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```Single Storm
The previous sections have shown that an entire storm can be characterized by just two
numbers: one related to the wave period and one to the wave height. It now becomes
important to predict these values from other data - such as geographical and meteorological
information.
Wave Prediction
In general, prediction models are based upon the following parameters:
² wind speed,
² distance over which the waves have travelled under that wind …eld, called fetch and
² duration of the wind speed.
Coastal engineers often add fourth parameter: the water depth. This is less important
for o¤shore engineering applications and will not be included here. Figure 5.41 shows the
relevant parameter relations for deep water.
Figure 5.41: Parameter Relations of a Fetch-Limited Fully Developed Sea
Signi…cant wave heights (m) are to be read o¤ along the logarithmic scale on the left. One
can enter the diagram with a wind speed (m/s) along the vertical axis on the right and
the fetch (km) chosen from the values written along the upper curve.
One then reads o¤ three remaining items:
5-52 CHAPTER 5. OCEAN SURFACE WAVES
² Wave Height H in meters, on the left of the …gure,
² Duration t in hours, needed to generate the wave under the chosen conditions on
the bottom of the …gure and
² Wave Period T in seconds, by interpolating between the dashed lines.
Most oceanographers consider a fully developed sea to be one in which - for a given wind
speed - the remaining wave conditions (height and period) are no longer in‡uenced by
either the storm duration or fetch length and thus one’s location. Even if one were to
travel around the globe with the constant wind …eld, one would …nd that the wave height
no longer increased. Fully developed sea conditions are represented in this …gure by the
triangular area on the right in which the wave height (for a given wind speed) is indeed
independent of the duration or the fetch.
Suppose, as an exercise with …gure 5.41, a wind speed of 10 m/sec (Beaufort force 5).
With a fetch of 60 km, the sea no longer increases after 6 hours. This sea is de…ned by a
signi…cant wave height of 1.5 meters with an average wave period of 4.8 seconds.
With a fetch of 600 km, the sea no longer increases after 40 hours. This sea is de…ned by
a signi…cant wave height of 2.0 meters with an average wave period of 6.4 seconds.
Notice that, if one were to wait longer at a given location than the time duration found
in this …gure, the wave height would not increase further even though the waves are not
oceanographically fully developed; they are limited in this case by the fetch.
Storm Wave Data
The table below, for ”Open Ocean Areas” and ”North Sea Areas” gives an indication of
an average relationship between the Beaufort wind scale (or the associated average wind
velocity) at 19.5 meters above the sea and the signi…cant wave height H1=3 and the average
wave periods T1 and T2, de…ned before. These data have been plotted in …gure 5.42.
Wave Sp ec tru m Param eter E st im ates
S ca le o f W ind Sp ee d Op en Oc ean A re as North Sea Areas
B eau fort at 19.5 m (B retsch neid er) (JONS WAP)
above se a
H1=3 T1 T2 H1=3 T1 T2 °
(kn) (m ) (s) (s) (m ) (s) (s) ( -)
1 2 .0 1 .10 5 .80 5 .35 0 .50 3.50 3 .25 3 .3
2 5 .0 1 .20 5 .90 5 .45 0 .65 3.80 3 .55 3 .3
3 8 .5 1 .40 6 .00 5 .55 0 .80 4.20 3 .90 3 .3
4 13 .5 1 .70 6 .10 5 .60 1 .10 4.60 4 .30 3 .3
5 19 .0 2 .15 6 .50 6 .00 1 .65 5.10 4 .75 3 .3
6 24 .5 2 .90 7 .20 6 .65 2 .50 5.70 5 .30 3 .3
7 30 .5 3 .75 7 .80 7 .20 3 .60 6.70 6 .25 3 .3
8 37 .0 4 .90 8 .40 7 .75 4 .85 7.90 7 .35 3 .3
9 44 .0 6 .10 9 .00 8 .30 6 .10 8.80 8 .20 3 .3
10 51 .5 7 .45 9 .60 8 .80 7 .45 9.50 8 .85 3 .3
11 59 .5 8 .70 10 .10 9 .30 8 .70 10.00 9 .30 3 .3
12 >64 .0 10 .25 10 .50 9 .65 10 .25 10.50 9 .80 3 .3
5.5. WAVE PREDICTION AND CLIMATOLOGY 5-53
0
1
2
3
4
5
6
7
8
9
10
11
12
0 1 2 3 4 5 6 7 8 9 10 11 12
H1/3
T2
T1
North Sea Areas
(JONSWAP)
Wave Period
Wave Height
Beaufort
S
ig
n
ifi
ca
nt
W
av
e
H
ei
gh
t
(
m
)
A
ve
ra
ge
P
e
rio
ds

(s
)
0
1
2
3
4
5
6
7
8
9
10
11
12
0 1 2 3 4 5 6 7 8 9 10 11 12
H1/3
T2
T1
Open Ocean Areas
(Bretschneider)
Wave Period
Wave Height
Beaufort
S
ig
ni
fic
an
t W
av
e
H
ei
gh
t
(
m
)
A
ve
ra
ge
P
er
io
ds

(s
)
Figure 5.42: Wave Spectrum Parameter Estimates
This table and …gure 5.42 show lower and shorter waves in North Sea Areas, when compared
at the same wind strength (Beau…ort number) with those in Open Ocean Areas.
Other open ocean de…nitions for the North Atlantic and the North Paci…c, obtained from
[Bales, 1983] and adopted by the 17th ITTC (1984) as a reliable relationship for these
areas, are given in the table below. The modal or central periods in this table correspond
with the peak period, Tp, as de…ned before.
5-54 CHAPTER 5. OCEAN SURFACE WAVES
Open Ocean Annual Sea State Occurrences from Bales (1983)
for the North Atlantic and the North Paci…c
Sea Signi…cant Sustained Probability Modal
State Wave Height H1=3 Wind Speed 1) of Sea State Wave Period Tp
Number (m) (kn) (%) (s)
(¡)
Range Mean Range Mean Range 2) Most 3)
Probable
North Atlantic
0 - 1 0.0 - 0.1 0.05 0 - 6 3 0 - -
2 0.1 - 0.5 0.3 7 - 10 8.5 7.2 3.3 - 12.8 7.5
3 0.50 - 1.25 0.88 11 - 16 13.5 22.4 5.0 - 14.8 7.5
4 1.25 - 2.50 1.88 17 - 21 19 28.7 6.1 - 15.2 8.8
5 2.5 - 4.0 3.25 22 - 27 24.5 15.5 8.3 - 15.5 9.7
6 4 - 6 5.0 28 - 47 37.5 18.7 9.8 - 16.2 12.4
7 6 - 9 7.5 48 - 55 51.5 6.1 11.8 - 18.5 15.0
8 9 - 14 11.5 56 - 63 59.5 1.2 14.2 - 18.6 16.4
>8 >14 >14 >63 >63 <0.05 18.0 - 23.7 20.0
North Paci…c
0 - 1 0.0 - 0.1 0.05 0 - 6 3 0 - -
2 0.1 - 0.5 0.3 7 - 10 8.5 4.1 3.0 - 15.0 7.5
3 0.50 - 1.25 0.88 11 - 16 13.5 16.9 5.2 - 15.5 7.5
4 1.25 - 2.50 1.88 17 - 21 19 27.8 5.9 - 15.5 8.8
5 2.5 - 4.0 3.25 22 - 27 24.5 23.5 7.2 - 16.5 9.7
6 4 - 6 5.0 28 - 47 37.5 16.3 9.3 - 16.5 13.8
7 6 - 9 7.5 48 - 55 51.5 9.1 10.0 - 17.2 15.8
8 9 - 14 11.5 56 - 63 59.5 2.2 13.0 - 18.4 18.0
>8 >14 >14 >63 >63 0.1 20.0 20.0
Note:
1) Ambient wind sustained at 19.5 m above surface to generate fully-developed seas.
To convert to another altitude h2, apply V2 = V1 ¢ (h2=19:5)1=7.
2) Minimum is 5 percentile and maximum is 95 percentile for periods given wave
height range.
3) Based on periods associated with central frequencies included in Hindcast Clima-
tology.
The above tables for the North Atlantic and North Paci…c Oceans also include information
on the long term climatology of the waves. This will be discussed in the next section.
5.5. WAVE PREDICTION AND CLIMATOLOGY 5-55
Notice that all the methods in this section actually link wave data to wind data. This
is quite common since wind data is often much more available than wave data or can be
predicted rather easily from other available meteorological data.
5.5.2 Long Term
Longer term wave climatology is used to predict the statistical chance that a given wave-
sensitive o¤shore operation - such as lifting a major top-side element into place - will be
delayed by sea conditions which are too rough. Chapter 11 will be devoted entirely to
various applications of this general topic in a broad sense. The current section treats the
necessary input data on wave climate.
In general, wave climatology often centers on answering one question: What is the chance
that some chosen threshold wave condition will be exceeded during some interval - usually
days, weeks or even a year? To determine this, one must collect - or obtain in some other
way such as outlined in the previous section - and analyze the pairs of data (H1=3 and
T) and possibly even including the wave direction, ¹, as well)```