GUIDE WAVE ANALYSIS AND FORECASTING - WMO

9.1 Introduction
Chapter 8 described methods of measuring waves and
explained how to analyse the results to obtain estimates
of values describing the sea state, such as the significant
wave height. These estimates are usually obtained from
records made routinely over 15–35 minutes at three-hour
intervals. This chapter describes ways of analysing and
presenting the results from such records collected over
many months or years in order to give a description of
the wave climate at the recording location. Other record
lengths or intervals may be used; for example, measurements
are sometimes made at hourly intervals. Some of
the results may vary with the recording interval and it is
advisable always to specify this interval when giving
wave climate statistics.
This chapter first describes the relevant sea-state
parameters and defines the term “return value” which is
widely used to specify extreme environmental values for
designing structures such as offshore oil platforms and
sea defences. Methods of plotting wave data and statistical
analyses of the data to illustrate the wave climate are
briefly explained, together with the use of these plots to
check for possible errors in the data. Various methods
which have been developed over the years to estimate
50- and 100-year return values of wave heights are then
outlined. Some publications recommended for further
reading — in addition to the references cited — are
listed and the chapter concludes with a section on wave
climatologies and a description of the process of wave
hindcasting (Section 9.6). Annex III to this Guide
contains formulae for the statistical distributions used in
this chapter.
9.2 Definitions
9.2.1 Sea-state parameters
The two parameters most widely used to describe sea
state are the significant wave height, – H1/3, and the mean
zero-upcrossing or zero-downcrossing wave period, T – z,
or their spectral equivalents Hm0 and Tm02 defined
in Section 1.3.8. The notations Hs and T – z are used
throughout this chapter to represent both pairs of
parameters — since the methods described are applicable
to both.
High waves are often of particular importance, and
another sea-state parameter which is commonly used is
the height of the highest wave most likely to occur
during a three-hour interval, Hmax,3h. Its value may be
estimated from Hs and T – z (see Section 1.3.6) assuming
CHAPTER 9
WAVE CLIMATE STATISTICS
D. Carter with V. Swail: editors
these values remain constant for three hours. H max,3h
varies only slowly with T – z and is about 1.9 H s. In recent
years the height of the maximum wave crest (relative to
mean water level) has been of great interest, particularly
to the oil industry (interested readers can find more
details in Barstow, 1995).
There are numerous measures of ocean wave
period, but T – z, which was originally chosen because it
could readily be estimated from an analogue wave trace,
remains the most popular for many applications.
9.2.2 Return value of wave height
Designers of structures which have to stand for many
years need an estimate of the severest conditions likely
to be experienced. The usual parameter chosen to
describe such conditions is either the 50- or the 100-year
return value of wave height, where the N-year return
value is defined as that which is exceeded on average
once every N years.
This definition assumes that wave climate will
remain unchanged over 50 or 100 years, which is most
unlikely. An alternative definition is the height with a
probability of two or one per cent, respectively, of being
exceeded by the highest wave during one year. This is
equivalent to the above definition, except it does not
allow for the very small probability that the rare 50- or
100-year event might occur more than once during a
year.
Return value is a statistical parameter, and the
engineer in his design has to allow for the possibility of
a wave greater than say the 100-year return value, or
even of several such waves, occurring within a few
years. Nevertheless, the concept of return value as a
design criterion has proved useful (but see, for example,
Borgman, 1963, on risk analysis). The wave height
specified for the return value can be either H s or H max,3h,
or even the height of an individual wave. Much of the
effort given to wave climate studies in recent years has
concentrated upon methods for estimating return values
of these parameters — see Section 9.4. Sometimes, the
return value of wave crest elevation is also required in
order to specify, for example, the base height of an oil
platform. (Elevation is measured from mean sea level;
wave height is measured from crest to trough — see
Section 1.2.1.) Note that the maximum crest height is
not half of H max, as would be the case for a sinusoidal
wave, because extreme waves tend to be quite asymmetric
with typical values of crest to total wave height of
around 0.6.