats for calculating wave
height and period given the wind speed, fetch length,
wind duration, and the effects of refraction and shoaling.
These curves differ little from those found in PNJ
except that the wave height and period are called the
characteristic wave height (Hc) and period (Tc) rather
than H – 1/3 and T – –
H1/3 , and mks units are used rather than
feet and knots. Both PNJ and GD are derived from
visually assessed data. The only difference between
“characteristic” and “significant” parameters (i.e. Hc and H – 1/3, and Tc and T – H1/3 ) is that Hc and Tc are biased
slightly high when compared to H – 1/3 and T – H1/3 , which
are assessed from instruments. However, the differences
are insignificant for all practical purposes, and Hc and Tc are used throughout this chapter to be consistent
with the GD curves.
Figure 4.1 shows the GD curves for deep water.
This figure is of the form introduced in Figure 3.1
(Section 3.2) and will be used in wave calculations in
this chapter. The PNJ curves are presented for comparison
in Annex IV. For example, in Figure 4.1, thick
dark lines represent the growth of waves along increasing
fetch, which is shown by thin oblique lines. Each
thick line corresponds to a constant wind speed. The
characteristic wave height, Hc, is obtained from the
horizontal lines and the characteristic period Tc from
the dotted lines. The vertical lines indicate duration at
which that stage of development will be reached. If the
duration is limited, the waves will not develop along the
thick dark lines beyond that point irrespective of the
fetch length.
It should be noted that the curves are nearly horizontal
on the right-side of the diagram. This implies that
for a given wind speed, the waves stop growing when the
duration or fetch is long enough.
Of the formulae which have been devised from
measured wave data, the most noteable are from the
JONSWAP experiment which was introduced in
Chapter 1, Section 1.3.9 (see also Figure 1.17 and
Equation 4.1).
In this chapter several manual forecasting examples
are presented. Each example is designed to show how to
make a forecast for a given set of circumstances and/or
requirements. Some empirical working procedures are
briefly mentioned in Section 4.2. These procedures have
proved their value in actual practice and are alluded to in
Sections 4.3 and 4.4. In Section 4.3 examples highlighting
the various aspects of computing wind waves are
explained. Examples of swell computations are given in
Section 4.4. In Sections 4.3 and 4.4 all the examples are
related to deep-water conditions. In Chapter 7 shallowwater
effects on waves will be discussed, and in Section
4.5 a few examples of manual applications related to
shallow (finite-depth) water conditions are presented.
Table 4.1 provides a summary of each example given,
and indicates the sub-section of Chapter 4 in which it
can be found.
The explanations given in this chapter and in
Chapter 2 provide, in principle, all the material