GUIDE WAVE ANALYSIS AND FORECASTING - WMO

TABLE 4.4
Additional wave information for Problem 4.3.3
Hc Tc u Tp –
TH1/3 Hmax (m) (s) (m/s) (s) (s) (m)
Point B 6 9.3 17.5 11.2 10 12
and the mean period is about 8 s. The wave propagation
rate is given by c = gT c/2π and the group velocity is
given by c g = c/2 in deep water. Since g/2π = 1.56 m/s 2
(or 3.03 kn/s) then the group velocity c g ≈ 0.78 T c m/s or
≈ 1.5 T c kn. Waves with T c = 8 s have c g ≈ 12 kn and, in
12 h, cover a distance of 144 n.mi., or 2.4° of latitude.
Dividing 2.4 by T c = 8 gives 0.3. This example shows
that the travel distance over 12 h, expressed in degrees of
latitude, is 0.3 T c. This is an easy formula to use to determine
how far upwind to put A.
H c equals 4.2 m at time t 0 at point A. To produce
waves of that height, a wind of 17.5 m/s needs an equivalent
duration of 8 h. H c at point B at t 0 + 12 h can be
determined by taking a total duration 8 h + 12 h = 20 h.
From Figure 4.1, H c = 6 m and T c = 9.3 s. Table 4.4
gives additional information.
4.3.4 Extrapolation of an existing wave field
with further development from an
increasing wind
Problem:
The situation at t0 is the same as in Figure 4.3, but now
the wind increases from 17.5 m/s at t0 to 27.5 m/s at
t0 + 12 h over the area which includes the distance AB.
Forecast the sea state at Point B.
Solution:
Because the increase in wind speed is so great, divide the
time period into two 6 h periods with winds increasing
from 17.5 m/s at t 0 to 22.5 m/s, and 22.5 m/s to 27.5 m/s,
respectively. Recalling Section 4.2.1, the corresponding
speeds used to compute the waves are 21 m/s (21.25)
and 26 m/s (26.25).
At t 0, H c equals 4.2 m. Waves grow to this height
with 21 m/s winds after 5 h. Over the first period then
the equivalent duration with u = 21 m/s is 5 h + 6 h =
11 h. At the end of the interval, H c = 6.5 m.
Waves would reach the 6.5 m height after an equivalent
duration of 5.5 h with a wind of 26 m/s. Over the
second 6 h period then, we may work with an equivalent
duration of 11.5 h and a wind of 26 m/s. Thus,
H c = 9.2 m, and T c = 10.6 s (see Table 4.5).
Actually these waves would have passed point B,
since the average wave period during the 12 h period in
this case was nearly 9 s. Their travel distance would be
slightly greater than 2.6° of latitude. This small adjustment
to the distance AB would not have influenced the
calculations. In routine practice the travel distances are
rounded to the nearest half degree of latitude.
WAVE FORECASTING BY MANUAL METHODS 47
TABLE 4.5
Values of parameters computed from Hc for Problem 4.3.4
4.4 Computation of swell
For most practical applications two different types of
situation need to be distinguished:
(a) Swell arriving at the point of observation from a
storm at a great distance, i.e. 600 n.mi. or more. In
this case, the dimensions of the wave-generating
area of the storm (e.g., tropical cyclone) can be
neglected for most swell forecasting purposes, i.e.
the storm is regarded as a point source. The important
effect to be considered is wave dispersion;
(b) Swell arriving at the point of observation from a
nearby storm. Swell fans out from the points along
a storm edge. Because of the proximity of the storm
edge, swell may reach the point of observation
from a range of points on the storm front. Therefore,
apart from wave dispersion, the effect of
angular spreading should also be considered.
In swell computations, we are interested in the
propagation of wave energy. Therefore, the group velocity
of individual wave components, as approximated by
representative sinusoidal waves, should be considered.
Since large distances are often involved, it is more
convenient to measure distances in units of nautical
miles (n.mi.) and group velocities in knots (kn). The
wave period T is measured in seconds as usual. We then
have (as in Section 1.3.2):
c
g
Hc Tc u Tp –
TH1/3 Hmax (m) (s) (m/s) (s) (s) (m)
Point B 9.2 10.6 27.5 13.2 11.9 18.4
c 1 gT 1
= = = 3. 03T = 1. 515T
(kn).
2 2 2π
2
(4.3)
4.4.1 Distant storms
In the case of a distant storm (Figure 4.4), the questions
to be answered in swell forecasting are:
(a) When will the first swell arrive at the point of
observation from a given direction?
(b) What is the range of wave periods at any given
time?
(c) Which wavelengths are involved? and, possibly
(d) What would the height of the swell be?
The known data to start with are the distance,
Rp (n.mi.), from the storm edge to the point of observation,
P, the duration, Dp, of wave generation in the
direction of P, and the maximum wave period in the
storm area.
Because they travel faster, the wave components
with the maximum period are the first to arrive at P.
Their travel time is: