Fróðskaparrit - 01.01.2007, Page 134

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VALIDATION OF THE ECMWF ANALYSIS WAVE DATA
FOR THE AREA AROUND THE FAROE ISLANDS
Validation procedure
The validation will consist of two steps.
The first step is the comparison of time se-
ries of model-results vs. measurements of
relevant parameters and spectra. The sec-
ond step is the computation of statistical
parameters from the fit of the two time se-
ries. Time series give a qualitative impres-
sion, where the temporal fit of peak events
etc. can be inspected. The strength of the
statistical parameters is to give objective
information on the model performance,
which can be used to compare different
sites and different time intervals.
As the model results correspond to real-
time values (analysis values of the
wind/wave model are assimilated to real
time data), the measured time series will
not be filtered/averaged before comparison
with the model results. The statistics are
derived from model output at locations as
close to the buoy positions as possible. The
comparison is made at model output times
vs. the closest measurement time. This
non-averaged time series comparison is
used here as it favours the point of view of
the end user, that it exemplifíes how well
the model replicates the sea state at a par-
ticular location at a particular time. The
downside of this type of time series com-
parison, is that it does not take into account
the spatial and temporal resolution of the
wave model (Bidlot et ai, 2002), nor re-
duce the inherent randomness of wave pa-
rameters derived from a point time series.
The wave parameters, which are used
for the model validation, are signifícant
wave height Hm0, peak wave period T and
average wave periods Tm0I and T ()r The
average wave period can be defíned in
many ways and depend on different spec-
tral moments e.g. Tm02 =,Jm0/m2 where
m„ = j~f"E(f)df ,/is frequency and E(f) en-
ergy spectrum. T is more sensitive to the
higher ‘wind-sea’ frequencies, which ad-
just to the local wind speed much faster
than the lower frequencies compared to the
altemative mean wave periods. For this
reason a higher level of scatter is to be ex-
pected in modelled Tm02 values vs. meas-
urements compared to T gi values vs.
measurements.
Statistical parameters
Given a set of N model predicted m and ob-
served o scalar values. If we assume that
the measured data are error free, an unreal-
istic but necessary assumption, the follow-
ing statistical parameters can be computed:
Mean error also known as bias:
I » _ _
Bias = — Z4(m,-°i) = m-o (2)
A /=!
where m and o represent the mean values
of the modelled and obseiwed values. The
scatter index, which is the normalized root
mean square error, is given as:
N
(3)
Another frequently used parameter to
quantify the relation between m and o is
the correlation coefficient:

Cor =
£(°,-o)2X(w,-w)
(4)