Part C | 26.3
586 Part C Coastal Design
tical errors for a specific storm, particularly in terms of
predictions of storm intensity and size, the predictions
appear to approximate certain statistical characteristics
of the storm population reasonably well, such as the
mean number of storms in an area. What is not so clear
is whether they capture the complex multivariate structure that is inherent in interrelationships among storm
characteristics, such as the interaction of rates of change
of these characteristics and the effect of land proximity.
The effect of the omission of these higher order interactions on the statistics of predicted extremes remains
a topic for future research.
26.3.5 Probabilistic Analyses
of Extratropical Storms
As noted earlier, extratropical storms tend to be more
frequent and affect larger coast regions than tropical cyclones due to the relatively large size of these storms.
Based on these two considerations, it has been assumed
that, for most coastal areas, the use of the historical
storm method is adequate for quantifying hazards/risks.
However, there are four reasons why this may not be
a justifiable assumption given the geometric complexity of many coastal areas, particularly inland areas such
as major bays and lakes:
In some areas, the use of in situ observations
to characterize the extremes may contain mixed
populations, with a few observations from storms
in which strong winds blow along the optimal
surge/wave generating direction mixed with many
other observations with winds from other directions.
In such situations, the former events often have
the appearance of outliers. Since a record length
of 3040 years may only contain a single interval
of intense storms in which winds line up with the
optimal generation direction, this creates a difficult
situation for the analysis of extremes and a difficult
situation for planners and engineers to assess.
Although the GPD is specifically derived to fit a distribution above a particular threshold, it is still subject to the statistical constraint that all the samples
are drawn from a homogeneous population. Like the
GEV, the GPD is still only a three-parameter distribution, and if too many small events are mixed
into the analysis, the upper tail of the distribution is
very likely to be misestimated. Thus, in applications
where researchers choose the lower limit to be given
by an arbitrary (pre-selected) number of events, this
can lead to a very poor estimation of the actual hazards/risks.
Earlier, we noted that storm characteristics and frequencies seem to be significantly influenced by
multidecadal variations in atmospheric circulation
patterns. In these situations, it is exceptionally difficult to quantify the effects of the climatic variability
and relatively short-term sample durations may not
be adequate for accurately quantifying expected
extremes. This is an especially important point relating to the difference between storm events that
can occur and storm events that have occurred.
Due to all of the issues raised in items 13 and
inherent effects of uncertainty on encounter probabilities, the use of historical storm methods for very
low probabilities, as is needed for certain critical
infrastructure vulnerability assessment and design,
is very difficult to justify without the inclusion of
some means to add substantial conservatism into the
analysis. Additional research developing a variation
of the JPM to fit extratropical storms would be very
valuable in meeting this need.
26.3.6 Future Directions
and Final Comments
Irish and Resio [26.40] show that the effects of storm
size, storm forward speed, landfall location, and storm
track angle at the coast on storm surges all have asymptotic upper limits in tropical cyclones. Although these
upper limits are site dependent, the forms of these limiters can be written in terms of some relatively simple
functions. This information can help simplify the estimation of very low probability extremes; since in this
very extreme range of surges, it reduces the surge probabilities back to a univariate distribution, in this case
a function of a single parameter, storm central pressure.
However, as emphasized previously, sampling uncertainty must still be considered in the estimation process.
It is likely that, in many areas, the inclusion of sampling
uncertainty within relatively small sample sizes will potentially make the estimates of central pressure for AEP
values of 10
6 unrealistically low. In such situations,
it will likely be necessary to combine probabilistic estimates with theoretically derived upper limits to be
able to estimate coastal surges. Presently, this theoretical upper limit, the MPI, is still developed via relatively
simplistic theoretical formulations combined with empirical envelopes of lowest observed central pressures
around the world [26.84–86]. In their present form, this
limit is estimated primarily as a function of sea surface temperature; however, more theoretical work will
likely show the importance of additional terms to the estimation of the MPI. It should certainly be recognized
that any estimate of an MPI will directly contain epistemic errors and indirectly contain alleatory errors due
to the sampling distribution used to derive and calibrate
theories.
586 Part C Coastal Design
tical errors for a specific storm, particularly in terms of
predictions of storm intensity and size, the predictions
appear to approximate certain statistical characteristics
of the storm population reasonably well, such as the
mean number of storms in an area. What is not so clear
is whether they capture the complex multivariate structure that is inherent in interrelationships among storm
characteristics, such as the interaction of rates of change
of these characteristics and the effect of land proximity.
The effect of the omission of these higher order interactions on the statistics of predicted extremes remains
a topic for future research.
26.3.5 Probabilistic Analyses
of Extratropical Storms
As noted earlier, extratropical storms tend to be more
frequent and affect larger coast regions than tropical cyclones due to the relatively large size of these storms.
Based on these two considerations, it has been assumed
that, for most coastal areas, the use of the historical
storm method is adequate for quantifying hazards/risks.
However, there are four reasons why this may not be
a justifiable assumption given the geometric complexity of many coastal areas, particularly inland areas such
as major bays and lakes:
In some areas, the use of in situ observations
to characterize the extremes may contain mixed
populations, with a few observations from storms
in which strong winds blow along the optimal
surge/wave generating direction mixed with many
other observations with winds from other directions.
In such situations, the former events often have
the appearance of outliers. Since a record length
of 3040 years may only contain a single interval
of intense storms in which winds line up with the
optimal generation direction, this creates a difficult
situation for the analysis of extremes and a difficult
situation for planners and engineers to assess.
Although the GPD is specifically derived to fit a distribution above a particular threshold, it is still subject to the statistical constraint that all the samples
are drawn from a homogeneous population. Like the
GEV, the GPD is still only a three-parameter distribution, and if too many small events are mixed
into the analysis, the upper tail of the distribution is
very likely to be misestimated. Thus, in applications
where researchers choose the lower limit to be given
by an arbitrary (pre-selected) number of events, this
can lead to a very poor estimation of the actual hazards/risks.
Earlier, we noted that storm characteristics and frequencies seem to be significantly influenced by
multidecadal variations in atmospheric circulation
patterns. In these situations, it is exceptionally difficult to quantify the effects of the climatic variability
and relatively short-term sample durations may not
be adequate for accurately quantifying expected
extremes. This is an especially important point relating to the difference between storm events that
can occur and storm events that have occurred.
Due to all of the issues raised in items 13 and
inherent effects of uncertainty on encounter probabilities, the use of historical storm methods for very
low probabilities, as is needed for certain critical
infrastructure vulnerability assessment and design,
is very difficult to justify without the inclusion of
some means to add substantial conservatism into the
analysis. Additional research developing a variation
of the JPM to fit extratropical storms would be very
valuable in meeting this need.
26.3.6 Future Directions
and Final Comments
Irish and Resio [26.40] show that the effects of storm
size, storm forward speed, landfall location, and storm
track angle at the coast on storm surges all have asymptotic upper limits in tropical cyclones. Although these
upper limits are site dependent, the forms of these limiters can be written in terms of some relatively simple
functions. This information can help simplify the estimation of very low probability extremes; since in this
very extreme range of surges, it reduces the surge probabilities back to a univariate distribution, in this case
a function of a single parameter, storm central pressure.
However, as emphasized previously, sampling uncertainty must still be considered in the estimation process.
It is likely that, in many areas, the inclusion of sampling
uncertainty within relatively small sample sizes will potentially make the estimates of central pressure for AEP
values of 10
6 unrealistically low. In such situations,
it will likely be necessary to combine probabilistic estimates with theoretically derived upper limits to be
able to estimate coastal surges. Presently, this theoretical upper limit, the MPI, is still developed via relatively
simplistic theoretical formulations combined with empirical envelopes of lowest observed central pressures
around the world [26.84–86]. In their present form, this
limit is estimated primarily as a function of sea surface temperature; however, more theoretical work will
likely show the importance of additional terms to the estimation of the MPI. It should certainly be recognized
that any estimate of an MPI will directly contain epistemic errors and indirectly contain alleatory errors due
to the sampling distribution used to derive and calibrate
theories.