Metocean Extreme and Operating Conditions 3.7 Extreme Criteria 71
Part A | 3.7
waves. The modulated waves alternate between series
of higher and lower waves than predicted by Gaussian statistics. The kurtosis of the wave trace becomes
greater than 3.0, and the extreme waves are higher
than the Rayleigh distribution. Steep random unidirectional waves in laboratory basins often show this
behavior. However, several numerical and laboratory
studies, such as that by Toffoli et al. [3.143], have shown
that modulational instabilities are much less effective
in producing large wave groups when the waves are
spread.
Rogue waves remain an active area of research and
it is too early to draw definite conclusions. Fortunately,
rogue waves may not have a big influence on extreme
wave heights for design. Almost by definition, they
have a low probability. The probability that a rogue
wave occurs during one of the sea states far out in the
distribution of significant wave height is even lower.
Haver [3.138] estimated the effect of adding rare rogue
waves to the short term distribution and found that it
had little effect on the risk of failure.
3.7.10 Extremely Rare Events
Designers now frequently request metocean criteria
with return periods of 100010 000 years. Deriving
these values from a few years of measurements is difficult, if not impossible, to justify. Even deriving such
rare events from historical hindcasts is problematic,
since reliable historical databases rarely extend beyond
50 years. Synthetic modeling certainly holds the most
promise for deriving rare events, but even with this technology it is difficult to overcome our ignorance of the
physical limits which probably occur for many metocean phenomena. This issue is discussed in more detail
in Sect. 3.7.5.
3.7.11 Quantifying Uncertainty
Uncertainty affecting the calculation of metocean extremes comes primarily from the noise and/or bias in
the numerical models or measurements used to generate
the peaks, and from the inability of the chosen extreme
distribution to fit the peaks – what is often referred to as
statistical uncertainty. The impacts of these two types
of errors on extreme value uncertainty are discussed in
more detail in Sect. 3.7.4.
Statisticians have extensively studied statistical uncertainty and developed numerous ways of quantifying
it, as discussed in Tucker and Pitt [3.135]. If the input
peaks come from a short time series and the extrapolation is lengthy (e.g., 2-y of measurements extrapolated
to a 100-y return period), then the statistical error can
be large.
One often sees fits to extreme distributions that
show confidence limits that are based on the statistical
uncertainty only. If the peaks are based on site-specific
measurements, the statistical uncertainty is fairly representative, but if the peaks come from measurements
some distance from the site or from models, then the
statistical uncertainty is probably much smaller than the
uncertainty from the input data source. Sections 3.4.1
to 3.4.3 can help quantify that error.
3.7.12 Stationarity
Nonstationarities can be thought of as low-frequency
processes that have been sampled at far less than their
Nyquist frequency. For example, if one has only a few
months of data to analyze, then nonstationarities will
arise from seasonal, annual, decadal, etc., time scales.
Innumerable papers and books have been written on
the topic, including a relatively recent one by Rao
et al. [3.144].
Issues regarding nonstationarities have always
plagued metocean analysis. The challenge is perhaps
greatest when dealing with the calculation of extreme
values (e.g., 100-y wind speed) where stationarity of
the underlying time series is assumed in almost any
analysis method and nonstationarities in the underlying
dataset will tend to be amplified. For storm extremes,
important sources of nonstationarities can come from
natural oscillations in the atmosphere like the North
Atlantic Oscillation or El Nino, which can cause substantial variations in storm severity over periods of
several decades [3.145]. In theory, the obvious solution
is to include many decades of historical storms in the
extreme value analysis, but such long time series are
available in only a few regions of the world and even
there, data quality from the older decades my be problematic and introduce other forms of bias [3.146].
Global warming is introducing strong nonstationarities in many variables, the most obvious being
atmospheric temperature. Projections from the IPCC
(Intergovernmental Panel on Climate Change) [3.147]
show that these nonstationarities or trends will increase rapidly over the coming decades and for longlived facilities, the changes will need to be considered.
A starting point for estimating nonstationarities is to use
projections from numerical models such as those provided by the IPCC [3.147]. However, these projections
do not consider all variables of interest to engineers
(e.g., waves) and use models with fairly large grid sizes
which can fail to capture important regional variability.
Fortunately, computer power is continuing to increase,
so the limits on grid size are starting to recede, allowing for the development of regional nested models with
smaller grid sizes [3.148].
Part A | 3.7
waves. The modulated waves alternate between series
of higher and lower waves than predicted by Gaussian statistics. The kurtosis of the wave trace becomes
greater than 3.0, and the extreme waves are higher
than the Rayleigh distribution. Steep random unidirectional waves in laboratory basins often show this
behavior. However, several numerical and laboratory
studies, such as that by Toffoli et al. [3.143], have shown
that modulational instabilities are much less effective
in producing large wave groups when the waves are
spread.
Rogue waves remain an active area of research and
it is too early to draw definite conclusions. Fortunately,
rogue waves may not have a big influence on extreme
wave heights for design. Almost by definition, they
have a low probability. The probability that a rogue
wave occurs during one of the sea states far out in the
distribution of significant wave height is even lower.
Haver [3.138] estimated the effect of adding rare rogue
waves to the short term distribution and found that it
had little effect on the risk of failure.
3.7.10 Extremely Rare Events
Designers now frequently request metocean criteria
with return periods of 100010 000 years. Deriving
these values from a few years of measurements is difficult, if not impossible, to justify. Even deriving such
rare events from historical hindcasts is problematic,
since reliable historical databases rarely extend beyond
50 years. Synthetic modeling certainly holds the most
promise for deriving rare events, but even with this technology it is difficult to overcome our ignorance of the
physical limits which probably occur for many metocean phenomena. This issue is discussed in more detail
in Sect. 3.7.5.
3.7.11 Quantifying Uncertainty
Uncertainty affecting the calculation of metocean extremes comes primarily from the noise and/or bias in
the numerical models or measurements used to generate
the peaks, and from the inability of the chosen extreme
distribution to fit the peaks – what is often referred to as
statistical uncertainty. The impacts of these two types
of errors on extreme value uncertainty are discussed in
more detail in Sect. 3.7.4.
Statisticians have extensively studied statistical uncertainty and developed numerous ways of quantifying
it, as discussed in Tucker and Pitt [3.135]. If the input
peaks come from a short time series and the extrapolation is lengthy (e.g., 2-y of measurements extrapolated
to a 100-y return period), then the statistical error can
be large.
One often sees fits to extreme distributions that
show confidence limits that are based on the statistical
uncertainty only. If the peaks are based on site-specific
measurements, the statistical uncertainty is fairly representative, but if the peaks come from measurements
some distance from the site or from models, then the
statistical uncertainty is probably much smaller than the
uncertainty from the input data source. Sections 3.4.1
to 3.4.3 can help quantify that error.
3.7.12 Stationarity
Nonstationarities can be thought of as low-frequency
processes that have been sampled at far less than their
Nyquist frequency. For example, if one has only a few
months of data to analyze, then nonstationarities will
arise from seasonal, annual, decadal, etc., time scales.
Innumerable papers and books have been written on
the topic, including a relatively recent one by Rao
et al. [3.144].
Issues regarding nonstationarities have always
plagued metocean analysis. The challenge is perhaps
greatest when dealing with the calculation of extreme
values (e.g., 100-y wind speed) where stationarity of
the underlying time series is assumed in almost any
analysis method and nonstationarities in the underlying
dataset will tend to be amplified. For storm extremes,
important sources of nonstationarities can come from
natural oscillations in the atmosphere like the North
Atlantic Oscillation or El Nino, which can cause substantial variations in storm severity over periods of
several decades [3.145]. In theory, the obvious solution
is to include many decades of historical storms in the
extreme value analysis, but such long time series are
available in only a few regions of the world and even
there, data quality from the older decades my be problematic and introduce other forms of bias [3.146].
Global warming is introducing strong nonstationarities in many variables, the most obvious being
atmospheric temperature. Projections from the IPCC
(Intergovernmental Panel on Climate Change) [3.147]
show that these nonstationarities or trends will increase rapidly over the coming decades and for longlived facilities, the changes will need to be considered.
A starting point for estimating nonstationarities is to use
projections from numerical models such as those provided by the IPCC [3.147]. However, these projections
do not consider all variables of interest to engineers
(e.g., waves) and use models with fairly large grid sizes
which can fail to capture important regional variability.
Fortunately, computer power is continuing to increase,
so the limits on grid size are starting to recede, allowing for the development of regional nested models with
smaller grid sizes [3.148].