GUIDE WAVE ANALYSIS AND FORECASTING - WMO

give large differences in the comparisons. Further, it
must be remembered that in situ measurements are only
estimates and individual spectral components may have
quite large uncertainty due to high sampling variability
in the estimates.
For these reasons, model validation studies are
usually performed in a statistical sense using all available
data, and are based on comparisons of derived
parameters. A common approach is to perform a regression
analysis on a set of important parameters such as
H s, T – z (or T p) and, if directional wave data are available,
the mean direction (for different frequency bands). In
addition, it may be useful to compare mean wave spectra
or cumulative distributions (of, for example, H s) for
simultaneous model results and measurements. Since the
wind field that drives the model is intimately related to
the model wave field, most evaluation studies also
include verification of wind speed and direction.
An important requirement for evaluation of a wave
model is the availability of reliable sea-state measurements
and related weather data. Most of the evaluation
studies reported in the last 15 years have used buoy data
for wind and wave measurements and have occasionally
used analysed weather maps for additional wind
information. A few earlier studies (e.g. Feldhausen et al.,
1973) have used visual ship reports for wave height to
make a qualitative evaluation of several wave hindcasting
procedures. More recently, satellite altimeter data
have been used to validate wave model results. For
example, Romeiser (1993) validated the global WAM
model (WAMDI Group, 1988; Komen et al., 1994) for a
one-year period using global data from the GEOSAT
altimeter.
Most verification studies have attempted to calculate
several statistical parameters and analysed the
magnitude and variation of these parameters to determine
the skill of a wave model. Among the parameters
that are most commonly used are:
• The mean error (ME) or bias;
• The root-mean-square error (RMSE);
• The Scatter Index (SI) defined as the ratio of RMSE
to the mean observed value of the parameter; and
• r, the sample linear correlation coefficient between
the model and the observed value.
A few studies have considered other statistical measures
to evaluate wave model performance such as the slope of
the regression line between model and observed values
or the intercept of the regression line on the y axis. The
four parameters as listed above are the best indicators of
the performance of a wave model.
Verification of operational wave models at
national Services of many countries is an ongoing
activity. At most Services, the initial verification of a
wave model is performed during the implementation
phase and the verification statistics are updated periodically
so as to monitor the model’s performance.
Table 6.1 shows the performance of a few wave models
which are presently in operational use at various
OPERATIONAL WAVE MODELS 73
national (international) organizations in different parts
of the world. The table presents verification statistics
for wind speed, wave height and peak period (where
available) in terms of four statistics, namely: ME,
RMSE, SI and r as defined above. The table includes a
variety of models developed over the last twenty years,
ranging from first generation (1G) to the recent third
generation (3G) models (see Section 5.5 for a discussion
of model classifications).
Verification statistics for many more models have
been summarized elsewhere by Khandekar (1989).
Based on these statistics, it may be concluded that a firstgeneration
wave model driven by winds obtained from a
weather prediction model can provide wave height
simulations with an RMS error of about 1.0 m and a
scatter index of around 35 per cent. The second- and
third-generation wave models, driven by winds from
operational weather prediction models, can provide wave
height simulations with RMS errors of about 0.5 m and
scatter indices of about 25 per cent. The third-generation
WAM model (see Section 5.5.4), which has run
operationally since early 1992 at the European Centre
for Medium-Range Weather Forecasts (ECMWF) in the
United Kingdom, generates wave height values with
RMS errors ranging from 0.4 m to 0.7 m in different
parts of world oceans, while the bias (or mean error)
ranges from 0.05 m to 0.2 m. Since these statistics were
generated further improvements have been made both to
the determination of wind fields and the wave models
themselves, so it is expected that the results of the verifications
will also be continually improving.
A sample wave height plot generated by the US
Navy’s GSOWM at a buoy location in the Gulf of
Alaska is shown in Figure 6.6. The figure shows wave
height variation in the Gulf of Alaska as measured by the
buoy and as modelled by the GSOWM. The GSOWM
was driven by winds from the GSCLI (Global Surface
Contact Layer Interface) boundary-layer model. The
figure also shows wave height variation simulated by the
WAM model, which was configured to run on a 1° x 1°
grid and was driven by surface wind stress fields generated
by the Navy Operational Global Atmospheric Prediction
System (NOGAPS). Also shown along with the
wave plots are wind and wave error statistics covering
the one-month period from 20 February to 20 March
1992. The GSOWM has a high bias of about 1 m in
its wave height simulation on the US west coast. This
bias is due to the model’s tendency to retain excess
low-frequency energy from swell waves which often
travel from the central Pacific to the US west coast.
Figure 6.7 shows the verification of the global wave
height field generated by the WAM model at ECMWF
against wave heights measured by the radar altimeter
aboard the satellite ERS-1 (see Section 8.5.2). The altimeter
wave heights plotted along the sub-satellite tracks
cover a six-hour window centred around the time for
which the model wave height field is valid. In general, the
model wave heights show an excellent agreement with