Environmental Engineering Reference
In-Depth Information
Fig. 2.29 Comparison of the observed and Gumbel-adapted distribution functions and densities
plus the 1-year extreme values
and
u
¼
b
=
a
¼þ
0
:
9039
=
0
:
7963
¼
1
:
1351 m
From this it follows that the standard deviation for the long-term wave distribution is
s
H
;
extr
¼
p
p
1
a
¼
1
:
28255
79628
¼
1
:
61 m
0
:
The observed data (“obs”) and the associated Gumbel values for the distribution function
and density are plotted in Figure 2.29. As we assume that the observed quasi-steady sea
states (H
s
) are related to T
s0
¼
3 h, they were supplemented by the values for 1 year
displaced by “ln(N
i
)/a”. The following applies here [24, 11]:
N
i
¼
8760 h
=
a
=
3h
¼
2920
We can see from Figure 2.29 that the observed data agrees very well with the Gumbel
distribution in the relevant range of high values. The 98% quantile value related to one
year is generally used as the characteristic value:
u
1
¼
u
3h
þ
ln
ð
N
Þ=
a
¼
1
:
1351
þ
ln
ð
2
:
920
Þ=
0
:
7963
¼
11
:
16 m
1
a
InðInð0
3
:
902
H
s;1;0:98
¼ H
s;k
¼ F
1
extr;1
ð0
:
98Þ¼u
1
:
98ÞÞ ¼ 11
:
16 þ
7963
¼ 16
:
06 m
0
:
Extrapolating for longer reference periods - 5 years for extreme wave loads according to
[24] or 50 years for the design working life of an offshore structure - is only permissible
when the observed sea state data for extreme values is available for longer periods of time -
at least 5 or 20 years. It should be remembered in this context that wind-generated waves
depend on the climatic conditions of the seasons, especially the frequency of severe storms
[17]. However, assuming that the observed 1-year extreme values correspond to the Gumbel
distribution computed above, then the result is the Gumbel distributions for the 5- and 50-
year extreme values shown in Figure 2.30.
