GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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be computed; the bias, RMS (root-mean-square) error
and scatter index (ratio of RMS error to mean measured
value) are particularly useful as measures of performance.
Continuous hindcasts typically show scatter
indices for significant wave height in the range of
0.25–0.30, while for peak-to-peak comparisons of storm
hindcasts they are often in the range of 0.12–0.16.
In addition, it is useful to construct 1-D spectral
plots of the respective observed and modelled spectra,
e.g. at peak wave height or within three hours. For
continuous wave measurements, an appropriate moving
average should be used on the recorded data (e.g. 6 or 7
point moving average). It is instructive to represent the
data with error bars indicating appropriate confidence
limits (for instance 95 per cent). See, for example,
Figure 5.4, where the 90 per cent confidence limits are
shown.
If 2-D spectral measurements are available, they
should be used to evaluate the model predicted values.
9.6.7 Extremal analysis
From the wave hindcast model, the following quantities
are available at all points and at each time step:
• H s — significant wave height;
• T p — spectral peak period;
• θ d — vector mean wave direction;
• W s — average wind speed;
• W d — wind direction.
The objective of the extreme analysis is to describe
extremes at all contiguous grid locations for the following
variables:
• H s versus annual exceedance probability or inverse
return period;
• W s versus annual exceedance probability;
• H m (maximum individual wave height) versus
annual exceedance probability.
Techniques for extremal analysis of these quantities are
described in preceding sections.
9.6.7.1 Extreme wave/crest height distribution
For the points at which a detailed extremal analysis is
performed, the maximum individual wave height may
GUIDE TO WAVE ANALYSIS AND FORECASTING
be estimated in each storm from the hindcast zeroth and
first spectral moments following Borgman’s (1973)
integral expression, which accounts for storm build-up
and decay. The integral may be computed for
two assumed maximum individual wave height
distributions:
(a) Rayleigh (as adapted by Cartwright and Longuet-
Higgins, 1956);
(b) Forristall (1978).
The same approach may be used to estimate the
maximum crest height at a site in a storm using the
empirical crest-height distribution of Haring and
Heideman (1978). The median of the resulting distributions
of H m, H c may be taken as the characteristic
maximum single values in a storm. The mean ratios of
H m/H s and H c/H s should be calculated and used to
develop a mean ratio to provide extremes of H m and H c
from fields of extreme H s.
9.6.7.2 Presentation of extremes
Fields of extremes of H s, H m, W s should be tabulated and
displayed as field plots (contour plots if necessary) of
numerical values.
Results of detailed extremal analysis at selected
grid locations should be presented in tabular form for
each analysed point and in graphical form. The graphical
display of extrapolations shall include the fitted line, the
confidence limits on the fit and the fitted points.
9.6.8 Available hindcast databases
Several hindcast databases have been created covering a
wide range of ocean basins. Most of these are continuous
hindcasts, a few are storm hindcasts. There are no
hybrid hindcast databases presently available. A list of
available hindcast databases, with their characteristics, is
shown in Table 9.3. These databases cover periods of
three years or longer (continuous) or 40 storms or more
(storm). It is not possible to include the many other hindcasts,
related to short periods for verification purposes or
to studies of particular events, in this publication.