Part C | 26.3
584 Part C Coastal Design
where represents the model used to convert the
parameters to an estimate of maximum surge for each
event as a function of (c p ; R max ; v f ; Â l ; x); however, it
is easy to see that this approach can be generalized to
any set of n parameters for which a response surface
can be defined, along with the multivariate probability
distribution. Variations on the methodology for evaluating the parameter probabilities and the storm set to be
simulated have been presented by Toro et al. [26.59],
Niedoroda et al. [26.73], Resio et al. [26.70], and
Irish et al. [26.74]. Each has its advantages and disadvantages, and as long as the multivariate probability
function is sufficiently resolved in the integration
process, the results should be in reasonable agreement
with each other.
Similar to the EST, this method is nonparametric
with respect to the form of the CDF; however, the type
of extrapolation used to extend the JPM result beyond
the record length is very different to that used by the historical storm method. As shown by Irish et al. [26.75],
the former of these is based on probability estimates
which are much more smoothly varying than the local surge response inherent in the historical data, which
means that when applied the JPM provides a significant
decrease in sampling uncertainty, when compared to the
historical storm method.
A potential advantage of the JPM over methods
which depend heavily on historical storms is that the
JPM attempts to consider all storms that might happen
in an area; whereas, the EST considered only storms
that did happen in that area. For example, the 100year return period storm set to contain a full suite of
(c p ; R max ; v f ; Â l ; x); whereas, the historical storm method
will have just one or two storms available in this parameter space. Assuming that, for the purpose of surge
generation, storm characteristics can be represented adequately by the set of parameters used, it is possible to
construct a Katrina-like storm (high intensity combined
with large size) even if one has not happened previously.
Likewise, it is possible to interpolate between re-curved
storms such as Hurricanes Opal and Wilma to understand probabilities of possible hurricane impacts in the
Tampa, Florida area, even though neither of these storms
produced significant surges in the Tampa area.
Perhaps the biggest controversy in JPM applications
during the 1970s and 1980s centered on the sufficiency of this five-dimension set of parameters used in
the joint-probability function to produce accurate wind
fields. In addition to this concern, the lack of data on
historical storms prior to 1950 made it very difficult
to derive representative distributions, even for extended
sections of coast. For example, information on storm
size (R max ) was lacking for most historical storms; consequently, a statistical estimate of R max (as a function
of latitude and central pressure) was frequently substituted for actual values in the probability distribution.
One wind field factor not considered in early JPM applications was the variable peakedness of tropical cyclone
wind fields. This term is represented in terms of the
Holland B parameter [26.76] in recent tropical cyclone
wind models.
It is clear that the number of primary dimensions
within the JPM must be capable of representing wind
fields to sufficient accuracy so that they provide reasonable, relatively unbiased skill when used to drive coastal
wave and surge models. For the case of extratropical
storms, there is no known simple set of parameters that
meets this criterion, and some extension of the EST or
POT method may be the suitable choice for such applications, at least for recurrence intervals which are not
too long (less than 100 years or so). For the case of tropical cyclones, dynamic models of tropical cyclone wind
fields [26.77, 78] have been shown to capture a substantial portion of the wind field structure, when driven
with the parameters listed above plus the Holland B
parameter.
An argument against using the parametric wind
fields in the JPM is that each historical tropical cyclone
will tend to exhibit some degree of deviation from the
theoretical parametric (planetary boundary layer) estimates. At any fixed time, such deviations could be produced by strong storm asymmetries, variations in R max
around the storm, enhanced spiral bands, etc. Hence,
a best-estimate wind field crafted by experts to assimilate all the observations in a given tropical cyclone will
typically represent the details of that particular storm
much more faithfully than is possible via a parameterized theoretical model. Such wind fields today are
produced primarily by groups like the National Oceanic
and Atmospheric Administration (NOAA) Hurricane
Research Division [26.79]. These wind fields are absolutely essential for advancing our understanding of
tropical cyclone winds relative to wave and surge forcing in offshore and coastal areas. An excellent discussion of the reconstruction of historical wind fields and
the impact of different approaches on model accuracies
can be found in [26.80].
It is obvious that best-estimate wind fields contain
an extremely large number of degrees of freedom in
their formulation. Given the relatively small number of
historical tropical cyclones, it is unlikely that we can
understand/quantify the probabilistic nature of all the
interrelated detailed factors that create these deviations.
If these details were absolutely critical to coastal wave
and surge estimation, we would be able to represent
a past tropical cyclone very accurately but would know
little about the probability of future tropical cyclones
unless we retained the same number of degrees of free-
584 Part C Coastal Design
where represents the model used to convert the
parameters to an estimate of maximum surge for each
event as a function of (c p ; R max ; v f ; Â l ; x); however, it
is easy to see that this approach can be generalized to
any set of n parameters for which a response surface
can be defined, along with the multivariate probability
distribution. Variations on the methodology for evaluating the parameter probabilities and the storm set to be
simulated have been presented by Toro et al. [26.59],
Niedoroda et al. [26.73], Resio et al. [26.70], and
Irish et al. [26.74]. Each has its advantages and disadvantages, and as long as the multivariate probability
function is sufficiently resolved in the integration
process, the results should be in reasonable agreement
with each other.
Similar to the EST, this method is nonparametric
with respect to the form of the CDF; however, the type
of extrapolation used to extend the JPM result beyond
the record length is very different to that used by the historical storm method. As shown by Irish et al. [26.75],
the former of these is based on probability estimates
which are much more smoothly varying than the local surge response inherent in the historical data, which
means that when applied the JPM provides a significant
decrease in sampling uncertainty, when compared to the
historical storm method.
A potential advantage of the JPM over methods
which depend heavily on historical storms is that the
JPM attempts to consider all storms that might happen
in an area; whereas, the EST considered only storms
that did happen in that area. For example, the 100year return period storm set to contain a full suite of
(c p ; R max ; v f ; Â l ; x); whereas, the historical storm method
will have just one or two storms available in this parameter space. Assuming that, for the purpose of surge
generation, storm characteristics can be represented adequately by the set of parameters used, it is possible to
construct a Katrina-like storm (high intensity combined
with large size) even if one has not happened previously.
Likewise, it is possible to interpolate between re-curved
storms such as Hurricanes Opal and Wilma to understand probabilities of possible hurricane impacts in the
Tampa, Florida area, even though neither of these storms
produced significant surges in the Tampa area.
Perhaps the biggest controversy in JPM applications
during the 1970s and 1980s centered on the sufficiency of this five-dimension set of parameters used in
the joint-probability function to produce accurate wind
fields. In addition to this concern, the lack of data on
historical storms prior to 1950 made it very difficult
to derive representative distributions, even for extended
sections of coast. For example, information on storm
size (R max ) was lacking for most historical storms; consequently, a statistical estimate of R max (as a function
of latitude and central pressure) was frequently substituted for actual values in the probability distribution.
One wind field factor not considered in early JPM applications was the variable peakedness of tropical cyclone
wind fields. This term is represented in terms of the
Holland B parameter [26.76] in recent tropical cyclone
wind models.
It is clear that the number of primary dimensions
within the JPM must be capable of representing wind
fields to sufficient accuracy so that they provide reasonable, relatively unbiased skill when used to drive coastal
wave and surge models. For the case of extratropical
storms, there is no known simple set of parameters that
meets this criterion, and some extension of the EST or
POT method may be the suitable choice for such applications, at least for recurrence intervals which are not
too long (less than 100 years or so). For the case of tropical cyclones, dynamic models of tropical cyclone wind
fields [26.77, 78] have been shown to capture a substantial portion of the wind field structure, when driven
with the parameters listed above plus the Holland B
parameter.
An argument against using the parametric wind
fields in the JPM is that each historical tropical cyclone
will tend to exhibit some degree of deviation from the
theoretical parametric (planetary boundary layer) estimates. At any fixed time, such deviations could be produced by strong storm asymmetries, variations in R max
around the storm, enhanced spiral bands, etc. Hence,
a best-estimate wind field crafted by experts to assimilate all the observations in a given tropical cyclone will
typically represent the details of that particular storm
much more faithfully than is possible via a parameterized theoretical model. Such wind fields today are
produced primarily by groups like the National Oceanic
and Atmospheric Administration (NOAA) Hurricane
Research Division [26.79]. These wind fields are absolutely essential for advancing our understanding of
tropical cyclone winds relative to wave and surge forcing in offshore and coastal areas. An excellent discussion of the reconstruction of historical wind fields and
the impact of different approaches on model accuracies
can be found in [26.80].
It is obvious that best-estimate wind fields contain
an extremely large number of degrees of freedom in
their formulation. Given the relatively small number of
historical tropical cyclones, it is unlikely that we can
understand/quantify the probabilistic nature of all the
interrelated detailed factors that create these deviations.
If these details were absolutely critical to coastal wave
and surge estimation, we would be able to represent
a past tropical cyclone very accurately but would know
little about the probability of future tropical cyclones
unless we retained the same number of degrees of free-