GUIDE WAVE ANALYSIS AND FORECASTING - WMO

the monsoon season of June to September than at other
times of the year. It would be preferable if this seasonal
cycle (or intra-annual variation) could be removed
before further statistical analysis, but wave data records
are generally too short for this to be done satisfactorily
(because of the large inter-annual variation superimposed
upon the intra-annual cycle) and the data are
usually analysed as a whole — although distribution
plots for each season are often produced (see, for
example, Jardine and Latham (1981) and Smith
(1984)). The seasonal cycle, which is of fixed length,
does not present quite the same problem as that of tropical
storms which occur with random frequency from
year to year.
When analysing data with a marked seasonal cycle,
it is essential to check that the number of data values
from each season is proportional to its length. Clearly,
analysis of, say, 18 months’ data would give a poor
indication of the wave climate for any site with a marked
intra-annual cycle unless this was taken into account.
However, even when given complete years of data, it is
still necessary to check that any gaps are uniformly
spread and that, for example, there are not more gaps
during the winter months.
It is difficult to make wave measurements — the
sea is often a hostile environment for electronic
equipment as well as for man — and long series of wave
data often contain gaps. Providing these occur at
random, they can generally be allowed for in the statistical
analysis. Stanton (1984), however, found that gaps
in measurements made by a Waverider buoy in the North
Atlantic off Scotland appeared particularly in high-sea
states, which poses considerable problems for the statistician
(see Stanton (1984) for further details). The
active avoidance by merchant ships of heavy weather
could also bias visual wave data statistics.
Seasonal cycles are not the only ones to be borne in
mind. Some sites can be routinely affected by a marked
sea or land breeze. Elsewhere, the state of the tide can
significantly affect the sea state — either by wavecurrent
interaction or, if the site is partially protected, by
the restricted water depth over nearby sandbanks. These
are largely diurnal or semi-diurnal cycles and hence are
of particular importance if the data set has only one or
two records per day.
9.4 Estimating return values of wave height
In this section we first discuss how to estimate the 50year
return value of significant wave height from wave
records at sites unaffected by tropical storms. The
methods are applicable not only to data sets of significant
wave height, – H 1/3, but also to data sets of the
spectral estimate, H m0. The notation H s50 will be used for
the 50-year return value of either. The same methods can
also be applied to other data sets — such as H max,3h —
and to obtain other return values such as the 100-year
value, H s100.
WAVE CLIMATE STATISTICS 105
Then we consider the estimation of the 50-year
return value of individual wave height and, finally,
briefly comment upon estimates of return values in areas
affected by tropical storms. The methods can also be
used to analyse “hindcast” wave heights (estimated from
observed wind fields using wave models described in
Chapter 6). See Section 9.6.2 for further details.
9.4.1 Return value of significant wave height
excluding tropical storms
9.4.1.1 Introduction
The method usually employed to estimate the 50-year
return value of significant wave height is to fit some
specified probability distribution to the few years’ data
and to extrapolate to a probability of occurrence of once
in 50 years. This method is commonly used for
measured in situ data and, recently, has been successfully
applied to satellite altimeter data (Carter, 1993;
Barstow, 1995). Sometimes, the distribution is fitted only
to the higher values observed in the data (i.e. the “upper
tail” of the distribution is fitted).
An alternative method, given considerably longer
data sets of at least five years, is that of “extreme value
analysis”, fitting, for example, the highest value
observed each year to an extreme value distribution. So,
if ten years of data are available — i.e. 29 220 estimates
of Hs if recorded at three-hour intervals and allowing for
leap years — only ten values would be used to fit the
extreme-value distribution, which illustrates why long
series of data are required for this method. (The advantage
of the method is explained below.) It is widely used
in meteorology, hydrology, and in sea-level analysis in
which records covering 20–30 years are not uncommon.
There are rarely sufficient data for it to be used for wave
analysis, but it has been applied, for example, to the
Norwegian hindcast data set (Bjerke and Torsethaugen,
1989) which covers 30 years.
F(.) will be used to represent a cumulative probability
distribution i.e.:
F(x) = Prob (X < x) , (9.1)
where X is the random variable under consideration.
In our case, the random variable is Hs which is
strictly positive so
F(0) = Prob (Hs < 0) = 0. (9.2)
Assuming a recording interval of three hours, so that
there are on average 2 922 values of Hs each year, the
probability of not exceeding the 50-year return value
Hs50 is given by
( ) =
F Hs50 1
1 – ≈ 0. 9999932.
50 × 2922
(9.3)
It is important to note that the value of F(H s50) depends
upon the recording interval. If 12-hour data are being
analysed, then: