GUIDE WAVE ANALYSIS AND FORECASTING - WMO

individual wave height derived using this assumption
are, therefore, likely to be too low. On the other hand, the
usual method of estimating the highest individual wave
height (assuming a narrow band sea with crest to trough
height equal to twice the crest elevation) over-estimates
this height. Errors from these two incorrect assumptions
tend to cancel out. For further details see Hogben and
Carter (1992).
Battjes (1972) gives a method, modified by Tucker
(1989), which avoids this assumption. Battjes derives
numerically the distribution of individual wave heights
from the H s – T – z scatter plot, assuming that, for a specified
significant wave height, the individual waves have a
Rayleigh distribution (Equation 1.16). The number of
individual waves during the year with this significant
wave height is obtained from the T – z distribution in the
scatter plot; summation gives the total number of waves
in the year. Extrapolation of the distribution of individual
wave heights to a probability of the one wave in the total
number in N years — using Weibull probability paper —
gives the N-year return value of individual wave height.
See Battjes (1972) or Tucker (1989, 1991) for details.
9.4.3 Return value of wave height in tropical
storms
The methods so far described for estimating return
values, such as Hs50 from a set of measurements, assume
that all the measurements in the set and all the estimated
extreme values come from the same probability distribution,
with the implication that they are generated by the
same physical processes. In particular, we have assumed
that very severe storms, which give rise to extreme
values, are essentially the same as other storms, merely
more violent examples. This assumption is obviously
invalid in parts of the world where extreme waves are
invariably associated with tropical storms. The analysis
of wave records from a site in such areas, using the
methods outlined in this chapter, may well describe the
general wave climate at the site but sensible estimates of
extreme conditions will not be obtained.
Unfortunately, without this assumption, it is not
possible to estimate long-term extremes using only a few
years’ measurements from one site because the relevant
data are insufficient. We might expect between five and
15 tropical storms in an area such as the Caribbean or
the South China Sea during a year, but some might pass
too far from the site to make any impact on the local
wave conditions. Severe storms are rare. For example,
Ward et al. (1978) estimate that only 48 severe hurricanes
— the only ones to “affect extreme wave statistics
significantly” — occurred in the Gulf of Mexico
between 1900 and 1974.
Estimates of return values of wave heights in areas
where extremes are dominated by tropical storms may
be obtained by analysing storm data from the whole area
and by constructing a mathematical model to give the
probability distribution of significant wave height. The
model usually consists of three basic parts:
WAVE CLIMATE STATISTICS 109
(a) The probability that a storm will occur in the area
(a Poisson distribution is assumed with an average
interval estimated from historical records);
(b) The probability that a storm centre will pass within
a specified distance of a site (a uniform distribution
is assumed over the area or part of it determined
from historical track records);
(c) The probability of the significant wave height
exceeding a particular value given a tropical storm
passing at a specified distance (from analysis of
wave data throughout the area or hindcast wind/
wave model results).
Parts (a), (b) and (c) can be put together to give the probability
distribution of maximum significant wave height
at any site but (c) may require modification to include
fetch-limited constraints.
Further details are given, for example, in Ward et al.
(1978) and Spillane and Dexter (1976). For estimating
the height of the highest individual wave in a tropical
storm, see Borgman (1973).
9.5 Further reading
Stanton (1984) applies many of the procedures and
methods discussed in this chapter to a set of wave data
obtained off north-west Scotland with a clear exposition of
the methods. Chapter 4 of Carter et al. (1986) expands
somewhat on many of the topics covered here and gives
further references, see also Goda (1979), which includes a
detailed comparison of the various expressions used for
wave period. Mathieson et al. (1994) recently published the
findings of an IAHR working group on this subject.
Information on fitting distributions can be found,
besides that given in Johnson and Kotz (1970), in NERC
(1975). A comparison of fitting methods for the FT-I is
described in Carter and Challenor (1983) and an application
of maximum likelihood to fit environmental data to
a generalized extreme-value distribution is given in
Challenor and Carter (1983).
Methods of estimating return wave height and
further information on fitting distributions are described
by Borgman and Resio (1982), by Isaacson and
Mackenzie (1981), on pages 529–544 in Sarpkaya and
Isaacson (1981), and by Carter and Challenor (1981(b))
which includes a summary of some plotting options for
use on probability paper.
9.6 Wave climatologies
Knowledge of the wave climatology for a specific location,
a region or an entire ocean basin is important for a
wide range of activities including:
(a) Design, planning and operability studies for
harbours, coastal structures including fish farms,
offshore structures such as oil platforms, and
vessels;
(b) Coastal erosion and sediment transport;
(c) Environmental studies, e.g. the fate of, and clean-up
procedures for, oil spills;
(d) Wave energy estimation;