Part A | 3.7
68 Part A Fundamentals
that this assumed independence does not lead to substantial errors for return intervals of up to roughly 100
years for the Gulf of Mexico hurricane population. That
is because the 100-y condition is strongly dependent
on the track crossing distance and much less dependent
on the other particulars of the storm. Unfortunately, for
rarer return periods beyond a few hundred years, pooling starts to yield increasingly biased results because
the longer return intervals become more sensitive to
the intensity of the stronger storms, and pooling does
nothing to increase that population of storms. When
pooling it is important not to extend the averaging grid
too widely else one can suppress real spatial gradients
like those suspected to exist in the Gulf of Mexico hurricane patterns, e.g., Cooper [3.124].
Another limitation with the historical method is that
it cannot easily be used to develop criteria involving the
rare combination of two relatively independent events.
A case in point is the superposition of the Loop Current (or one of its detached eddies) and a hurricane.
Recent simulations by Cooper and Stear [3.125] suggest these events happen roughly every 4 years. When
they do, a number of potential nonlinear interactions
can occur such as wave focusing [3.126], amplification of mid-water currents [3.13], and intensification
of the hurricane [3.124]. The first two phenomena depend strongly on the distance between the hurricane and
Loop, and there are virtually no comprehensive measurements of the wave and current field in joint events.
Hence, historical events are missing.
3.7.3 Synthetic Storm Modeling
The previous section pointed out two major weaknesses
of the historical approach. To address these weaknesses,
researchers have looked at various means of generating so-called synthetic storms; that is, storms that did
not actually occur but could have occurred. Georgiou
et al. [3.127] describe one of the first efforts. They
first fit standard storm parameters like intensity and radius to standard distribution functions (e.g., lognormal).
They then drew randomly from these distributions to
construct synthetic storms whose probability was calculated from the underlying distributions of the storm
parameters. Once the combination of storm parameters
was selected, these were input into a standard parametric wind model that could calculate the detailed wind
field along the historical tracks. Because the probability distributions of each hurricane parameter is at most
weakly dependent on the other parameters (e.g., radius
to maximum wind is only weakly correlated to intensity), the overall probability of a given synthetic storm
scales roughly as the product of the probability of the
individual parameters. Hence the method can generate
rare (low probability) synthetic storms using a combination of storm parameters that are well away from the tail
of their respective probability distributions and hence
have relatively low uncertainty.
While the early models went a long way in reducing statistical uncertainty of the longer return period
estimates, they continued to utilize historical tracks
to estimate the frequency of storm passage and they
assumed that the change in storm parameters was independent of that track. This latter assumption is clearly
problematic in places like the Gulf of Mexico, where
the warm waters of the Loop Current likely affect
storm intensity as do nearby land masses. To partially
address these limitations, Vickery et al. [3.128] used statistical properties of track heading, track speed, and
intensity, combined with a regression model to generate synthetic storms. This approach allows for the
generation of thousands of years of storms with low statistical uncertainty. Emanuel et al. [3.129] investigated
stochastic techniques to generate many synthetic storm
tracks and a deterministic model to calculate storm intensity along each of those tracks. They investigated
two track models. Their first model was conceptually
similar to that of Vickery et al. [3.128], while their
second track generation method accounted for largescale weather, including vertical shear and steering
flow. Once Emanuel et al. [3.129] had constructed the
tracks, they used a deterministic model to calculate
the parameters, including intensity and radius. Vickery et al. [3.130] used a track model that accounts for
large-scale weather but in a more deterministic fashion
than Emanuel et al. [3.129], by using NCEP reanalysis.
To calculate the storm parameters they used a statistical intensity model that incorporated atmospheric
inputs, much as Emanuel et al. [3.129] did, but Vickery
et al. [3.130] also included ocean temperature feedback.
Perhaps the biggest challenge in using these models
is determining whether some of the more extreme synthetic storms are realistic. The next section addresses
this point.
3.7.4 Modeling Versus Measurements
In an ideal world, the ocean would be covered with
measurement sites that have operated for centuries. In
the real world, the metocean specialist is often faced
with developing criteria where there are no measurements at the site, or if there are, they may only be a year
or less in duration. Extrapolating such a short record to
return intervals of a few decades or more will usually result in large statistical uncertainty at best, and at worst,
large biases. On the other hand, numerical model hindcasts spanning many decades now cover most of the
world, as discussed in Sect. 3.4. Depending on the hor-
68 Part A Fundamentals
that this assumed independence does not lead to substantial errors for return intervals of up to roughly 100
years for the Gulf of Mexico hurricane population. That
is because the 100-y condition is strongly dependent
on the track crossing distance and much less dependent
on the other particulars of the storm. Unfortunately, for
rarer return periods beyond a few hundred years, pooling starts to yield increasingly biased results because
the longer return intervals become more sensitive to
the intensity of the stronger storms, and pooling does
nothing to increase that population of storms. When
pooling it is important not to extend the averaging grid
too widely else one can suppress real spatial gradients
like those suspected to exist in the Gulf of Mexico hurricane patterns, e.g., Cooper [3.124].
Another limitation with the historical method is that
it cannot easily be used to develop criteria involving the
rare combination of two relatively independent events.
A case in point is the superposition of the Loop Current (or one of its detached eddies) and a hurricane.
Recent simulations by Cooper and Stear [3.125] suggest these events happen roughly every 4 years. When
they do, a number of potential nonlinear interactions
can occur such as wave focusing [3.126], amplification of mid-water currents [3.13], and intensification
of the hurricane [3.124]. The first two phenomena depend strongly on the distance between the hurricane and
Loop, and there are virtually no comprehensive measurements of the wave and current field in joint events.
Hence, historical events are missing.
3.7.3 Synthetic Storm Modeling
The previous section pointed out two major weaknesses
of the historical approach. To address these weaknesses,
researchers have looked at various means of generating so-called synthetic storms; that is, storms that did
not actually occur but could have occurred. Georgiou
et al. [3.127] describe one of the first efforts. They
first fit standard storm parameters like intensity and radius to standard distribution functions (e.g., lognormal).
They then drew randomly from these distributions to
construct synthetic storms whose probability was calculated from the underlying distributions of the storm
parameters. Once the combination of storm parameters
was selected, these were input into a standard parametric wind model that could calculate the detailed wind
field along the historical tracks. Because the probability distributions of each hurricane parameter is at most
weakly dependent on the other parameters (e.g., radius
to maximum wind is only weakly correlated to intensity), the overall probability of a given synthetic storm
scales roughly as the product of the probability of the
individual parameters. Hence the method can generate
rare (low probability) synthetic storms using a combination of storm parameters that are well away from the tail
of their respective probability distributions and hence
have relatively low uncertainty.
While the early models went a long way in reducing statistical uncertainty of the longer return period
estimates, they continued to utilize historical tracks
to estimate the frequency of storm passage and they
assumed that the change in storm parameters was independent of that track. This latter assumption is clearly
problematic in places like the Gulf of Mexico, where
the warm waters of the Loop Current likely affect
storm intensity as do nearby land masses. To partially
address these limitations, Vickery et al. [3.128] used statistical properties of track heading, track speed, and
intensity, combined with a regression model to generate synthetic storms. This approach allows for the
generation of thousands of years of storms with low statistical uncertainty. Emanuel et al. [3.129] investigated
stochastic techniques to generate many synthetic storm
tracks and a deterministic model to calculate storm intensity along each of those tracks. They investigated
two track models. Their first model was conceptually
similar to that of Vickery et al. [3.128], while their
second track generation method accounted for largescale weather, including vertical shear and steering
flow. Once Emanuel et al. [3.129] had constructed the
tracks, they used a deterministic model to calculate
the parameters, including intensity and radius. Vickery et al. [3.130] used a track model that accounts for
large-scale weather but in a more deterministic fashion
than Emanuel et al. [3.129], by using NCEP reanalysis.
To calculate the storm parameters they used a statistical intensity model that incorporated atmospheric
inputs, much as Emanuel et al. [3.129] did, but Vickery
et al. [3.130] also included ocean temperature feedback.
Perhaps the biggest challenge in using these models
is determining whether some of the more extreme synthetic storms are realistic. The next section addresses
this point.
3.7.4 Modeling Versus Measurements
In an ideal world, the ocean would be covered with
measurement sites that have operated for centuries. In
the real world, the metocean specialist is often faced
with developing criteria where there are no measurements at the site, or if there are, they may only be a year
or less in duration. Extrapolating such a short record to
return intervals of a few decades or more will usually result in large statistical uncertainty at best, and at worst,
large biases. On the other hand, numerical model hindcasts spanning many decades now cover most of the
world, as discussed in Sect. 3.4. Depending on the hor-