Statistical Characterization of Hazards and Risk in Coastal Areas 26.A Appendix: Glossary of Probability and Risk Terms 587
Part C | 26.A
26.4 Summary
On the one hand, we can see that considerable progress
has been made in the estimation of hazards and associated risks in coastal areas over the last 100 years.
Like all decision-making processes which become codified, it is difficult to change a methodology used for
such estimates very quickly; hence engineering practice has often significantly lagged the recognized state
of the art of our understanding of coastal hazards and
risks, tending to wait until the occurrence of a natural disaster, such as Hurricane Katrina and the tsunami
affecting Fukushima, Japan, to foster a willingness to
change. Prudent design concepts in areas with critical
infrastructure and communities that can be affected by
hazards/risks must continue to consider the effects of
both alleatory and epistemic uncertainty.
While the discussion herein focuses primarily on
the coastal storm problem, the key concepts translate
to the wide array of hazards impacting the coast. While
each of these hazards will have its own unique set of
physical characteristics and statistical challenges, the
general concepts discussed here are appropriate for
evaluating their probability and risk, as well as for understanding the factors contributing to uncertainty in
these extreme estimates.
26.5 Nomenclature
a
specified limit or coefficient
b
specified limit or coefficient
c
coefficient
c p
storm central pressure
d
coefficient
k
coefficient
n; m
indices
p.x/
probability density function
q
coefficient
v f
storm forward speed
x
variable
x c
coefficient
AEP
annual exceedance probability
CDF
cumulative distribution function
EST
empirical simulation technique
ETM
empirical track method
F.x/
cumulative distribution function
GEV
generalized extreme value distribution
GPD
generalized Pareto distribution
JPM
joint probability method
MPI
maximum possible intensity
N
total number of items
P
probability of exceedance
PDF
probability density function
PMH probable maximum hurricane
POT
peaks over threshold
Pr.A/ probability of event A occurring
Pr.BjA/ probability of a consequence (B) occurring
given that event A occurred
R
risk
R max
storm radius to maximum winds
SPH
standard project hurricane
T
return period (or return interval)
T
0
dimensionless return period (or return interval)
"
coefficient
"
0
coefficient
" Á
deviation from deterministic surge estimate
Á
surge value
 l
storm track angle relative to coast at landfall
sampling frequency
coefficient
y
reduced Gumbel variate
distribution standard deviation
T
rms error at return period T
0
T
dimensionless root-mean-square error at dimensionless return period T
0
26.A Appendix: Glossary of Probability and Risk Terms
Confidence intervals: A confidence interval is a statistical representation of how certain one is that
a given variable will lie within a given range. A confidence interval includes two components – the
interval (the value will be between x and y) and
the level of certainty (a 90% confidence interval
indicates one can say that there is a 90% probability the value will fall between the cited interval.
As the interval gets smaller, the certainty that the
values will fall within the interval goes down. Confidence intervals are related to uncertainty in that they
are a statistical method of measuring uncertainty of
Part C | 26.A
26.4 Summary
On the one hand, we can see that considerable progress
has been made in the estimation of hazards and associated risks in coastal areas over the last 100 years.
Like all decision-making processes which become codified, it is difficult to change a methodology used for
such estimates very quickly; hence engineering practice has often significantly lagged the recognized state
of the art of our understanding of coastal hazards and
risks, tending to wait until the occurrence of a natural disaster, such as Hurricane Katrina and the tsunami
affecting Fukushima, Japan, to foster a willingness to
change. Prudent design concepts in areas with critical
infrastructure and communities that can be affected by
hazards/risks must continue to consider the effects of
both alleatory and epistemic uncertainty.
While the discussion herein focuses primarily on
the coastal storm problem, the key concepts translate
to the wide array of hazards impacting the coast. While
each of these hazards will have its own unique set of
physical characteristics and statistical challenges, the
general concepts discussed here are appropriate for
evaluating their probability and risk, as well as for understanding the factors contributing to uncertainty in
these extreme estimates.
26.5 Nomenclature
a
specified limit or coefficient
b
specified limit or coefficient
c
coefficient
c p
storm central pressure
d
coefficient
k
coefficient
n; m
indices
p.x/
probability density function
q
coefficient
v f
storm forward speed
x
variable
x c
coefficient
AEP
annual exceedance probability
CDF
cumulative distribution function
EST
empirical simulation technique
ETM
empirical track method
F.x/
cumulative distribution function
GEV
generalized extreme value distribution
GPD
generalized Pareto distribution
JPM
joint probability method
MPI
maximum possible intensity
N
total number of items
P
probability of exceedance
probability density function
PMH probable maximum hurricane
POT
peaks over threshold
Pr.A/ probability of event A occurring
Pr.BjA/ probability of a consequence (B) occurring
given that event A occurred
R
risk
R max
storm radius to maximum winds
SPH
standard project hurricane
T
return period (or return interval)
T
0
dimensionless return period (or return interval)
"
coefficient
"
0
coefficient
" Á
deviation from deterministic surge estimate
Á
surge value
 l
storm track angle relative to coast at landfall
sampling frequency
coefficient
y
reduced Gumbel variate
distribution standard deviation
T
rms error at return period T
0
T
dimensionless root-mean-square error at dimensionless return period T
0
26.A Appendix: Glossary of Probability and Risk Terms
Confidence intervals: A confidence interval is a statistical representation of how certain one is that
a given variable will lie within a given range. A confidence interval includes two components – the
interval (the value will be between x and y) and
the level of certainty (a 90% confidence interval
indicates one can say that there is a 90% probability the value will fall between the cited interval.
As the interval gets smaller, the certainty that the
values will fall within the interval goes down. Confidence intervals are related to uncertainty in that they
are a statistical method of measuring uncertainty of