Fróðskaparrit - 01.01.2007, Side 130

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VALIDATION OF THE ECMWF ANALYSIS WAVE DATA
FOR THE AREA AROUND THE FAROE ISLANDS
to verify that the ECMWF wave model
(henceforth called EW4) is well suited to
provide boundary conditions and forcing
for a high-resolution local wave model.
The four periods, which are chosen for
this validation, are centred around the
largest wave heights, recorded in the de-
ployment time of the directional waverider
WVD-4 south of Faroe Islands (Figure 1).
Each period spans one month, such that the
general skill of the EW4 model can be in-
vestigated in average and extreme circum-
stances.
The ECMWF wave model
The wave model at ECMWF is a slightly
adapted version of the WAM cycle 4 model
(ECMWF, 2004, Janssen, 2004, Janssen et
al., 2005). WAM is a third generation wave
model, which solves the wave transport
equation explicitly without any ad hoc as-
sumption on the shape of the wave energy
spectrum. The basic transport equation in
Cartesian co-ordinates is:
ðe
(1)
where F(a,Q) is the wave energy spectrum,
t is time, a is the intrinsic angular fre-
quency, 0 is the wave direction measured
clockwise from true north, c and c are
propagation velocities in geographical
space, ca and c0 are the propagation veloci-
ties in frequency and directional space re-
spectively. If Sto=0, Eq. 1 gives the local
rate of change of wave energy density due
to spatial propagation, and depth induced
shoaling and refraction. The effects of cur-
rents on the wave transport equation are
omitted here as the effects of currents on
oceanic scales are usually negligible
(Komen et al., 1994).
The right hand side of Eq. 1 represents
all effects of generation, dissipation and
wave-wave interactions. The total source
term can be expressed as Sto=Sjn+ Sds + Snl,
where S.n is the wind input, Sds is the wave
dissipation and Snl is the Discrete Interac-
tion Approximation (DIA) to the non-lin-
ear quadruplet wave-wave interactions.
More detailed information on the WAM
model and its source terms can be found in
Komen et al. (1994).
Direct application of the WAM model
to global scales will result in numerical
difficulties with the areas close to the poles
(as the distance in latitude direction de-
creases, this causes problems with the
CFL-criterion). This problem is solved in
the ECMWF-WAM (EW4) model by using
an irregular spherical grid, where the dis-
tance in latitude direction is more or less
fixed to its value at the equator (ECMWF,
2004). As the model results validated here
are derived from a regular spherical 0.25°
by 0.25° grid as disseminated by ECMWF,
some interpolation has been made in
the parameter values. The 2D-wave spectra
are not interpolated, but set equal to
the closest point from the staggered grid
(find more information on the ECMWF
wave model interpolation schemes on
http://www.ecmwf.int).
A weather or sea state forecast is essen-
tially an initial value problem. Given the
initial state, the further development in
time can be calculated. The problem is,