Statistical Characterization of Hazards and Risk in Coastal Areas 26.3 Historical Perspective 583
Part C | 26.3
that would only happen much less often than the time
span of the sample record. It is intuitive that even the
1 000 000-year event must happen in some 10-year sample, so the historical treatment for these points was to
consider them as not representative of the record length
within which they were sampled. Such points were
typically simply omitted from the distribution fitting
process; however, it seems obvious that this omission
for all points in a region neglects a potentially valuable
piece of information from all of the analyses in an area.
26.3.4 The Development
of Alternative Methods
The tragedy of Hurricane Katrina emphasized the point
that reliable estimates of coastal hazards and risks
should include the effects of all storms that can occur
in an area and not just the events that occurred within
a particular historical sample. However, as early as the
1970s, this had been recognized, and alternative methods started to be developed which afforded improved
estimates of coastal hazards and risks. Probably the two
most widely used of these methods have been the joint
probability method (JPM), along with a derivative of
the JPM termed the JPM-OS (joint probability method
optimal sampling), and a second approach which, in
this handbook, we will term the empirical track method
(ETM). Material from a US Army Corps of Engineers
White Paper [26.65] and a reduced version of the White
Paper [26.66] will form a substantial portion of our
discussions of these developments, and a considerable
amount of details on the specifics can be found there.
The Development
of the Joint Probability Method (JPM)
The JPM was developed for application to coastal
surges in the 1970s [26.67, 68] and subsequently extended by a number of investigators [26.38, 69] in an
attempt to circumvent problems related to limited historical records. In this approach, information characterizing a small set of storm parameters was analyzed from
a relatively broad geographic area. In applications of
this method in the 1970s and 1980s, the JPM assumed
that storm characteristics were constant along the entire section of coast from which the sample was drawn.
This assumption is inconsistent with more recent studies (Fig. 26.9) which show that storm frequencies vary
substantially in this area.
The JPM used a set of parameters, including central
pressure, radius of maximum wind speed, storm forward speed, storm landfall location, and the angle of the
storm track relative to the coast, to generate parametric
wind fields. Furthermore, initial applications of the JPM
assumed that the values of these five parameters varied
only slowly in storms approaching the coast; therefore,
the values of these parameters at landfall could be used
to estimate the surge at the coast, and these values could
be treated as a constant during the approach of a storm
to the coast. Recent data shows that this is not a good
assumption [26.70, 71]; specifically, these studies suggest that tropical cyclones decay as they approach land.
Kimball [26.72] has shown that such decay is consistent
with the intrusion of dry air into a tropical cyclone during its approach to land, although other hypotheses for
this consistent decay in intensity, such as the lack of energy production from parts of the tropical cyclone over
land and increased drag in these areas have also been
advanced. In any event, the evidence appears rather
convincing that major tropical cyclones begin to decay
substantially before they make landfall, rather than only
after landfall as previously assumed.
The initial formulation of the JPM used computer
simulations of straight-line tracks with constant parametric wind fields to define the maximum surge value
for selected combinations of the basic five storm parameters. Each of these maximum values was associated
with a probability
p.c p ; R max ; v f ; Â l ; x/ ;
(26.20)
where c p is the central pressure, R max is the radius of
maximum wind speed, v f is the forward velocity of the
storm, Â l is the angle of the track relative to the coast
at landfall, and x is the distance between the point of
interest and the landfall location.
These probabilities were treated as discrete increments and the CDF was defined as
F.x/ D
X
p ijklm jx ijklm < x ;
(26.21)
where the subscripts denote the indices of the five parameters used to characterize the tropical cyclones.
The JPM represents a straightforward application of
the response surface method for estimating extremes.
In this method, the response of a particular variable
(such as waves and surges) is derived as a function of
several parameters, such as the set (c p ; R max ; v f ; Â l ; x)
used in the above example. Given that the multivariate probability of the five-parameter space is known
and a method for defining the response from this set
of variables is known, the equation for the CDF for the
response can be written for this example as
F.Á/ D
Z Z Z Z Z
p.c p ; R max ; v f ; Â l ; x/
HŒÁ .c p ; R max ; v f ;  l ; x/
dc p dR max dv f d l dx ;
(26.22)
Part C | 26.3
that would only happen much less often than the time
span of the sample record. It is intuitive that even the
1 000 000-year event must happen in some 10-year sample, so the historical treatment for these points was to
consider them as not representative of the record length
within which they were sampled. Such points were
typically simply omitted from the distribution fitting
process; however, it seems obvious that this omission
for all points in a region neglects a potentially valuable
piece of information from all of the analyses in an area.
26.3.4 The Development
of Alternative Methods
The tragedy of Hurricane Katrina emphasized the point
that reliable estimates of coastal hazards and risks
should include the effects of all storms that can occur
in an area and not just the events that occurred within
a particular historical sample. However, as early as the
1970s, this had been recognized, and alternative methods started to be developed which afforded improved
estimates of coastal hazards and risks. Probably the two
most widely used of these methods have been the joint
probability method (JPM), along with a derivative of
the JPM termed the JPM-OS (joint probability method
optimal sampling), and a second approach which, in
this handbook, we will term the empirical track method
(ETM). Material from a US Army Corps of Engineers
White Paper [26.65] and a reduced version of the White
Paper [26.66] will form a substantial portion of our
discussions of these developments, and a considerable
amount of details on the specifics can be found there.
The Development
of the Joint Probability Method (JPM)
The JPM was developed for application to coastal
surges in the 1970s [26.67, 68] and subsequently extended by a number of investigators [26.38, 69] in an
attempt to circumvent problems related to limited historical records. In this approach, information characterizing a small set of storm parameters was analyzed from
a relatively broad geographic area. In applications of
this method in the 1970s and 1980s, the JPM assumed
that storm characteristics were constant along the entire section of coast from which the sample was drawn.
This assumption is inconsistent with more recent studies (Fig. 26.9) which show that storm frequencies vary
substantially in this area.
The JPM used a set of parameters, including central
pressure, radius of maximum wind speed, storm forward speed, storm landfall location, and the angle of the
storm track relative to the coast, to generate parametric
wind fields. Furthermore, initial applications of the JPM
assumed that the values of these five parameters varied
only slowly in storms approaching the coast; therefore,
the values of these parameters at landfall could be used
to estimate the surge at the coast, and these values could
be treated as a constant during the approach of a storm
to the coast. Recent data shows that this is not a good
assumption [26.70, 71]; specifically, these studies suggest that tropical cyclones decay as they approach land.
Kimball [26.72] has shown that such decay is consistent
with the intrusion of dry air into a tropical cyclone during its approach to land, although other hypotheses for
this consistent decay in intensity, such as the lack of energy production from parts of the tropical cyclone over
land and increased drag in these areas have also been
advanced. In any event, the evidence appears rather
convincing that major tropical cyclones begin to decay
substantially before they make landfall, rather than only
after landfall as previously assumed.
The initial formulation of the JPM used computer
simulations of straight-line tracks with constant parametric wind fields to define the maximum surge value
for selected combinations of the basic five storm parameters. Each of these maximum values was associated
with a probability
p.c p ; R max ; v f ; Â l ; x/ ;
(26.20)
where c p is the central pressure, R max is the radius of
maximum wind speed, v f is the forward velocity of the
storm, Â l is the angle of the track relative to the coast
at landfall, and x is the distance between the point of
interest and the landfall location.
These probabilities were treated as discrete increments and the CDF was defined as
F.x/ D
X
p ijklm jx ijklm < x ;
(26.21)
where the subscripts denote the indices of the five parameters used to characterize the tropical cyclones.
The JPM represents a straightforward application of
the response surface method for estimating extremes.
In this method, the response of a particular variable
(such as waves and surges) is derived as a function of
several parameters, such as the set (c p ; R max ; v f ; Â l ; x)
used in the above example. Given that the multivariate probability of the five-parameter space is known
and a method for defining the response from this set
of variables is known, the equation for the CDF for the
response can be written for this example as
F.Á/ D
Z Z Z Z Z
p.c p ; R max ; v f ; Â l ; x/
HŒÁ .c p ; R max ; v f ;  l ; x/
dc p dR max dv f d l dx ;
(26.22)