(9) The EST simulation approach is to perform N-repetitions of M-years of simulation; for example,

100 simulations of a 200-year sequence of storms. Details of the EST are given in Borgman and Scheffner

(1991). The number of storms simulated per year is specified according to a Poisson probability law of the

form:

(II-5-25)

for *n *= 0,1,2,3,.... Equation II-5-25 defines the probability of having N storm events in *T *years. The variable

λ defines the mean frequency of observed events per time period. For the example shown for the coast of

Delaware, the value of λ was chosen to be 0.32 events per year, computed as the ratio of 33 observed events

above some selected threshold intensity over a 104-year period.

(10) A 10,000-element array is initialized to the above Poisson distribution. The number corresponding

to 0 storms per year from Equation II-5-25 is 0.7234; thus, if a random number selection is less than or equal

to 0.7234 on an interval of 0.0 to 1.0, then no hurricanes would occur during that year of simulation. If the

random number is between 0.7234 and 0.7234 + *P*[*N*=1] = 0.7234 + 0.2343 = 0.9577, one event is selected.

Two events for 0.9577 + 0.0379 = 0.9956, etc. When one or more storms are indicated for a given year, they

are randomly selected from the expanded training set. In this manner, a randomly selected number of storms

per year is computed for each year to generate a 200-year simulation.

(11) Each 200-year sequence is rank ordered, a cumulative pdf computed, and a frequency-of-occurrence

relationship developed according to the approach described above. However, in the EST, tail functions

(Borgman and Scheffner 1991) are used to define probabilities for events larger than the largest the 200-year

simulation.

(12) This computation is repeated 100 times, resulting in 100 individual pdfs from which 100 stage-

frequency relationships are computed. This family of curves is averaged and the standard deviation

computed, resulting in the generation of a stage-frequency relationship containing a measure of variability

of data spread about the mean. This variation is well-suited to the development of design criteria requiring

the quantification of the element of risk associated with the frequency predictions. A computed stage-

frequency relationship for a coastal station in the Delaware study is shown in Figure II-5-27.

(c) EST - extratropical storm application.

(1) Extratropical events cannot be easily parameterized; therefore, the multi-parameter application of

the EST is not appropriate for events such as northeasters. An alternate small-parameter application of the

EST (Palermo et al. 1998) was used for this class of events. Northeasters have a much greater frequency of

occurrence than hurricanes. For example, several northeasters impact large regions of the east coast every

year. The existing WIS database of northeasters represents an adequate population of storms from which

frequency-of-occurrence relationships can be computed.

(2) The extratropical EST approach is conceptually simpler than the multi-parameter version used for

hurricanes because parameters such as tidal phase, wave height, and wave period are specified as input

vectors. In this approach, a database of extratropical events is assembled and respective surge elevations

computed for each storm in the training set using numerical modeling techniques. If 20-30 years of reliable

storm surge elevation data are available for a particular location, the numerical modeling phase may not be

necessary. The extratropical analogy to the tropical implementation is that there are fewer input vectors. The

database of response vectors is combined with tide, rank ordered, and a pdf is computed.

Water Levels and Long Waves

II-5-49

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