GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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broader for a longer period. Because of the wide range
of energetic periods, the swell will also have a less regular
appearance.
4.4.3 Swell arriving at a point of observation
from a nearby storm.
As pointed out in the introduction to Section 4.4, swell,
fanning out from different points of a nearby storm edge
(less than 600 n.mi.), may reach the observation point.
When forecasting swell from a nearby storm, therefore,
the effect of angular spreading should be considered in
addition to wave dispersion.
For swell estimates:
• The sea state in the fetch area which has influence
on the forecast point must be computed;
• The distance from the leading edge of the fetch area
to the observation point measured;
• The period of the spectral peak, and the range of
wave periods about the peak found;
• The arrival time of the swell at the forecast point
determined;
• The range of periods present at different times
calculated; and
• The angular spreading factor and the wave dispersion
factor at each forecast time determined.
The angular spreading can be calculated by using
the width of the fetch area and the distance from the
fetch area to the forecast point in Figure 3.3 (see also
Section 3.3). This factor is a percentage of the energy,
so, when applied to a wave height the square root must
be taken.
From the JONSWAP results, Hasselman et al.
(1976) proposed a relation between sea-surface variance
(wave energy) and peak frequency for a wide range of
growth stages. Transforming their results into terms of
Hm0 and fp gives
H m0 = 0.414 f p –2 (fpu) 1/3 . (4.9)
Equation 4.9 together with the
JONSWAP spectrum (Figure 1.17)
and PNJ can be used to find the
wave dispersion factor at each
forecast time at the forecast point.
Figures 3.4(a) and (b) illustrate
how the wave spectrum disperses
over time. This is illustrated in the
following example.
Problem:
Figure 4.6 shows the storm that
produced waves which we want to
forecast at Casablanca. A review of
previous weather charts showed
that, in the past 24 h, a cold front
had been moving eastward. It travelled
slowly, but with sufficient
speed to prevent any waves from
GUIDE TO WAVE ANALYSIS AND FORECASTING
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moving out ahead of the fetch. At chart time, the front was
slowing down, and a secondary low started to develop. The
forecast indicated that, as the secondary low intensified,
the wind in the fetch area would change to become a crosswind
from the south. It was also expected that the front
would continue its movement, but the westerly winds in
the rear would decrease in strength. At chart time the welldeveloped
sea that existed in the fetch area would no
longer be sustained by the wind.
The fetch area (hatched area in Figure 4.6) was
480 n.mi. long and 300 n.mi. wide at chart time. The
winds in the area were WNW. The distance to
Casablanca from the leading edge of the fetch (R c) is
600 n.mi. Determine all of the swell characteristics at
Casablanca and their direction.
Solution:
During the past 24 h, the average wind speed was
u = 15 m/s in the fetch area; for that wind Hc = 4.8 m,
and Tc = 8.6 s. From Equation 4.1, Tp = 10.1 s, and the
range of important wave periods is from 14.4 s down to
5.0 s (2 fp to 0.7 fp). The first waves with a period of 14.4 s will arrive at
the coast at
0. 660 x 600
t = = 27. 5h
14.4
after chart time. Also, the waves with a period of 14.4 s
cease to arrive at the coast in
( ) =
0. 660 x 480 + 600
t =
14.4
49. 5h.
Since the time to get from the rear of the fetch area
for the wave components with T = 14.4 s is less than
24 h, Equations 4.5 and 4.6 are used to determine the
range of frequencies at each forecast time at Casablanca.
These ranges are shown in Table 4.9.
The angular spreading factor is determined from
the ratio of R c to the fetch width, i.e. 600/300 = 2. For
Figure 4.6 — Weather situation over the North Atlantic at t = 0
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Casablanca