Metocean Extreme and Operating Conditions 3.7 Extreme Criteria 69
Part A | 3.7
izontal resolution of the model grid, the nearest model
element to the site of interest is often only a few kilometers away. Thus the best strategy for developing extreme
design criteria at site is often to use available measurements to calibrate a hindcast model that has been run
for several decades, rather than to do an extreme analysis on the measurements themselves.
3.7.5 Accounting for Physical Limits
Whether one uses the historical method or synthetic
modeling to estimate extremes, extrapolation of some
form is almost always being used to estimate criteria well beyond any observed storms. This raises the
concern that the method can be generating values that
cannot be physically attained in the real world. Perhaps
the clearest example of this danger is the case where
a metocean specialist tries to fit a Weibull distribution
(historical method) to waves measured during a 2-y
long measurement program in a water depth where
wave breaking can occur for the stronger storms. Fitting
this kind of data with a classic historical method can
yield 100-y estimates that are unrealistically high because those waves would have broken in the real world.
The problem, of course, is that the extreme distributions
are purely statistical functions with no physical basis.
One solution to this potential problem is to use
numerical models that include the necessary physics
to account for the limits. This can be a practical and
straight forward solution for the example of breaking
waves cited above. In that case, hindcasting storms over
many decades using a wave model that accounts for
breaking is usually a quick and effective solution.
Regrettably, incorporating physical limits into numerical models is not straightforward when the physics
are not well understood. A case in point is calculating
extremely rare hurricane conditions, say the 10 000 year
significant wave height. Cardone and Cox [3.131] applied a third-generation wave model to strong storms
and found that the wave heights trended toward an
asymptotic limit. However, it is debatable whether the
asymptotic limit is generated by real physical limits or
artificial ones imposed by the model equations. There
is no way to be sure, as wave and wind measurements
during the events considered by Cardone and Cox have
not been recorded. Another approach used by Vickery
et al. [3.130] applied the concept of the maximum
probable storm intensity. Emanuel [3.132] and others
provide evidence that such limits appear to exist.
3.7.6 Seasonality
Fixed offshore facilities are designed for year-round
conditions but there are some instances where metocean conditions are needed for seasonal construction or
drilling. If the operation is, say, planned for only the
three months of summer, then only the metocean conditions for those months need to be considered. More
specifically, if a 1%=y risk of failure is desired (expected failure of once every 100-y), then the extreme
values of metocean conditions in 100 years of summers
should be calculated.
However, caution must be exercised when considering seasonality for a drilling rig or operations which
will continue year-around. To illustrate this point, consider the question of how one might combine seasonal
criteria to calculate the annual survival rate. Assume that
the target reliability is an average 99% survival rate (1%
failure rate) each year. One might be tempted to use the
99% probability value for each season, but more careful consideration reveals this will badly overestimate the
survivability. That is because the annual survival rate is
given by the probability that the rig will survive the summer and the fall and the winter and the spring. It follows
that if the extremes in each season are statistically independent, then the annual survival probability is given
by the product of the seasonal probabilities, or 0:99
4
D
0:96; 4% less than the annual target survival rate of 99%.
An obvious solution to this shortfall is to use the 0.9975
probability for each of the four seasons, which yields an
annual survival rate 99% D 99:75
4 .
3.7.7 Directionality
Directional metocean specifications are sometimes desired when a structure is considerably stronger or
less prone to motion in some directions than others.
The considerations in this case are similar to those
for seasonal specifications, especially the concept that
the total survival probability from all individual directions should not be significantly different from the
omnidirectional survival probability. Using the same
arguments given in the previous discussion on seasonality, it is clear that using the n-y metocean criteria
in each direction bin will give a much lower survival
probability than using the n-y omni-directional criteria [3.133].
The simplest way to insure a reasonable result is to
make the probabilities in all of the direction bins equal.
So, for example, if the target annual survivability is 99%
and four direction bins are used, then the target survival
probability in each of these four bins should be 99:75%.
3.7.8 Combining Long and Short-Term
Distributions
Estimating extreme values of individual wave and crest
heights requires combining a long-term extreme value
Part A | 3.7
izontal resolution of the model grid, the nearest model
element to the site of interest is often only a few kilometers away. Thus the best strategy for developing extreme
design criteria at site is often to use available measurements to calibrate a hindcast model that has been run
for several decades, rather than to do an extreme analysis on the measurements themselves.
3.7.5 Accounting for Physical Limits
Whether one uses the historical method or synthetic
modeling to estimate extremes, extrapolation of some
form is almost always being used to estimate criteria well beyond any observed storms. This raises the
concern that the method can be generating values that
cannot be physically attained in the real world. Perhaps
the clearest example of this danger is the case where
a metocean specialist tries to fit a Weibull distribution
(historical method) to waves measured during a 2-y
long measurement program in a water depth where
wave breaking can occur for the stronger storms. Fitting
this kind of data with a classic historical method can
yield 100-y estimates that are unrealistically high because those waves would have broken in the real world.
The problem, of course, is that the extreme distributions
are purely statistical functions with no physical basis.
One solution to this potential problem is to use
numerical models that include the necessary physics
to account for the limits. This can be a practical and
straight forward solution for the example of breaking
waves cited above. In that case, hindcasting storms over
many decades using a wave model that accounts for
breaking is usually a quick and effective solution.
Regrettably, incorporating physical limits into numerical models is not straightforward when the physics
are not well understood. A case in point is calculating
extremely rare hurricane conditions, say the 10 000 year
significant wave height. Cardone and Cox [3.131] applied a third-generation wave model to strong storms
and found that the wave heights trended toward an
asymptotic limit. However, it is debatable whether the
asymptotic limit is generated by real physical limits or
artificial ones imposed by the model equations. There
is no way to be sure, as wave and wind measurements
during the events considered by Cardone and Cox have
not been recorded. Another approach used by Vickery
et al. [3.130] applied the concept of the maximum
probable storm intensity. Emanuel [3.132] and others
provide evidence that such limits appear to exist.
3.7.6 Seasonality
Fixed offshore facilities are designed for year-round
conditions but there are some instances where metocean conditions are needed for seasonal construction or
drilling. If the operation is, say, planned for only the
three months of summer, then only the metocean conditions for those months need to be considered. More
specifically, if a 1%=y risk of failure is desired (expected failure of once every 100-y), then the extreme
values of metocean conditions in 100 years of summers
should be calculated.
However, caution must be exercised when considering seasonality for a drilling rig or operations which
will continue year-around. To illustrate this point, consider the question of how one might combine seasonal
criteria to calculate the annual survival rate. Assume that
the target reliability is an average 99% survival rate (1%
failure rate) each year. One might be tempted to use the
99% probability value for each season, but more careful consideration reveals this will badly overestimate the
survivability. That is because the annual survival rate is
given by the probability that the rig will survive the summer and the fall and the winter and the spring. It follows
that if the extremes in each season are statistically independent, then the annual survival probability is given
by the product of the seasonal probabilities, or 0:99
4
D
0:96; 4% less than the annual target survival rate of 99%.
An obvious solution to this shortfall is to use the 0.9975
probability for each of the four seasons, which yields an
annual survival rate 99% D 99:75
4 .
3.7.7 Directionality
Directional metocean specifications are sometimes desired when a structure is considerably stronger or
less prone to motion in some directions than others.
The considerations in this case are similar to those
for seasonal specifications, especially the concept that
the total survival probability from all individual directions should not be significantly different from the
omnidirectional survival probability. Using the same
arguments given in the previous discussion on seasonality, it is clear that using the n-y metocean criteria
in each direction bin will give a much lower survival
probability than using the n-y omni-directional criteria [3.133].
The simplest way to insure a reasonable result is to
make the probabilities in all of the direction bins equal.
So, for example, if the target annual survivability is 99%
and four direction bins are used, then the target survival
probability in each of these four bins should be 99:75%.
3.7.8 Combining Long and Short-Term
Distributions
Estimating extreme values of individual wave and crest
heights requires combining a long-term extreme value